# Integral Field Spectroscopy of 13 Tidal Disruption Event Hosts from the ZTF
Survey

Erica Hammerstein Department of Astronomy, University of Maryland, College
Park, MD 20742, USA  Astrophysics Science Division, NASA Goddard Space Flight
Center, 8800 Greenbelt Rd, Greenbelt, MD 20771, USA  Center for Research and
Exploration in Space Science and Technology, NASA/GSFC, Greenbelt, MD 20771,
USA  S. Bradley Cenko Astrophysics Science Division, NASA Goddard Space Flight
Center, 8800 Greenbelt Rd, Greenbelt, MD 20771, USA  Joint Space-Science
Institute, University of Maryland, College Park, MD 20742 USA  Suvi Gezari
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218,
USA  Department of Physics and Astronomy, Johns Hopkins University, 3400 N.
Charles St., Baltimore, MD 21218, USA  Sylvain Veilleux Department of
Astronomy, University of Maryland, College Park, MD 20742, USA  Joint Space-
Science Institute, University of Maryland, College Park, MD 20742 USA  Brendan
O’Connor Department of Physics, The George Washington University, Washington,
DC 20052, USA  Astronomy, Physics and Statistics Institute of Sciences
(APSIS), The George Washington University, Washington, DC 20052, USA
Department of Astronomy, University of Maryland, College Park, MD 20742, USA
Astrophysics Science Division, NASA Goddard Space Flight Center, 8800
Greenbelt Rd, Greenbelt, MD 20771, USA  Sjoert van Velzen Leiden Observatory,
Leiden University, Postbus 9513, 2300 RA, Leiden, The Netherlands  Charlotte
Ward Department of Astrophysical Sciences, Princeton University, Princeton, NJ
08544, USA  Yuhan Yao Cahill Center for Astrophysics, California Institute of
Technology, MC 249-17, 1200 E California Boulevard, Pasadena, CA, 91125, USA
Matthew Graham Department of Astronomy, California Institute of Technology,
1200 E. California Blvd, Pasadena, CA, 91125, USA

###### Abstract

The host galaxies of tidal disruption events (TDEs) have been shown to possess
peculiar properties, including high central light concentrations, unusual
star-formation histories, and “green” colors. The ubiquity of these large-
scale galaxy characteristics among TDE host populations suggests they may
serve to boost the TDE rate in such galaxies by influencing the nuclear
stellar dynamics. We present the first population study of integral field
spectroscopy for thirteen TDE host galaxies across all spectral classes and
X-ray brightnesses with the purpose of investigating their large-scale
properties. We derive the black hole masses via stellar kinematics (i.e., the
$M-\sigma$ relation) and find masses in the range $5.0\lesssim\log(M_{\rm
BH}/M_{\odot})\lesssim 8.3$, with a distribution dominated by black holes with
$M_{\rm BH}\sim 10^{6}M_{\odot}$. We find one object with $M_{\rm BH}\gtrsim
10^{8}M_{\odot}$, above the “Hills mass”, which if the disrupted star was of
solar type, allows a lower limit of $a\gtrsim 0.66$ to be placed on its spin,
lending further support to the proposed connection between featureless TDEs
and jetted TDEs. We also explore the level of rotational support in the TDE
hosts, quantified by $(V/\sigma)_{e}$, a parameter which has been shown to
correlate with stellar age and may explain the peculiar host galaxy
preferences of TDEs. We find that the TDE hosts exhibit a broad range in
$(V/\sigma)_{e}$ following a similar distribution as E+A galaxies, which have
been shown to be overrepresented among TDE host populations.

††journal: ApJ††facilities: LDT (LMI), Keck:II (KCWI)††software: GALFIT, KCWI-
DRP, CWITools, GIST, ppxf

##  1 Introduction

It is generally accepted that most, if not all, massive galaxies host a
supermassive black hole (SMBH) in their nucleus which play important roles in
the evolution and properties of their host galaxies (e.g. Kormendy &
Richstone, 1995; Magorrian & Tremaine, 1999; Ho, 2008; Gültekin et al., 2009;
Kormendy & Ho, 2013; Veilleux et al., 2005; Fabian, 2012; Veilleux et al.,
2020). This is evident from scaling relations between the SMBH mass and host
galaxy properties such as the bulge velocity dispersion (e.g. Ferrarese &
Merritt, 2000; Gebhardt et al., 2000) or bulge luminosity (e.g. Dressler,
1989; Magorrian et al., 1998). These objects can announce their presence most
prominently through sustained accretion of nuclear gas and dust as active
galactic nuclei (AGN), but many more SMBHs lie dormant, making the study of
these objects more difficult. The tidal disruption of a star by the central
SMBH, known as a tidal disruption event (TDE), provides a unique way to gain
insights on the population of distant and mostly quiescent SMBHs.

A TDE occurs when a star passes sufficiently close (i.e., within the tidal
radius) to a SMBH such that the tidal forces felt by the star are stronger
than its own self-gravity, resulting in the star being torn apart and roughly
half of that stellar debris being eventually accreted by the black hole,
creating a luminous flare of radiation potentially visible from Earth (Rees,
1988; Evans & Kochanek, 1989; Ulmer, 1999). TDEs were only a theoretical
prediction just $\sim$50 yrs ago (Hills, 1975; Lidskii & Ozernoi, 1979), and
we now have observational evidence of these events from the radio to X-rays,
with the largest samples of TDEs discovered in the optical using surveys such
as iPTF (Blagorodnova et al., 2017, 2019; Hung et al., 2017), ASAS-SN (Holoien
et al., 2014, 2016a, 2016b, 2019a; Wevers et al., 2019; Hinkle et al., 2021),
Pan-STARRS (Gezari et al., 2012; Chornock et al., 2014; Holoien et al., 2019b;
Nicholl et al., 2019), SDSS (van Velzen et al., 2011), and ZTF (van Velzen et
al., 2019b, 2021; Hammerstein et al., 2023; Yao et al., 2023). While the light
curves and spectra of TDEs offer important clues to the formation of the
accretion disk, winds, and jets, the host galaxies of these transients provide
insights into SMBH–galaxy co-evolution, galaxy evolution and mergers, and the
dynamics of galaxy nuclei. Understanding the environments that are most likely
to host TDEs will even lead to more efficient discovery and follow-up during
the era of the Vera Rubin Observatory, which is predicted to observe hundreds
to even thousands of new TDEs a year (van Velzen et al., 2011).

TDEs have also been shown to be observed preferentially in E+A or post-
starburst galaxies (Arcavi et al., 2014; French et al., 2016; Law-Smith et
al., 2017; Hammerstein et al., 2021a), whose optical spectra are characterized
by little to no H$\alpha$ or [O II] emission and strong Balmer absorption,
indicating the presence of stars formed within the past Gyr but no current
star formation activity. Typical E+A overrepresentation (i.e., the ratio
between the fraction of TDE hosts that are E+As to the fraction of all
galaxies that are E+As) ranges widely depending on the study, with some
population studies finding an overrepresentation of over 100 (Law-Smith et
al., 2017) and others finding an overrepresentation of just 22 (Hammerstein et
al., 2021a). E+A galaxies are also known to have large bulge-to-light ratios,
high Sérsic indices, and high concentration indices (Yang et al., 2008), all
of which have been shown to greatly enhance the TDE rate in these galaxies by
making more stars available in the nuclear region to be tidally disrupted
(Stone & van Velzen, 2016; Stone & Metzger, 2016; French et al., 2020a).

Several previous studies have aimed to characterize the environments that are
most likely to host TDEs and have shown that certain large-scale galaxy
properties are indeed linked with higher TDE rates. Graur et al. (2018) found
that TDE host galaxies have higher stellar mass surface density and lower
velocity dispersions as compared to a sample of galaxies not known to host
recent TDEs. Law-Smith et al. (2017) examined a sample of TDE host galaxies in
comparison to the local galaxy population and found that all of the TDE hosts
in their sample reside below the star formation main sequence, have bluer
bulge colors, high Sérsic indices and high bulge-to-light ratios compared to
galaxies of similar masses. Hammerstein et al. (2021a) found that 61% of TDE
host galaxies in their sample were in the green valley between the star-
forming “blue cloud” and the passive “red sequence” of galaxies, compared to
only 13% of SDSS galaxies. They also found that while most green valley
galaxies have Sérsic indices comparable to blue cloud galaxies, the TDE hosts
had higher Sérsic indices most similar to red, passive galaxies. All of these
properties are indicative of systems which have undergone a merger that
produce concentrated central stellar distributions and can indeed enhance the
TDE rate (Stone & van Velzen, 2016; Stone & Metzger, 2016; French et al.,
2020a).

In this paper, we present integral field spectroscopy (IFS) of a sample of 13
TDE host galaxies from the Zwicky Transient Facility (ZTF) survey in order to
obtain their black hole masses and understand their large-scale kinematics and
stellar populations, the latter of which we compare to several other galaxy
populations, including E+A galaxies. Integral field spectroscopy provides
spatially resolved spectra which gives a study such as this one an edge over
long-slit spectroscopy when attempting to probe various size scales of the TDE
host galaxies. In Section 2, we describe the observations of the 13 TDEs in
our sample as well as the subsequent data reduction and analysis methods. We
present the results of the kinematic and stellar population analysis and
discuss these results in Section 3. We discuss the results pertaining to the
black hole mass in Section 4 and those pertaining to the stellar kinematics
and populations in Section 5. We close with our conclusions in Section 6.

##  2 Observations & Data Analysis

We selected our host galaxy sample from the ZTF-I TDEs published in van Velzen
et al. (2021) and Hammerstein et al. (2023), with the intention of
constructing a sample which includes multiple TDE spectral classes and X-ray
brightnesses. We point to van Velzen et al. (2021) for a full description of
the ZTF TDE search, although we note that the method for discovering TDEs is
agnostic to host galaxy type apart from filtering out known AGN. While this
search is thus agnostic to host galaxy type, we do note that our selection of
TDE hosts from the ZTF sample, designed to include TDEs from all
classifications, will not follow the true observed rate of each type of TDE.
However, this is likely not relevant for the study presented here as we do not
make conclusions by comparing the TDE types. We show SDSS and Pan-STARRS
images of each of the host galaxies in Figure 1.

Figure 1: SDSS and Pan-STARRS gri images of the thirteen TDE host galaxies,
with the yellow rectangle representing the positioning of the KCWI field of
view. All images are $34\arcsec\times 34\arcsec$ while the KCWI field of view
is $8\farcs 4\times 20\farcs 4$.

Our sample of thirteen TDEs includes all four TDE spectral classes (for a
description of all classes, see Hammerstein et al., 2023), with 2 TDE-H, 8
TDE-H+He, 2 TDE-He, and 1 TDE-featureless, 6 of which are also X-ray detected
TDEs. The hosts span redshifts in the range $0.015\leq z\leq 0.345$ and have
stellar masses in the range $9.56\leq\log(M_{\rm gal}/M_{\odot})\leq 11.23$,
both of which we take from the published values of van Velzen et al. (2021)
and Hammerstein et al. (2023).

In Figure 2 we show the rest-frame, extinction corrected $u-r$ color from
Hammerstein et al. (2023) derived from fitting the host SED for the TDE host
galaxies as a function of host galaxy stellar mass. We also include a
background sample of 955 galaxies from the SAMI Galaxy Survey DR3 (Croom et
al., 2021), which provides spatially resolved stellar kinematic and population
information, discussed further in Section 5. The galaxies in the SAMI sample
were selected to span the plane of mass and environments, with the redshifts
spanning $0.004\leq z\leq 0.095$, masses between $10^{7}-10^{1}2M_{\odot}$,
magnitudes with $r_{\rm pet}<19.4$, and environments from isolated galaxies to
groups and clusters (Bryant et al., 2015). $\sim$54% of the TDE hosts are in
the green valley compared to just $\sim$20% of the background galaxies, in
line with previous findings (e.g., Hammerstein et al., 2021a; Sazonov et al.,
2021; Hammerstein et al., 2023; Yao et al., 2023). We summarize the properties
of the host galaxies and include references to the first TDE classification in
Table 1.

Figure 2: The rest-frame, extinction corrected $u-r$ color as a function of
host galaxy mass for the TDE host galaxies and a sample of 955 galaxies from
the SAMI survey. The dashed green lines indicate the location of the green
valley, the location of which we take from Hammerstein et al. (2023). The
colors and shapes of the points indicate the spectral class of TDE for each
event. IDs are listed in Table 1. The TDE hosts are typically less massive
than the background sample and more often reside in the green valley compared
to the background galaxies ($\sim$54% vs. $\sim$20%). Table 1: Sample of TDE
Host Galaxies

ID | Name | RA | Dec. | First TDE Classification | Spectral Class | Redshift | $\log(M_{\rm gal}/M_{\odot})$ | $m_{r}$
---|---|---|---|---|---|---|---|---
1 | AT2018zr | 07:56:54.55 | +34:15:43.6 | Tucker et al. (2018) | TDE-H | 0.075 |  $10.01_{-0.14}^{+0.08}$ | 18.02 |
2 | AT2018bsi | 08:15:26.63 | +45:35:32.0 | Gezari et al. (2018) | TDE-H+He | 0.051 |  $10.62_{-0.07}^{+0.05}$ | 15.50 |
3 | AT2018hyz | 10:06:50.88 | +01:41:33.9 | Dong et al. (2018) | TDE-H+He | 0.046 |  $9.96_{-0.16}^{+0.09}$ | 16.96 |
4 | AT2018lni | 04:09:37.65 | +73:53:41.7 | van Velzen et al. (2021) | TDE-H+He | 0.138 |  $10.10_{-0.13}^{+0.10}$ | 19.46 |
5 | AT2018lna | 07:03:18.65 | +23:01:44.7 | van Velzen et al. (2019c) | TDE-H+He | 0.091 |  $9.56_{-0.14}^{+0.11}$ | 19.51 |
6 | AT2019azh | 08:13:16.95 | +22:38:53.9 |  van Velzen et al. (2019a)aaSee also Hinkle et al. (2021). | TDE-H+He | 0.022 |  $9.74_{-0.05}^{+0.08}$ | 14.51 |
7 | AT2019ehz | 14:09:41.91 | +55:29:27.8 | Gezari et al. (2019) | TDE-H | 0.074 |  $9.81_{-0.12}^{+0.09}$ | 18.72 |
8 | AT2019qiz | 04:46:37.88 |  $-$10:13:34.9 | Siebert et al. (2019) | TDE-H+He | 0.015 |  $10.01_{-0.12}^{+0.10}$ | 14.17 |
9 | AT2020ddv | 09:58:33.42 | +46:54:40.4 | Gezari et al. (2020b) | TDE-He | 0.160 |  $10.30_{-0.16}^{+0.13}$ | 19.37 |
10 | AT2020ocn | 13:53:53.80 | +53:59:49.7 | Gezari et al. (2020a) | TDE-He | 0.070 |  $10.28_{-0.17}^{+0.13}$ | 17.57 |
11 | AT2020qhs | 02:17:53.95 |  $-$09:36:50.9 | Hammerstein et al. (2023) | TDE-featureless | 0.345 |  $11.23_{-0.07}^{+0.07}$ | 19.40 |
12 | AT2020wey | 09:05:25.91 | +61:48:09.1 | Arcavi et al. (2020) | TDE-H+He | 0.027 |  $9.63_{-0.22}^{+0.18}$ | 16.61 |
13 | AT2020zso | 22:22:17.13 |  $-$07:15:58.9 | Ihanec et al. (2020) | TDE-H+He | 0.057 |  $10.05_{-0.12}^{+0.09}$ | 17.03 |

Note. — Labels used in figures, RA and Dec, TDE classification references,
spectral classes, redshifts, host galaxy stellar masses, and host galaxy
apparent $r$-band magnitudes for the thirteen objects in our sample. All
spectral classifications, redshifts, and host galaxy stellar masses are based
on those provided in van Velzen et al. (2021) and Hammerstein et al. (2023).
Host magnitudes are derived from Pan-STARRS. X-ray detected events are bolded.

###  2.1 Large Monolithic Imager and GALFIT

We obtained optical imaging of the host galaxies in our sample using the Large
Monolithic Imager (LMI) mounted on the 4.3-m Lowell Discovery Telescope (LDT)
in Happy Jack, AZ. Data were obtained on 2022-10-30, 2022-11-30, and
2023-02-13 (PIs: Hammerstein, O’Connor) under clear skies and good observing
conditions (seeing $\sim$1″). The targets were observed in the SDSS $r$-band
filter with varying exposure times depending on the galaxy brightness, e.g.,
from 50 s for $r\approx 14$ AB mag to 200 s for $r\approx 19.5$ AB mag. The
chosen exposure times lead to a high signal-to-noise ratio (SNR) for each
galaxy, which when combined with the spatial resolution of LMI allow for an
improved morphological analysis when compared to available archival data
(e.g., SDSS). We were able to observe all thirteen host galaxies through this
program. We reduced the LMI data using a custom python pipeline (see Toy et
al., 2016; O’Connor et al., 2022) to perform bias subtraction, flat-fielding,
and cosmic ray rejection. The observations for each galaxy, including
observation date and exposure time, are described in Table 2. Given that the
LMI observations were obtained several years after peak for all objects, we do
not expect that the transient will contribute any appreciable flux to the
photometry that may affect the fitting performed here.

We use GALFIT (Peng et al., 2002) to perform 2D fits to the host galaxy
photometry and obtain morphological parameters such as the effective radius,
ellipticity, and position angle of the host galaxies. Because we are
interested in exploring galaxy properties at several different scales, we
perform two fits with two different models. The first model includes a Sérsic
component and exponential disk component which is used to obtain a bulge
effective radius ($R_{\rm e,bulge}$). This radius is used to mask a region in
the IFU data for obtaining the bulge velocity dispersion and subsequently the
black hole mass. The second fit includes a single Sérsic component, used to
obtain the effective radius of the entire galaxy light profile ($R_{\rm
e,gal}$). We use this radius to mask the region for general kinematic and
stellar population analysis. We fit all galaxies using these two models with
the exception of AT2019qiz. The prominent bar in AT2019qiz required the
addition of another component in order to isolate the bulge of the galaxy.
Instead, we used a model which includes an exponential disk and two Sérsic
components, one for the bulge and one for the bar, which was sufficient to
isolate the bulge and obtain the bulge effective radius. Some galaxies
required additional components to mask out nearby stars or faint galaxies in
the fitting window, which we included when necessary. We present the results
of this fitting, namely the galaxy and bulge effective radii, in Table 3 and
show an example fit and residuals in Figure 3.

Figure 3: A 29″$\times$29″ cutout of the LMI observations of the host galaxy
of AT2018bsi, shown with the GALFIT model and residuals. All images are on the
same scale. GALFIT is able to model the host galaxy reasonably well with the
residuals showing potential dust lane or spiral arm features which are not as
straightforward to model with GALFIT and for the purposes of the study
presented here, are unimportant. In the left panel we show two ellipses
representing the fitted bulge effective radius ($R_{\rm e,bulge}$, cyan) and
the disk effective radius (where the relationship between the effective radius
and the scale length of the disk is $R_{\rm e,disk}=1.678R_{\rm s,disk}$,
white). Table 2: Summary of LMI observations

Name | Obs. Date |  Exp. Time (s)
---|---|---
AT2018zr | 2022 Oct. 31 | 150
AT2018bsi | 2022 Dec. 01 | 55
AT2018hyz | 2022 Dec. 01 | 80
AT2018lni | 2022 Dec. 01 | 200
AT2018lna | 2022 Oct. 31 | 200
AT2019azh | 2022 Oct. 31 | 70
AT2019ehz | 2023 Feb. 13 | 120
AT2019qiz | 2022 Dec. 01 | 50
AT2020ddv | 2022 Oct. 31 | 200
AT2020ocn | 2022 Dec. 01 | 100
AT2020qhs | 2022 Dec. 01 | 200
AT2020wey | 2022 Oct. 31 | 80
AT2020zso | 2022 Dec. 01 | 60

Note. — Summary of observations obtained with LMI, including the observation
date and exposure time. All observations were performed using the SDSS
$r$-band filter.

###  2.2 Keck Cosmic Web Imager and GIST

We present Keck Cosmic Web Imager (KCWI; Morrissey et al., 2018) observations
of thirteen TDE host galaxies selected from the ZTF-I sample of TDEs. Integral
field spectra were obtained on the night of 2021-12-25 under clear weather
conditions (seeing $\sim 0.8\arcsec$) as part of program ID N096 (PI: Gezari).
Observations for each object, described in Table 3, were obtained using the
small ($8\farcs 4\times 20\farcs 4$) slicer and ‘BM’ grating, which gives a
nominal resolution of $R_{\rm 0}=8000$ and an average bandpass of 861 Å. Three
different central wavelengths were used to ensure that important host galaxy
stellar absorption lines were observed for each galaxy. The final
configurations are as follows:

  * i.

C1: Small slicer, ‘BM’ grating, central wavelength of 4200 Å.

  * ii.

C2: Small slicer, ‘BM’ grating, central wavelength of 4800 Å.

  * iii.

C3: Small slicer, ‘BM’ grating, central wavelength of 5200 Å.

In Figure 1, we overplot the KCWI pointing for each observed galaxy. Three
host galaxies, AT2018bsi, AT2019azh, and AT2019qiz, have angular sizes larger
than the KCWI field-of-view. For each of these galaxies we obtained sky
exposures offset from the host galaxy in order to perform sky subtraction.

The observations were reduced using the standard procedure of the KCWI data
reduction pipeline (Neill et al., 2023) which includes bias subtraction, flat
fielding, cosmic ray removal, sky subtraction, wavelength calibration,
heliocentric correction, and flux calibration. We used CWITools (O’Sullivan &
Chen, 2020) to apply a WCS correction to the KCWI data in ‘src_fit’ mode,
which fits 1D profiles to the spatial data to find the peak of the source and
then applies a correction to the WCS such that the peak aligns with the input
coordinates.

We use the Galaxy IFU Spectroscopy Tool (GIST; Bittner et al., 2019) modified
to work with KCWI data to obtain the stellar kinematic and population
information. The GIST pipeline performs all necessary steps to analyze the
KCWI IFU spectra with ppxf (Cappellari, 2022), including spatial masking and
binning, SNR determination and masking, stellar kinematic analysis, and
stellar population analysis. The X-shooter library of simple stellar
population models (XSL; Verro et al., 2022) offers the best spectral
resolution ($\sigma\sim 13$ km s-1, $R\sim 10000$) and wavelength coverage
(3500 Å– 24800 Å) which matches our KCWI observations ($\lambda_{\rm
obs,min}=3768$ Å in configuration C1 and $\lambda_{\rm obs,max}=5624$ Å in
configuration C3), meaning we can fit the entire spectral range for each host
galaxy. The XSL provides several options for initial mass functions (IMF) and
isochrones. We choose the set of models that utilizes the Salpeter IMF
(Salpeter, 1955) and PARSEC/COLIBRI isochrones (Bressan et al., 2012; Marigo
et al., 2013), which includes stellar populations with ages above 50 Myr and
metallicities in the range $-2.2<$ [Fe/H] $<+0.2$, normalized to obtain mass-
weighted stellar population results.

We run the GIST pipeline three times for each host galaxy, each time using
different binning and masking criteria. We spatially mask and bin the spaxels
for the three different fits as follows:

  * i.

Bulge $\sigma$ fit: Mask all spaxels outside of $R_{\rm e,bulge}$ obtained
from GALFIT; combine remaining spaxels into one bin.

  * ii.

Galaxy $(V/\sigma)_{e}$ fits: Mask all spaxels outside of $R_{\rm e,gal}$
obtained from GALFIT; apply no binning.

  * iii.

Stellar population fit: Mask all spaxels outside of $R_{\rm e,gal}$ obtained
from GALFIT; combine remaining spaxels into one bin.

We are motivated to perform three different fits for several reasons. The
first is so that our black hole masses are determined only from the bulge
velocity dispersions, with the bulge effective radius determined from the two
component GALFIT fit. The second is so that our determination of the large-
scale kinematics and stellar population properties follows most closely the
methods of van de Sande et al. (2018), who perform two fits within an ellipse
that encloses half of the projected total galaxy light: one which is similar
to our galaxy $(V/\sigma)_{e}$ fit and one which is similar to our stellar
population fit. We present and discuss the results of this analysis in the
next sections.

Table 3: Summary of KCWI observations

Name | Config. |  Exp. Time (s) |  $\Delta t_{\rm obs-peak}$ (days)
---|---|---|---
AT2018zr | C1 | $2\times 900$ | 1372
AT2018bsi | C1 | $2\times 150$ | 1362
AT2018hyz | C1 | $2\times 600$ | 1150
AT2018lni | C2 | $2\times 1800$ | 1097
AT2018lna | C1 | $2\times 1500$ | 1067
AT2019azh | C1 | $2\times 100$ | 1008
AT2019ehz | C1 | $2\times 1000$ | 960
AT2019qiz | C1 | $2\times 500$ | 807
AT2020ddv | C2 | $2\times 1500$ | 655
AT2020ocn | C1 | $2\times 600$ | 585
AT2020qhs | C3 | 1350, 500 | 511
AT2020wey | C1 | $2\times 200$ | 418
AT2020zso | C1 | 300, 600 | 386

Note. — Summary of observations obtained with KCWI, including the instrument
configuration, exposure times, and days post-peak from the tidal disruption
flare. $t_{\rm peak}$ is taken from Hammerstein et al. (2023). The
configuration notation is described in Section 2.2.

##  3 Results

We present the results of our kinematic and stellar population analysis on the
KCWI spectra of the 13 TDE host galaxies. We summarize our main results in
Table 3. In Figure 4, we show a white light image of the host galaxy of
AT2019azh and example output maps from GIST, including the line-of-sight
velocity and velocity dispersion as well as the stellar population age and
metallicity. In Figure 5, we show the bins constructed by GIST, as well as two
example spectra and ppxf fits from different bins. The output we show in
Figures 4 and 5 involves no spatial masking like that described in Section
2.2, but instead masks spaxels below the isophote level which has a mean SNR
of 2.2. This particular fit is not used for any analysis and is for
illustrative purposes only. In the following sections, we discuss our results
on obtaining the black hole masses and characterizing the host galaxy stellar
kinematics and populations.

Table 4: Results from photometric and kinematic analysis

Name | kpc$/\arcsec$ |  $R_{\rm e,gal}$ (″) |  $R_{\rm e,bulge}$ (″) |  $\sigma_{\star}$ (km s-1) | $\log(M_{\rm BH}/M_{\odot})$ | (V/$\sigma)_{e}$
---|---|---|---|---|---|---
AT2018zr | 1.35 | 3.14 | 1.50 | 49.79 $\pm$ 4 | 5.56 $\pm$ 0.76 | 0.52 $\pm$ 0 |
AT2018bsi | 1.00 | 10.32 | 1.84 | 117.54 $\pm$ 8 | 7.14 $\pm$ 0.62 | 0.93 $\pm$ 0 |
AT2018hyz | 0.90 | 2.25 | 1.16 | 66.62 $\pm$ 3 | 6.10 $\pm$ 0.67 | 0.12 $\pm$ 0 |
AT2018lni | 2.44 | 0.95 | 0.58 | 56.40 $\pm$ 5 | 5.79 $\pm$ 0.75 | 0.22 $\pm$ 0 |
AT2018lna | 1.70 | 1.93 | 0.96 | 36.43 $\pm$ 4 | 4.98 $\pm$ 0.83 | 0.78 $\pm$ 0 |
AT2019azh | 0.45 | 16.36 | 4.24 | 68.01 $\pm$ 2 | 6.13 $\pm$ 0.66 | 0.88 $\pm$ 0 |
AT2019ehz | 1.41 | 2.95 | 1.51 | 46.65 $\pm$ 11 | 5.44 $\pm$ 0.98 | 0.37 $\pm$ 0 |
AT2019qiz | 0.31 | 14.85 | 2.27 | 71.85 $\pm$ 1 | 6.23 $\pm$ 0.65 | 0.71 $\pm$ 0 |
AT2020ddv | 2.76 | 1.48 | 0.80 | 57.81 $\pm$ 10 | 5.83 $\pm$ 0.85 | 0.09 $\pm$ 1 |
AT2020ocn | 1.34 | 2.35 | 0.28 | 81.00 $\pm$ 8 | 6.46 $\pm$ 0.70 | 0.36 $\pm$ 0 |
AT2020qhs | 4.89 | 3.44 | 1.21 | 215.46 $\pm$ 44 | 8.26 $\pm$ 0.83 | 0.53 $\pm$ 0 |
AT2020wey | 0.55 | 4.18 | 0.87 | 53.54 $\pm$ 4 | 5.69 $\pm$ 0.74 | 0.40 $\pm$ 0 |
AT2020zso | 1.10 | 4.32 | 1.08 | 61.80 $\pm$ 4 | 5.96 $\pm$ 0.71 |  |

Note. — The results from our photometric and kinematic analysis of the LMI and
KCWI data, including the galaxy and bulge half light radii measured from
GALFIT, the bulge velocity dispersion and derived black hole mass, and the
ratio of ordered rotation to random stellar motion (V/$\sigma)_{e}$.

Figure 4: An example output from GIST of the host galaxy of AT2019azh. The
left panel shows an unbinned white light image of the KCWI observation. The
panels on the right depict the output maps from GIST, which show the ppxf-
derived line-of-sight velocity, velocity dispersion, and stellar population
ages and metallicities. This fit involves no spatial masking like that
described in Section 2.2, but instead masks spaxels below the isophote level
which has a mean SNR of 2.2. This particular fit is not used for any analysis
and is for illustrative purposes only.

Figure 5: Example ppxf fits to the host galaxy of AT2019azh output from GIST.
The left panel shows the bins constructed with GIST where the color represents
the bin to which each spaxel belongs. Bins are constructed using the Voronoi
binning method (Cappellari & Copin, 2003) to reach a threshold SNR for each
bin, in this case SNR $\sim 10$. The two panels on the right show the spectra
(purple and teal lines) and ppxf fits (black lines) from the outlined bins on
the left. We show the uncertainties on the spectra in gray.

##  4 Black hole masses

We derive the black hole masses through the $M_{\rm BH}-\sigma$ relation of
Gültekin et al. (2009), assuming that this relation holds valid for all
galaxies in this sample:

$\log(M_{\rm
BH}/M_{\odot})=8.12+4.24\log\left(\frac{\sigma}{200~{}\mathrm{km~{}s^{-1}}}\right)$
(1)

We propagate the uncertainties on the velocity dispersion through this
relation and add them linearly with the intrinsic scatter on the relation to
obtain the uncertainty on the black hole mass.

In Figure 6, we show the distribution of black hole masses for the entire
sample in addition to the subsamples of X-ray bright and X-ray faint events.
We find that the distribution peaks at $\log(M_{\rm BH}/M_{\odot})=5.96$ with
a range of masses $4.98\leq\log(M_{\rm BH}/M_{\odot})\leq 8.26$, which is
consistent with previous studies performing a similar analysis (e.g., Wevers
et al., 2017, 2019; Yao et al., 2023). We examine whether the populations of
X-ray bright and X-ray faint events show any significant difference in their
black hole mass distributions by performing an Anderson-Darling test and find
that we cannot reject the null hypothesis that the X-ray bright and X-ray
faint samples are drawn from the same distribution in black hole mass
($p$-value $\geq 0.25$). This is consistent with several previous studies
(e.g., Wevers et al., 2019; French et al., 2020b; Hammerstein et al., 2023)
which largely found no significant difference in the black hole, host galaxy,
or even light curve properties between X-ray bright and X-ray faint TDEs. This
lack of difference between X-ray bright and X-ray faint populations may be
explained by the unifying theory of Dai et al. (2018), which posits that
whether or not X-rays are observed in a particular TDE is a matter of viewing
angle effects.

In Figure 7, we show the derived black hole masses as a function of host
galaxy stellar mass along with several empirical relations from the
literature. Reines & Volonteri (2015) derived the relations for AGN and
inactive galaxies, while Greene et al. (2020) derived the relations for late,
early, and all galaxy types. Importantly, Greene et al. (2020) used upper
limits in their calculations which are crucial for including low-mass systems,
such as the ones that host TDEs, in the relation. We also show the fitted
relation from Yao et al. (2023), which was derived by fitting a linear
relation between $M_{\rm gal}$ and $M_{\rm BH}$ for the TDE hosts in their
sample. Rather interestingly, the TDE hosts most closely follow the relation
for late-type galaxies, despite very few being classified as such. This could
be explained by the very few low-mass early-type galaxies used in deriving the
relations for early-type galaxies and all galaxy types. Alternatively, this
may be caused by our choice in $M_{\rm BH}-\sigma$ relation, although each
scaling will have its own resulting offset.

Figure 6: Distribution of black hole masses for the host galaxies in our
sample. We show the entire sample in black, with the divisions on X-ray bright
vs. X-ray faint in purple and orange, respectively. The distribution peaks at
$\log(M_{\rm BH}/M_{\odot})=5.96$, consistent with previous results for
similar analyses. We find no significant difference in black hole masses
between the X-ray bright (6 total) and X-ray faint (7 total) events. Figure 7:
The black hole mass as a function of the host galaxy stellar mass. We show
several derived $M_{\rm BH}-M_{\rm gal}$ relations. Black dashed and long-
dashed lines show the relations from Reines & Volonteri (2015) derived from
AGN host galaxies and inactive galaxies, respectively. The blue dashed,
dotted, and dot-dashed lines show the relations from Greene et al. (2020)
derived from late-type galaxies, early-type galaxies, and all galaxy types,
respectively. We also showed the fitted relation from Yao et al. (2023), which
was fit only for TDE hosts. Labels for each TDE are in Table 1.

###  4.1 Comparisons to previous measurements

All objects in our sample have previously measured black hole masses through a
variety of methods, although only three have previously measured velocity
dispersions. We compare our estimate of the black hole mass derived from the
bulge velocity dispersion and $M_{\rm BH}-\sigma$ relation with previous
estimates using the same method.

AT2019azh: Yao et al. (2023) derived the black hole mass for AT2019azh by
fitting the optical ESI spectrum using ppxf. They found
$\sigma_{\star}=67.99\pm 2.03$ km s-1, corresponding to a black hole mass of
$\log(M_{\rm BH}/M_{\odot})=6.44\pm 0.33$ using the $M_{\rm BH}-\sigma$
relation of Kormendy & Ho (2013). Our value of $\sigma_{\star}=68.01\pm 2.02$
km s-1 is consistent with that of Yao et al. (2023).

AT2020wey: Yao et al. (2023) also measured the velocity dispersion of the host
galaxy of AT2020wey in the same manner as AT2019azh, finding
$\sigma_{\star}=39.36\pm 2.79$ km s-1. We find a significantly higher value
for the velocity dispersion of $\sigma_{\star}=53.54\pm 4.75$ km s-1. It is
possible that with the small effective radius of AT2020wey (see Table 3), the
long-slit spectra used to derive the velocity dispersion in Yao et al. (2023)
are inclusive of stars much farther from the bulge effective radius and thus
have lower velocity dispersions. This can explain the discrepancy we see here.

AT2019qiz: Nicholl et al. (2020) fit the late time X-shooter spectrum of
AT2019qiz using ppxf and found $\sigma_{\star}=69.7\pm 2.3$ km s-1. Our value
for the velocity dispersion is marginally higher, $\sigma_{\star}=71.85\pm
1.93$ km s-1, but still consistent within the uncertainties of the two
measurements.

All objects in our sample also have at least one estimate of the black hole
mass obtained from fitting the TDE light curve with the MOSFiT (Guillochon et
al., 2018) TDE model (Mockler et al., 2019). The TDE model fits each TDE by
generating bolometric light curves via hydrodynamical simulations and passing
them through viscosity and reprocessing transformation functions to create the
the single-band, observed light curves. MOSFiT then uses the single-band light
curves to fit the multi-band input data to estimate the light-curve properties
and information on the disrupted star in addition to the mass of the SMBH.
Hammerstein et al. (2023) used MOSFiT to fit the light curves of every object
in our sample, but found no significant correlation with the host galaxy mass.

We now reexamine any potential correlation using the derived black hole mass
instead. In Figure 8, we show the MOSFiT black hole mass as a function of the
black hole mass we have derived here. The gray dashed line indicates a one-to-
one relationship. While we do find a weak, positive correlation between the
MOSFiT masses and the masses we derive here, it is not significant. As our
$M_{\rm BH}-\sigma$ derived black hole masses are so well correlated with the
host galaxy masses from Hammerstein et al. (2023), it is not surprising that
we do not find a significant correlation between the MOSFiT masses and our
masses. Given that the MOSFiT mass are typically orders of magnitude larger
than those inferred through the $M_{\rm BH}-\sigma$ relation, it is possible
that an underestimation of the black hole mass due to uncertainties of the
relation at such low velocity dispersions is causing the discrepancy.
Additional updates to the MOSFiT TDE model, which will be presented in Mockler
& Nicholl et al. (2023, in prep), may also help to address the discrepancies.

Hammerstein et al. (2023) also estimated the black hole mass using the TDEmass
code (Ryu et al., 2020) which assumes that circularization happens slowly, and
that the UV/optical emission arises from shocks in the intersecting debris
streams instead of in an outflow or wind. Again, they found no significant
correlation between the SMBH mass and the host galaxy mass. We show the
TDEmass SMBH mass as a function of the SMBH mass derived from stellar
kinematics in Figure 8, with gray dashed line indicates a one-to-one
relationship. We note that the mass for AT2020qhs (ID 11) was not able to be
determined with TDEmass. We find no significant correlation between the
TDEmass values for the black hole mass and the ones we derive here.

While it is not surprising that the MOSFiT and TDEmass values do not agree, as
they derive the black hole mass using differing assumptions on the origin of
the UV/optical emission, the lack of any correlation with host galaxy
properties is puzzling. Previous studies (e.g., Ramsden et al., 2022; Mockler
et al., 2019) which derive the black hole mass from MOSFiT have found weak
correlations between the SMBH mass and properties such as the bulge mass and
host galaxy stellar mass, but parameters such as the bulge mass can be
difficult to determine for TDE host galaxies without sensitive imaging given
their masses and redshifts. On the other hand, studies like Wevers et al.
(2019) have confirmed a disparity between SMBH masses measured using MOSFiT
and those from host scaling relations such as $M_{\rm BH}-\sigma$. The lack of
correlation is not entirely discouraging, as there is indeed some correlation
between light curve properties such as rise and fade timescale and the black
hole mass (van Velzen et al., 2021; Nicholl et al., 2022; Hammerstein et al.,
2023; Yao et al., 2023), and perhaps indicates a need to revisit the exact
ways in which the properties of the black hole are imprinted onto the observed
TDE light curves.

Figure 8: Top panel: The black hole mass derived from MOSFiT as a function of
the black hole mass we derive from host kinematics. The gray dashed line
indicates a one-to-one relationship. We do not find a significant correlation
between the two measurements. Bottom panel: The black hole mass derived from
TDEmass as a function of the black hole mass we derive from host kinematics.
The gray dashed line indicates a one-to-one relationship. We do not find a
significant correlation between the two measurements. Labels for each TDE are
in Table 1.

###  4.2 Correlations with TDE light curve properties

Many previous studies have found significant correlations between the light
curve properties of TDEs and the black hole mass or, more often, the host
galaxy mass. van Velzen et al. (2021) found a correlation between the decay
timescale and host galaxy stellar mass, which Hammerstein et al. (2023)
further confirmed with a larger sample. This is consistent with many previous
results in the literature (e.g., Blagorodnova et al., 2017; Wevers et al.,
2017). Hammerstein et al. (2023) additionally found a weak correlation between
the rise timescale and the host galaxy stellar mass as well as between the
peak luminosity and the host galaxy stellar mass.

We now reexamine the correlations with host galaxy stellar mass presented in
Hammerstein et al. (2023). Between the SMBH mass and the decay rate for the 13
TDEs, we find a weak positive correlation with a Kendall’s tau test, but the
$\tau=0.23$ correlation is not significant with $p$-value $=0.31$. The
Kendall’s tau test between the SMBH mass and the rise results in $\tau=0.23$,
but again is not significant with a $p$-value $=0.31$. We no longer find a
correlation between the black hole mass and the peak blackbody luminosity.
While we generally find the same trends as previous works, our smaller sample
size weakens our ability to make significant conclusions and the disappearance
of significant correlations here should be interpreted with caution.

The black hole mass now makes it possible to compare the peak blackbody
luminosity of the TDE light curves with the Eddington luminosity implied by
the black hole mass. We define the Eddington luminosity as $L_{\rm Edd}\equiv
1.25\times 10^{38}(M_{\rm BH}/M_{\odot})$ and take values for the peak
blackbody luminosity from Hammerstein et al. (2023) measured using the peak
UV/optical SED. In Figure 9, we show the peak blackbody luminosity as a
function of the Eddington luminosity, with solid, dashed, and dotted curves
representing lines of constant Eddington ratio.

All of our events are consistent with being at or below the Eddington
luminosity (solid line), apart from AT2018lna (ID 5), with its blackbody
luminosity significantly super-Eddington even at the maximum extent of its
uncertainties. We note that this is also the lowest mass object in our sample
with $\log(M_{\rm BH}/M_{\odot})=4.98\pm 0.83$. The apparent significantly
super-Eddington luminosity may be due to the large uncertainty on the
calibration of $M_{\rm BH}-\sigma$ relation at such low velocity dispersions,
although without larger samples of dynamically measured masses for
intermediate mass black holes, this problem is hard to constrain (for a review
on such measurements, see Greene et al., 2020). The mass for AT2018lna should
thus be interpreted with caution. Super-Eddington mass fallback rates are not
unexpected for black holes with such low masses, with duration of
$\dot{M}/M_{\rm Edd}>1$ longer for smaller black holes (De Colle et al.,
2012). AT2018lna, the lowest mass black hole and the one with the largest
Eddington ratio, does indeed follow this expected relation, its bolometric
luminosity staying above Eddington for much longer than the other objects in
this sample when examing the light curve fits of Hammerstein et al. (2023).

AT2020qhs is an outlier in black hole mass, but not necessarily an outlier in
its Eddington ratio. Wevers et al. (2019) found that the TDE candidate
ASASSN-15lh possessed similar qualities and that the observed emission is
consistent with the peak Eddington ratio and luminosity of a maximally
spinning Kerr black hole. As we discuss in Section 4.3, a non-negligible spin
may explain the properties of AT2020qhs.

Yao et al. (2023) found a correlation between the Eddington ratio
($\lambda_{\rm Edd}\equiv L_{\rm bb}/L_{\rm Edd}$) and the black hole mass
which was inconsistent with the expected ratio between the peak fallback rate
and Eddington accretion rate. Instead, they found a much shallower relation
between $\dot{M}_{\rm fb}/\dot{M}_{\rm Edd}$ and the black hole mass, which
they attribute to either Eddington-limited accretion or that the UV/optical
luminosity only captures a fraction of the total bolometric luminosity. We
report similar findings here, with a moderate negative correlation between
$\lambda_{\rm Edd}$ and $M_{\rm BH}$ resulting from a Kendall’s tau test
($\tau=-0.56$, $p$-value = 0.007). In Figure 10, we show $\log(\lambda_{\rm
Edd})$ as a function of $M_{\rm BH}$, along with the fitted relations from Yao
et al. (2023) (solid line, fitted for all 33 TDEs in their sample:
$\dot{M}_{\rm fb}/\dot{M}_{\rm Edd}\propto M_{\rm BH}^{-0.49}$, dashed line,
correcting for selection bias by only fitting objects with $z<0.24$:
$\dot{M}_{\rm fb}/\dot{M}_{\rm Edd}\propto M_{\rm BH}^{-0.72}$) and the
expected relation $\dot{M}_{\rm fb}/\dot{M}_{\rm Edd}\propto M_{\rm
BH}^{-3/2}$. Visual inspection shows that the relation for our sample may be
steeper than that found by Yao et al. (2023).

Figure 9: The peak blackbody luminosity as a function of the Eddington
luminosity implied by the black hole mass. The solid, dashed, and dotted lines
indicate constant Eddington ratios. We find that nearly all TDEs in our sample
are consistent with being at or below the Eddington limit, with the exception
of AT2018lna. This object has the lowest velocity dispersion in our sample and
the black hole mass should be interpreted with caution. Labels for each TDE
are in Table 1. Figure 10: The Eddington ratio as a function of black hole
mass. The dotted line is the expected Eddington ratio for the peak fallback
accretion rate and the solid and dashed lines are the fitted relations from
Yao et al. (2023) where $\dot{M}_{\rm fb}/\dot{M}_{\rm Edd}\propto M_{\rm
BH}^{-0.49}$ and $\dot{M}_{\rm fb}/\dot{M}_{\rm Edd}\propto M_{\rm
BH}^{-0.79}$, respectively. We find a moderate negative correlation between
$\lambda_{\rm Edd}$ and the black hole mass, with the relation shallower than
the expected $\lambda_{\rm Edd}\propto M_{\rm BH}^{-3/2}$, but likely steeper
than that obtained by Yao et al. (2023). Labels for each TDE are in Table 1.

###  4.3 AT2020qhs and the TDE-featureless class

We now turn our attention specifically to AT2020qhs (ID 11), which is a
notable event for several reasons. AT2020qhs is a member of the new class of
featureless TDEs put forth by Hammerstein et al. (2023). These events are
characterized by optical spectra showing a strong blue continuum but with no
broad Balmer or He II emission typical of the optical spectra of TDEs. The
peak flare luminosities of these events are several orders of magnitude larger
than those of broad-line TDEs, but the rise and fade timescales are similar to
the other spectral classes. The host galaxies of TDE-featureless events are
typically more massive than broad-line TDEs, suggestive of a higher central
black hole mass. Indeed, we find that AT2020qhs possesses the highest black
hole mass in our sample, with $\log(M_{\rm BH}/M_{\odot})=8.26$. Yao et al.
(2023) measured the velocity dispersions for two additional TDE-featureless
events, AT2020acka (Hammerstein et al., 2021b; Yao et al., 2023) and AT2021ehb
(Gezari et al., 2021; Yao et al., 2022), and found corresponding black hole
masses of $\log(M_{\rm BH/}/M_{\odot})=8.23\pm 0.40$ and $\log(M_{\rm
BH}/M_{\odot})=7.16\pm 0.32$, respectively. If we use the Greene et al. (2020)
$M_{\rm BH}-M_{\rm gal}$ relation for late-type galaxies to estimate the black
hole masses for the remaining three featureless events in the Hammerstein et
al. (2023) sample, AT2018jbv, AT2020riz, and AT2020ysg, we obtain masses
within the range $\log(M_{\rm BH}/M_{\odot})=$ 6.48 – 7.70, which are still
among the highest masses of those obtained here.

The dependence of the tidal radius and the Schwarzschild radius on the black
hole mass is such that above $\sim 10^{8}M_{\odot}$ (sometimes called the
“Hills mass”; Hills, 1975), a solar-type star will typically pass beyond the
black hole’s event horizon undisturbed, producing no visible flare. While the
black hole mass for AT2020qhs is above this limit, it is still possible to
produce an observable TDE around a SMBH of this size. The Hills mass may be
exceeded through the disruption of giant stars, although the long timescales
and lower luminosities of these events makes it less likely that they will be
detected and noted by traditional TDE search methods (Syer & Ulmer, 1999;
MacLeod et al., 2012). This explanation for such a high black hole mass seems
unlikely, as the TDE-featureless class is shown to have the highest
luminosities of any TDE class while the timescales for these events are
comparable to other classes of TDEs (Hammerstein et al., 2023).

A more favorable explanation is that the SMBH of AT2020qhs possesses a non-
negligible spin which serves to increase the Hills mass (Kesden, 2012), as was
similarly suggested for the TDE candidate ASASSN-15lh (Leloudas et al., 2016).
It has been shown, however, that such SMBHs will contribute only marginally to
the overall TDE rate (Stone & Metzger, 2016). The low predicted rates of
spinning SMBHs amongst TDEs may not be a large concern, as Hammerstein et al.
(2023) noted that most of the TDE-featureless events occur at high redshifts,
implying that a larger volume is needed to observe them and hinting at their
rarity. Following the work of Kesden (2012) and under the assumption that the
disrupted star was of solar type, we can place a lower limit on the spin of
the AT2020qhs black hole of $a\gtrsim 0.66$.

We do note, however, that the disruption of a higher mass star can potentially
explain the black hole mass of AT2020qhs. Leloudas et al. (2015) also
addressed this for ASASSN-15lh, finding that only star masses greater than
$\sim 3M_{\odot}$ can be disrupted by a non-rotating Schwarzschild black hole.
These events are also rare (Stone & Metzger, 2016; Kochanek, 2016), but may be
a plausible explanation for AT2020qhs flare. Mockler et al. (2022) used
measurements of the N III to C III ratio in UV spectra to infer the masses of
the disrupted stars, finding that the observed ratios necessitate the
disruption of more massive stars in the post-starburst hosts they targeted.
Larger samples of UV spectra for all TDE types and black hole masses are
needed to further investigate whether this is the case for TDE-featureless
events such as AT2020qhs.

Spin has been invoked to explain other phenomena observed in TDEs, such as the
launching of relativistic jets. Recently, Andreoni et al. (2022) reported the
discovery of a jetted TDE in the ZTF survey, concluding that a high spin is
likely required to produce such jets. They put a lower limit on the spin
parameter of $a\gtrsim 0.3$. Andreoni et al. (2022) also noted the
similarities between AT2022cmc and the TDE-featureless class, with the
comparable peak flare luminosities and similar lack of broad emission lines in
spectra suggesting a connection between the two classes of events. They
propose that TDE-featureless events may be jetted TDEs observed off-axis, but
further multi-wavelength follow-up of these events is needed to confirm this
hypothesis. Nonetheless, the black hole masses AT2020qhs and AT2020acka imply
SMBHs with rapid spins and further bolster the possible connection between
jetted TDEs and the TDE-featureless class.

##  5 Galaxy kinematics and stellar populations

We now investigate the kinematic properties on the scale of the effective
radius of the entire galaxy light profile ($R_{\rm e,gal}$). Our fits using
ppxf yield velocities and velocity dispersions, which can be used to estimate
the level of rotational support the TDE hosts possess, quantified by the ratio
of ordered to random stellar motion $(V/\sigma)_{e}$, where lower values of
$(V/\sigma)_{e}$ indicate a higher degree of random stellar motions. We adopt
the formula of Cappellari et al. (2007), defined for integral field data:

$\left(\frac{V}{\sigma}\right)^{2}_{e}\equiv\frac{\langle
V^{2}\rangle}{\langle\sigma^{2}\rangle}=\frac{\Sigma_{n=1}^{N}F_{n}V_{n}^{2}}{\Sigma_{n=1}^{N}F_{n}\sigma_{n}^{2}},$
(2)

where $F_{n}$ is the flux contained within the $n$th bin, while $V_{n}$ and
$\sigma_{n}$ are the mean measured velocity and velocity dispersion within
that bin. In Figure 11 we show the $(V/\sigma)_{e}$ for the thirteen TDE host
galaxies as a function of stellar population age. We also show the same
comparison sample of galaxies as in Figure 2. The top and side panels of
Figure 11 show the distribution of galaxies in the red sequence, which hosts
largely quiescent, elliptical galaxies, the blue cloud, which hosts primarily
star-forming galaxies, and the green valley, which hosts recently quenched
galaxies, defined from Figure 2, E+A galaxies, and the TDE hosts. E+A galaxies
from the SAMI survey were selected using the H$\alpha$ equivalent width and
Lick H$\delta_{\rm A}$ absorption index using values presented in the MPA+JHU
catalogs (Brinchmann et al., 2004). We note that only a third of the galaxies
in the SAMI survey have a counterpart in the MPA+JHU catalog. The H$\alpha$
equivalent width is limited to $<4.0$ Å and the H$\delta_{A}$ index is limited
to H$\delta_{\rm A}-\sigma$(H$\delta_{\rm A})>4.0$ Å to isolate post-starburst
galaxies.

Figure 11: The ratio between stellar ordered rotation and random orbital
motion of the TDE host galaxies, defined as $(V/\sigma)_{e}$, as a function of
galaxy stellar mass, with the color of the points/pixels corresponding to the
stellar population age. The median uncertainty on the TDE host galaxy values
is shown in the top left. Galaxies from the SAMI galaxy survey are shown in
the background, with the mean stellar population age of galaxies within a
pixel used to determine the pixel color. White contours represent the number
density of background galaxies. The top and side panels show the distribution
of the TDE hosts and the red sequence, green valley, blue cloud, and E+A
galaxies in the background sample obtained by kernel density estimation. We
find that the TDE hosts are generally lower mass than most of the background
sample, with a larger spread in $(V/\sigma)_{e}$ than green valley or red
sequence galaxies but a distribution similar to E+A galaxies. Labels for each
TDE are in Table 1.

van de Sande et al. (2018) found a strong correlation between the ratio of
ordered rotation to random stellar motion and the stellar population age of a
galaxy, such that younger stellar populations are predominantly rotationally
supported as in late-type galaxies while older stellar populations are
pressure supported by random stellar motions as in early-type galaxies. They
also found that $(V/\sigma)_{e}$ is linked to the observed shape (quantified
by the ellipticity $\epsilon$). These correlations link a galaxy’s star
formation history with its merger history, as mergers will enhance the
formation of bulges which in turn lowers a galaxy’s $(V/\sigma)_{e}$ and
ellipticity. We find that the TDE host galaxies largely follow this same
relation between $(V/\sigma)_{e}$ and stellar population age, apart from two
outliers AT2019azh and AT2020zso (IDs 6 and 13, respectively). AT2019azh is a
known E+A galaxy, which have been shown to have varied central stellar
population ages and young stellar populations not necessarily confined to the
nucleus (Norton et al., 2001; Pracy et al., 2009). This may affect the
measurement of the host galaxy stellar population age in the central regions
in unforeseen ways.

The close link between the merger history, stellar population age, and stellar
kinematics is very likely a driving factor behind post-starburst color (used
as a proxy for stellar population age) and morphology, and may help explain
the TDE preference for such environments. Even before van de Sande et al.
(2018) noted the connection between stellar kinematics and stellar population
age, Schawinski et al. (2010) found that low-mass morphologically early type
galaxies in the green valley, which is thought to contain more recently
quenched galaxy populations, are linked to mergers which rapidly ushered their
migration from the star-forming blue cloud to the green valley and which
changed their shape from disk to spheroidal. Schawinski et al. (2014)
subsequently found that these systems have classic post-starburst populations.
However, the majority of galaxies migrate into the green valley through a slow
decline in star formation rate likely as a result of gas supply shut off and
retain hence their disk shape. The population of green, spiral-like galaxies
is noted in Hammerstein et al. (2021a), who compared 19 TDE hosts to red
sequence, green valley, and blue cloud galaxies, finding that the TDE hosts
are inconsistent with the majority of green valley galaxies which maintained
their disk-like morphology inferred through the Sérsic index.

Given the rate enhancement of TDEs in green valley (and E+A) galaxies, one
could expect that TDE host galaxies also cluster in a specific region of
$(V/\sigma)_{e}$. However, we observe a relatively large spread in
$(V/\sigma)_{e}$. The TDE hosts are more evenly distributed in
$(V/\sigma)_{e}$ with a median value of 0.52. We compare the distribution of
the TDE host galaxies in $(V/\sigma)_{e}$ and mass to the red sequence, green
valley, and blue cloud galaxies. We find that the TDE hosts, while
predominantly green, are generally less massive than the majority of green
valley galaxies. This is in agreement with the findings of Hammerstein et al.
(2021a) for a larger sample of 19 TDE host galaxies from ZTF. The green valley
and red sequence distributions in $(V/\sigma)_{e}$ peak around $\sim 0.2$,
indicating that these galaxies are dominated by random stellar motions. In
general, we expect a negligible contribution to the TDE rate from stars on
circular orbits. This could lead one to conclude that at a fixed stellar mass,
a low $(V/\sigma)_{e}$ might imply a higher TDE rate. However, we should note
that the stars within the SMBH sphere of influence (radius $\sim 1$ parsec)
contribute only a tiny fraction to the stellar light within the effective
radius. Hence the large spread in the $(V/\sigma)_{e}$ that we observe for the
TDE host galaxies cannot directly be translated into a spread in the TDE rate.
We thus arrive at the somewhat puzzling observation that the TDE rate appears
to be correlated more strongly with the global colors of the host galaxy than
the $(V/\sigma)_{e}$ at its effective radius.

Galaxies that are most certainly dominated by random stellar motions and have
stellar populations older than 10 Gyr (i.e., early-type galaxies), have a mean
$(V/\sigma)_{e}=0.22$. Although three TDE hosts have values around or below
this level, they have stellar population ages younger than 10 Gyr at $\sim
7.1$ Gyr. The older, more massive galaxies which are dominated by random
stellar motions may also host black holes which exceed the Hills mass, which
could explain why the TDE hosts with lower $(V/\sigma)_{e}=0.22$ have younger
stellar populations than galaxies with similar kinematics. The difference in
age between galaxies dominated by random stellar motions and the TDE hosts of
similar $(V/\sigma)_{e}$ implies that the TDE rate likely declines as a galaxy
ages despite the increase in the degree of random motion, although the precise
reason, whether it be black hole growth beyond the Hills mass or otherwise,
and the connection this has with nuclear dynamics is not yet clear given the
indirect relationship that these global properties have with factors
influencing the TDE rate in the nucleus.

The E+A distribution in $(V/\sigma)_{e}$ has a mean value of 0.49, similar to
the TDE hosts’ median value of 0.52. The E+A mass distribution also peaks at
$\log(M_{\rm gal}/M_{\odot})=10.07$, while the median TDE host galaxy mass is
$\log(M_{\rm gal}/M_{\odot})=10.09$. It is clear that the TDE host galaxies
are likely consistent with the same population of galaxies as post-starburst
galaxies, which has been suggested previously (e.g., Law-Smith et al., 2017;
Hammerstein et al., 2021a). We can also rule out that the TDE hosts come from
the same population as red sequence galaxies. An Anderson-Darling test
comparing the $(V/\sigma)_{e}$ of red sequence galaxies to the TDE hosts
reveals that the null hypothesis that the two are drawn from the same parent
population can be rejected ($p$-value = 0.02). The same cannot be said,
however, when comparing green valley galaxies and blue cloud galaxies to the
TDE hosts.

The TDE host galaxies also differ in age when compared to the E+A galaxies,
with the former having a median stellar population age of 6.12 Gyr, while the
E+A galaxies have a mean stellar population age of 2.82 Gyr. One possible
conclusion from this is that the TDE host galaxies are post-merger, similar to
E+As, but the younger stellar populations produced in the merger-induced
starburst having subsided meaning the ages of the stellar populations are
older but the other factors which enhance the TDE rate in E+A galaxies (e.g.,
nuclear star clusters, high central stellar concentrations) remain. Future
observations which search for merger signatures, such as in French et al.
(2020b), for larger samples of TDEs will be able to confirm the prevalence of
post-merger galaxies among TDE host populations. The GALFIT residuals for
several galaxies from the LMI data presented here do show remaining features,
although differentiating normal dust lane features from true merger signatures
like tidal features is difficult. Stone et al. (2018) examined factors which
enhance TDE rates in post-starburst galaxies, such as SMBH binaries, nuclear
stellar overdensities, radial orbit anisotropies, and delay between the
initial starburst and the enhancement of the TDE rate due to these factors.
This delay time between the initial post-merger starburst and the enhancement
of the TDE rate could help to explain why the TDE hosts show older ages but
similar global stellar dynamics to the younger post-starburst galaxies.

##  6 Conclusions

We have presented the first sample study of IFU observations of thirteen TDE
host galaxies from the ZTF survey in order to investigate their kinematic
properties and infer their black hole masses. Our main conclusions are as
follows:

  * •

The black hole mass distribution peaks at $\log(M_{\rm BH}/M_{\odot})=5.96$,
consistent with theoretical predictions that TDE populations are dominated by
lower mass SMBHs and past observational findings.

  * •

There is no significant statistical difference between the X-ray bright and
X-ray faint population of TDEs in our sample, which further supports the
unifying theory of Dai et al. (2018) that proposes viewing angle effects as
the factor which determines X-ray brightness in a TDE.

  * •

We find no significant correlation between the black hole masses derived from
$M_{\rm BH}-\sigma$ and the black hole masses derived from MOSFiT or TDEmass.
This may indicate a need to revisit the way that the black hole mass is
imprinted on the light curves of TDEs.

  * •

The Eddington ratio is moderately correlated with the black hole mass,
although the correlation is likely shallower than the expected relation
between the peak fallback accretion rate and the black hole mass, similar to
the findings of Yao et al. (2023).

  * •

We find that the event AT2020qhs, a member of the TDE-featureless class, has
the highest black hole mass of the sample: $\log(M_{\rm BH}/M_{\odot})=8.26\pm
0.83$, above the Hills mass for the disruption of a solar type star. We
suggest that the SMBH at the center of this event is rapidly spinning and,
assuming that the disrupted star was of solar type, put a lower limit on the
spin of $a\gtrsim 0.66$. This further supports the proposed connection between
jetted TDEs and the TDE-featureless class put forth by Andreoni et al. (2022).

  * •

We investigate the large-scale kinematics of the TDE host galaxies,
particularly the ratio of ordered rotation to random stellar motions
$(V/\sigma)_{e}$, and find that the TDE hosts show similar distributions in
$(V/\sigma)_{e}$ to E+A galaxies but older stellar populations. This may
indicate that TDE host galaxies, like E+A galaxies, are post-merger galaxies
with the younger stellar populations produced in the merger-induced starburst
having subsided, leaving only the older stellar populations. The delay time
between post-merger starburst and TDE rate enhancement may also explain the
discrepancy in age (e.g., Stone et al., 2018)

EH acknowledges support by NASA under award number 80GSFC21M0002. These
results made use of the Lowell Discovery Telescope (LDT) at Lowell
Observatory. Lowell is a private, non-profit institution dedicated to
astrophysical research and public appreciation of astronomy and operates the
LDT in partnership with Boston University, the University of Maryland, the
University of Toledo, Northern Arizona University and Yale University. The
Large Monolithic Imager was built by Lowell Observatory using funds provided
by the National Science Foundation (AST-1005313). The data presented here were
obtained at the W. M. Keck Observatory, which is operated as a scientific
partnership among the California Institute of Technology, the University of
California and the National Aeronautics and Space Administration. The
Observatory was made possible by the generous financial support of the W. M.
Keck Foundation. The authors wish to recognize and acknowledge the very
significant cultural role and reverence that the summit of Mauna Kea has
always had within the indigenous Hawaiian community. We are most fortunate to
have the opportunity to conduct observations from this mountain. The SAMI
Galaxy Survey is based on observations made at the Anglo-Australian Telescope.
The Sydney-AAO Multi-object Integral field spectrograph (SAMI) was developed
jointly by the University of Sydney and the Australian Astronomical
Observatory. The SAMI input catalogue is based on data taken from the Sloan
Digital Sky Survey, the GAMA Survey and the VST ATLAS Survey. The SAMI Galaxy
Survey is supported by the Australian Research Council Centre of Excellence
for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number
CE170100013, the Australian Research Council Centre of Excellence for All-sky
Astrophysics (CAASTRO), through project number CE110001020, and other
participating institutions. The SAMI Galaxy Survey website is http://sami-
survey.org. The data analysis in this paper was performed on the Yorp and
Astra clusters administered by the Center for Theory and Computation, part of
the Department of Astronomy at the University of Maryland.

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