The Open Journal of Astrophysics submitted XXX; accepted YYY

# Imprints of interaction processes in the globular cluster system of NGC 3640

Ana I. Ennis⋆1,2 Juan P. Caso†3,4,5 Lilia P. Bassino‡5 1Waterloo Centre for
Astrophysics, University of Waterloo, 200 University Ave W, Waterloo, Ontario
N2L 3G1, Canada  2Perimeter Institute for Theoretical Physics, Waterloo,
Ontario N2L 2Y5, Canada  3Instituto de Astrofísica de La Plata (CCT La Plata –
CONICET, UNLP), Paseo del Bosque S/N, B1900FWA La Plata, Argentina  4Consejo
Nacional de Investigaciones Científicas y Técnicas, Godoy Cruz 2290, C1425FQB,
Ciudad Autónoma de Buenos Aires, Argentina  5Facultad de Ciencias Astronómicas
y Geofísicas de la Universidad Nacional de La Plata, Paseo del Bosque S/N,
B1900FWA La Plata, Argentina

###### Abstract

We present a wide-field study of the globular cluster systems (GCS) of the
elliptical galaxy NGC 3640 and its companion NGC 3641, based on observations
from Gemini Multi-Object Spectrograph/Gemini. NGC 3640 is a shell galaxy which
presents a complex morphology, which previous studies have indicated as the
sign of a recent ‘dry’ merger, although whether its nearest neighbour could
have had an influence in these substructures remains an open question. In this
work, we trace the spatial distribution of the globular clusters (GCs) as well
as their colour distribution, finding a potential bridge of red GCs that
connects NGC 3640 to its less massive companion, and signs that the blue GCs
were spatially disturbed by the event that created the shells.

###### keywords:

Early-type galaxies (429), Galaxies (573), Globular star clusters (656)

##  1 Introduction

Mergers are essential parts of the current $\Lambda$ Cold Dark Matter
paradigm, in which dark matter haloes and galaxies are mainly formed through
hierarchical assembly (Peebles, 1982; Blumenthal et al., 1984; Davis et al.,
1985). In particular, the early evolution of early-type galaxies (ETGs) is
dominated by major mergers involving large amounts of gas (Naab et al., 2007).
Once they become quiescent, they continue to grow their mass and size through
minor dry mergers, with little to no star formation (Naab et al., 2009, e.g.).
Aside from being the driving forces behind the mass growth of a galaxy,
mergers shape the morphology of galaxies (Hopkins et al., 2010; Kannan et al.,
2015, e.g), feed central supermassive black holes, and potentially trigger
central starbursts (Ellison et al., 2011; Satyapal et al., 2014). As such,
they are important components of any galaxy formation model.

The frequency of major mergers experienced by a galaxy is influenced by the
local density where it resides, as evidenced by the dependence of the fraction
of passive galaxies and stellar mass functions with it (e.g. McNaught-Roberts
et al., 2014; Etherington et al., 2017). Although this relation is nuanced, it
is clear that higher-density environments show larger rates of galaxy mergers,
with groups being the most active type of environment.

Tidal features are the most direct evidence of recent mergers, and they have
been widely used to characterize the impact of these events on the properties
of galaxies. Photometric analysis has shown, for example, that blue ETGs are
more likely to present morphological disturbances (Tal et al., 2009; Kaviraj
et al., 2011, e.g), hinting at the presence of younger stellar populations as
a consequence of recent mergers. However, most of the signatures of accretion
events are found in the form of low surface brightness structures, which
require long exposures to be analysed.

Globular clusters (GCs) located in the halo of galaxies are helpful tools when
it comes to tracing the occurrence of recent mergers since they are bright and
they are connected to the underlying stellar population, acting as fossil
records of the evolutionary history of their host galaxy and carrying in their
properties valuable information about its accretion events. In regions where
the stellar halo is too faint, GCs have been used as tracers of stellar
streams and tidal tails (Napolitano et al., 2022), and when structures can be
detected, the colours and positions of the GCs connected to them can shed
further light on their origin (Lim et al., 2017; D’Abrusco et al., 2022, e.g).
Since GCs are sparse even in massive galaxies and tidal features are hard to
detect, studying this connection requires deep, wide-field observations. In
nearby ETGs, rich underlying substructure is related with GC systems with
unusual colour and luminosity distributions (e.g. Sesto et al., 2016; Bassino
& Caso, 2017), and the presence of young GCs (e.g. Strader et al., 2004;
Woodley et al., 2010).

The elliptical galaxy NGC 3640, located at a distance of 27 Mpc according to
the results from the surface brightness fluctuation method (SBF) (Tully et
al., 2013), is part of a loose group conformed by approximately eight galaxies
(Madore et al., 2004). This group is thought to be dynamically young since no
X-ray emission was detected by ROSAT above $3\,\sigma$ of the background level
(Osmond & Ponman, 2004). NGC 3640 has an absolute magnitude of
$\textrm{M}_{\textrm{B}}=-20.93$ (Tal et al., 2009), and it has been
classified as both E3 (de Vaucouleurs et al., 1991) and T3 (Kormendy, 1982),
the latter being defined as a type for galaxies with very prominent
companions, making the probability of tidal effects very high. Its close
companion, NGC 3641 is classified as a compact elliptical (cE) in de
Vaucouleurs et al. (1976), and it is located at a projected angular distance
of $2^{\prime}5$ South. If we consider the distance to NGC 3640 as the mean
distance to the group, this corresponds to a physical distance of
$19\,\textrm{kpc}$.

Prugniel et al. (1988) (P88 for the rest of this work) present the first
analysis dedicated to the morphology of this galaxy and its kinematics. Using
photometry, they analyse the surface brightness profile of NGC 3640,
identifying signatures of a recent merger in the shape of the isophotes and in
the residual structures. A previous work had already shown the isophotes to be
boxy (Bender et al., 1988), and more recently, NGC 3640 has even been referred
to as an example of ‘extreme boxyness’ (Michard & Prugniel, 2004). In P88,
they also detect a dust lane along the minor axis, a feature that has been
identified in remnants of merger processes with large quantities of gas and
dust. With additional long-slit spectroscopic data, P88 characterize NGC 3640
as a fast rotator ($V/\sigma=1.5)$, which can also be a consequence of an
interaction or merging process. In comparison with other galaxies thought to
be merger remnants, they argue NGC 3640 appears to be at a more advanced stage
of relaxation, though it lacks strong nuclear radio emission, which is
expected to be ignited after the merging has been completed. Since NGC 3640
shows very small amounts of gas and dust according to P88, the merger it
experienced is thought to have been ‘dry’.

Figure 1: Representation of the observed GMOS fields plotted over a colored
image from the Digitized Sky Survey 2, obtained from the Aladin Sky Atlas.

Later on, Schweizer & Seitzer (1992) include NGC 3640 in a sample of galaxies
they analyze using an index defined in their work to quantify features
connected to mergers. Out of the 35 ellipticals in the sample, NGC 3640
presents one of the highest values of this index, meaning it is among the most
disturbed galaxies. Assuming this disturbance is owed to NGC 3640 being the
result of a disk-disk merger, they use its UBV colour to date this merger,
concluding it could be a ‘young’ elliptical, i.e. less than 7 Gyr old.
However, they point out in their work that the presence of NGC 3641 could have
had a significant influence in the disturbances detected in NGC 3640,
especially considering the high interactivity between galaxies in small
groups. Michard & Prugniel (2004) support the idea of NGC 3640 having been
formed in a major merger based on its morphology and on their analysis of its
stellar population indicators, which indicate the presence of a relatively
small young population, in comparison with other highly disturbed galaxies. In
addition, two different works performed analysis of the stellar population of
NGC 3640 using long-slit spectra. While Denicoló et al. (2005) estimate a
nuclear age of 2.5 Gyr, the reanalysis of the same data by Brough et al.
(2007) finds an older (4 Gyr), less metal-rich center, which they estimate to
be within $1.5\sigma$ of their results. Overall, their analysis points to NGC
3640 having undergone a dissipational merger 7.5 Gyr ago, and presenting a
younger central age that would imply a more recent ‘wet’ merger.

NGC 3640 shows then a large number of peculiarities, including a collection of
signs that point at it having undergone a relatively recent merging process.
Though several of these signs have been associated with a major disk-disk
merger, none of the analyses rule out interactions with the less massive
galaxies in the group as the cause of some of the tidal disturbances. The
compactness of NGC 3641 could be another hint of interaction since it could be
a consequence of tidal stripping. This is inconclusive since NGC 3641 is
located to the South of NGC 3640, while the major axis of NGC 3640 is oriented
East to West, and its classification as a cE is unclear. There are many open
questions about the evolutionary history of NGC 3640, particularly in terms of
its interaction with NGC 3641. In this work, we study the globular cluster
system (GCS) of both galaxies, looking for clues that can help us untangle the
interactions that have shaped NGC 3640.

In Section 2, we describe the data and the reduction process. In Sections 3
and 4 we analyse several properties of the GCS of NGC 3640 and NGC 3641,
respectively. In Section 5 we focus on the connection between the spatial
distribution of GCs and the low surface brightness structures. In Section 6 we
discuss the results. Finally, in Section 7 we summarize our results.

##  2 Data acquisition and reduction

###  2.1 Observations

Filter |  $\lambda$ [nm] | Exposition time [s]
---|---|---
$g^{\prime}$ | 475 | 4 x 650
$r^{\prime}$ | 630 | 4 x 270
$i^{\prime}$ | 780 | 4 x 240
Table 1: Exposition times for each filter, identical for both fields.

The observations for this work were taken utilizing the Gemini Multi-Object
Spectrograph Camera (GMOS) on Gemini North (Program GN-2016A-Q-69, PI: L.
Bassino) on February 10th, 2016, in imaging mode. The field of view of GMOS is
of $5.5\,\rm{arcmin}\times 5.5\,\rm{arcmin}$, and we used a binning of
$2\times 2$, which results in a resolution of $0.146\,\rm{arcsecpix}^{-1}$.
The seeing for these observations was $\approx 0.75$ across all filters. We
observed two fields as shown in Figure 1, one containing both galaxies and an
adjacent one with which we aimed to cover the entire extension of the GCS and
calculate the background contamination. We also observed the Landolt field of
standard stars SA 104 (Landolt, 1992), using the magnitudes obtained in the
GMOS filters by Jørgensen (2009).

Figure 2: From top to bottom, the error in magnitude, $\chi^{2}$ and the
sharpness value obtained from PSF photometry for the $g^{\prime}$ filter for
reference. Solid lines indicate the chosen limits, with the limit in magnitude
applied to the selections in the following tests.

###  2.2 Data reduction and point-source selection

We used the DRAGONS Data Reduction Software (Labrie et al., 2019) to correct
the observations using bias and flat-field images obtained from the Gemini
Archive 111https://archive.gemini.edu/, and then to combine all of the images
corresponding to each field in each filter. Images in the filter $i^{\prime}$
presented a fringe pattern which was corrected using a blank field from the
Archive. We then proceeded to subtract a model of the integrated light from
both galaxies using the median filter task in SciPy. We ran it twice with
different-sized windows (100 and 50 pixels), allowing for the detection of
point-like sources in the inner region. Finally, we used geomap and geotran in
IRAF to geometrically transform the final images, taking them all to the same
reference system and cropping the edges.

The first catalog of globular cluster candidates present in the field was
built using Source Extractor (Bertin & Arnouts, 1996). We used two filters,
Gaussian and Mexhat ones, since the latter has proven to be more effective in
crowded regions. Combining the outcome of both, we obtained approximately 4000
objects. Considering GCs appear as unresolved point-like sources at this
distance, we use the classifier $CLASS\\_STAR$, which estimates the
probability of the detected source being point-like. In this case, we
eliminate from the sample objects with $CLASS\\_STAR>0.5$ as to clear it of
extended objects, mainly background galaxies and saturated stars.

We obtained aperture photometry for these objects using the tasks in the
DAOPHOT package in IRAF. After selecting $\sim 30$ of the brightest objects in
each filter, for each field correspondingly, we built the spatially variable
corresponding point-spread function (PSF) and obtained PSF photometry of our
sample with the task ALLSTAR.

Figure 3: Completeness fraction in the $i^{\prime}$ filter for three
concentric annular regions, with the corresponding fit. Circles and a solid
line indicate the inner region; triangles and a dashed line, the intermediate
region; and squares and a dotted line, the outer region.

Besides calculating instrumental magnitudes with their errors, this task
provides us with statistical parameters that characterize the goodness of the
fit. In particular, it calculates the sharpness and the chi-squared. In the
completeness test described in the following section, we obtained the
distribution of parameters for a large number of artificial sources, and
selected constraints for these parameters, as shown in Figure 2. After
applying this selection, we obtain a total of $1576$ point-like sources.

###  2.3 Completeness test

In the dim end of the magnitudes range, we estimate the limiting value by
performing a completeness test. We build a catalog of 32000 objects, with
magnitudes assigned so that they cover the range of magnitudes and colours
expected for old GCs, and positions that cover both fields, distributed evenly
over 200 copies of the original image. Using the PSF obtained before, we add
them as fake stars to our raw data. Then, we proceed to perform the same data
reduction process as before, detecting point-like sources and performing PSF
photometry in the same manner as for our GC candidates. This allows us to
obtain the set of statistical parameters that return the highest fraction of
sources while still providing a good fit.

We divide the area into three concentric annular regions to take into
consideration any radial variations in the completeness, and we estimate the
fraction of recovered sources per magnitude bin for each of these regions.
Then, we fit a function to the completeness fraction estimated for each
region, which will be used later on to apply a more detailed completeness
correction (Figure 3). This is particularly relevant in the inner region, in
which the intrinsic brightness of the galaxy causes the completeness fraction
to be lower than in other areas of the image. Finally, we determine the
overall limit as the magnitude at which this fraction is of $\sim 80\%$ for
the intermediate and outer regions, which in this case is
$i^{\prime}_{0}=24.7$.

###  2.4 Photometric calibration

We transform the instrumental magnitudes to the standard system by using the
equations corresponding to the E2V-DD detector obtained from the Gemini
Observatory website222http://http://www.gemini.edu/, described in Equation 1,
and a field of standard stars, SA 104. We calculated the zero points and
colour terms by fitting a curve to the relation between our photometry of the
standard stars and their standard magnitudes (see Table 2). In the case of the
median atmospheric extinction coefficients, $k_{CP}$, we used the ones
provided by the Gemini Observatory website, corresponding to the median value
at Mauna Kea.

$\begin{split}m_{\rm std}=&m_{\rm
zero}-2.5\,\log_{10}\left(N(e-)/\textrm{exptime}\right)\\\
&-k_{CP}(\textrm{airmass}-1.0)\end{split}$ (1)

Filter | Zero-point | Colour term
---|---|---
g’ | $28.08\pm 0.06$ | $0.06\pm 0.09*(g^{\prime}-r^{\prime})$
r’ | $28.23\pm 0.11$ | $0.01\pm 0.18*(g^{\prime}-r^{\prime})$
i’ | $28.35\pm 0.03$ | $0.13*(r^{\prime}-i^{\prime})$
Table 2: Zero-point and colour term values obtained for each filter. The
colour term used for the $i^{\prime}$ filter was obtained from the Gemini
website since the quality of the observations of the standard stars field in
said filter did not allow for a good fit. Figure 4: Colour-colour diagrams for
two different combinations of filters, showing all sources present in the
field as grey crosses, and those that satisfy all the criteria to be
considered GC candidates are highlighted with pink squares. The limits shown
in solid lines are estimated based on values from the literature.

###  2.5 GC candidate selection

In Figure 4, we show the colour-colour diagrams of the entire sample of point-
like sources detected in the field. We use colour limits to identify GC
candidates, following Bassino & Caso (2017), in the three classic colour
combinations. The limits in $(g^{\prime}-i^{\prime})$ are shown in the colour-
magnitude diagram (Figure 6), where we add the limit obtained from the
completeness test, corresponding to $80\%$, in the dim end of the magnitudes
axis. The colour limits correspond to $0.4<(g^{\prime}-i^{\prime})_{0}<1.5$,
$0.3<(g^{\prime}-r^{\prime})_{0}<1.2$ and
$-0.05<(r^{\prime}-i^{\prime})_{0}<0.5$. In addition, we limit the error in
magnitude to $<0.15$, and we exclude objects brighter than $M_{i}=21.5$, which
at the estimated distance for NGC 3640 corresponds to $M_{V}=-11$, which is
the limit at which the probability of finding GCs becomes very low (Harris et
al., 2014). Objects brighter than this limit that fall in this colour range
are more likely to be ultra-compact dwarfs, and as such, we treat them as
potential contaminants.

Figure 5: Spatial distribution of all GC candidates across both fields. Orange
dots and green diamonds indicate sources attributed to NGC 3640 and NGC 3641
respectively. The centre of each galaxy is shown in large symbols with thick
edges.

Since we cannot estimate radial velocity measurements from photometry alone,
initially we separate GC candidates according to their spatial distribution,
as shown in Figure 5. The relation between the stellar mass of the galaxy and
the extension of the GCS shown in Equation 9 in Caso et al. (2019) results in
a value of $21\,kpc$ for the extension of the GCS of NGC 3641. However, the
fact that NGC 3641 is a compact elliptical means that the estimated extension
of the GCS that corresponds to the effective radius of the galaxy is far
smaller. Since existing scaling relations are inconclusive for cE galaxies, we
initially attribute all GC candidates within a radius of $75^{\prime\prime}$
of the center of NGC 3641 to its GCS, and the rest to NGC 3640, though this
separation is by no means conclusive.

Figure 6: Left: Colour-magnitude diagram for all sources, shown as grey
crosses. The GC candidates attributed by galactocentric distance to NGC 3641
are shown as green diamonds, while those attributed to NGC 3640 are
represented by orange dots. In pink we show the error bars for the mean error
in magnitude bins ($0.4$ mag). Right: Colour-magnitude diagram for background
sources.

##  3 The GCS of NGC 3640

###  3.1 Colour-magnitude diagram

In Figure 6 we show the colour-magnitude diagram of the point-like sources in
the field and the GCs associated with each galaxy. NGC 3641 presents
intermediate colours in comparison with NGC 3640, covering a smaller range in
general. In particular, NGC 3641 almost lacks blue GCs. It is reasonable to
expect those to have been accreted first if these galaxies have interacted.

NGC 3640 covers a range typical of GCS in massive ETGs, and towards the
brighter end, two subpopulations are evident.

The right panel shows the background sources, located in the region selected
as background based on the radial distribution described in the following
section. The contamination level is even across the entire colour range.

###  3.2 Radial distribution

In Figure 7 we show the radial distribution for the GC candidates across both
fields attributed to NGC 3640. We estimate the background level considering
the flattening of the distribution in the outer regions, at
$r_{gal}=3.7^{\prime}$, obtaining a contamination correction of
$8\,\textrm{GC}\,\textrm{arcmin}^{-2}$ which was applied throughout the
analysis.

We fit a Hubble-Reynolds law to the background corrected profile, resulting in
the following profile:

$n(r)=1.88\left(1+\left(\frac{r}{1.16}\right)^{2}\right)^{-2.06}$ (2)

Extrapolating this function to the value at which it reaches $20\%$ of the
background level, we calculate a total extension of the system of $31\,{\rm
kpc}$ ($\approx 4^{\prime}$).

Integrating the profile up to this point, we obtain the total population up to
our completeness level, resulting in $\approx 310\,$GCs.

In addition, in Figure 8, we show the radial distribution for GC candidates
split into red and blue subpopulations, following the separation described in
the following Section. We fit Hubble-Reynolds laws to both profiles, obtaining
core radii of $0.72$ for blue GCs and $1.8$ for red GCs. The red subpopulation
appears heavily concentrated towards the centre of the galaxy, whereas the
blue one extends to the outer region in a steeper manner. These behaviours are
consistent with what is expected if we consider red GCs to be mostly formed
in-situ, and blue GCs to come from accretion processes that increase their
density in the outer halo.

Figure 7: Radial distribution for GC candidates attributed to NGC 3640.
Crosses describe the raw sample, while orange circles show the background
corrected distribution, with a grey, larger circle indicating those considered
for the fit. The dash-dotted line shows the level at which $20\%$ of the
background density is reached, and the dashed curve, the Hubble-Reynolds law
fit.

Figure 8: Radial distribution for GC candidates attributed to NGC 3640, for
the blue (top) and red (bottom) subpopulations. Crosses describe the raw
sample, while circles show the background corrected distribution. The dash-
dotted horizontal line indicates $20\%$ of the background level, and the
dashed curve, the Hubble Reynolds law.

###  3.3 Colour distribution

In Figure 9 we show the histogram of the colour distribution for the GCs
attributed to NGC 3640, as well as the background correction. Since the
background sources show a homogeneous distribution across the colour range, we
consider the background correction negligible in terms of fitting the
subpopulations.

Figure 10 shows the density probability functions of the colour distribution
for the GCs attributed to NGC 3640, as well as the inner
($r_{gal}<75^{\prime\prime}$) and outer ($r_{gal}>75^{\prime\prime}$) regions.
These smoothed distributions use a Gaussian kernel, with a bandwidth of $0.5$.

We use the Gaussian Mixture Modeling code (GMM, Muratov & Gnedin (2010)) to
estimate the probability of the distribution being bimodal in all samples. The
output provided by GMM includes both the parameters for the best fit of
Gaussian functions ($\mu$ and $\sigma$, as well as the fraction of sources
attributed to each mode) and statistical tests that estimate the confidence
level of the multi-modal fit. These statistical tests are the kurtosis of the
distribution, which quantifies its peakedness, and D, which is a parameter
that is calculated by assuming bimodality and measuring the distance between
the estimates means, weighed by the broadness of each mode. D is expected to
be greater than 2 in bimodal distributions. A unimodal distribution would
result in a stronger peak, which would in turn be reflected in positive values
for the kurtosis.

In Table 3, we show the results for each sample. When considering the entire
population of GCs attributed to NGC 3640, the result is a negative kurtosis
and a $D>2$, meaning a bimodal distribution, with modal values similar to
those in other massive early-type galaxies (Harris et al., 2009; Forbes et
al., 2011).

Both regions are statistically bimodal according to this fit. The means of the
subpopulations in the inner region are redder than when considering the entire
sample, in particular for the red subpopulation. The outer region presents
bluer means for both subpopulations than the entire sample, and is more likely
to be contaminated by GCs connected to NGC 3641.

Sample | $\mu$ | $\sigma$ | Red fraction | Kurtosis | D
---|---|---|---|---|---
| Blue | Red | Blue | Red |  |  |
NGC $3640$ | $0.85\pm 0.04$ | $1.19\pm 0.05$ | $0.15\pm 0.02$ | $0.14\pm 0.02$ | $0.35$ | $-0.56$ | $2.27\pm 0.24$
NGC 3640 (inner) | $0.92\pm 0.05$ | $1.24\pm 0.05$ | $0.14\pm 0.03$ | $0.12\pm 0.02$ | $0.30$ | $-0.56$ | $2.54\pm 0.39$
NGC 3640 (outer) | $0.79\pm 0.05$ | $1.13\pm 0.06$ | $0.14\pm 0.02$ | $0.16\pm 0.02$ | $0.48$ | $-0.60$ | $2.22\pm 0.29$
Table 3: Parameters for the Gaussian functions resulting from the bimodal fit
performed using GMM for the different samples. Figure 9: Colour distribution
for the full sample of GC candidates attributed to NGC 3640 shown in orange.
Black lines represent the background distribution, and white lines the
corrected distribution.  Figure 10: Smoothed olour distributions for the full
sample of GC candidates attributed to NGC 3640 (top). In the middle panel, the
inner region (left), and in the bottom, the outer region of NGC 3640. Blue
solid curves and red dashed curves represent the best fit from GMM for bimodal
Gaussian distributions for each sample.

###  3.4 Luminosity function

The luminosity function of globular cluster systems is widely used as a
distance estimator due to the universality of the absolute magnitude of its
turn-over. The SBF distance to NGC 3640 is $26.9$ Mpc, which results in a
turn-over magnitude of $V_{0}=24.75$. Using the transformations from Faifer et
al. (2011), and a mean $(g-i)$ value of 1, we can transform to approximately
$i_{0}=24.1$, which is well within our completeness range, allowing us to
estimate our own measurement of the distance to compare with the literature
value.

In Figure 11, we show the luminosity function for GC candidates associated
with NGC 3640, after applying a completeness and background correction.
Fitting a Gaussian function to our distribution results in a turn-over value
of $i_{0}=23.74\pm 0.02$, which is within error from the SBF distance. The
dispersion of the Gaussian is $\sigma_{L}=0.68\pm 0.02$. In Harris et al.
(2014), the GCLF is proposed to have an intrinsic width of
$\sigma_{L}=0.52-0.55\,\textrm{dex}$. The difference between these two values
may be due to contamination from NGC 3641.

Due to this slight difference, we choose to use the turn-over value from SBF
to estimate the percentage of GCs within our completeness range in relation to
the total population, which in this case is $74\%$. Combining this result with
the number obtained from the integration of the radial distribution, we can
estimate the total number of GCs for NGC 3640, $N_{GC}\approx 350$.

Figure 11: Luminosity function for the GC candidates associated with NGC 3640.
Orange lines show the original distribution, with orange solid blocks showing
the result after correcting for completeness and subtracting the background,
indicated in dashed gray lines. The dashed curve and vertical line correspond
to the fit performed in this work and its corresponding turn-over magnitude,
while the dash-dotted is the fit obtained with the distance from the
literature, with its fixed turn-over magnitude shown as a dash-dotted vetical
line. All fits were done using only the shown magnitude range according to the
completeness test, with the corrected distribution.

##  4 The GCS of NGC 3641

###  4.1 Radial distribution

In Figure 12 we show the radial distribution for the GCs within
$75^{\prime\prime}$ of the centre of NGC 3641, with a Hubble-Reynolds law fit
up to the imposed limit. If we extrapolate this profile to the same level we
used for NGC 3640, we obtain an estimate for the population of NGC 3641 up to
the completeness level of $\approx 100$ GCs.

Figure 12: Radial distribution for GC candidates attributed to NGC 3641. Grey
crosses describe the raw sample, while green dots show the background
corrected distribution. A dashed curve shows the Hubble profile. A horizontal
line indicates the same background level as in previous figures.

###  4.2 Colour distribution

In Figure 13 we show the colour distribution for GCs associated with NGC 3641.
Analogously to the previous section, we use GMM and in this case obtain a
negative kurtosis ($-0.384$) but the value of D is significantly smaller than
2 ($1.74$), indicating an unimodal distribution is a better fit. The mean for
the distribution is $1.05$, with $\sigma=0.16$. In the bimodal fit, the
fraction of red GCs is $0.84$, with a mean of $1.09$, showing most of the GCs
surrounding NGC 3641 can be considered red. This is reasonable considering we
are only analysing objects really close to the galaxy, where red GCs are
expected to be dominant, and also because if NGC 3640 is actually stripping
its GCs, it would have stripped mainly blue ones which are more external.

Figure 13: Smoothed colour distribution for GC candidates associated to NGC
3641. A black curve indicates the unimodal distribution resulting from the GMM
fit.

###  4.3 Luminosity function

In Figure 14 we show the luminosity function of GC candidates associated to
NGC 3641. We perform a similar analysis as with NGC 3640, performing the fit
of a Gaussian function both using the turn-over from the literature (in this
case, the same one as for NGC 3640), and then fitting our own value. We find
an almost exact match, although our luminosity function is noisy, with a
dispersion larger than usual ($0.9$), and showing bumps towards the brighter
end which may be due to contamination from NGC 3640.

An integration of the luminosity function results in a total population of
$\approx 135$ GC.

Figure 14: Luminosity function for the GC candidates associated to NGC 3641.
Dashed green lines show the background distribution, black solid bars indicate
the result from subtracting it from the raw distribution (green bars). The
dot-dashed curve shows the Gaussian fit.

##  5 Spatial distribution and tidal features

The panels of Figure 15 show the contours of the spatial distribution of the
GC candidates located across the field containing both galaxies, separated by
colour, placing the limit in $(g^{\prime}-i^{\prime})=1$, drawn on top of
residual images. These were obtained modelling both galaxies using the ELLIPSE
task in iraf, and subtracting it from the image.

Figure 15: Smoothed distribution of GC candidates across the entire field
separated between blue (top) and red (bottom), with density contours plotted
in solid lines. Crosses in both panels show the individual positions, and the
background is the residuals image of the field obtained in the $i^{\prime}$
filter after modelling both galaxies with the task ELLIPSE and subtracting
them from the raw image.

In the top panel, we can see that the blue GCs are extended across the entire
field. The contours follow one of the strongest substructures, identified by
P88 as ‘A’. This behaviour may indicate that the interaction that caused the
shell-like structure in ‘A’ also pushed the blue GCs in this direction.

The red GCs are more concentrated towards the region between both galaxies,
and their density maps reveal a bridge that connects them. In combination with
the overdensity in the colour distribution of NGC 3640 that matches the
population of GCs associated to NGC 3641, this seems to indicate that NGC 3640
is accreting GCs from its neighbour, and this process is ongoing.

Figure 16: Image in the $i^{\prime}$ filter resulting from subtracting the
model of the surface brightness profile of both galaxies. Circles indicate GC
candidates across the entire field with their colours shown in a gradient, and
polygons indicate the location of the shells following the nomenclature given
in P88.

Figure 17: Histogram of GCs located in the regions defined as shells. Top
image shows each shell separately, bottom one shows the combination of all the
histograms, following the same color scheme as in the polygons in the previous
Figure.

##  6 Discussion

###  6.1 GCs as tracers of substructures

In the current paradigm of ETG evolution, both major and minor mergers play
important roles at different stages of galaxy evolution. Gas-rich major
mergers dominate the early stages, while minor mergers become more relevant
during the second phase of evolution, where ETGs grow their mass by accretion
with very low to null rates of star formation (Oser et al., 2010; Naab et al.,
2007; Hilz et al., 2012). These encounters leave traces behind as different
types of substructures, e.g. streams, shells, tails, and plumes (Mancillas et
al., 2019)[and references within]. We identify the substructures in NGC 3640
as shells since they are approximately semi-circular and concentric, mostly
located on the northwest corner of the galaxy. Mancillas et al. (2019)
attributes the fact that shells tend to accumulate on one side of the galaxy
to the consequences of a satellite accretion event, where the arc is formed
after the satellite falls into the central potential. In general, shells are
expected to form after mergers with a 4:1 mass ratio at most, i.e.
intermediate- to major-mass mergers (Pop et al., 2018; Karademir et al.,
2019), and they survive around 4 Gyr. This upper limit for the timing of the
accretion event is consistent with previous analyses of NGC 3640 which date
the structures and parts of the stellar population (see Section 1).

The mergers the host galaxy undergoes shape the GCS. They may increase the
population by either forming new GCs if there is enough gas involved and if
the conditions are violent enough, or accreding old GCs from satellite
galaxies. They may also alter their spatial distribution, redistributing them
to the halo (Choksi & Gnedin, 2019; Dornan & Harris, 2023).

D’Abrusco et al. (2022) study statistically significant structures in the
spatial distributions of the GCS of a variety of Fornax galaxies, concluding
they are relics of accreted GC systems that are overlaid on the smooth
distribution of the GCs belonging to the host galaxy. Following their
analysis, we show in Figure 17 the colour distribution for the GCs that
correspond spatially to the shells detected in the galaxy, identified in
Figure 16. In shell F, located in the direction of NGC 3641, we find most GCs
have a similar color, around $0.9$, bluer than those associated to NGC 3641.
In substructures A and E, blue GCs dominate, while the region covered by
substructure B/C/D has a wider color distribution, although it is also
dominated by blue objects, including GCs with colors bluer than $0.7$.

This analysis is based on the distribution observed in 2D being representative
of the physical position of the objects in the real, 3D Universe. D’Abrusco et
al. (2022) argue that the risk of the 2D structures being merely projection
effects is small. This is due to previous studies like Woodley & Harris (2011)
showing through simulations that the probability of misidentifying a 2D
subgroup is $1\%$, and to the fact that the identified structures present
complex morphologies that a smooth 3D spatial distribution cannot explain.

###  6.2 Paucity of GCs in the inner region

The Hubble-Reynolds profile fit to the projected radial distribution of the
GCS of NGC 3640 has a core radius of $r_{0}=1.16\,\textrm{arcmin}=9.07\,kpc$.
Considering NGC 3640 has a stellar mass of $log{M_{\star}}=11.2$ (Karachentsev
et al., 2015) we can place it in the context of the $r_{0}$ vs. $M_{\star}$
relation studied in Caso et al. (2024) for a sample of early-type galaxies in
HST/ACS archival date. Given that Gemini data is not comparable in terms of
depth with HST/ACS, even after a thorough completeness analysis, this number
might be slightly enlarged in comparison to those in the sample in Caso et al.
(2024). However, it is clear NGC 3640 has a larger core radius than most
galaxies in the sample, especially for those with similar masses. This implies
the GCS of NGC 3640 is flatter up to a larger galactocentric radius, which can
also be seen by simple visual inspection of the projected spatial distribution
in Figure 16, where the paucity of GCs near the centre of the galaxy is
apparent.

The highest core radius value in the HST/ACS sample (Caso et al., 2024)
corresponds to NGC 4406 (M86), a galaxy that presents an offset peak in its
GCS connected to a potential disturbance caused by a satellite dwarf galaxy,
and a shell that is both seen in the low-surface brightness analysis (Mihos et
al., 2017) and the GC spatial structure (Lambert et al., 2020). The two
following galaxies are NGC 1316 and NGC 4472 (M49), both having undergone
late, major mergers. Numerical simulations of hierarchical galaxy formation
including GCs have shown that mergers or large accretion events such as being
tidally stripped are the most frequent causes of GCs being redistributed to
the halo (Kravtsov & Gnedin, 2005; Kruijssen & Cooper, 2012; Rieder et al.,
2013). Using the E-MOSAICS suite of cosmological simulations, Kruijssen (2015)
and more recently Keller et al. (2020) have both shown that mergers play a
vital role in the survival of GCs since they eject them to the outskirts where
the interstellar medium is less dense and they are less prone to experience
tidal shocks.

It follows then that the connection between lower values of core radius for
the GCS and galaxies that show substructures that imply major mergers not long
in the past is a physical one. Large accretion events directly affect the
radial distribution of GCs, not so much through the creation of young GCs but
through the flattening of the inner region due to redistribution. In Table 3,
we show that the red fraction increases as we move away from the central
region. In the current paradigm of GC formation, blue GCs are expected to
dominate in the outer region since a large fraction of them comes from
accretion of satellite galaxies, while most red GCs are thought to have formed
in-situ. This difference can be interpreted as a sign of redistribution
mechanisms at play.

###  6.3 The bridge?

The possibility of NGC 3640 and NGC 3641 interacting is not discussed in
previous work, mainly due to the observations focusing on the central regions
NGC 3640. In terms of integrated light, we do not detect a significant
overdensity that can be interpreted as a stream between the two, but it could
potentially be fainter than our magnitude limit. Since GCs have been shown to
trace stellar streams (Blom et al., 2014; Napolitano et al., 2022, e.g.), it
is reasonable to interpret the overdensity detected between the two galaxies
as a hint that there might be a stream between them. Previous works in other
galaxies have also found potential bridges made of GCs as tracers of
interactions, such as Bassino et al. (2006) connecting NGC 1387 and NGC 1399,
and Wehner et al. (2008) with NGC 3311 and NGC 3309. We see that the colours
of the GCs spatially situated between both galaxies are mainly intermediate,
closer to the peak of the population associated with NGC 3641, perhaps due to
being members of its GCS that are being accreted by the more massive galaxy.
As is originally mentioned in P88, the compactness of NGC 3641 implies a high
angular momentum interaction. Although they refrain from interpreting anything
more conclusive, they point out that the dust lane in NGC 3640 is oriented in
the direction of its neighbour, which is encouraging.

Solid evidence of the interaction can only be obtained through spectroscopy,
which would allow us to confirm membership of the GCs as well as to analyze
their kinematics, which might confirm the connection between the two galaxies.

##  7 Conclusions

We perform a wide-field photometric study of the GCS of NGC 3640 and NGC 3641,
using data obtained from GMOS/Gemini. We attribute GCs to the GCS of each
galaxy based on projected distance, and analyze each of them separately. NGC
3640 presents a bimodal GCS, with blue GCs that extend towards the outer
regions of the field, and red GCs concentrated towards the centre. The
luminosity function allows us to estimate a total population of $\approx 350$
GCs. In NGC 3641 we find a unimodal distribution, with GCs in an intermediate
colour range in relation to the subpopulations in NGC 3640.

Finally, we identify a potential connection between the spatial distribution
of the GCs and the shell-like structures around NGC 3640, which hints at a
major merger having disrupted the GCS. We also indicate the potential presence
of a bridge formed by red GCs that connect both galaxies, indicating they may
be currently interacting. Further spectroscopic studies are necessary to
solidify these claims.

## Acknowledgements

This research was supported in part by Perimeter Institute for Theoretical
Physics. Research at Perimeter Institute is supported by the Government of
Canada through the Department of Innovation, Science and Economic Development
and by the Province of Ontario through the Ministry of Research and
Innovation. This work was funded with grants from Consejo Nacional de
Investigaciones Científicas y Técnicas de la República Argentina, Agencia
Nacional de Promoción Cientf́ica y Tecnológica, and Universidad Nacional de La
Plata (Argentina). This work made use of AstroPy (Astropy Collaboration et
al., 2013, 2018, 2022), MatPlotLib (Hunter, 2007), NumPy (Harris et al., 2020)
Pandas (McKinney, 2010), PhotUtils (Bradley et al., 2023), SciKit (Pedregosa
et al., 2011) and SciPy (Virtanen et al., 2020).

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