11institutetext: Departamento de Astrofísica, Universidad de La Laguna,
E-38200, La Laguna, Tenerife, Spain
11email<EMAIL_ADDRESS>22institutetext: Instituto de Astrofísica de
Canarias E-38205, La Laguna, Tenerife, Spain 33institutetext: Sub-Department
of Astrophysics, Department of Physics, University of Oxford, Denys Wilkinson
Building, Keble Road, Oxford OX1 3RH, UK 44institutetext: Departamento de
Física Teórica, Atómica y Óptica, Universidad de Valladolid, E-47011
Valladolid, Spain 55institutetext: Instituto de Astrofísica e Ciências do
Espaço, Universidade de Lisboa, OAL, Tapada da Ajuda, PT1349-018 Lisbon,
Portugal 66institutetext: Instituto Nacional de Astrofísica, Óptica y
Electrónica (INAOE), Luis Enrique Erro No. 1, Tonantzintla, Puebla, CP 72840,
México 77institutetext: Consejo Nacional de Ciencia y Tecnología, Av.
Insurgentes Sur 1582, 03940 México City, México 88institutetext: Faculty of
Physics, Ludwig-Maximilians-Universität, Scheinerstr. 1, 81679 Munich, Germany
99institutetext: Main Astronomical Observatory, National Academy of Sciences
of Ukraine, 27 Akademika Zabolotnoho St, 03680, Kyiv, Ukraine
1010institutetext: Departamento de Física de la Tierra y Astrofísica,
Universidad Complutense de Madrid, E-28040 Madrid, Spain 1111institutetext:
Instituto de Física de Partículas y del Cosmos IPARCOS, Fac. de Ciencias
Físicas, Universidad Complutense de Madrid, E-28040 Madrid, Spain
1212institutetext: Max Planck Institute for Astronomy, Königstuhl 17, 69117,
Heidelberg, Germany

# The massive relic galaxy NGC 1277 is dark matter deficient

From dynamical models of integral-field stellar kinematics out to five
effective radii

Sébastien Comerón 1122 Ignacio Trujillo 2211 Michele Cappellari 33 Fernando
Buitrago 4455 Luis E. Garduño 66 Javier Zaragoza-Cardiel 6677 Igor A.
Zinchenko 8899 Maritza A. Lara-López 10101111 Anna Ferré-Mateu 2211 and Sami
Dib 1212

According to the $\Lambda$CDM cosmology, present-day galaxies with stellar
masses $M_{\star}>10^{11}\,{\rm M}_{\odot}$ should contain a sizable fraction
of dark matter within their stellar body. Models indicate that in massive
early-type galaxies (ETGs) with $M_{\star}\approx 1.5\times 10^{11}\,{\rm
M}_{\odot}$ dark matter should account for $\sim 15\%$ of the dynamical mass
within one effective radius ($1\,R_{\rm e}$) and for $\sim 60\%$ within
$5\,R_{\rm e}$. Most massive ETGs have been shaped through a two-phase
process: the rapid growth of a compact core was followed by the accretion of
an extended envelope through mergers. The exceedingly rare galaxies that have
avoided the second phase, the so-called relic galaxies, are thought to be the
frozen remains of the massive ETG population at $z\gtrsim 2$. The best relic
galaxy candidate discovered to date is NGC 1277, in the Perseus cluster. We
used deep integral field George and Cynthia Mitchel spectrograph (GCMS) data
to revisit NGC 1277 out to an unprecedented radius of 6 kpc (corresponding to
$5\,R_{\rm e}$). By using Jeans anisotropic models constructed with JAM we
recovered the dark matter fraction of NGC 1277 within $5\,R_{\rm e}$, $f_{\rm
DM}(5\,R_{\rm e})$, and found it to be negligible ($f_{\rm DM}(5\,R_{\rm
e})<0.07$; two-sigma confidence level), which is in strong tension with the
$\Lambda$CDM expectation for a massive ETG. Since the lack of an extended
envelope would reduce dynamical friction and prevent the accretion of an
envelope, we propose that NGC 1277 lost its dark matter very early or that it
was dark matter deficient ab initio. We discuss our discovery in the framework
of recent proposals suggesting that some relic galaxies may result from dark
matter stripping as they fell in and interacted within galaxy clusters.
Alternatively, NGC 1277 might have been born in a high-velocity collision of
gas-rich proto-galactic fragments, where dark matter left behind a disc of
dissipative baryons. We speculate that the relative velocities of $\approx
2000\,{\rm km\,s^{-1}}$ required for the latter process to happen were
possible in the progenitors of the present-day rich galaxy clusters.

###### Key Words.:

Galaxies: elliptical and lenticular, cD – Galaxies: evolution – Galaxies:
formation – Galaxies: individual: NGC 1277 – Galaxies: individual: NGC 1278 –
Galaxies: kinematics and dynamics

##  1 Introduction

The first proposed formation scenarios for massive early-type galaxies (ETGs)
suggested a monolithic collapse (Larson, 1969) similar to what had been
posited for the oldest stellar populations in the Milky Way (Eggen et al.,
1962). These models fell out of fashion with the advent of hierarchical
formation models within a cold dark matter cosmology (White & Rees, 1978;
Klypin & Shandarin, 1983). However, recent computational studies assuming a
$\Lambda$CDM cosmology indicate that nature borrows from both scenarios and
that the actual massive ETG formation process is two-phase (Naab et al., 2009;
Oser et al., 2010; Johansson et al., 2012; Lackner et al., 2012; Zolotov et
al., 2015; Rodriguez-Gomez et al., 2016). First, the massive ETG progenitors
suffer a dissipative collapse that results in a compact rotating object (known
as blue nugget) whose star formation is rapidly quenched (Huang et al., 2013;
Dekel & Burkert, 2014; Zolotov et al., 2015; Martín-Navarro et al., 2019;
Lapiner et al., 2023), perhaps due to active galactic nucleus (AGN) feedback
(e.g., Choi et al., 2018). Then, the passive evolution of the stellar
population turns the blue nugget into a red one, while an extended pressure-
supported envelope is formed through the mostly dry accretion of surrounding
systems.

This two-phase formation narrative is supported by observations indicating
that passively-evolving galaxies at high redshift were much more compact than
local massive ETGs (Daddi et al., 2005; Zirm et al., 2007; Cimatti et al.,
2008; Toft et al., 2017; Kubo et al., 2018), and have grown by a factor of
roughly four in effective radius since redshift $z\sim 2$ (Trujillo et al.,
2006, 2007; Buitrago et al., 2008; van der Wel et al., 2011; Szomoru et al.,
2012). Further credence to this framework is given by the fact that stellar
envelopes have been shown to grow with cosmic time (Damjanov et al., 2011;
Ryan et al., 2012; van der Wel et al., 2014; Bai et al., 2014; Buitrago et
al., 2017). Also, the recently identified compact, star-forming, and
presumably rotating Ultra-red Flattened Objects (Nelson et al., 2022) could be
dust-shrouded blue nuggets, which would give additional evidence for the two-
phase formation scenario.

Both models and observations indicate that red nuggets are the evolved
remnants of the infant massive galaxies, offering a sneak peek to the epoch at
which the first giant galaxies assembled, at $z\gtrsim 2$. Since red nuggets
are expected to survive within at least a fraction of massive galaxies
(Pulsoni et al., 2021), they can be examined and resolved in nearby galaxies.
However, this often comes at the expense of suffering contamination from the
envelope. Local red nuggets embedded within elliptical or even disc galaxies
have been studied through structural decompositions (Huang et al., 2013;
Graham et al., 2015; de la Rosa et al., 2016; Costantin et al., 2021) and
resolved stellar populations (Yıldırım et al., 2017; Martín-Navarro et al.,
2018; Ferré-Mateu et al., 2019; Barbosa et al., 2021). Also, some red nuggets
could be identified with the kinematically-decoupled components (KDCs) often
observed in the central regions of slow rotators ETGs (see review by
Cappellari, 2016). Cleaner nuggets can be studied at intermediate and high $z$
(e.g., Damjanov et al., 2009, 2013, 2014; van Dokkum et al., 2009; Auger et
al., 2011; Stockton et al., 2014; Hsu et al., 2014; Saulder et al., 2015;
Oldham et al., 2017; Charbonnier et al., 2017; Buitrago et al., 2018;
Scognamiglio et al., 2020; Spiniello et al., 2021a, b; Lisiecki et al., 2023;
D’Ago et al., 2023), but the price to pay is to suffer from cosmological
dimming and poor angular resolution.

Local red nuggets that have somehow avoided accreting an envelope are
therefore key to access good-quality uncontaminated data from the progenitors
of massive ETGs. They constitute snapshots of galaxies that have evolved
passively, and whose growth stopped at a freezing redshift $z_{\rm f}>1$. Such
galaxies are exceedingly rare (see the number density estimates in Quilis &
Trujillo, 2013) and have been named ‘relic galaxies’ since the study by
Trujillo et al. (2009). Ironically, no relic galaxy was found in the study
defining them. Later searches were more successful, and nowadays a few tens of
candidates and spectroscopically confirmed relics are known (Trujillo et al.,
2014; Ferré-Mateu et al., 2015, 2017; Spiniello et al., 2021a, b).

The detailed study of NGC 1277 has provided a unique insight into the extreme
conditions under which nuggets grow. Martín-Navarro et al. (2015) found that
the initial mass function (IMF) of NGC 1277 is bottom-heavy throughout the
galaxy, which implies a large stellar mass-to-light ratio $\Upsilon_{\star}$,
as confirmed by Yıldırım et al. (2015). Similar although slightly less extreme
properties have also been confirmed for two more relic galaxies (Ferré-Mateu
et al., 2017). Also, dynamical modelling has unveiled that virtually no dark
matter is necessary to explain the stellar kinematics in the innermost parts
of NGC 1277 (Yıldırım et al., 2015).

NGC 1277 is a fast rotator, a property that is common among relic galaxies
(Yıldırım et al., 2017). It is found in a cluster environment, which is in
agreement with the expectations from some cosmological simulations (Stringer
et al., 2015; Peralta de Arriba et al., 2016) and observational findings
(Poggianti et al., 2013; Buitrago et al., 2018; Baldry et al., 2021). The
reason for this environmental preference has been posited to be that the high
relative velocities between cluster galaxies are efficient at preventing
prolonged interactions. However, other evolutionary pathways are also possible
(Buitrago et al., 2018; Tortora et al., 2020).

NGC 1277 was originally reported to have an unexpectedly massive black hole
with $M_{\rm BH}=17\times 10^{9}\,{\rm M}_{\odot}$ from Schwarzschild
dynamical modelling based on rather low spatial resolution long-slit data (van
den Bosch et al., 2012). However, a reanalysis of the same data by Emsellem
(2013) using an $N$-body particle realization based on the Jeans Anisotropic
Modelling (JAM; Cappellari, 2008) formalism suggested that the black hole was
likely overestimated and proposed $M_{\rm BH}\approx 5\times 10^{9}\,{\rm
M}_{\odot}$. This lower value of $M_{\rm BH}$ was later confirmed with higher
spatial resolution integral fiel data from both Schwarzschild (Walsh et al.,
2016) and JAM models (Krajnović et al., 2018). Even the lower black hole mass
estimates place NGC 1277 more than one order of magnitude above the scaling
relations linking the mass of the black hole with the luminosity of the
spheroid (the $M_{\rm BH}-L$ relation; Gültekin et al., 2009; Sani et al.,
2011). A possible explanation for this anomaly is that the black hole assembly
occurs chiefly during the early collapse phase, with little to no mass
increase during the envelope growth period (Trujillo et al., 2014; Ferré-Mateu
et al., 2015, 2017). Since the scaling relations are established using mostly
ETGs that have undergone an envelope growth, NGC 1277 would naturally have a
lower mass than regular massive ETGs hosting black holes with a similar mass.
Alternatively, the mass of the central black hole in NGC 1277 might have been
overestimated and be as low as $M_{\rm BH}=1.2\times 10^{9}\,{\rm M}_{\odot}$
(Graham et al., 2016) due to the degeneracy between the black hole mass and
$\Upsilon_{\star}$ in the central parts of the galaxy (see also Emsellem,
2013). Additionally, a black hole mass of $M_{\rm BH}\approx 5\times
10^{9}\,{\rm M}_{\odot}$ would be consistent with the $M_{\rm BH}-\sigma$
relation (Ferrarese & Merritt, 2000; Gebhardt et al., 2000) for a stellar
velocity dispersion of $400\,{\rm km\,s^{-1}}$ at the centre of the galaxy
(van den Bosch et al., 2012).

We revisit NGC 1277 with new deep spectroscopic data obtained with the George
and Cyhthia Mitchel spectrograph (GCMS), an integral field spectrograph at the
2.7 m Harlan J. Smith telescope at the McDonald Observatory (Hill et al.,
2008; Tufts et al., 2008). These data are a significant improvement over
single-slit observations (Trujillo et al., 2014; Martín-Navarro et al., 2015)
and integral field observations with a narrower radial coverage than ours
($13\arcsec$ versus $18\arcsec$; Yıldırım et al., 2015, 2017). This is
critical to explore the outskirts of the galaxy, where dark matter is expected
to contribute the most to the mass budget, and test the claims that a dark
matter halo is not required to describe the stellar kinematics. An additional
advantage of our dataset is that the field of view simultaneously covers NGC
1278, a regular massive ETG in the Perseus cluster with a mass similar to that
of NGC 1277. Thus, we can study a relic galaxy alongside an object that has
undergone the complete two-phase evolution with exactly the same instrumental
setup, enabling a straightforward comparison of their properties. In order to
mitigate the coarse GCMS $\sim 4^{\prime\prime}$ angular resolution and better
constrain the kinematics in the vicinity of the central black hole, we are
complementing our data with kinematics of the inner
$1\aas@@fstack{\prime\prime}6\times 1\aas@@fstack{\prime\prime}6$ of NGC 1277
obtained by Walsh et al. (2016) using the adaptive-optics-assisted Near-
infrared Integral Field Spectrometer (NIFS; McGregor et al., 2003) at the
Gemini North telescope.

In this paper, we examine the stellar kinematics of NGC 1277 and NGC 1278 and
produce detailed dynamical Jeans models with JAM111We used v6.3.2 of the
Python package JamPy, available from https://pypi.org/project/jampy/.
(Cappellari, 2008, 2020). We assume that the distance to the galaxies is 68.4
Mpc, based on the average of the two distances derived from the turn-over of
the globular cluster luminosity function by Beasley et al. (2018). At this
distance, $1\arcsec$ corresponds to $332\,{\rm pc}$. In order to be consistent
with the dark matter halo parametrisation from Child et al. (2018, see Sect.
5.2), we assume a Hubble-Lemaître constant of $H_{0}=71\,{\rm
km\,s^{-1}\,Mpc^{-1}}$.

The goal of this article is to describe the dark matter distribution of NGC
1277 out to an unprecedented radius of five effective radii ($5\,R_{\rm e}$,
corresponding to 6 kpc). Because of the relic nature of the target, this is
equivalent to studying the dark matter halo properties of a massive ETG at
$z\gtrsim 2$. The results of the experiment provide tight constraints to test
the accuracy of the dark matter distributions that are predicted by the
$\Lambda$CDM model.

This paper is organised as follows: in Sect. 2 we describe the GCMS data and
their reduction process. In Sect. 3 we detail how the stellar kinematics and
the multi-Gaussian expansion (MGE) models of the Hubble Space Telescope (HST)
images and mass maps were obtained. In Sect. 4 we describe the Jeans dynamical
modelling of NGC 1277 and NGC 1278. We discuss our results in Sect. 5 and
present our summary in Sect. 6. We also include Appendix A, where we discuss
the accuracy of our black hole mass determination if we ignore the high-
resolution HST and NIFS data. This is crucial to assess the feasibility of the
black hole mass determination for the progenitors of relic galaxies at high
redshift using adaptive optics-assisted or James Webb Space Telescope (JWST)
data.

##  2 Data and data reduction

Figure 1:  Map of the median intensity (left panel) and S/N per spectral pixel
of 1.1 Å (right panel) in the wavelength range
$4400\,{\rm\AA}-6650\,{\rm\AA}$. The coordinates are centered in NGC 1277 and
are in arcseconds. The black continuous shapes denote the effective radii of
the galaxies as measured in Sect. 3.2. The effective radius of NGC 1277 has
been de-circularised assuming an axial ratio $q^{\prime}_{\star}=0.6$, as
determined from an ellipse fit to the outer regions of the galaxy (see Sect.
3.2). The dashed circle indicates the location of the galaxy that is in the
line of sight of NGC 1277 (Sect. 3.1).

The George Mitchell and Cynthia spectrograph (GCMS; formerly known as
VIRUS-P), is hosted at the 2.7 m Harlan J. Smith telescope at the McDonald
Observatory (Tufts et al., 2008; Hill et al., 2008). The integral field unit
comprises 246 $4\aas@@fstack{\prime\prime}16$ in diameter fibres that are
distributed in a fixed pattern with a filling factor of roughly 1/3. The total
field of view of the instrument is of $100\arcsec\times 102\arcsec$. At the
distance of NGC 1277, the fibre diameter corresponds to 1.3 kpc and the field
of view is $\sim 30\,{\rm kpc}$ per side.

The data were taken with the ‘red setup’ on 29–31 December 2019 as part of the
Metal-THINGS programme (Lara-López et al., 2021, 2023). The observations were
made with the VP1 grism and covered the $4400\,{\rm\AA}-6800\,{\rm\AA}$
spectral range with a spectral resolution of 5.3 Å. In order to ensure a high
filling factor, a three-pointing dither pattern was followed, resulting in a
738-fibre coverage of the field of view. The dithering pattern was designed so
as to avoid the position of the fibres to overlap within each three-pointing
dataset.

Ten three-point dither datasets were taken, each with an exposure time of 900
s per dither for a total of 9000 s (2.5 hours) per position. Throughout the
acquisition, the seeing varied between 1$\aas@@fstack{\prime\prime}$7 and
3$\aas@@fstack{\prime\prime}$5\. Only one of the datasets had a seeing above
$2\aas@@fstack{\prime\prime}8$. We checked that ignoring the latter dataset
did not improve the quality of the recovered kinematics.

The basic data reduction (bias subtraction, flat frame correction, and
wavelength calibration) was performed using P3D222The software can be obtained
from https:/p3d.sourceforge.io. (Sandin et al., 2010). The sky emission of the
ten datasets was estimated by computing the median spectrum of a few hand-
picked sky fibres. After the sky subtraction, the datasets were flux-
calibrated using IRAF (Tody, 1986) and combined to produce a final science-
ready data product with a single spectrum for each of the 738 fibre locations
(from now on and for the sake of brevity we will simply call them fibres) in
the field of view. We cropped the reddest portion of the spectrum, above the
rest frame 6650 Å, to avoid some calibration problems on that portion of the
spectrum. Nine fibres in the south-eastern corner of the field of view have
problematic spectra and were excluded from further analysis. Figure 1 shows
maps of the median spectral intensity and the signal-to-noise ratio (S/N) per
spectral pixel of 1.1 Å. The S/N was obtained by estimating the noise with the
DER_SNR algorithm by Stoehr et al. (2008) and comparing it to the median
intensity.

##  3 Galaxy resolved kinematics and MGE modelling

###  3.1 The resolved kinematics of NGC 1277 and NGC 1278

The kinematics of the field were obtained with pPXF333We used v7.4.5 of the
pPXF package available from https://pypi.org/project/ppxf/. (Cappellari &
Emsellem, 2004; Cappellari, 2022). This code fits the spectra with a linear
combination of spectral energy distribution templates convolved with a line-
of-sight velocity distribution (LOSVD). The templates were drawn from the
E-MILES single stellar population models444The E-MILES spectral energy
distribution libraries can be downloaded from
http://research.iac.es/proyecto/miles/pages/spectral-energy-distributions-
seds/e-miles.php. (Vazdekis et al., 2015), which uses the MILES (Sánchez-
Blázquez et al., 2006; Falcón-Barroso et al., 2011) and CaT (Cenarro et al.,
2007) stellar templates. We used the models with a Kroupa initial mass
function (Kroupa, 2001) and BaSTI isochrones (Pietrinferni et al., 2004, 2006,
2009, 2013; Cordier et al., 2007), but the choice of a specific library plays
little effect in the precise determination of the kinematics. To speed up the
processing, we excluded the templates that, a priori, would not describe a
massive ETG, that is those with low metallicity ($[{\rm Z}/{\rm H}]<-0.35$)
and young ages ($<1\,{\rm Gyr}$). We have tested that producing the fits with
the complete MILES model library would not introduce significant changes in
the derived kinematics.

We only fitted the first two momenta of the LOSVD, that is the mean recession
velocity and the velocity dispersion $[v,\sigma]$. The characterisation of
higher-order momenta requires high-S/N data, which would go against our goal
of covering as much of NGC 1277 as possible. In some lines of sight, two
objects appear in projection, so their spectra should be fitted with two sets
of templates with distinct kinematics. This is why each spectrum was at first
fitted with single sets of templates with initial values $[v=5066\,{\rm
km\,s^{-1}},\sigma=250\,{\rm km\,s^{-1}}]$ (corresponding to the redshift
$z=0.016898$ of NGC 1277; Falco et al., 1999), $[v=6066\,{\rm
km\,s^{-1}},\sigma=250\,{\rm km\,s^{-1}}]$ (roughly the velocity of NGC 1278),
$[v=4066\,{\rm km\,s^{-1}},\sigma=50\,{\rm km\,s^{-1}}]$ (the velocity of a
small galaxy overlapping with part of the western side of NGC 1277; see Fig.
1), and $[v=-34\,{\rm km\,s^{-1}},\sigma=50\,{\rm km\,s^{-1}}]$ (this is a
velocity compatible with that of Galactic objects and it was chosen so to
describe foreground stars), and with pairs of sets of templates combining the
above initial values. The best fit was chosen based on the chi-squared values
after penalising by a factor 1.1 fits with two sets of templates. The latter
factor was manually selected after extensively testing which value was
required not to use two templates in fitting spectra where a visual inspection
clearly indicated the presence of a single object.

A necessary input of the Jeans modelling (Sect. 4) is a $V_{\rm
rms}\equiv\sqrt{V^{2}+\sigma^{2}}$ map, where $V$ is the velocity corrected
for the mean recession velocity of the galaxy $v_{\rm rec}$ ($V\equiv v-v_{\rm
rec}$). The recession velocity was obtained by assuming a symmetric rotation
curve and by finding the average of the peak velocities of the receding and
the approaching sides. We obtained a recession velocity of $v_{\rm
rec}=5097\,{\rm km\,s^{-1}}$ for NGC 1277 and $v_{\rm rec}=6072\,{\rm
km\,s^{-1}}$ for NGC 1278.

Figures 2 and 3 show the $V$, $\sigma$, and $V_{\rm rms}$ maps for NGC 1277
and NGC 1278, respectively. We are only plotting the fibres that were used for
the Jeans modelling, that is those with high enough S/N (${\rm S/N}>7$ per
spectral pixel), low kinematic errors ($\epsilon\left(V_{\rm
rms}\right)<65\,{\rm km\,s^{-1}}$; formal errors as derived by pPXF), and for
which pPXF has converged to reasonable $\sigma$ values ($10\,{\rm
km\,s^{-1}}<\sigma<350\,{\rm km\,s^{-1}}$). Furthermore we only selected those
with $V$ within $400\,{\rm km\,s^{-1}}$ of $v_{\rm rec}$ for NGC 1277 and
within $60\,{\rm km\,s^{-1}}$ for NGC 1278. Those values are selected to be
slightly larger than the amplitude of the rotation curve of the galaxies.
Overall, the maps include 47 fibres for NGC 1277 and 183 for NGC 1278. The
coverage of NGC 1277 is roughly elliptical in shape, with a semi-major axis of
$\sim 18^{\prime\prime}$ (6 kpc at the distance of NGC 1277, corresponding to
five effective radii as measured in Sect. 3.2) and a semi-minor axis of $\sim
10^{\prime\prime}$ (3.5 kpc). The coverage of NGC 1278 is roughly circular,
with a radius of $\sim 30^{\prime\prime}$ (10 kpc, or roughly three effective
radii).

Figure 2:  From left to right, $V$, $\sigma$, and $V_{\rm rms}$ linearly
interpolated maps of NGC 1277. The dashed line in the left panel indicates the
kinematic major axis determined with kinemetry. The black circle indicates the
size of the GCMS fibres and the black crosses indicate their centres. The grey
contours denote isophotes separated by $0.5\,{\rm mag\,arcsec^{-2}}$ intervals
obtained from an HST F625W image. The axes are in units of arcseconds. Figure
3:  Same as Fig. 2, but for NGC 1278. In order to highlight the kinematic
structures, the colour scales differ from those in Fig. 2. In this case, the
isophotes are based on an HST F850LP image, which is the one used for the MGE
modelling detailed in Sect. 3.2. Since for this galaxy $V\ll\sigma$, the
$V_{\rm rms}$ map is virtually identical to the $\sigma$ map.

Because of the large angular size of the fibres compared to the size of NGC
1277, we had to devise a method to pinpoint the centre of the galaxy in the
CGMS data. We aligned the GCMS data with an HST Advanced Camera for Surveys
(ACS; Ford et al., 1998) F850LP image (programme ID GO 14215; Trujillo et al.,
2015) by comparing the flux of the fibres selected for the Jeans modelling
with that within circular apertures in the image with the same radius as the
fibres. The HST image had previously been convolved with a Gaussian kernel
with a sigma of one arcsecond so to match the seeing of the GCMS observations.
The CGMS fluxes were calculated in the $6150\,{\rm\AA}-6650\,{\rm\AA}$
spectral range. We excluded bluer wavelengths in order to avoid a too large
wavelength difference between the integral field and the HST data. Ideally, an
HST image in a wavelength matching that of the CGMS data should have been
used, but unfortunately the available ACS F625W image (programme ID GO 10546;
Fabian, 2005) does not fully cover NGC 1278. The determination of the exact
alignment was obtained by minimising

$L=\sum_{i}\left(\frac{F_{\rm GCMS,i}-F_{\it HST,i}}{F_{\rm
GCMS,i}}\right)^{2},$ (1)

where $F_{\rm GCMS,i}$ and $F_{\it HST,i}$ denote the flux for the $i^{\rm
th}$ bin in the CGMS fibre and the corresponding HST area, respectively. The
minimisation was performed with the adaptive Metropolis et al. (1953) for
Bayesian analysis code (adamet555We used v2.0.7 of the Python package adamet,
available from https://pypi.org/project/adamet/.; Cappellari et al., 2013b),
which is an implementation of the algorithm by Haario et al. (2001). As an
alternative method for the GCMS data registration, we aligned four bright
stars in the HST with their GCMS counterparts. The alignment differences
between the two methods were of $0\aas@@fstack{\prime\prime}5$ only. We
decided to use the former registration method, but we have checked that using
the latter alignment does not significantly change any of the results obtained
from the JAM fit (Sects. 4.1 and 4.2).

We determined the major axis of the galaxies kinematically by running the
kinemetry tilted ring code666We used the IDL v4.2 of the code available here
https://www.aip.de/en/members/davor-krajnovic/kinemetry/. (Krajnović et al.,
2006) over the $V$ maps. The major axis position angles were extracted by
averaging the orientation of the tilted rings over radial ranges where it is
roughly flat ($3\arcsec\leq R\leq 14\arcsec$ for NGC 1277 and $10\arcsec\leq
R\leq 23\arcsec$ for NGC 1278). We find the position angles $\overline{{\rm
PA}}=96\aas@@fstack{\circ}0$ and $\overline{{\rm PA}}=86\aas@@fstack{\circ}5$
for NGC 1277 and NGC 1278, respectively (Fig. 4). The kinematic position angle
for NGC 1277 is close to the photometric value of ${\rm
PA}=92\aas@@fstack{\circ}7$ reported in van den Bosch et al. (2012) and of
${\rm PA}=96\aas@@fstack{\circ}0$ from HyperLeda777The HyperLeda database is
hosted at http://leda.univ-lyon1.fr/. (Makarov et al., 2014).

Figure 4:  Position angle as a function of distance along the major axis for
the kinemetry tilted ring models of NGC 1277 (left) and NGC 1278 (right). The
error bars correspond to the one-sigma uncertainties. The vertical dashed
lines indicate the radial interval over which the kinematical axis was
determined. Its estimated value is indicated by the number in the lower part
of the panels and the horizontal dotted lines. Figure 5:  Velocity (top-row
panels) and $\sigma$ (lower-row panels) profiles for NGC 1277 (left-column
panels) and NGC 1278 (right-column panels) as measured along the kinematic
major axes. The black data points denote our measurements obtained from fibres
whose centre is within the fibre radius ($2\aas@@fstack{\prime\prime}05$) of
the kinematic major axis. The data in crimson come from Ferré-Mateu et al.
(2017).

We constructed velocity and velocity dispersion profiles using the information
from the fibres that are crossed by the kinematic major axis. Figure 5
displays the rotation and the velocity dispersion curves for NGC 1277 in black
(left panels). The profiles for NGC 1278 are also shown for reference. As a
sanity check to assess the quality of our kinematic determination we also plot
the previous long-slit measurements of NGC 1277 from Ferré-Mateu et al. (2017)
in crimson (right panels). Our $\sigma$ profile agrees remarkably well with
that in Ferré-Mateu et al. (2017) except for the central peak which we are
missing, most likely due to beam smearing. The same effect might explain the
smaller amplitude of our rotation curve. The fact that both galaxies are shown
with the same velocity and angular scales highlights the differences between
the two: NGC 1277 is a compact fast rotator with a central $\sigma$ cusp,
while NGC 1278 is an extended barely-rotating object with a much more uniform
$\sigma$.

###  3.2 MGE models of HST images and mass maps

The density of the luminous tracers whose kinematics dominate the spectral
range that we are studying (stars in our case) is a necessary input for JAM.
Also, since we aim to obtain dark matter distributions, we also need to know
the baryonic mass distributions to disentangle both kinds of matter.

To trace the luminosity of NGC 1277, we used an HST ACS F625W image with a
Galactic extinction correction $A_{\rm F625W}=0.365\,{\rm mag}$ (Schlafly &
Finkbeiner, 2011). The filter was selected because it is within the spectral
range from which we obtained the kinematics ($4400\,{\rm\AA}-6650\,{\rm\AA}$),
so it is representative of the stellar population that dominates the stellar
kinematics that we are tracing with our instrumental set-up. Unfortunately,
NGC 1278 is only partially covered by the exposure. To model this galaxy, we
instead used the ACS F850LP image with a correction $A_{\rm
F850LP}=0.205\,{\rm mag}$. This is not ideal, because this band falls outside
the CGMS spectral range, and as a consequence does not exactly correspond to
the stellar population of the luminous tracers. Because the F850LP image
covers both galaxies, it is used as a proxy for the $z$ band in the colour
maps (see below). The HST images reveal that both galaxies have a tiny
circumnuclear dust ring smaller than $1\arcsec$ in radius which is visually
similar to some of those described in Lauer et al. (2005) and Comerón et al.
(2010).

The mass maps for both galaxies were constructed by combining the above-
mentioned F850LP frame and an extinction-corrected F475W image ($A_{\rm
F475W}=0.538$) from the same programme. Equating F475W to the $g$ band and
F850LP to the $z$ band (Ryon, 2022) and assuming a Chabrier (2003) IMF, Table
A1 from Roediger & Courteau (2015) provides the following relation for the
$g$-band mass-to-light ratio:

${\rm log}\left(\Upsilon_{\star g}\right)=-1.132+1.116(g-z).$ (2)

We applied the mass-to-light ratio map to the F475W image to obtain the mass
surface density map. We considered an absolute solar magnitude of $M_{\odot
g}=5.11\,{\rm mag}$ (Willmer, 2018). Because of the strong evidence for a
bottom-heavy IMF in red nuggets (Martín-Navarro et al., 2015; Ferré-Mateu et
al., 2017), which is consistent with the tendency for the densest galaxies to
have the heaviest IMF (Figure 12 in Cappellari et al., 2013a), the mass
density map was corrected from a Chabrier to a Salpeter (1955) IMF with the
following recipe from Cimatti et al. (2008)

${\rm log}\left(M_{\star}\right)({\rm Salpeter})={\rm
log}\left(M_{\star}\right)({\rm Chabrier})+0.23.$ (3)

This recipe does not account for the mass of stellar remnants.

Table 1: Parameters of the MGE decompositions of the surface brightness maps
of NGC 1277 and NGC 1278

${\rm log}\,I_{0}\,({\rm log}\,({\rm L}_{\odot}\,{\rm pc^{-2}}))$ | $\sigma_{\star}\,({\rm arcsec})$ | $q^{\prime}_{\star}$
---|---|---
NGC 1277 (F625W)
5.061 | 0.019 | 0.892
4.524 | 0.111 | 0.896
4.226 | 0.249 | 0.888
3.951 | 0.705 | 0.479
3.628 | 0.892 | 0.809
3.127 | 1.597 | 0.723
2.975 | 2.276 | 0.450
2.860 | 3.418 | 0.450
2.675 | 6.197 | 0.450
1.785 | 12.847 | 0.475
1.493 | 12.847 | 0.950
NGC 1278 (F850LP)
4.627 | 0.025 | 1.000
4.153 | 0.173 | 1.000
3.663 | 0.480 | 1.000
3.706 | 0.793 | 0.828
3.369 | 1.609 | 0.803
3.225 | 3.076 | 0.800
2.882 | 7.604 | 0.800
1.543 | 18.938 | 0.800
2.172 | 18.938 | 1.000
888$I_{0}$ stands for the central surface brightnesses of the projected
Gaussian components, $\sigma_{\star}$ denotes their dispersion, and
$q^{\prime}_{\star}$ their projected axial ratio. An approximate conversion
between the F850LP and F625W surface brightnesses can be obtained by dividing
the NGC 1278 $I_{0}$ values by 1.7 (corresponding to $r-z=0.74$, and
accounting for the different brightness of the Sun in the two bands).

Table 2: Parameters of the MGE decompositions of the surface mass density maps
of NGC 1277 and NGC 1278

${\rm log}\,\Sigma_{0}\,({\rm log}\,({\rm M}_{\odot}\,{\rm pc^{-2}}))$ | $\sigma_{\star}\,({\rm arcsec})$ | $q^{\prime}_{\star}$
---|---|---
NGC 1277
5.619 | 0.031 | 0.750
5.366 | 0.101 | 0.750
5.083 | 0.239 | 0.750
4.559 | 0.662 | 0.750
4.779 | 0.701 | 0.400
4.371 | 1.077 | 0.750
3.903 | 2.325 | 0.483
3.543 | 2.629 | 0.599
3.420 | 4.838 | 0.400
3.283 | 7.150 | 0.427
2.239 | 12.861 | 0.536
2.332 | 12.861 | 0.750
NGC 1278
4.631 | 0.233 | 0.900
4.511 | 0.630 | 0.900
4.005 | 1.444 | 0.811
3.825 | 2.998 | 0.800
3.428 | 7.280 | 0.804
2.862 | 17.127 | 0.900
999Same as Table 1, but with $\Sigma_{0}$ indicating the projected central
surface mass densities of the Gaussian components.

Both the surface brightness and the mass density distributions were
parametrised using an MGE (Emsellem et al., 1994; Cappellari, 2002). The fits
were made with the MgeFit101010We used v5.0.14 of the MgeFit Python package
from https://pypi.org/project/mgefit/. software by Cappellari (2002). This
approach describes galaxies as a superposition of two-dimensional Gaussian
components which, by knowing the inclination of the galaxy, can be deprojected
into three-dimensional oblate axi-symmetric Gaussian components. We fixed the
major axis of the MGE components to correspond to those of the kinematic axes
measured in Sect. 3.1.

A detailed characterisation of the surface brightness and mass distributions
requires knowledge about the point spread functions (PSFs). They were modelled
using Tiny Tim (Krist, 1995; Krist et al., 2011) and assuming that the targets
sit at the centre of the chip. For the mass map, we adopted the PSF of the
reddest filter used to build it, that is F850LP.

Given that the outer regions of the galaxies contain pixels with no well-
defined colours due to negative fluxes introduced by random fluctuations and
the background subtraction, we only modelled a region slightly larger than
that covered by our good-quality integral field data, that is, an ellipse with
${\rm PA}=96\aas@@fstack{\circ}0$ (from the kinematic major axis) and with
semi-axes $a=520\,{\rm pixels}$ ($26\arcsec$) and $b=312\,{\rm pixels}$
($15\aas@@fstack{\prime\prime}6$) for NGC 1277 (the ellipticity comes from the
shape of the outer isophotes as obtained by fitting elliptical isophotes as in
Jedrzejewski, 1987), and a circle with a radius $a=760\,{\rm pixels}$
($38\arcsec$) for NGC 1278. Still, the surface mass density map contained a
significant number of outliers in the outskirts of the galaxies. We identified
them by studying the statistical properties in boxes of $10\,{\rm
pixels}\times 10\,{\rm pixels}$ in the outer half of the radius range to be
fitted with MGE. Specifically, we looked for pixels that were at least two
standard deviations above the median value in the box and we filtered them by
replacing their value with the median. Finally, point sources, overlapping
galaxies, and the near side of the dust rings of both galaxies, were masked.

Tables 1 and 2 show the parameters of the MGE decompositions of the surface
brightness and mass density maps of the two galaxies, respectively. The
magnitude of the Sun in $r$ (F625W) and $z$ (F850LP) was assumed to be
$M_{\odot r}=4.65\,{\rm mag}$ and $M_{\odot z}=4.50\,{\rm mag}$, respectively
(Willmer, 2018). Figures 6 and 7 allow a direct visual comparison of the
isophotes of the original HST images (in black) and those from the model (in
red).

Figure 6:  In black, isophote plot derived from the HST F625W image of NGC
1277 with $0.5\,{\rm mag\,arcsec^{-2}}$ intervals. The corresponding MGE model
isophotes are indicated in red. The blue ellipse denotes the extent of the
region that was used to produce the MGE models. The grey circles indicate the
position of the fibres that were used for the dynamical analysis. Figure 7:
Same as Fig. 6, but for NGC 1278 and the HST F850LP image. Figure 8:  Major-
(continuous line and coordinate $x$) and minor-axis (dashed line and
coordinate $y$) surface brightness profiles of NGC 1277 (left panel; in F625W)
and NGC 1278 (right panel; in F850LP). Black lines come from our MGE fit and
green ones come from Emsellem (2013) after a correction for extinction. The
vertical grey lines indicate the maximum extent of the fitting area along the
major (continuous) and the minor axis (dashed). For NGC 1278 the minor and
major axis surface brightness profiles are nearly undistinguishable. The grey
curves in the right panel correspond to the F625W surface brightness profiles
calculated under the assumption that $r-z=0.74$ (see text). Figure 9:  Major-
(continuous line and coordinate $x$) and minor-axis (dashed line and
coordinate $y$) stellar surface density profiles of NGC 1277 (left panel) and
NGC 1278 (right panel). The vertical grey lines are as in Fig. 8. The surface
density estimates were calculated by deriving pixel-to-pixel mass-to-light
ratios from colours following the prescriptions in Roediger & Courteau (2015),
and assuming a Salpeter IMF.

As a sanity check, we compared our MGE major- and minor-axis surface
brightness profiles for NGC 1277 to those in Emsellem (2013). We corrected the
latter for Galactic extinction to be directly comparable with ours. The
profiles were computed following Eq. 1 in Cappellari (2002)

$I(x,y)=\sum_{j}I_{0j}\,{\rm
exp}\left[-\frac{1}{2\sigma_{{\star}j}^{2}}\left(x^{2}+\frac{y^{2}}{q^{\prime}_{{\star}j}}\right)\right],$
(4)

where the sum is made over all the Gaussian components $j$, $x$ and $y$ are
coordinates in the plane of the sky (in the directions of the major and the
minor axis of the galaxy, respectively), and $I_{0j}$, $\sigma_{{\star}j}$,
and $q^{\prime}_{{\star}j}$ are the central surface brightness, the dispersion
(size), and the projected axial ratio of the MGE components. The results are
shown in Fig. 8.

Overall, the agreement between our parametrisation of the surface brightness
map of NGC 1277 and that from Emsellem (2013) is rather good. The apparently
large difference within the central $0\aas@@fstack{\prime\prime}1$ only
affects the central pixel. The other small discrepancies within the central
$1\arcsec$ can be attributed to differences in the handling of the small
nuclear dust ring. Some large differences are seen at the edges of the fitting
range, where the surface brightness profiles computed from our fit can be, at
very specific radii, a factor of two or more above that obtained from Emsellem
(2013). This occurs at a surface brightness of $\sim 25\,{\rm
mag\,arcsec^{-2}}$ and might be a consequence of small differences in sky
subtraction and masking strategies.

The total F625W luminosity of our NGC 1277 model can be calculated as
(Cappellari et al., 2013b, Eq. 10)

$L=\sum_{j}L_{j}=\sum_{j}2\pi
I_{0j}\sigma_{{\star}j}^{2}q_{{\star}j}^{\prime},$ (5)

where $L_{j}$ is the total luminosity of each of the individual Gaussian
components, resulting in $L=2.2\times 10^{10}\,{\rm L}_{\odot r}$, whereas
that estimated in Emsellem (2013) is (after the extinction correction)
$L=2.4\times 10^{10}\,{\rm L}_{\odot r}$. The differences between the two
parametrisations are comparable to those found between van den Bosch et al.
(2012) and Emsellem (2013).

Our models show that NGC 1278, as expected, is more extended than NGC 1277.
The central surface brightness of NGC 1278 is smaller than in NGC 1277, again
indicating that the latter is a much more centrally concentrated object. The
total F850LP luminosity of our NGC 1278 model is $L=8.3\times 10^{10}\,{\rm
L}_{\odot z}$. Given $r-z=0.74$ ($r-z=0.90$, when not accounting for
differential extinction) as measured from a circular aperture
$15^{\prime\prime}$ in radius centered in NGC 1278 in SDSS DR16 images
(Ahumada et al., 2020), this corresponds to $L\approx 4.8\times 10^{10}\,{\rm
L}_{\odot r}$, which is roughly two times the luminosity of NGC 1277 at the
same band.

The circularised luminosity integrated within a cylinder of radius $R$ of an
MGE model can be written as (Cappellari et al., 2013b, Eq. 11)

$L(R)=\sum_{j}L_{j}\left[1-{\rm
exp}\,\left(-\frac{R^{2}}{2\sigma_{{\star}j}^{2}q_{{\star}j}^{\prime}}\right)\right].$
(6)

This expression can be used to find the effective radius of the galaxies by
setting $L(R_{\rm e})=L/2$. For NGC 1277 we obtain $R_{\rm
e}=3\aas@@fstack{\prime\prime}5$ (corresponding to 1.2 kpc) and for NGC 1278
we find $R_{\rm e}=11\aas@@fstack{\prime\prime}7$ (corresponding to 3.9 kpc).
These values highlight again the extreme compactness of NGC 1277 when compared
to a regular massive ETG. Our determination of the effective radius of NGC
1277 is comparable with the values of $R_{\rm e}=1.6\,{\rm kpc}$ obtained by
van den Bosch et al. (2012), $R_{\rm e}=\left(1.2\pm 0.1\right)\,{\rm kpc}$ by
Ferré-Mateu et al. (2017), and $R_{\rm e}=\left(1.3\pm 0.1\right)\,{\rm kpc}$
by Yıldırım et al. (2017). Because the two galaxies differ in luminosity by a
factor of roughly two, it might be convenient to describe their compactness in
terms of their effective radius relative to the radius of a given isophote. We
chose $R_{23}$, the circularised radius of the $23\,{\rm mag\,arcsec^{-2}}$
extinction-corrected F625W isophote. The circularised surface brightness
profile was computed by setting $q^{\prime}_{\star j}\rightarrow 1$ and
$\sigma_{\star j}\rightarrow\sigma_{\star j}\sqrt{q^{\prime}_{\star j}}$ in
Eq. 4 as suggested in Cappellari et al. (2009). We obtained $R_{\rm 23}/R_{\rm
e}=4.9$ and $R_{23}/R_{\rm e}=2.8$ for NGC 1277 and NGC 1278, respectively.

Using the data in Table 2 we derived the surface density profiles (Fig. 9),
which we found to follow rather closely the surface brightness profiles except
for the inner arcsecond, where the colours differ from the rest of the galaxy
due to the presence of dust rings. These profiles have to be taken with some
care, since they are made under the assumption of a Salpeter IMF. Different
IMFs might result in significant $\Upsilon_{\star}$ changes (see Sects. 4 and
5.1 for a dynamical determination of $\Upsilon_{\star}$). Under this IMF
assumption we use an expression analogous to Eq. 5,

$M_{\star}=\sum_{j}M_{\star
j}=\sum_{j}2\pi\Sigma_{0j}\sigma_{{\star}j}^{2}q_{{\star}j}^{\prime},$ (7)

to find a total stellar mass of $M_{\star}=1.3\times 10^{11}\,{\rm M}_{\odot}$
for NGC 1277 (compatible with the value of $M_{\star}=\left(1.3\pm
0.2\right)\times 10^{11}\,{\rm M}_{\odot}$ in Yıldırım et al., 2017) and of
$M_{\star}=2.7\times 10^{11}\,{\rm M}_{\odot}$ for NGC 1278.

##  4 JAM dynamical modelling

We used the Jeans Anisotropic Modelling (JAM111111We used v6.3.2 of the Python
package JamPy, available from https://pypi.org/project/jampy/.) code to
produce dynamical models of the galaxies. Given MGE models of the luminous
tracer and mass distributions, a galaxy inclination ($i$), and an anisotropy
parameter ($\beta_{z}$ or $\beta_{r}$) that can be different for each MGE
component, JAM computes the projected first and second moments of the velocity
distribution of the dynamical tracers (stars in our case). JAM solves the
Jeans equations to describe the motions of star in a state of hydrodynamical
equilibrium (Jeans, 1922) by assuming either a cylindrically- (Cappellari,
2008) or a spherically-aligned velocity ellipsoid (Cappellari, 2020). The
definition of the anisotropy parameter varies depending on the chosen
alignment. In the cylindrically-aligned case, with coordinates $(R,z,\theta)$,
the anisotropy parameter is defined as $\beta_{z}\equiv
1-\overline{V_{z}^{2}}/\overline{V_{R}^{2}}$, whereas for the spherically-
aligned case with coordinates $(r,\theta,\phi)$, $\beta_{r}\equiv
1-\overline{V_{\theta}^{2}}/\overline{V_{r}^{2}}$ ($V_{z}$, $V_{R}$,
$V_{\theta}$, and $V_{\rm r}$ stand for the velocities along the $z$, $R$,
$\theta$, and $r$ coordinates, respectively). We fitted the JAM models to the
$V_{\rm rms}$ values obtained from the GCMS and NIFS observations using
adamet. Before running the fits, we rotated the $V_{\rm rms}$ maps so that the
major axis of the galaxy determined in Sect. 3.1 lied horizontally.

Tests of JAM using high-resolution $N$-body simulations (Lablanche et al.,
2012) and lower-resolution cosmological hydrodynamical simulations (Li et al.,
2016) have confirmed its good accuracy when using high-S/N data, and
negligible bias in reproducing the total mass profiles. More recently, JAM was
compared in detail against the Schwarzschild (1979) method using samples of
both observed galaxies, with circular velocities from interferometric
observations of the CO gas, and numerical simulations respectively. These
studies consistently found that the JAM method produces even more accurate
(smaller scatter versus the true values) density profiles (Figure 8 in Leung
et al., 2018) and enclosed masses (Figure 4 in Jin et al., 2019) than the more
general Schwarzschild models. This may be due to the JAM assumption acting as
an empirically-motivated prior and reducing the degeneracies of the dynamical
inversion. These extensive tests justify our choice of JAM for this study.

In general, our density models introduced into adamet include the dark matter
halo, the stellar component, and a central mass to account for the
supermassive black hole. The latter is introduced as a minute MGE component
with a Gaussian sigma of $0\aas@@fstack{\prime\prime}01$.

We assumed spherical dark matter haloes described by a Navarro-Frenk-White
profile (Navarro et al., 1996, 1997, NFW profile)

$\rho_{\rm DM}=\frac{\rho_{\rm s}}{\frac{r}{r_{\rm s}}\left(1+\frac{r}{r_{\rm
s}}\right)^{2}},$ (8)

where $r$ is the three-dimensional radius, $r_{\rm s}$ is the break radius,
and $\rho_{\rm s}$ is a normalisation density. In order to reduce the number
of free parameters, we set $r_{\rm s}=100\,{\rm kpc}$, which is a reasonable
estimate for massive elliptical galaxies calculated from the stellar-to-halo
mass relation from Girelli et al. (2020) and the halo mass-concentration
relations from Klypin et al. (2011) and Child et al. (2018, see Sect. 5.2 for
further details). As discussed in Cappellari et al. (2013b), the choice of a
break radius is irrelevant because simulations systematically predict them to
be found well outside the outermost regions sampled by the dynamical tracers.
To include the dark matter halo in our JAM models, we fitted the analytic form
of the halo with the mge_fit_1d routine in the MgeFit package, which produces
an accurate MGE approximation. The dark matter halo Gaussian components were
characterised by their mass $M_{{\rm DM}\,j}$ and dispersion $\sigma_{{\rm
DM}\,j}$.

The three-dimensional stellar mass distribution fed into JAM was that from the
MGE stellar mass density models (Sect. 3.2). The intrinsic axial ratio of the
Gaussian components was obtained by assuming an inclination angle $i$
(Cappellari, 2008, Eq. 14)

$q_{{\star}j}=\frac{\sqrt{q_{{\star}j}^{\prime 2}-{\rm cos}^{2}\,i}}{{\rm
sin}\,i}.$ (9)

Once the intrinsic axial ratios of the components were computed, the volume
density of stars was described as

$\rho_{\star}(R,z)=\alpha\sum_{j}\frac{M_{\star
j}}{\left(\sqrt{2\pi}\sigma_{{\star}j}\right)^{3}q_{\star j}}\,{\rm
exp}\,\left[-\frac{1}{2\sigma_{{\star}j}^{2}}\left(R^{2}+\frac{z^{2}}{q_{{\star}j}^{2}}\right)\right],$
(10)

where $R$ is the projection of the radius in the mid-plane of the galaxy, and
where the formula from Cappellari (2008) is scaled with the so-called mismatch
parameter (Cappellari et al., 2012), which is defined as

$\alpha\equiv\frac{\Upsilon_{\star}}{\Upsilon_{\rm
Salpeter}}=\frac{M_{\star}/L}{\left(M_{\star}/L\right)_{\rm
Salpeter}}=\frac{M_{\star}}{\left(M_{\star}\right)_{\rm Salpeter}}.$ (11)

The mismatch parameter describes the stellar mass-to-light ratio with respect
to that expected from a Salpeter IMF.

In practice, the parameters that we fitted by feeding JAM models into adamet
are:

  * •

The intrinsic axial ratio of the flattest MGE component of the stellar model,
$q_{\star\,{\rm min}}$. It is related to the projected axial ratio
$q_{\star\,{\rm min}}^{\prime}$ and the inclination $i$ through Eq. 9. Fitting
this parameter is equivalent to fit the inclination $i$.

  * •

The shape of the velocity ellipsoid, parametrised by either $\beta_{z}$ or
$\beta_{r}$.

  * •

The mismatch parameter, that accounts for deviations from the Salpeter IMF
that was assumed while constructing the stellar mass maps (Sect. 3.2). Finding
this parameter is equivalent to a dynamical determination of the stellar mass-
to-light ratio.

  * •

The black hole mass, $M_{\rm BH}$.

  * •

The dark matter halo density normalisation. We introduced it as $f_{\rm
DM}(6\,{\rm kpc})$, the fraction of matter that is dark within the inner 6 kpc
of the galaxy. The mass within 6 kpc was calculated as $M(6\,{\rm
kpc})=M_{\star}(6\,{\rm kpc})+M_{\rm DM}(6\,{\rm kpc})+M_{\rm BH}$. The
seemingly arbitrary 6 kpc radius corresponds to the radial coverage of the
GCMS data of NGC 1277.

We adopted constant priors on all parameters during the adamet Bayesian
modelling. For most of the parameters, we refined the bounds of the fitting
range after running the fit several times and examining the posterior
probability distributions. In other cases, the boundaries come from physical
limitations. For example, $M_{\rm BH}$ and $f_{\rm DM}(6\,{\rm kpc})$ cannot
be smaller than zero. Also, the intrinsic axial ratio of the flattest MGE
component cannot be larger than the projected one, setting an upper boundary
$q_{\star\,{\rm min}}=q^{\prime}_{\star\,{\rm min}}$. Finally, to avoid
unphysically thin components, we assume a minimum possible axial ratio for the
flattest component at $q_{\star\,{\rm min}}=0.05$.

In order to calculate the mass of spherical dark matter halo MGEs within a
specific radius we used the following expression from Cappellari (2008, Eq.
49)

$M_{\rm DM}(r)=\sum_{j}M_{{\rm DM}\,j}\left[{\rm
erf}\,\left(\frac{r}{\sqrt{2}\sigma_{{\rm
DM}\,j}}\right)-\frac{\sqrt{\frac{2}{\pi}}r}{\sigma_{{\rm DM}\,j}}{\rm
exp}\,\left(-\frac{r^{2}}{2\sigma_{{\rm DM}\,j}^{2}}\right)\right],$ (12)

where erf stands for the error function. For the flattened stellar MGE
components, the mass contained within a radius $r$ is given by the following
expression adapted from Cappellari et al. (2013b, Eq. 15)

$M_{\star}(r)=\alpha\sum_{j}M_{\star j}\left[{\rm erf}\,\left(h_{\star
j}\right)-2h_{\star j}{\rm exp}\,\left(-h_{\star
j}^{2}\right)/\sqrt{\pi}\right],$ (13)

where we accounted for the mismatch parameter and where

$h_{\star j}=\frac{r}{\sqrt{2}\sigma_{\star j}q_{\star j}^{1/3}}.$ (14)

The instrumental pixel size and the seeing are accounted for by JAM. Since the
pixels considered by JAM are square, for GCMS we assumed a pixel size of
$3\aas@@fstack{\prime\prime}7$, equivalent in surface to our
$4\aas@@fstack{\prime\prime}16$ in diameter fibres. We also assumed a PSF
sigma of one arcsecond. For the NIFS data the situation is more complicated,
because the data points correspond to the centre of Voronoi bins with variable
size. We set the pixel size to the actual value for NIFS,
$0\aas@@fstack{\prime\prime}05$, because the data for the central region of
NGC 1277 (the most sensitive to the black hole dynamics) has enough signal to
remain unbinned. We used the same NIFS PSF parametrisation as Krajnović et al.
(2018, Appendix A), that is an inner component with a Gaussian sigma
$0\aas@@fstack{\prime\prime}05$ and weight 0.65 and an outer component with
sigma $0\aas@@fstack{\prime\prime}40$ and a weight 0.35.

###  4.1 Dynamical modelling of NGC 1277

Figure 10:  Dynamical modelling of the NIFS $V_{\rm rms}$ map of NGC 1277
assuming a cylindrically-aligned velocity ellipsoid (fit cA1). The corner plot
shows the probability distribution of the fitted parameters marginalised over
either two parameters for the contour plots, and over one for the histograms.
In the contour plots blue regions correspond to the three-sigma confidence
level and white regions denote maximum likelihood. The top-right corner shows
the $V_{\rm rms}$ map and the fit, with grey isophotes indicating F625W
contours separated by $0.5\,{\rm mag\,arcsec^{-2}}$ and the black crosses
indicating the centre of the bins. The indentations in the isophotes are a
clear sign of the presence of the dust ring, whose near side was masked while
producing the MGE models. The fitted parameters were $q_{\star\,{\rm min}}$,
$\beta_{z}$, $\alpha$, and $M_{\rm BH}$, whereas the dark matter fraction
$f_{\rm DM}(6\,{\rm kpc})$ was fixed to zero. Figure 11:  As Fig. 10, but this
time the fitted $V_{\rm rms}$ map is that of the GCMS data, $f_{\rm
DM}(6\,{\rm kpc})$ ($f_{\rm DM}(1.5\,R_{\rm e})$) is a free parameter and the
central black hole mass is fixed to $M_{\rm BH}=4.70\times 10^{9}\,{\rm
M}_{\odot}$ (fit cA2).

For NGC 1277 we have both GCMS and NIFS data. A particularity of the NIFS
dataset is that the spaxel with the largest $\sigma$ does not correspond to
the coordinate centre as provided by Walsh et al. (2016). This small offset of
$0\aas@@fstack{\prime\prime}02$ was corrected before running the fits.

Figure 12:  Major- (blue) and minor-axis (red) $V_{\rm rms}$ profiles for the
NIFS data of NGC 1277 (symbols) and the cA1 fit (continuous line). The error
bars represent one-sigma $V_{\rm rms}$ formal uncertainties as obtained by
pPXF (see Sect. 3.1). We selected the bins whose centres are within a cone
with an aperture of $30^{\circ}$ centered in the major (minor) axis. Figure
13:  Same as Fig. 12, but this time for the GCMS data, the cA2 fit, and for
fibres whose centre is within a fibre radius ($2\aas@@fstack{\prime\prime}05$)
of the major and minor axes.

We tested three fitting approaches to check the internal consistency and gauge
the uncertainties:

  1. A

_Successively fit the NIFS and the GCMS data:_ We first fitted the NIFS data
(A1; Fig. 10). Since the field of view of the instrument only covers the inner
0.5 kpc of NGC 1277, we assumed the dynamical effect of dark matter to be
negligible and fixed $f_{\rm DM}(6\,{\rm kpc})=0$. Indeed, the dark matter
fraction within 0.5 kpc expected for a dark matter halo typical of a galaxy
with the mass of NGC 1277 (see Sect. 5.2) is $\sim 0.5\%$. Then, we fitted the
GCMS data with the black hole mass $M_{\rm BH}$ fixed to the value obtained in
A1 (A2; Fig. 11). The rationale for this is that the black hole sphere of
influence (Peebles, 1972) is small compared to the field of view covered by
the GCMS data ($\sim 130\,{\rm pc}$ or $\sim 0\aas@@fstack{\prime\prime}4$ for
a $M_{\rm BH}=5\times 10^{9}\,{\rm M}_{\odot}$ and for a central velocity
dispersion $\sigma=400\,{\rm km\,s^{-1}}$) and we should not expect the latter
to help constraining the black hole mass. When fitting for black hole masses
with JAM, it is always recommended to restrict the field of view to the
smallest region required to break the $M/L-$black hole degeneracy (e.g.,
Thater et al., 2022) not to risk biasing the black hole mass due to gradients
in the velocity ellipsoid and the mismatch parameter, or due the choice of a
parametrisation for the dark matter halo. In other words, a good global fit
might be reached at the expense of a poor fit of the central region, resulting
in a bad determination of the black hole mass. This approach is very different
from the one usually employed with Schwarzschild models, which need large
radii kinematics to constrain the orbital distribution and reduce degeneracies
in the black hole mass.

  2. B

_Simultaneous fit of the NIFS and the GCMS data:_ Both sets of data were
fitted simultaneously (plot not shown). We multiplied the uncertainties of
$V_{\rm rms}$ in the NIFS dataset by a factor 2.5 so both datasets have a
roughly equal weight in the chi-squared value (the same procedure was followed
in Cappellari et al., 2015 to merge data from SLUGGS and ATLAS3D).

  3. C

_Fitting the GCMS data alone:_ For this fit, we excluded the NIFS data (plot
not shown). As detailed in the description of approach A, this procedure is
not recommended because we run into the risk of biasing the black hole mass
estimate. However, because we do not have NIFS data for NGC 1278, producing
this fit allows for a direct comparison between the two galaxies.

We denote fits made assuming a cylindrically-aligned velocity ellipsoid with a
‘c’ prefix, and those with a spherically-oriented one with an ‘s’. As
discussed in Cappellari (2020), no single alignment holds for a full galaxy. A
cylindrically-oriented ellipsoid is only found in the case of a plane-parallel
potential, whereas a spherically-oriented one is found for a strictly
spherical one. Nevertheless, a cylindrically-oriented ellipsoid is a rather
good approximation for a disc, especially close to the mid-plane (Cappellari
et al., 2007; Cappellari, 2008). Since the Schwarzschild (1979) dynamical
modelling by Yıldırım et al. (2015) does not show signs of a galaxy-wide
pressure-supported component, we assumed a cylindrical alignment for our
fiducial fit of NGC 1277 (cA).

The fitted parameters for all the approaches are listed in Table 3. For
parameters whose maximum likelihood values are not close to the boundary of
the fitting interval, we present them as ${\rm value}\pm{\rm sigma}/2$, where
sigma has been calculated as the interval between the 15.86 and 84.14
percentiles. In some cases, in particular for $f_{\rm DM}(6\,{\rm kpc})$ and
$q_{\rm\star min}$, the probability distribution may peak close to the
boundary of the fitting interval imposed by physics. We detected those cases
are those where $\left|{\rm value}-{\rm boundary}\right|<{\rm sigma}/2$. In
such cases, we determined one-sigma upper (lower) limits based on the 68.28
(31.72) percentile.

Table 3: JAM model fit parameters for NGC 1277

|  | Fitting approach | $q_{\star\,{\rm min}}$ |  $\beta_{z}$ or $\beta_{r}$ |  $\beta_{z,{\rm out}}$ or $\beta_{r,{\rm out}}$ | $\alpha$ | $M_{\rm BH}$ | $f_{\rm DM}(6\,{\rm kpc})$
---|---|---|---|---|---|---|---|---
|  |  |  |  |  |  | $\left(10^{9}\,{\rm M}_{\odot}\right)$ | $f_{\rm DM}(5\,{R_{\rm e}})$
Cylindric |  Single $\beta_{z}$ | cA1 NIFS only | $<0.08$ | $-0.26\pm 0.03$ | $-$ | $1.187\pm 0.012$ | $4.70\pm 0.11$ | 0
cA2 GCMS fixed $M_{\rm BH}$ | $0.36\pm 0.03$ | $0.00\pm 0.06$ | $-$ | $1.211\pm 0.014$ | 4.70 | $<0.03$
cB NIFS+GCMS | $>0.38$ | $-0.14\pm 0.03$ | $-$ | $1.194\pm 0.013$ | $5.0\pm 0.2$ | $<0.009$
cC GCMS all free | $0.36\pm 0.04$ | $-0.01\pm 0.07$ | $-$ | $1.20\pm 0.03$ | $4.9\pm 0.9$ | $<0.03$
Two $\beta_{z}$ | cA2$\beta_{z}$ GCMS fixed $M_{\rm BH}$ | $0.35\pm 0.03$ | $0.02\pm 0.09$ | $0.01\pm 0.06$ | $1.208\pm 0.015$ | 4.70 | $<0.03$
cB$\beta_{z}$ NIFS+GCMS | $>0.35$ | $-0.27\pm 0.06$ | $-0.05\pm 0.05$ | $1.188\pm 0.017$ | $5.3\pm 0.3$ | $<0.03$
cC$\beta_{z}$ GCMS all free | $0.35\pm 0.04$ | $0.06\pm 0.13$ | $0.01\pm 0.07$ | $1.21\pm 0.03$ | $4.7\pm 1.0$ | $<0.03$
Spherical |  Single $\beta_{r}$ | sA1 NIFS only | $0.092\pm 0.015$ | $0.48\pm 0.03$ | $-$ | $1.178\pm 0.010$ | $1.9\pm 0.2$ | 0
sA2 GCMS fixed $M_{\rm BH}$ | $0.34\pm 0.02$ | $0.25\pm 0.06$ | $-$ | $1.300\pm 0.016$ | 1.9 | $<0.05$
sB NIFS+GCMS | $0.30\pm 0.02$ | $0.34\pm 0.08$ | $-$ | $1.240\pm 0.016$ | $2.6\pm 0.5$ | $0.08\pm 0.04$
sC GCMS all free | $0.35\pm 0.02$ | $0.13\pm 0.16$ | $-$ | $1.25\pm 0.05$ | $3.6\pm 1.6$ | $<0.04$
Two $\beta_{r}$ | sA2$\beta_{r}$ GCMS fixed $M_{\rm BH}$ | $0.33\pm 0.02$ | $0.34\pm 0.10$ | $0.24\pm 0.07$ | $1.307\pm 0.019$ | 1.9 | $<0.05$
sB$\beta_{r}$ NIFS+GCMS | $0.30\pm 0.03$ | $0.36\pm 0.07$ | $0.21\pm 0.11$ | $1.27\pm 0.02$ | $2.4\pm 0.5$ | $<0.07$
sC$\beta_{r}$ GCMS all free | $0.35\pm 0.02$ | $0.2\pm 0.4$ | $0.2\pm 0.2$ | $1.27\pm 0.07$ | $3.0\pm 1.8$ | $<0.05$

121212Fits cA1 and cA2 are shown in Figs. 10 and 11, respectively. Values in
boldface were fixed for the fit. The grey background indicates our fiducial
fit. The errors and the upper and lower limits correspond to formal one sigma
uncertainties (see text).

We first comment on the fiducial fit, cA. When fitting the NIFS data only we
find a black hole mass $M_{\rm BH}=(4.70\pm 0.11)\times 10^{9}\,{\rm
M}_{\odot}$ (Fig. 10), which is essentially the same as $M_{\rm BH}=(4.54\pm
0.11)\times 10^{9}\,{\rm M}_{\odot}$ obtained by Krajnović et al. (2018) with
the same data. The fitted values for $q_{\star\,{\rm min}}$ and $\beta$ are
also the same within the uncertainties. The subsequent GCMS data fit with a
fixed $M_{\rm BH}$ (Fig. 11) yields a negligible dark matter fraction with
$f_{\rm DM}(6\,{\rm kpc})<0.03$. Reassuringly we find that the mismatch
parameter is very similar for the NIFS and the GCMS fits ($\alpha=1.187\pm
0.012$ versus $\alpha=1.211\pm 0.014$). This is relevant, since a large
difference between the two would require considering an $\alpha$ varying with
radius. The determination of the mismatch parameter allows us to re-evaluate
the stellar mass of NGC 1277 to $M_{\star}\approx 1.6\times 10^{11}\,{\rm
M}_{\odot}$.

In Figs. 12 and 13 we compare the major- and minor-axis $V_{\rm rms}$ profiles
of the NIFS and GCMS data to those derived from the cA1 and cA2 fits,
respectively. The agreement between the data and the fits is generally good,
especially for the GCMS data (cA2), where the fitted $V_{\rm rms}$ passes
close to most of the observed data points when accounting for three-sigma
error bars. The central small $V_{\rm rms}$ peak is also well captured by the
fit.

Both fitting approaches cB and cC yield very similar values for several of the
parameters, with negligible dark matter fractions within 6 kpc, a mismatch
parameter $\alpha\approx 1.2$, and black hole mass in the range $4.5\times
10^{9}\,{\rm M}_{\odot}\lesssim M_{\rm BH}\lesssim 5.0\times 10^{9}\,{\rm
M}_{\odot}$. It is noteworthy that the high angular resolution NIFS data do
not seem to be required to obtain a reasonable black hole mass estimate with a
formal error bar smaller than 20%. This coincidence is probably due to the
fact that we are introducing high angular resolution information through the
MGE models of the luminosity and the surface brightness distributions (see
Appendix A) and highlights the importance of high angular resolution
information to properly constrain the mass of the central black hole. A
further reason for the concordance is that the mismatch parameter does not
vary much with radius, as indicated by the small difference in the $\alpha$
values fitted in cA1 and cA2.

The intrinsic flattening of the flattest component $q_{\star\,{\rm min}}$
shows significant differences between fitting approaches. This parameter is
found to be in the range between $q_{\star\,{\rm min}}=0.050$ and
$q_{\star\,{\rm min}}=0.4$, which corresponds to an inclination between
$i=67\degr$ and $i=90\degr$. The intermediate $q_{\star\,{\rm min}}$ values
given by fits cA2 and cC correspond to $i\approx 79\degr$, which is very close
to the value deduced from the shape of the circumnuclear dust ring
($i=75\degr$; van den Bosch et al., 2012). The value of $q_{\star\,{\rm
min}}<0.08$ obtained from fitting the NIFS data only is considerably off the
other values, probably because the NIFS FOV covers a region where the dominant
MGE components are nearly round (Table 2), hence offering little constraining
power on the flatness of the galaxy.

The parameter $\beta_{z}$ is significantly smaller when fitting the NIFS data
alone than when fitting the NIFS and GCMS data simultaneously. The largest
positive $\beta_{z}$ values correspond to the fits where GCMS data only are
used. This suggests a radial variation of the shape of the velocity ellipsoid.
To explore this effect, we repeated all the fits where GCMS data are used, but
this time we considered two $\beta_{z}$ parameters. The first one corresponded
to stellar MGE components with a sigma smaller than the effective radius
$R_{\rm e}$, whereas the second one ($\beta_{z,{\rm out}}$) described the more
extended components. The fits with two $\beta_{z}$ values are denoted with the
suffix ‘$\beta_{z}$’. The results of the fits (Table 3) indicate that allowing
for radial variations in $\beta_{z}$ does not have a significant effect in
either $\alpha$, $M_{\rm BH}$, or $f_{\rm DM}(6\,{\rm kpc})$.

Following Cappellari (2020), we also fitted the data assuming a spherically-
aligned velocity ellipsoid (with an anisotropy parameter $\beta_{r}$) in order
to have a better grasp of the uncertainties. The results remain broadly the
same as with the cylindrically-aligned models (Table 3) and a negligible dark
matter fraction is also recovered here except for fit sB, which combines the
NIFS and the GCMS data. In this case, the need for dark matter might partly
come from the fact that JAM finds a relatively low inclination of $i=73\degr$
which is lower than for the other fits accounting for the GCMS data. The other
large differences between these fits and those made assuming a cylindrically-
aligned velocity ellipsoid arise in the black hole mass and the mismatch
parameter determination, with the former being lower and the latter being
higher than in the fiducial fit. Because all the fits result in a similar
baryonic (black hole plus stellar) mass within 6 kpc, this is at least partly
the consequence of the degeneracy between $M_{\rm BH}$ and $\alpha$.

We have also made experiments with dark matter profiles other than NFW, such
as the generalised NFW profile or the Einasto profile (Einasto, 1965). In all
cases, the resulting dark matter fraction $f_{\rm DM}(6\,{\rm kpc})$ has been
found to be compatible with zero. We also checked that uncertainties of the
order of $0\aas@@fstack{\prime\prime}5$ in the determination of the centre of
NGC 1277 within the field of view of the GCMS (see Sect. 3.1) do not affect
our results.

Figure 14:  Same as Fig. 10, but this time for the GCMS $V_{\rm rms}$ map of
NGC 1278 assuming a spherically-aligned velocity ellipsoid (fit sB). The
isophotes come from a F850LP image. This is our fiducial fit for NGC 1278,
where the fitted parameters are $q_{\star\,{\rm min}}$, $\beta_{r}$, $\alpha$,
and $M_{\rm BH}$, and $f_{\rm DM}(6\,{\rm kpc})$ ($f_{\rm DM}(1.5\,R_{\rm
e})$). Figure 15:  Same as Fig. 12 but for NGC 1278 with GCMS data, and the SB
fit. Because the galaxy is nearly spherical, we included data from all the
fibres and sorted them according to their distance to the centre.

To sum up, the results of nearly all our fitting approaches broadly coincide
with those of the fiducial fit cA (with a cylindrically-aligned velocity
ellipsoid and a single $\beta_{z}$). This fit yields a mismatch parameter
$\alpha=1.211\pm 0.014$ (giving a probably too optimistically well-constrained
stellar mass of $M_{\star}\approx(1.63\pm 0.02)\times 10^{9}\,{\rm
M}_{\odot}$) and a black hole mass $M_{\rm BH}=\left(4.70\pm 0.11\right)\times
10^{9}\,{\rm M}_{\odot}$. We also find a negligible dark matter fraction
within 6 kpc ($5\,R_{\rm e}$), $f_{\rm DM}(6\,{\rm kpc})<0.03$. We stress
that, almost irrespectively of the fitting approach, we find that dark matter
has a negligible dynamical effect within the inner 6 kpc of NGC 1277.

###  4.2 Dynamical modelling of NGC 1278

In order to fit the NGC 1278 kinematics we need to rely on the GCMS data only.
This means that, contrary to the case of NGC 1277, we lack high angular
resolution data able to provide tight constraints on the black hole mass. For
these fits we followed two approaches:

  1. A

_Fit where the central black hole mass is fixed by scaling relations:_ We use
the $M_{\rm BH}-M_{\star}$ scaling relation in the Eq. 15 from Sahu et al.
(2019) relating the black hole mass to the total stellar mass of elliptical
galaxies (the plot for fit A is not shown). By introducing the total stellar
mass $M_{\star}=2.7\times 10^{11}\,{\rm M_{\odot}}$ (Sect. 3.2) we obtained
$M_{\rm BH}=1.3\times 10^{9}\,{\rm M}_{\odot}$. However, because the residual
mean square of the relation is 0.48 dex, $M_{\rm BH}$ is expected to be in the
rather large range between $M_{\rm BH}\approx 4\times 10^{8}\,{\rm M}_{\odot}$
and $M_{\rm BH}\approx 4\times 10^{9}\,{\rm M}_{\odot}$. Alternatively, we
could have used the $M_{\rm BH}-\sigma$ relation. Assuming the expression in
Eq. 7 from Kormendy & Ho (2013) and a central velocity dispersion
$\sigma=285\,{\rm km\,s^{-1}}$ we obtained a virtually identical black hole
mass of ($M_{\rm BH}=1.4\times 10^{9}\,{\rm M}_{\odot}$ with a 0.29 dex
scatter in the relation).

  2. B

_Fit with no constraints:_ We left all the parameters free, including the
black hole mass $M_{\rm BH}$. We chose it to be our fiducial fit (Fig. 14)
because the large scatter in the black hole scaling relations (see item A)
could introduce a bias when fixing the black hole mass.

Table 4: JAM model fit parameters for NGC 1278

|  | Fitting approach | $q_{\star\,{\rm min}}$ |  $\beta_{z}$ or $\beta_{r}$ |  $\beta_{z,{\rm out}}$ or $\beta_{r,{\rm out}}$ | $\alpha$ | $M_{\rm BH}$ | $f_{\rm DM}(6\,{\rm kpc})$
---|---|---|---|---|---|---|---|---
|  |  |  |  |  |  | $\left(10^{9}\,{\rm M}_{\odot}\right)$ | $f_{\rm DM}(1.5\,{R_{\rm e}})$
Cylindric |  Single $\beta_{z}$ | cA $M_{\rm BH}$ fixed | $>0.76$ | $0.026\pm 0.014$ | $-$ | $1.174\pm 0.019$ | 1.3 | $0.044\pm 0.014$
cB all free | $>0.77$ | $0.023\pm 0.013$ | $-$ | $1.10\pm 0.03$ | $3.9\pm 0.8$ | $0.077\pm 0.018$
Two $\beta_{z}$ | cA$\beta_{z}$ $M_{\rm BH}$ fixed | $>0.71$ | $0.12\pm 0.04$ | $-0.09\pm 0.03$ | $1.20\pm 0.02$ | 1.3 | $0.045\pm 0.014$
cB$\beta_{z}$ all free | $>0.70$ | $0.11\pm 0.05$ | $-0.07\pm 0.03$ | $1.18\pm 0.03$ | $1.7\pm 0.9$ | $0.058\pm 0.018$
Spherical |  Single $\beta_{r}$ | sA $M_{\rm BH}$ fixed | $>0.76$ | $0.42\pm 0.07$ | $-$ | $0.91\pm 0.06$ | 1.3 | $0.25\pm 0.05$
sB all free | $>0.76$ | $0.41\pm 0.09$ | $-$ | $0.94\pm 0.07$ | $1.1\pm 1.0$ | $0.23\pm 0.05$
Two $\beta_{r}$ | sA$\beta_{r}$ $M_{\rm BH}$ fixed | $>0.77$ | $0.38\pm 0.08$ | $0.29\pm 0.14$ | $1.01\pm 0.10$ | 1.3 | $0.19\pm 0.07$
sB$\beta_{r}$ all free | $>0.77$ | $0.41\pm 0.09$ | $0.25\pm 0.14$ | $1.06\pm 0.10$ | $0.3\pm 1.0$ | $0.16\pm 0.07$

131313Fit sB is shown in Fig. 14. Values in boldface were fixed for the fit.
The grey background indicates our fiducial fit. The errors and the upper and
lower limits correspond to formal one sigma uncertainties (see text in Sect.
4.1).

The baryon distribution in NGC 1278 is found to be nearly circular in
projection (Table 2), which might be indicative of a far from flattened
baryonic matter distribution. We tested this hypothesis by calculating the
projected angular momentum within an effective radius to check whether NGC
1278 is a slow rotator, as follows. First, we estimated the projected angular
momentum within $R_{\rm e}$ (Emsellem et al., 2007, Eq. 6)

$\lambda_{R_{\rm
e}}=\frac{\sum_{i=1}^{N}F_{i}R_{i}\left|V_{i}\right|}{\sum_{i=1}^{N}F_{i}R_{i}\sqrt{V_{i}^{2}+\sigma_{i}^{2}}},$
(15)

where the sums are made over the fibres within $R_{\rm e}$, $R_{i}$ are the
distances of the fibres to the centre of NGC 1278, and $F_{i}$ are the fluxes
at those distances based on the MGE model calculated using the circularised
version of Eq. 4 (see Sect. 3.2). We found $\lambda_{R_{\rm e}}=0.094$. Then,
we measured the ellipticity of the MGE model using the routine
mge_half_light_isophote included in JAM and obtained $\varepsilon_{\rm
e}=0.19$. Finally, we applied the test proposed in Eq. 19 in (Cappellari,
2016), who suggested that galaxies fulfilling

$\lambda_{R_{\rm e}}<0.080+\varepsilon_{\rm e}/4,$ (16)

as it is the case for NGC 1278, are slow rotators. Since this test proves that
NGC 1278 is not likely to be a very flattened object, we chose a spherically-
aligned velocity ellipsoid for our fiducial fit. We present the results in
Table 4. As for NGC 1277, the fits are labelled with prefixes ‘c’ and ‘s’ so
to denote the velocity alignments and a suffix ‘$\beta_{z}$’ or ‘$\beta_{r}$’,
respectively, if they were produced assuming two different values for the
shape of the velocity ellipsoid. Here we assumed that $\beta_{r,{\rm out}}$
and $\beta_{z,{\rm out}}$ affect the shape of the MGE components with
$\sigma_{\star}$ larger than the effective radius, $R_{\rm
e}=11\aas@@fstack{\prime\prime}7$.

Our fiducial fit sB (Fig. 14) yields a significant fraction of dark matter
within 6 kpc, $f_{\rm DM}(6\,{\rm kpc})=0.23\pm 0.05$. This fraction does not
change if we keep the black hole mass fixed (fit sA). The fiducial fit yields
a mismatch parameter $\alpha=0.94\pm 0.07$, which implies that the stellar
mass-to-light ratio compatible with that expected from a Salpeter IMF. In
principle, changes in $\alpha$ modify the $M_{\rm BH}$ obtained in the $M_{\rm
BH}-M_{\star}$ scaling relation that is introduced as a constant in sA, but
since $\alpha\approx 1$, the shift in $M_{\rm BH}$ would be very small. The
value of $M_{\rm BH}=(1.1\pm 1.0)\times 10^{9}\,{\rm M}_{\odot}$ obtained in
the fiducial fit is compatible with what is expected from the scaling
relations.

All the fits yield a $q_{\star\,{\rm min}}$ value peaking at the boundary of
the fitting range ($q_{\star\,{\rm min}}=0.8$). Since NGC 1278 is likely to be
near-spherical, this is a poorly-defined parameter and not much importance
should be attached to this coincidence.

Contrarily to NGC 1277, where $f_{\rm DM}(6\,{\rm kpc})$ was consistently
found to be negligible irrespective of the kind of fit, the fraction of dark
matter within 6 kpc in NGC 1278 is found to vary depending on whether a
cylindrically- or a spherically-aligned velocity ellipsoid is assumed. The
former orientation yields dark matter fractions $f_{\rm DM}(6\,{\rm
kpc})\approx 0.05\pm 0.02$ and the latter have $f_{\rm DM}(6\,{\rm
kpc})\approx 0.20\pm 0.05$. Fits with low $f_{\rm DM}(6\,{\rm kpc})$
compensate the lack of dark matter by increasing the baryonic mass through an
increase in $\alpha$ from $\alpha\approx 0.9-1.0$ (slightly smaller than that
expected for a Salpeter IMF) to up to $\alpha\approx 1.2$ (indicating a
bottom-heavy IMF comparable to that obtained for NGC 1277). For our fiducial
fit, a zero dark matter fraction is disfavoured at a more than four-sigma
level, but a strong covariance is seen between $\alpha$ and $f_{\rm
DM}(6\,{\rm kpc})$ (Fig. 14). Hence, an independent determination of $\alpha$
would be desirable in order to confirm the presence of a significant dark
matter fraction. Such an evidence was obtained from line index indicators,
showing a much bottom-lighter IMF in NGC 1278 than in NGC 1277 (companion
paper Ferré-Mateu et al. in prep.).

Figure 15 shows the radial $V_{\rm rms}$ profile. The agreement between the
observation and the fit in the central region ($R\lesssim 15^{\prime\prime}$)
is remarkable. At larger radii, the error bars in $V_{\rm rms}$ for the
individual fibres becomes as large as a few tens of ${\rm km\,s}^{-1}$, which
causes a large scatter. Yet, the fit passes roughly through the middle of the
data cloud. The reason why such data points with large error bars are not
abundantly found for NGC 1277 is the abruptness of the surface brightness
profile, which causes the radial range of fibres with barely acceptable
kinematic fits to be very narrow.

As for NGC 1277, we checked whether registration errors of the GCMS data of
the order of $0\aas@@fstack{\prime\prime}5$ would have an impact on the
results. We found that the uncertainties in $\alpha$ and $f_{\rm DM}(6\,{\rm
kpc})$ introduced by the centering error are smaller than the formal one-sigma
error bars of the fit.

In summary, for NGC 1278 we find a dark matter fraction $f_{\rm DM}(6\,{\rm
kpc})=0.23\pm 0.05$ and a black hole mass $M_{\rm BH}=(1.1\pm 1.0)\times
10^{9}\,{\rm M}_{\odot}$. The excess parameter is $\alpha=0.94\pm 0.07$
(compatible with a Salpeter IMF), which yields a total stellar mass
$M_{\star}=(2.5\pm 0.2)\times 10^{11}\,{\rm M}_{\odot}$.

##  5 Discussion

###  5.1 The mass-to-light ratio and the IMF of the stellar component of NGC
1277 and NGC 1278

Figure 16:  Circularised mass-to-light ratio $\Upsilon_{\star r}$ as a
function of the radius for NGC 1277 and NGC 1278, in blue and red
respectively. The vertical lines indicate the limit of the GCMS kinematic
data, The right axis shows the correspondence with the absolute value of the
outer exponent of a bimodal IMF, $\Gamma_{\rm b}$, for a stellar population
with an age of 13.0 Gyr and a metallicity $[{\rm Z}/{\rm H}]=0.26$. The
horizontal black dashed lines denote the range of $\Gamma_{\rm b}$ values
found by Martín-Navarro et al. (2015) and Ferré-Mateu et al. (2017) for NGC
1277. The surface brightness of NGC 1278 has been converted to F625W as in
Sect. 3.2. The correspondence between $\Upsilon_{\star r}$ and $\Gamma_{\rm
b}$ is only roughly valid for NGC 1277 because NGC 1278 is slightly younger
and less metallic (Ferré-Mateu et al. in prep).

Our determination of the stellar mass of NGC 1277 and NGC 1278 makes it
possible to provide constraints on the IMF. Our fiducial fit of NGC 1277
yields a stellar mass-to-light ratio in F625W (similar to the $r$ band)
$\Upsilon_{\star r}=7.4\,{\rm M}_{\odot}/{\rm L}_{\odot r}$. After converting
the F850LP surface brightnesses to F625W through $r-z=0.74$ (measured from
SDSS images, Sect. 3.2), we find $\Upsilon_{\star r}=5.6\,{\rm M}_{\odot}/{\rm
L}_{\odot r}$ for NGC 1278.

If we know $\Upsilon_{\star}$, the age of the stellar population, and its
metallicity we can obtain information about the shape of the IMF from
photometric predictions based on spectral energy distributions. Here, we used
those based on E-MILES (Vazdekis et al., 2012)141414The E-MILES spectral
energy distributions can be downloaded from
http://research.iac.es/proyecto/miles/pages/photometric-predictions-based-on-
e-miles-seds.php. computed using BaSTI isochrones. These predictions are made
assuming an IMF lower cutoff at $0.1\,{\rm M}_{\odot}$ and an upper cutoff at
$100\,{\rm M}_{\odot}$. The $\Upsilon_{\star}$ inferences account for the
stellar remnants (contrarily to the mass maps derived in Sect 3.2, with
respect to which the mismatch parameter $\alpha$ from our fits was
calculated). Based on Martín-Navarro et al. (2015) and Ferré-Mateu et al. (in
prep) we assume an age of 13.0 Gyr and a metallicity of $[{\rm Z}/{\rm
H}]=0.26$ for NGC 1277.

Under the assumption of a bimodal IMF with a turning point at $0.4\,{\rm
M}_{\odot}$ defined as in Vazdekis et al. (1996), and where $-\Gamma_{\rm b}$
corresponds to the exponent of the power law in the high-end of the IMF, we
obtain $\Gamma_{\rm b}=2.54$. This value is very similar with that found by
Martín-Navarro et al. (2015) and Ferré-Mateu et al. (2017), where the index
varied between $\Gamma_{\rm b}\approx 3.05$ at the centre of NGC 1277 and
$\Gamma_{\rm b}\approx 2.5$ at a radius of about $1.4\,R_{\rm e}$. The fact
that both line indices and dynamical modelling yield compatible results makes
the inference of a bottom-heavy IMF for NGC 1277 very robust.

In Fig. 16 we plot the stellar mass-to-light ratio at F625W as a function of
the radius for NGC 1277 and NGC 1278. Here we define $\Upsilon_{\star r}$ as
the ratio of the circularised surface density and the surface brightness MGE
models corrected (multiplied) by the mismatch parameter. The right axis
indicates the corresponding absolute value of the outer exponent of a bimodal
IMF, $\Gamma_{\rm b}$, obtained from the E-MILES photometric predictions for a
stellar population with age 13.0 Gyr, metallicity $[{\rm Z}/{\rm H}]=0.26$
(this is roughly valid for NGC 1277 only, because NGC 1278 is slightly younger
and less metallic; Ferré-Mateu et al. in prep.). If the mismatch parameter,
$\alpha$, were constant with radius as assumed in the JAM fits, the wiggles in
$\Upsilon_{\star}$ would imply a genuine variation of the mass-to-light ratio.
However, the observed changes in $\Gamma_{\rm b}$, are a combination of real
variations driven by small radial changes in $\alpha$, and apparent variations
due to small radial trends of the stellar population age and abundances.
Nevertheless, it is reassuring to see that for most of the radial range, the
estimated $\Gamma_{\rm b}$ index for NGC 1277 falls within the range of values
obtained in Martín-Navarro et al. (2015) and Ferré-Mateu et al. (2017). In NGC
1278, $\Upsilon_{\star}$ is systematically lower than in NGC 1277 at all
radii. This is line with the finding that relic galaxies have a bottom-heavier
IMF than regular ETGs of a similar properties (Martin-Navarro et al., 2023).

Interestingly, the excess parameter of $\alpha\approx 1.2$ found in NGC 1277
is virtually identical to $\alpha=1.19$ measured at the centre of massive ETGs
by Gu et al. (2022). This is in agreement with the idea that some massive ETGs
host a rather untouched red nugget at their centre, which would be the remains
of the first-phase of formation at their centre (de la Rosa et al., 2016;
Ferré-Mateu et al., 2019; Barbosa et al., 2021). NGC 1278, with $\alpha\approx
1.0$, has a mismatch parameter below the average in Gu et al. (2022). It would
be interesting to check in future work whether allowing for a radial-dependent
$\alpha$ would show indications of a negative mismatch parameter gradient.

###  5.2 The dark matter haloes of NGC 1277 and NGC 1278

In this subsection we compare the fitted dark matter haloes to the
expectations from models and simulations. To do so, two pieces of information
are required:

  1. 1)

A stellar-to-halo mass relation (SHMR) providing a dark halo mass as a
function of the measured stellar mass.

  2. 2)

A parametrisation of the shape of the dark matter halo as a function of its
mass.

We adopted the SHMR from Girelli et al. (2020), who used abundance matching to
relate the observed stellar mass of galaxies in the COSMOS field to dark
matter halo masses extracted from dustgrain-_pathfinder_ $\Lambda$CDM
simulation (Giocoli et al., 2018). They offer SHMRs at different redshifts,
which allows us to check $z=0$ galaxies, but also to test whether the relic
galaxy NGC 1277 has properties compatible with those of galaxies at $z\sim
2-3$. In this context, the dark matter halo mass $M_{\rm 200}$ is defined as
the mass enclosed within a radius $r_{200}$ where the average density is a
factor $\Delta=200$ times the critical density of the Universe

$\rho_{\rm c}=\frac{3H_{0}^{2}}{8\pi G}.$ (17)

Throughout this paper, the stellar masses in Girelli et al. (2020) have been
consistently shifted by 0.23 dex, so to convert their assumed Chabrier (2003)
IMF into a Salpeter (1955) one. This is because for both NGC 1277 and NGC 1278
the mismatch parameter with respect to a Salpeter (1955) IMF is $\alpha\approx
1$.

Using the SMHR parametrisation in Eq. 6 of Girelli et al. (2020) and the
parameters from their Table 2, we produced Montecarlo runs to estimate the
dark matter halo mass accounting for the statistical uncertainties of the
parameters and in the galaxy stellar mass (from our mismatch parameter
uncertainties). The uncertainties were assumed to have a Gaussian
distribution.

Once the masses of the dark matter haloes were estimated, we parametrised
their shape using Eq. 18 in Child et al. (2018). This expression gives the NFW
dark matter halo concentration, defined as $c_{200}=r_{200}/r_{\rm s}$, as a
function of the stellar-to-halo mass ratio $M_{\star}/M_{200}$. We adopted the
free parameters from the “Stack, NFW” fit in their Table 1. We can then
reformulate Eq. 8 as a function of the concentration

$\rho_{\rm DM}=\frac{\rho_{\rm c}}{3A_{\rm
NFW}}\frac{1}{\frac{r}{r_{200}}\left(\frac{1}{c_{200}}+\frac{r}{r_{200}}\right)^{2}},$
(18)

where $A_{\rm NFW}$ can be written as

$A_{\rm NFW}={\rm ln}\,\left(1+c_{200}\right)-\frac{c_{200}}{1+c_{200}}.$ (19)

Concentration uncertainties were computed from Montecarlo runs accounting for
one-sigma error bars from our fit and those from the parameters in Girelli et
al. (2020) and Child et al. (2018).

Figure 17:  Three-dimensional cumulative mass profiles of NGC 1277 for the
baryonic component (stars plus black hole, in purple), the fitted dark matter
halo (in black), and the predicted dark matter halo profiles for two different
freezing redshifts (in blue and red for low and high $z_{\rm f}$,
respectively) based on the SMHR parametrisation by Girelli et al. (2020) and
the dark matter halo parametrisation by Child et al. (2018). The bands
correspond to 95.4% confidence intervals. The baryonic component can be
further subdivided into the black hole (dotted purple line) and the stellar
component (dashed purple line). The grey vertical line indicates $r=6\,{\rm
kpc}$ ($18^{\prime\prime}$), that is the radius within which we have kinematic
data. Figure 18:  Same as Fig. 17, but for NGC 1278. The dashed grey line
indicates the radius out to which we have kinematic data, that is 10 kpc or
$30^{\prime\prime}$.

In Fig. 17 we display the cumulative baryonic (stellar plus black hole) and
dark matter mass profiles from our fiducial fit to NGC 1277. We include 95.4%
confidence interval (two sigma) bands for both profiles. Since the $f_{\rm
DM}(6\,{\rm kpc})$ probability distribution peaks at zero (the border of the
fitting interval) we calculated the confidence intervals as the 95.4
percentile rather than the interval between the 2.3 and the 97.7 percentiles.
We also display the predicted dark matter halo profiles for freezing redshifts
$z_{\rm f}=0$ and $z_{\rm f}=3$, as well as the 95.4% confidence intervals
based on the Montecarlo simulations. The predicted dark matter halo profiles
for both redhifts are very similar because the stellar mass of NGC 1277
roughly corresponds to that where the SHMR for all the redshifts intersect
(Fig. 12 in Girelli et al., 2020).

The cumulative mass profiles in Fig. 17 indicate that within 6 kpc (equivalent
to $5R_{\rm e}$, which is the radius traced by our kinematic data), NGC 1277
has a mass-follows-light behaviour, with a maximum allowed dark matter
fraction (at a two-sigma level) of $f_{\rm DM}(6\,{\rm kpc})=0.07$. This is in
tension with $f_{\rm DM}(6\,{\rm kpc})=0.09$ predicted for both freezing
redshifts $z_{\rm f}=0$ and $z_{\rm f}=3$. However, it is compatible with the
minimum two-sigma mass fractions allowed by the models according to our
Montecarlo runs based on the Girelli et al. (2020) and Child et al. (2018)
works ($f_{\rm DM}(6\,{\rm kpc})=0.03$). The negligible amount of dark matter
within 6 kpc, and hence the tension between the fit and the expectations, is a
common feature among all except one of the experiments listed in Table 3. Our
results are compatible with those from Yıldırım et al. (2015), who found a
fraction of dark matter within the effective radius, $f_{\rm DM}(R_{\rm e})$
compatible with zero.

The discrepancy between the fitted and the expected dark matter fraction for
NGC 1277 arises from a combination of several factors. The extreme compactness
of NGC 1277 might make it baryon-dominated over most of its disc, so it may
become hard to characterise the dynamical effects of the underlying dark
matter distribution. Also, the reported formal error bars ignore the
systematics that might be introduced by the hypotheses used in the Jeans
modelling. However, those systematics are probably small, as indicated by the
overall good agreement of the $f_{\rm DM}(6\,{\rm kpc})$ values yielded by the
fits made assuming a cylindrical and a spheroidal velocity ellipsoid (see
Cappellari, 2020). Finally, it is possible that a large fraction of the
discrepancy is due to the extreme nature of NGC 1277 and to an early freezing
redshift that resulted in the lack of the accretion of dark matter-rich
satellites to form an envelope.

Contrary to the case of NGC 1277, Fig. 18 shows that the dark matter profile
obtained in our fiducial fit of NGC 1278 falls above to the $z_{\rm f}=0$
prediction. The fitted dark matter profile is in a strong tension with what
would be expected for a $z_{\rm f}=3$ galaxy.

One might be tempted to use the fact that NGC 1277 lacks detectable dark
matter to speculate about the possibility of the (in)existence of Milgromian
dynamics (Milgrom, 1983) or other alternatives to the $\Lambda$CDM paradigm.
However, given a centrally-concentrated baryonic mass of $M_{\star}\approx
1.6\times 10^{11}\,{\rm M}_{\odot}$ and an acceleration constant
$a_{0}=1.24\times 10^{-10}\,{\rm m\,s^{-2}}$ (McGaugh, 2011), we should
explore the dynamics at a radius $R=13\,{\rm kpc}$ (about twice the radius
that we cover) to be able to probe the fully Milgromian regime. Therefore our
data do not permit studying the Milgromian regime unless the Newtonian-
Milgromian transition were not abrupt.

In summary, we find that the fact that the extreme relic galaxy NGC 1277 has
no detectable dark matter within five effective radii is at odds with the
expectations from models. On the other hand, we find that the regular massive
ETG NGC 1278 has a dark matter halo perfectly compatible with the models.

###  5.3 The dark matter fraction within one and five effective radii and
within 6 kpc

Figure 19:  Dark matter fraction within the effective radius, $f_{\rm
DM}(R_{\rm e})$, as a function of the stellar mass for NGC 1277 and NGC 1278
(star symbols). The error bars represent one sigma confidence intervals (that
corresponding to NGC 1277 is smaller than the symbol size). Circles correspond
to the 103 ATLAS3D galaxies with good fits in Cappellari et al. (2013b) and
the diamond symbols correspond to the data for a sample of 161 passive
galaxies from the SAMI Galaxy Survey from Santucci et al. (2022). The colour
coding of the symbols indicates the effective radius of the galaxies as
indicated by the side-bar. The ATLAS3D data points were derived by merging the
galaxy distances from Cappellari et al. (2011), the effective radii and
luminosities from (Cappellari et al., 2013b), and the $f_{\rm DM}(R_{\rm e})$
and $\Upsilon_{\star}$ values from Cappellari et al. (2013a). The effective
radii for the SAMI galaxies were kindly provided by G. Santucci. The green
line indicates the relation derived from JAM models with a fixed
cosmologicaly-motivated NFW dark matter halo from Cappellari et al. (2013b).
The red line and confidence band correspond to the fit represented in Fig. 7
from Santucci et al. (2022). The black line shows a prediction of the
$M_{\star}-f_{\rm DM}(R_{\rm e})$ relation made by combining the dark matter
haloes derived from the SHMR from Girelli et al. (2020) and the dark matter
halo parametrisation from Child et al. (2018) with the $R_{\rm e}$ values
derived from a linear fit (Eq. 20) to the size measurements for galaxies with
a morphological type $T\leq-1$ in Trujillo et al. (2020). The latter relation
was calculated assuming a de Vaucouleurs (1948) profile for the stellar
component and it is complemented by a one-sigma uncertainty band calculated
using a Montecarlo simulation. For the Trujillo et al. (2020) and the Santucci
et al. (2022) data and the Girelli et al. (2020) SHMR, the stellar masses were
corrected by a factor 0.23 dex to convert the assumed Chabrier (2003) IMF into
a Salpeter (1955) one (see Eq. 3 in Sect. 3.2). Figure 20:  Dark matter
fraction within five effective radii $f_{\rm DM}(5\,R_{\rm e})$ for NGC 1277
(star) with the 95.4% confidence interval indicated by a vertical line. The
black line indicates the predicted $M_{\star}-f_{\rm DM}(5\,R_{\rm e})$
relation based on the dark matter haloes profiles and $R_{\rm e}$ values
derived as in Fig. 19. The grey shades indicate the 68.3% (darker) and 95.4%
(lighter) confidence intervals of the relation calculated using a Montecarlo
simulation. A de Vaucouleurs (1948) profile was assumed for the stellar
density profile of the galaxies. Figure 21:  Same as Fig. 20, but this time
for the dark matter fraction enclosed within 6 kpc, $f_{\rm DM}(6\,{\rm
kpc})$, and including the data point corresponding to NGC 1278.

In this section, we compare the fitted dark matter fractions of NGC 1277 and
NGC 1278 with those of other massive ETGs from the literature, as well as with
expectations from combining theoretical models with measurements of the sizes
of massive ETGs. Our deep observations allow us to explore as far as
$5\,R_{\rm e}$ for NGC 1277 and $3\,R_{\rm e}$ for NGC 1278. However, studies
of large samples (e.g., Cappellari et al., 2013b; Santucci et al., 2022),
typically only cover the central regions of the galaxies. Thus, here we
compare the dark matter fractions within $R_{\rm e}$, $f_{\rm DM}(R_{\rm e})$.
Given the small radius probed by these studies and the increased fraction of
baryons as we approach the central regions of galaxies, this dark matter
fraction comparison is of limited interest because these previous studies
sampled radii where dark matter usually plays a minor role.

In Fig. 19, we compare the dark matter fractions $f_{\rm DM}(R_{\rm e})$ for
NGC 1277 and NGC 1278 to the values obtained for a subsample of 103 galaxies
from the ETG survey ATLAS3D (Cappellari et al., 2011) shown in the top panel
of Fig. 10 from Cappellari et al. (2013b) and a sample of 161 passive galaxies
from the SAMI Galaxy Survey (Croom et al., 2012; Bryant et al., 2015) shown in
Fig. 7 from Santucci et al. (2022). The former data points correspond to the
fits deemed to be good by the authors and come from JAM models similar to
ours. The stellar masses of the galaxies from Santucci et al. (2022) were
positively shifted by 0.23 dex to convert their assumed Chabrier (2003) IMF
into a Salpeter (1955) one as we do in Sect. 3.2. Fig. 19 also shows two
$M_{\star}-f_{\rm DM}(R_{\rm e})$ relations derived from the above-mentioned
works. The green line comes from the lower panel in Fig. 10 in Cappellari et
al. (2013b), and was derived from JAM fits where the NFW halo parameters were
fixed to cosmologicaly-motivated values obtained from Moster et al. (2010).
The red line indicates the fit from Fig. 7 in Santucci et al. (2022) and is
again shifted by 0.23 dex.

Figure 19 also displays a third $M_{\star}-f_{\rm DM}(R_{\rm e})$ relation
(black line) that was obtained from the dark matter haloes predicted by
combining the SHMR from Girelli et al. (2020 , which is corrected to a
Salpeter IMF too) and the dark matter halo parametrisation from Child et al.
(2018 , see Sect. 5.2). In order to assign an effective radius to each galaxy
stellar mass, we produced a linear fit between ${\rm log}\,R_{\rm e}$ and
${\rm log}\,M_{\star}$ using the observational data for ETGs (Hubble-Reynolds
type $T\leq 1$) from Trujillo et al. (2020). After correcting $M_{\star}$ by
0.23 dex to shift the IMF to a Salpeter one, we obtained

${\rm log}\,R_{\rm e}=-5.0+0.51\,{\rm log}\,M_{\star},$ (20)

where $R_{\rm e}$ is in kpc and $M_{\star}$ in ${\rm M}_{\odot}$. To estimate
the fraction $X_{\star}(r=R_{\rm e})$ of the stellar mass that is found within
a three-dimensional radius $r=R_{\rm e}$ we assumed a Sérsic (1963) profile
with an index $n=4$ (a de Vaucouleurs, 1948 profile). The fraction $X_{\star}$
for the $n=4$ specific case was calculated by combining Eqs. 30 and 41 and
from Baes & Gentile (2011)

$X_{\star}(r)=1.523\left(\frac{r}{R_{\rm
e}}\right)^{2}G^{8,1}_{1,9}\left[\begin{array}[]{cc}0&\\\
\@vec{b},&-1\end{array}\left|0.7132\left(\frac{r}{R_{\rm
e}}\right)^{2}\right.\right],$ (21)

where $G$ is the Meijer G function (Meijer, 1936) and

$\@vec{b}=\left(\frac{1}{8},\frac{2}{8},\frac{3}{8},\frac{4}{8},\frac{5}{8},\frac{6}{8},\frac{7}{8},\frac{1}{2}\right).$
(22)

We found that for a de Vaucouleurs (1948) profile $X_{\star}(R_{\rm
e})=0.415$. The $M_{\star}-f_{\rm DM}(R_{\rm e})$ relation is complemented by
a one-sigma uncertainty band that was calculated with a Montecarlo simulation
using the uncertainties quoted by Girelli et al. (2020) and Child et al.
(2018), as well as an intrinsic sigma of 0.057 in ${\rm log}\,R_{\rm e}$ from
Table 3 in Trujillo et al. (2020).

We found that the $f_{\rm DM}(R_{\rm e})$ value for NGC 1278 is compatible
with the $M_{\star}-f_{\rm DM}(R_{\rm e})$ relation from Santucci et al.
(2022). If the confidence intervals in the relation from Cappellari et al.
(2013b) were similar to those in Santucci et al. (2022), then the dark matter
fraction in NGC 1278 would be compatible with that relation too. We also found
that $f_{\rm DM}(R_{\rm e})$ in NGC 1278 matches the expectation from
combining the effective radii measured by Trujillo et al. (2020) and the dark
matter halo models discussed in Sect. 5.2. The fact that NGC 1278 falls below
two of the $M_{\star}-f_{\rm DM}(R_{\rm e})$ relations while it has a denser
dark matter halo than the expectation for its mass (Fig. 18) is because is
because its effective radius ($R_{\rm e}=3.9\,{\rm kpc}$) is smaller than the
average for ETGs of its mass ($R_{\rm e}=6.5\,{\rm kpc}$ from Eq. 20).

NGC 1277 is well below the three $M_{\star}-f_{\rm DM}(R_{\rm e})$ relations
shown in Fig. 19 with $f_{\rm DM}(R_{\rm e})<0.007$ (95.4% confidence
interval). The expected dark matter fraction of a galaxy with the stellar mass
of NGC 1277 is $f_{\rm DM}(R_{\rm e})=0.14^{+0.06}_{-0.05}$ at a one-sigma
confidence level and $f_{\rm DM}(R_{\rm e})=0.14^{+0.12}_{-0.09}$ at a two-
sigma confidence level. Calculating $f_{\rm DM}(R_{\rm e})$ is another way of
demonstrating the dark matter deficient nature of this object in comparison
with other galaxies with a similar stellar mass. However, as NGC 1277 is very
compact, we emphasise that its extreme lack of dark matter is only fully
demonstrated by finding little to no dark matter within 6 kpc ($5\,R_{\rm
e}$).

If two galaxies have the same dark matter halo and the same stellar mass, the
most compact one has the smallest $f_{\rm DM}(R_{\rm e})$. We colour-coded the
symbols in Fig. 19 according to their $R_{\rm e}$ to check whether galaxies
with a small $f_{\rm DM}(R_{\rm e})$ are exclusively compact ($R_{\rm
e}\approx 1\,{\rm kpc}$). We find that galaxies with a small $f_{\rm
DM}(R_{\rm e})$ can be relatively extended (with effective radii of a few
kpc), and that some compact galaxies have a non-negligible central dark matter
fraction. Therefore, the reason why Cappellari et al. (2013b) and Santucci et
al. (2022) find galaxies with $f_{\rm DM}(R_{\rm e})\approx 0$ cannot be
solely the compactness of the objects. Instead, these small $f_{\rm DM}(R_{\rm
e})$ values are likely because the fraction of dark matter within $1\,R_{\rm
e}$ is so small, that it becomes hard to constrain it. Indeed, ATLAS3D was
designed to observe galaxies out to $1\,R_{\rm e}$ (Cappellari et al., 2011)
and most of the Santucci et al. (2022) galaxies are covered out to less than
$2\,R_{\rm e}$ (see their Fig. 1). Figure 4 in Cappellari et al. (2015)
illustrates this point by showing that, whereas the stellar and the total mass
profiles of massive ETGs do not differ much in the inner $1\,R_{\rm e}$, the
stellar density profile falls much faster than the total one in the outskirts.
Hence, our large radial coverage ($5\,R_{\rm e}$ for NGC 1277 and $3\,R_{\rm
e}$ for NGC 1278) ensures a precision in the characterisation of the dark
matter component that cannot be achieved if we are limited to the inner
$1-2\,R_{\rm e}$.

To stress the importance of the fact that we find little to no dark matter
within $5\,R_{\rm e}$ for NGC 1277, in Fig. 20 we compare the properties of
NGC 1277 with a $M_{\star}-f_{\rm DM}(5\,R_{\rm e})$ relation computed by
combining the works by Child et al. (2018), Girelli et al. (2020), and
Trujillo et al. (2020) as done for the $M_{\star}-f_{\rm DM}(R_{\rm e})$
relation in black in Fig. 19. This time the fraction of the stellar mass lying
within the radius of interest is $X_{\star}(5\,R_{\rm e})=0.842$.
Additionally, we used a Montecarlo simulation to estimate 68.3% and 95.4%
confidence intervals, yielding $f_{\rm DM}(5\,R_{\rm e})=0.57^{+0.07}_{-0.10}$
and $f_{\rm DM}(5\,R_{\rm e})=0.57^{+0.13}_{-0.24}$, respectively for an ETG
with the stellar mass of NGC 1277. This is incompatible with the two-sigma
limit $f_{\rm DM}(5\,R_{\rm e})<0.07$ obtained from our dynamical fit (Sect.
5.2).

As NGC 1277 is very compact compared to a typical galaxy of its mass (1.2 kpc
versus 5.3 kpc from the $M_{\star}-R_{\rm e}$ relation derived from Trujillo
et al., 2020), the lack of dark matter within $5\,R_{\rm e}$ could be
interpreted as a consequence of the high density of the stellar component. To
emphasise that NGC 1277 is genuinely dark matter deficient, the dark matter
fraction within a given physical radius could be checked instead. In Fig. 21
we compare $f_{\rm DM}(6\,{\rm kpc})$ for NGC 1277 and NGC 1278 with that of a
prediction calculated as for Figs. 19 and 20. Here, $X_{\star}(6\,{\rm kpc})$
had to be computed in a galaxy by galaxy basis, as this fraction varies as a
function of $6\,{\rm kpc}/R_{\rm e}$. We again show that, whereas NGC 1278
falls within the expected trend, NGC 1277 is below it. Although the
discrepancy between the fit and the prediction is not as large as for the
$M_{\star}-f_{\rm DM}(5\,R_{\rm e})$ relation, a tension is still found
($f_{\rm DM}(6\,{\rm kpc})<0.07$ two-sigma limit versus $f_{\rm DM}(6\,{\rm
kpc})=0.16\pm 0.05$ and $f_{\rm DM}(6\,{\rm kpc})=0.16\pm 0.10$ at 68.3% and
95.4% confidence intervals, respectively).

The decaying rotation curve of NGC 1277 (Fig. 5) bears a qualitative
resemblance with those of the high-redshift massive star-forming galaxies
studied by Genzel et al. (2017). The latter six galaxies are also found to be
dark matter-poor, with $f_{\rm DM}(R_{\rm e})\lesssim 0.2$ and compatible with
zero in four cases. However, these galaxies cannot be straightforwardly
compared to NGC 1277. The reason is that the typical effective radius in the
Genzel et al. (2017) sample is $R_{\rm e}\approx 8\,{\rm kpc}$, so these
objects are not nearly as compact as NGC 1277. Also, in five out of six
galaxies, the data coverage stops at $\approx 2\,R_{\rm e}$, so it misses the
galactic outskirts where dark matter is presumed to be playing a major role
and might be able to provide tight constraints on $f_{\rm DM}(R_{\rm e})$.

In conclusion, we find that NGC 1277 lacks dark matter within $1\,R_{\rm e}$,
$5\,R{\rm e}$, and $6\,{\rm kpc}$ when compared to the expectations from
models. On the other hand, we find that NGC 1278 behaves according to what is
expected for a massive ETG.

###  5.4 How could a compact dark matter-deficient galaxy form?

We have found evidence that, in addition to being the best massive relic
candidate in the local Universe, NGC 1277 is dark matter deficient (it has a
fraction of dark matter within $5\,R_{\rm e}$ of less than 7%, whereas the
expected value is $\sim 60\%$; Sect. 5.3 and Fig. 20). The principle of
parsimony suggests that the two oddities have a common cause (or that one is
the consequence of the other). However, another relic, Mrk 1216 (Ferré-Mateu
et al., 2017), has been found to contain significant fractions of dark matter
within $R_{\rm e}$ (Yıldırım et al., 2015; Buote & Barth, 2019). The situation
poses a conundrum: either 1) relic galaxies can form with largely different
dark matter contents, or 2) NGC 1277 and Mrk 1216 are different kinds of
objects born and/or evolved under different circumstances. The latter
possibility is supported by Ferré-Mateu et al. (2017), who found Mrk 1216 to
be the galaxy with the smallest ‘degree of relicness’ among their three-galaxy
sample (which includes NGC 1277). They also found that the burst of star
formation that generated the bulk of the baryonic mass in Mrk 1216 was more
extended in time than for the other galaxies in the sample, as well as traces
of recent accretion. As a consequence, they posit that Mrk 1216 is a relic
that is on its way to become a ‘regular’ massive ETG (see also Yıldırım et
al., 2015).

How did NGC 1277, one of the densest known galaxies, form within a not so
dense dark matter halo? This seems counterintuitive and, according to a study
by Flores-Freitas et al. (2022) based on the TNG50 cosmological simulation
(Pillepich et al., 2019; Nelson et al., 2019), the progenitors of present-day
massive relic galaxies inhabited at $z\sim 4$ dark matter haloes that were
more massive than those of an average quiescent galaxy progenitor with a
similar stellar mass. Also, Figure 7 in Lapiner et al. (2023) shows that
simulations predict that even the most compact blue nuggets have non-
negligible dark matter fractions ($f_{\rm DM}(R_{\rm e})\gtrsim 0.1$).

If it is possible for a few rare galaxies not to have dark matter, it becomes
easy to explain why they do not undergo the envelope accretion phase. In the
absence of a halo, nearby galaxies undergo parabolic flybys instead of
spiralling-in due to dynamical friction (Chandrasekhar, 1943). This hypothesis
would hold even if we had underestimated $f_{\rm DM}(5\,R_{\rm e})$, because
the stripping of the outskirts of the halo (see discussion below) would still
be a plausible mechanism to explain the lack of accretion. On the other hand,
regular massive ETGs like NGC 1278 are effective at cannibalising small dark
matter rich-galaxies, which impacts both $R_{\rm e}$ and $f_{\rm DM}$ (see,
e.g., Hilz et al., 2012; Tortora & Napolitano, 2022). If we assume that the
lack of an envelope in NGC 1277 is due to a dark matter deficiency, it must
have either lost its dark matter early (before significant accretion occurred)
or was dark matter deficient ab initio. Hence, the big question about NGC 1277
shifts from ‘how did it avoid to accrete an envelope?’ to ‘why is it dark
matter deficient?’.

A possible way to generate a dark matter-poor galaxy that resembles a massive
relic was proposed by Flores-Freitas et al. (2022). They used the TNG50
cosmological simulation to identify five relic analogues, of which the one
residing in subhalo 6 is the purest and the most similar to NGC 1277. The
simulated galaxy is born in isolation within a massive $\sim 10^{12}\,{\rm
M}_{\odot}$ dark matter halo that is significantly stripped as it enters a
cluster. As the galaxy loses most ($\sim 90\%$) of its dark matter, it also
leaves behind most of its gas, which prevents further star formation from
happening. During this process, the stellar body of the galaxy remains mostly
intact, as it loses only about $20\%$ of its mass. The resulting galaxy has
1.4 times more mass in dark matter than in stars (Flores-Freitas et al.,
2022), and virtually all the dark matter outside a radius of 30 kpc has been
stripped away (Flore-Freitas, private communication). This phenomenon is
similar to the stripping of dark matter of satellites as they interact with
their main galaxy (Engler et al., 2021). Moreno et al. (2022) also explored
simulated dwarf satellite galaxies that lose most of their dark matter as they
have a close interaction with their parent galaxy. They proposed that in such
events the stellar component is harder to remove than the dark matter one
because stellar orbits are more circular than those of dark matter particles.
Hence, repeated interactions would be efficient at stripping dark matter
particles when they are close to their apocentre.

The main caveat of the Flores-Freitas et al. (2022) scenario is given by the
authors themselves. Indeed, as subhalo 6 falls within the cluster, the
apparent stripping might in part be caused by some of the material being
assigned to the parent halo. Thus, the mass loss could be an artefact
introduced by the algorithm assigning particles to the different dark matter
haloes. Another problem is that, whereas the outer parts of the halo are
efficiently stripped, the dark matter mass within the inner 6 kpc diminishes
by a factor of less than two (Flores-Freitas; private communication), so the
mechanism does not seem sufficient to remove most of the dark matter from the
central parts of the galaxy. On the other hand, the stripping of the outer
parts of the halo would probably be sufficient to greatly reduce dynamical
friction and perhaps prevent the accretion of an envelope. A possible way
around all these caveats is that subhalo 6 contains the best relic analogue
within the TNG50 volume, but this volume of $1.4\times 10^{5}\,{\rm Mpc}^{3}$
is relatively small compared to the observed local number density of relics
(three in $5\times 10^{6}\,{\rm Mpc}^{3}$; Ferré-Mateu et al., 2017) and might
be insufficient to cover the most rare and extreme objects. Hence it is likely
that a larger simulation volume would uncover even better relic analogues more
closely resembling NGC 1277.

A scenario similar to that put forward by Flores-Freitas et al. (2022) was
given by Yu et al. (2018). These authors studied the Illustris simulation
(Vogelsberger et al., 2014) searching for dark matter-deficient galaxies. They
found a galaxy akin to NGC 1277 that is, compact ($R_{\rm e}\approx 2\,{\rm
kpc}$), massive ($M_{\star}=9.42\times 10^{10}\,{\rm M}_{\odot}$), and with a
total dark matter mass fraction below 0.1. According to Yu et al. (2018), a
strong interaction with the environment at redshift $z<1$ would have stripped
about half of the stars from the galaxy and most of its dark matter (their
Fig. 2). The result would be a dense compact galaxy with little dark matter.
Only one such galaxy is found within the $(106.5\,{\rm Mpc})^{3}\approx
1.2\times 10^{6}\,{\rm Mpc}^{3}$ Illustris box, which is tantalisingly close
to the observational density constraints by Ferré-Mateu et al. (2017) and of
the same order of magnitude as the number density of relics estimated by
Quilis & Trujillo (2013). It is also compatible with the estimated density of
massive ultra-compact galaxies for the $z<0.3$ Universe of $(1.0\pm 0.4)\times
10^{-6}\,{\rm Mpc}^{-3}$ from Buitrago et al. (2008) and the lower limit for
the relic density of one relic within $10^{7}\,{\rm Mpc}^{3}$ from Spiniello
et al. (2021b).

A possible caveat of the work by Yu et al. (2018) is that the Illustris
simulation yields lower dark matter fractions for ETGs than those measured
through gravitational lensing (Mukherjee et al., 2022). Another caveat is
that, since the mass loss in their scenario occurred quite late ($z<1$), the
interaction should have stripped both the envelope and the population of blue
globular clusters (found to be absent in Beasley et al., 2018). This
possibility is discussed in Beasley et al. (2018) and found to be unlikely
because, whereas tidal stripping could explain the lack of an envelope, it
could not explain the extreme density of the centre of the galaxy. As a
consequence, they conclude that NGC 1277 was already dense and compact at
birth. To strengthen the argument, we find that NGC 1278 has signs of a
relatively young ($<10\,{\rm Gyr}$) accreted stellar population all the way to
its centre (Ferré-Mateu et al. in prep) which should be observed in NGC 1277
too if it had lost its envelope long after the blue nugget phase. Additional
caveats of a process such as that described in Yu et al. (2018) affecting NGC
1277 at a relatively late time ($z\lesssim 1$) is that it is hard to imagine
how the stripped core of an ETG could become rotation-dominated. Furthermore,
NGC 1277 lacks shells and streams (Trujillo et al., 2014), which indicates a
paucity of interactions affecting the stellar component in the last few Gyr
(Mancillas et al., 2019). Therefore, the only way to reconcile the stripping
hypothesis with the observations is by assuming that the dark matter loss
occurred very early (as seen in the work by Flores-Freitas et al., 2022),
before NGC 1277 had time to accrete a significant envelope.

In a bottom-up hierarchical paradigm, galaxies grow by mergers. In the early
Universe, galaxies were richer in gas than nowadays and mergers as well as
cold streams caused a wet compaction that led to the formation of the compact
high-redshift galaxies known as blue nuggets (see, e.g., Lapiner et al.,
2023). It is possible that for a few major mergers the geometry of the
encounter (impact parameter and relative velocity) were such that the
collisionless dark matter would escape the system. The escape velocity from a
$10^{11}\,{\rm M}_{\odot}$ body at a distance of $1\,{\rm kpc}$ is $\approx
1000\,{\rm km\,s^{-1}}$, so under this hypothesis the relative velocity of the
two bodies should be of the order of $2000\,{\rm km\,s^{-1}}$ in order to
remove the dark matter from the system. Whereas these relative velocities can
hardly be found in the field, they are consistent with the high-velocity tail
within rich clusters. For example the Perseus cluster where NGC 1277 resides,
is a rich cluster (Völk & Atoyan, 2000) with a velocity dispersion of
$\sigma=1288^{+90}_{-77}\,{\rm km\,s^{-1}}$ (Girardi et al., 1993). Hence, we
speculate that infrequent high-velocity collisions during the proto-cluster
phase are possible. Indeed, assuming a Hubble-Lemaître parameter at $z=2$,
$H(z=2)\approx 200\,{\rm km\,s^{-1}}$, we obtain from the relations in
Ferragamo et al. (2022) that to reach a velocity dispersion of $1000\,{\rm
km\,s^{-1}}$ (so a few outliers have velocities of $2000\,{\rm km\,s^{-1}}$),
a cluster mass of $3\times 10^{14}\,{\rm M}_{\odot}$ is sufficient. This mass
is less than half the current mass of the Perseus cluster, $M=8.5\times
10^{14}\,{\rm M}_{\odot}$ (Mathews et al., 2006).

In this scenario high-velocity collision scenario, the situation would be
somewhat similar to that of the Bullet Cluster (Clowe et al., 2004; Markevitch
et al., 2004), where dissipative matter (gas) is left behind. However, the
analogy cannot be pushed too far because the gas in the blue nugget progenitor
fragments would be orders of magnitude denser and cooler than that in the
intra-cluster medium.

In the high-velocity encounter framework, the difference between the
progenitor of NGC 1277 and that of a blue nugget on its way to become a
regular ETG would be that the latter keeps most of its dark matter. This might
be because the mergers that generated the progenitors of regular ETGs were
mostly minor (as suggested by Zolotov et al., 2015) or because the relative
velocity of the merging fragments was not large enough to prevent the dark
matter from falling back.

The high-velocity merger hypothesis has of course several caveats. The first
one is that NGC 1277 looks like the passively-evolved product of the average
blue nugget which is presumed to have a regular fraction of dark matter. As a
consequence, if our suggestion is valid, young massive ETGs should look
similar irrespective of their dark matter content. This is not completely
unreasonable because the dark matter fraction in the central regions of blue
nuggets massive ETGs is often small (Lapiner et al., 2023 and Fig. 19,
respectively). However, it remains to be seen whether the lack of a dense
extended dark matter halo would not result in the loss of many of the baryons
at the onset of intense star formation. Another problem of this scenario is
related to the time-scales involved in the process. On one hand, intense star
formation would likely be triggered by the collision. On the other hand, the
star formation time-scale should be longer than the dynamical time-scale
($\tau_{\rm dyn}\sim 1/\sqrt{G\overline{\rho}}\sim 40\,{\rm Myr}$, where
$\overline{\rho}$ is the average density of NGC 1277) for the gas to have time
to settle in a disc in order to produce a mostly rotation-supported stellar
body. Also, the density of the gas should have been high enough to ensure a
fast cooling to prevent the escape of a large fraction of the gas shock-heated
by the collision.

A third possibility to explain the apparent lack of dark matter in NGC 1277 is
a strong departure from a NFW dark matter profile. Our data do not reach the
depth required to probe the matter distribution beyond 6 kpc. This leaves the
door open for a halo with a core much flatter than that predicted by a NFW
profile. It is known that density fluctuations introduced by AGN and stellar
feedback at the centre of galaxies can erase cusps (e.g., Martizzi et al.,
2013). The extremely massive central black hole could have powered the
feedback, but such processes are also efficient at expelling baryons, so they
should have occurred after most of the gas was transformed into stars.
Therefore it is unclear how an extremely concentrated stellar component could
sit within a halo that is more cored than average. Furthermore, a cored halo
would not prevent dynamical friction from happening, so it would fail to
naturally explain the absence of an envelope.

NGC 1277 is similar to a gigantic rotating globular cluster, where the stars
are the main contributor to the mass. Our favoured hypothesis to explain the
formation of such a peculiar object is that NGC 1277 was born with little dark
matter or that it lost most of it very early at or soon after its blue nugget
phase. A plausible mechanism for that is that most of the dark matter of the
galaxy was lost through interactions as it entered and moved through the
Perseus cluster. Alternatively, NGC 1277 could have formed in a high-velocity
collision of gas-rich fragments, where baryons coalesced and formed stars as
dark matter left the system because of its velocity exceeding the escape one.

##  6 Summary and conclusions

Relic galaxies are fascinating objects thought to be the frozen remains of the
high redshift massive ETGs ($z\gtrsim 2$). Whereas the vast majority of
massive ETGs have suffered a complex merger history and have accreted an
envelope, relic galaxies are thought to be the untouched and passively-evolved
descendants of the blue nuggets observed in the early Universe. Very few relic
galaxies are known, the most pristine of which is NGC 1277 (Trujillo et al.,
2014). NGC 1277 is a massive (stellar mass $M_{\star}\approx 1.6\times
10^{11}\,{\rm M}_{\odot}$) and centrally concentrated (effective radius
$R_{\rm e}\approx 1.2\,{\rm kpc}$) galaxy in the Perseus cluster.

We have revisited NGC 1277 using data from the fibre spectrograph GCMS at the
2.7 m Harlan J. Smith telescope (Fig. 1). The data are of unprecedented
interest because 1) the long 2.5 hour exposure allows us to study the
outskirts of the galaxy (going from a radius of $13^{\prime\prime}$ in
literature studies up to $18^{\prime\prime}$ here), and 2) the field of view
covers the regular massive ETG NGC 1278, so we can study both a relic galaxy
and a fully evolved ETG with exactly the same observational setup. In order to
complement the GCMS data of NGC 1277, we use kinematics of the innermost
$1\aas@@fstack{\prime\prime}6\times 1\aas@@fstack{\prime\prime}6$ of the
galaxy obtained by Walsh et al. (2016) using the AO-assisted NIFS integral
field spectrograph.

Our aim was to produce dynamical models of both NGC 1277 and NGC 1278 and
recover their mass distribution. We used HST images to compute colour-derived
mass density maps to be able to disentangle the dark and the baryonic matter.
Both the surface brightness and the surface density maps were parametrised
using multi-Gaussian expansions (MGEs; Tables 1 and 2 and Figs. 8 and 9)
produced with the code by Cappellari (2002).

We fitted the $V_{\rm rms}\equiv\sqrt{V^{2}+\sigma^{2}}$ maps of the two
galaxies (Figs. 2 and 3) by feeding Jeans anisotropic models provided by JAM
(Cappellari, 2008, 2020) into the adamet Bayesian analysis code (Cappellari et
al., 2013b). For each galaxy, we fitted (among other parameters) the mismatch
parameter indicating how the mass-to-light ratio compares to that expected
from a Salpeter (1955) IMF, $\alpha$, and the dark matter fraction within 6
kpc, $f_{\rm DM}(6\,{\rm kpc})$. The 6 kpc radius matches the maximum coverage
of the good-quality GCMS data of NGC 1277 and corresponds to five effective
radii ($5\,R_{\rm e}$).

Our fits (Figs. 10 and 11) show that NGC 1277 has a large mismatch parameter
$\alpha\approx 1.2$, which is a consequence of a bottom-heavy IMF. Our most
surprising result is that there is little to no dark matter within the
explored radius and that the maximum (95.4% confidence interval) permissible
dark matter fraction within 6 kpc (corresponding to $5\,R_{\rm e}$) is $f_{\rm
DM}(6\,{\rm kpc})=0.07$ (Fig. 17), which is in tension with the $f_{\rm
DM}(6\,{\rm kpc})=0.09$ expectation based on the $\Lambda$CDM cosmology as
obtained from stellar-to-halo mass relations by Girelli et al. (2020) and the
dark matter halo shape parametrisation in Child et al. (2018). This low dark
matter fraction is on an even stronger tension with the prediction of $f_{\rm
DM}(5\,R_{\rm e})\sim 0.6$ (Fig. 20) obtained from combining the above two
works with a $M_{\star}-R_{\rm e}$ relation for massive ETGs extracted from
the data in Trujillo et al. (2020).

NGC 1278 has a mismatch parameter $\alpha\approx 1$, which indicates a
shallower IMF slope than for NGC 1277 (Fig. 14). The dark matter fraction of
NGC 1278 is $f_{\rm DM}(6\,{\rm kpc})=0.23\pm 0.05$, which is slightly above
the expectations from the $\Lambda$CDM cosmology (Fig. 18).

The large mismatch parameter of NGC 1277 indicates a large stellar mass-to-
light ratio, $\Upsilon_{\star r}=7.4\,{\rm M_{\odot}}/L_{\odot r}$. This
provides a dynamically-derived constraint to the IMF that is compatible with
the bottom-heavy IMFs determined by Martín-Navarro et al. (2015) and Ferré-
Mateu et al. (2017) using line indices (Fig. 16).

The lack of a dynamically significant dark matter component in NGC 1277
confirms the findings by Yıldırım et al. (2015). The fact that one of the
galaxies with the densest stellar component lies within an underdense dark
matter halo is extremely puzzling. On the other hand it explains why it has
not accreted an envelope, since the lack of an extended dark matter component
would shut down dynamical friction and hence the spiralling down of nearby
dwarf galaxies. Hence, we propose that NGC 1277 either lost its dark matter
early, before it accreted a significant envelope, or was dark matter deficient
ab initio.

A possible way to create a dark matter-poor object such as NGC 1277 has been
proposed by Flores-Freitas et al. (2022) who, based on the TNG50 simulation,
posited that relic galaxy analogues may have lost a large fraction of their
dark matter through interactions with the environment as they entered a
cluster. A similar scenario has been proposed by Yu et al. (2018) based on a
search for dark matter deficient galaxies in the Illustris simulation. It is
suggestive that the density of compact, massive and dark matter deficient
galaxies in the Illustris simulation is very close to that found in the local
Universe by Ferré-Mateu et al. (2017, one in $\approx 1.2\times 10^{6}\,{\rm
Mpc}^{3}$ versus three in $\approx 5\times 10^{6}\,{\rm Mpc}^{3}$) and
compatible with other density estimates by Buitrago et al. (2018) and
Spiniello et al. (2021b). Simulations have also shown a similar mechanism at
work for dwarf galaxies through interactions with their parent galaxies
(Engler et al., 2021; Moreno et al., 2022). Alternatively, an NGC 1277-like
object could have been born in a high-velocity collision of gas-rich objects
where dark matter would have escaped the system leaving behind a rotating
stellar body (blue nugget). The high relative velocities required for this
process to work could only be found in a cluster-like environment and we
speculate that they might have been possible in the progenitors of the rich
galaxy clusters at $z\sim 2$.

We have found that NGC 1277 lacks any detectable dark matter within 6 kpc
(corresponding to five effective radii, $5\,R_{\rm e}$) of its centre. Massive
dark matter-deficient galaxies are unexpected within the framework of the
consensus cosmological model $\Lambda$CDM. We propose that the galaxy was dark
matter deficient ab initio or soon after birth and that the relic nature of
NGC 1277 stems from the lack of an extended halo. In order to confirm this
hypothesis more deep integral field studies of pure relic galaxies are
required. It would also be interesting to check whether even deeper
observations of NGC 1277 can find traces of a tenuous dark matter halo by
finding a flattening of the rotation curve at a radius $\gtrsim 10\,{\rm
kpc}$.

###### Acknowledgements.

We thank Giulia Santucci for kindly sharing information about Fig. 7 in
Santucci et al. (2022). We thank Rodrigo Flores-Freitas Ana L. Chies-Santos
for sharing valuable insights about the intricacies of their work in Flores-
Freitas et al. (2022). SC is indebted to all the participants at the “Cosmic
nuggets – A feast of compact and massive Galaxies across the Universe”, in
particular Dr. Claudia Pulsoni, for the useful idea exchanges and for the
references that were essential for the discussion in this paper. SC also
thanks Drs. Jorge Sánchez Almeida, Alexandre Vazdekis, and Claudio dalla
Vecchia for enlightening discussions. SC and MALL acknowledge support from the
Ramón y Cajal programme funded by the Spanish Government (references
RYC2020-030480-I and RYC2020-029354-I). SC acknowledges funding from the State
Research Agency (AEI-MCINN) of the Spanish Ministry of Science and Innovation
under the grants “The structure and evolution of galaxies and their central
regions” with reference PID2019-105602GB-I00/10.13039/501100011033, and “Thick
discs, relics of the infancy of galaxies” with reference PID2020-113213GA-I00.
IT acknowledges support from the ACIISI, Consejería de Economía, Conocimiento
y Empleo del Gobierno de Canarias and the European Regional Development Fund
(ERDF) under grant with reference PROID2021010044 and from the State Research
Agency (AEI-MCINN) of the Spanish Ministry of Science and Innovation under the
grant PID2019-107427GB-C32 and IAC project P/300624, financed by the Ministry
of Science and Innovation, through the State Budget and by the Canary Islands
Department of Economy, Knowledge and Employment, through the Regional Budget
of the Autonomous Community. FB also acknowledges support from the grants
PID2020-116188GA-I00 and PID2019-107427GB-C32 by the Spanish Ministry of
Science and Innovation. MALL acknowledges support from the Spanish grant
PID2021-123417OB-I00. AFM has received support from the Spanish Ministry
grants CEX2019-000920-S, PID2021-123313NA-I00 and RYC2021-031099-I. This
research was supported by the International Space Science Institute (ISSI) in
Bern, through ISSI International Team project No. 505 (The Metal-THINGS Survey
of Nearby Galaxies). Based on observations made with the NASA/ESA Hubble Space
Telescope, and obtained from the Hubble Legacy Archive, which is a
collaboration between the Space Telescope Science Institute (STScI/NASA), the
Space Telescope European Coordinating Facility (ST-ECF/ESA) and the Canadian