# The Relation between Globular Cluster Systems and Supermassive Black Holes in Spiral Galaxies. III. The Link to the M •-M * Correlation

Rosa A. González-Lópezlira, Luis Lomelí-Núñez, Yasna Ordenes-Briceño, Laurent Loinard, Stephen Gwyn, Karla Alamo-Martínez, Gustavo Bruzual, Ariane Lançon, Thomas H. Puzia

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Rosa A. González-Lópezlira, Luis Lomelí-Núñez, Yasna Ordenes-Briceño, Laurent Loinard, Stephen Gwyn, et al.. The Relation between Globular Cluster Systems and Supermassive Black Holes in Spiral Galaxies. III. The Link to the M •-M * Correlation. The Astrophysical Journal, 2022, 941, 10.3847/1538-4357/ac982e. insu-03926795

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# The Relation between Globular Cluster Systems and Supermassive Black Holes in Spiral Galaxies. III. The Link to the M·-M* Correlation

Rosa A. González-Lópezlira¹, Luis Lomelí-Núñez²,³, Yasna Ordenes-Briceño⁴, Laurent Loinard³, Stephen Gwyn⁵, Karla Alamo-Martínez⁶, Gustavo Bruzual³, Ariane Lançon⁷, and Thomas H. Puzia⁴

¹Instituto de Radioastronomía y Astrofísica, UNAM, Campus Morelia, Michoacán, C.P. 58089, Mexico; r.gonzalez@irya.unam.mx

²Instituto Nacional de Astrofísica, Óptica y Electrónica, Luis Enrique Erro 1, Tonantzintla, Puebla, C.P. 72840, Mexico

³Instituto de Radioastronomía y Astrofísica, UNAM, Campus Morelia, Michoacán, C.P. 58089, Mexico

⁴Instituto de Astrofísica, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, 7820436 Macul, Santiago, Chile

⁵Herzberg Institute of Astrophysics, National Research Council of Canada, Victoria, BC V9E 2E7, Canada

⁶Departamento de Física, División de Ciencias e Ingenierías, Universidad de Guanajuato, 37150, León, Mexico

⁷Observatoire Astronomique de Strasbourg, Université de Strasbourg, CNRS, UMR 7550, 11 rue de l'Université, F-67000 Strasbourg, France

*Received 2021 August 8; revised 2022 September 14; accepted 2022 October 3; published 2022 December 12*

## Abstract

We continue to explore the relationship between the total number of globular clusters (GCs), N<sub>GC</sub>, and the central black hole mass, M<sub>•</sub>, in spiral galaxies. We present here results for the Sab galaxies NGC 3368, NGC 4736 (M94), and NGC 4826 (M64), and the Sm galaxy NGC 4395. The GC candidate selection is based on the (u<sup>*</sup> - i<sup>′</sup>) versus (i<sup>′</sup> - K<sub>s</sub>) color-color diagram, and i<sup>′</sup>-band shape parameters. We determine the M<sub>•</sub> versus N<sub>GC</sub> correlation for these spirals, plus NGC 4258, NGC 253, M104, M81, M31, and the Milky Way. We also redetermine the correlation for the elliptical sample in Harris et al., with updated galaxy types from Sahu et al. Additionally, we derive the total stellar galaxy mass, M<sub>*</sub>, from its two-slope correlation with N<sub>GC</sub>, and fit M<sub>•</sub> versus M<sub>*</sub> for both spirals and ellipticals. We obtain log M<sub>•</sub> ∝ (1.01 ± 0.13) log N<sub>GC</sub> for ellipticals, and log M<sub>•</sub> ∝ (1.64 ± 0.24) log N<sub>GC</sub> for late-type galaxies (LTGs). The linear M<sub>•</sub> versus N<sub>GC</sub> correlation in ellipticals could be due to statistical convergence through mergers, unlike the much steeper correlation for LTGs. However, in the M<sub>•</sub> versus total stellar mass (M<sub>*</sub>) parameter space, with M<sub>*</sub> derived from its correlation with N<sub>GC</sub>, M<sub>•</sub> ∝ (1.48 ± 0.18) log M<sub>*</sub> for ellipticals, and M<sub>•</sub> ∝ (1.21 ± 0.16) log M<sub>*</sub> for LTGs. The observed agreement between ellipticals and LTGs in this parameter space may imply that black holes and galaxies coevolve through *calm* accretion, active galactic nuclei feedback, and other secular processes.

*Unified Astronomy Thesaurus concepts:* Galaxy formation (595); Galaxy evolution (594); Spiral galaxies (1560); Globular star clusters (656); Star clusters (1567); Classical black holes (249); Black holes (162)

*Supporting material:* machine-readable tables

## 1. Introduction

It is widely accepted that all massive galaxies contain a supermassive black hole (SMBH). In spheroidal systems, the masses of the SMBHs, M<sub>•</sub>, correlate with other properties of their host galaxies: the bulge luminosity (the M<sub>•</sub>-L<sub>bulge</sub> relation, e.g., Kormendy 1993; Kormendy & Richstone 1995), the bulge mass (the M<sub>•</sub>-M<sub>bulge</sub> relation, e.g., Dressler 1989; Magorrian et al. 1998), the bulge stellar velocity dispersion (the M<sub>•</sub>-σ<sub>*</sub> relation, e.g., Ferrarese & Merritt 2000; Gebhardt et al. 2000), and the dark matter halo mass (Spitler & Forbes 2009). Today, the M<sub>•</sub>-σ<sub>*</sub> relation is known to have a ≈0.6 dex scatter and to depend on the galaxy's merger history (Bogdán et al. 2018; Sahu et al. 2019b), and the M<sub>•</sub>-M<sub>bulge</sub> relation depends on the morphology of the galaxy (Savorgnan et al. 2016; van den Bosch 2016; Sahu et al. 2019a). Graham (2012), Graham & Scott (2013), Scott et al. (2013), and Davis (2019a) find that there are correlations between M<sub>•</sub> and the luminosity and mass of the bulge, but that the slope is steeper for spiral bulges with a Sérsic profile than for early-type galaxies (ETGs), irrespective of whether the latter are better fitted by a Sérsic or a core-Sérsic profile.

Exciting as these correlations are because of the clues that they may provide regarding galaxy formation and assembly, and about their possible coevolution with the central black hole, they are not without controversy. While Ferrarese (2002), Baes et al. (2003), and Davis et al. (2019b) state that M<sub>•</sub> correlates with the disk maximum rotation velocity and hence with the dark matter halo mass, Kormendy & Bender (2011) retort that black holes do not correlate directly with dark matter haloes, and that a correlation appears only if the galaxy has a bulge. Likewise, Kormendy et al. (2011) contend that black holes do not correlate with either disks or pseudobulges. Davis et al. (2018) argue that M<sub>•</sub> actually correlates with the disk mass, albeit with a low correlation coefficient, r = 0.3.

Investigating the limits and deviations of these scaling relations, i.e., at high and low masses, may be particularly useful for uncovering the processes that are involved in the formation and evolution of galaxies and their black holes. For example, the log M<sub>•</sub> versus log M<sub>*</sub> correlation, with M<sub>*</sub> being the total galaxy stellar mass, has been explored in both ETGs and late-type galaxies (LTGs). Van den Bosch (2016), Davis (2019a), and Sahu et al. (2019a) find that the slope for LTGs is between 70% and 100% steeper than the nearly linear one followed by ETGs. Davis et al. (2019a) rules out that such a steep correlation in LTGs could be due to statistical convergence through hierarchical galaxy formation (Peng 2007; Jahnke & Macciò 2011); in addition, as the LTG in their sample sit on the

<figure><img src="image_3.png" /></figure>

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<table><caption>**Table 1**
Observation Log</caption><thead><tr><th>Galaxy</th><th>Filter</th><th>λ<sub>cen</sub><sup>a</sup></th><th>FWHM<sup>b</sup></th><th>Exposure s</th><th>Camera</th><th>Pixel Size arcsec</th><th>Program</th><th>Date</th></tr></thead><tbody><tr><td rowspan="4">NGC 3368</td><td>u* (302)</td><td>3537 Å</td><td>867 Å</td><td>5200</td><td>Megacam</td><td>0.186</td><td>18AF99</td><td>2018 June 16</td></tr><tr><td>g' (401)</td><td>4873 Å</td><td>1455 Å</td><td>1000</td><td>Megacam</td><td>0.186</td><td>19AF03</td><td>2019 March 4</td></tr><tr><td>i' (702)</td><td>7776 Å</td><td>1508 Å</td><td>1600</td><td>Megacam</td><td>0.186</td><td>11AC08</td><td>2011 March 1</td></tr><tr><td>K<sub>s</sub></td><td>2.15 μm</td><td>0.33 μm</td><td>1660</td><td>WIRCam</td><td>0.307</td><td>17AF12</td><td>2017 April 18</td></tr><tr><td rowspan="4">NGC 4395</td><td>u* (302)</td><td>3537 Å</td><td>867 Å</td><td>1500</td><td>Megacam</td><td>0.186</td><td>18AF99</td><td>2018 June 14</td></tr><tr><td>g' (402)</td><td>4720 Å</td><td>1520 Å</td><td>400</td><td>Megacam</td><td>0.186</td><td>18AF04</td><td>2018 May 23</td></tr><tr><td>i' (703)</td><td>7764 Å</td><td>1554 Å</td><td>200</td><td>Megacam</td><td>0.186</td><td>19AF03</td><td>2019 April 3</td></tr><tr><td>K<sub>s</sub></td><td>2.15 μm</td><td>0.33 μm</td><td>460</td><td>WIRCam</td><td>0.307</td><td>18AF98</td><td>2018 July 12</td></tr><tr><td rowspan="4">NGC 4736</td><td>u* (302)</td><td>3537 Å</td><td>867 Å</td><td>6900</td><td>Megacam</td><td>0.186</td><td>18AF99</td><td>2018 May 23, June 12</td></tr><tr><td>g' (401)</td><td>4873 Å</td><td>1455 Å</td><td>1645</td><td>Megacam</td><td>0.186</td><td>19AF03</td><td>2019 March 4</td></tr><tr><td>r' (601)</td><td>6282 Å</td><td>1219 Å</td><td>3304</td><td>Megacam</td><td>0.186</td><td>13AS03</td><td>2013 February 15</td></tr><tr><td>i' (702)</td><td>7776 Å</td><td>1508 Å</td><td>1127</td><td>Megacam</td><td>0.186</td><td>13AS03</td><td>2013 February 13, 15</td></tr><tr><td rowspan="4">NGC 4826</td><td>u* (302)</td><td>3537 Å</td><td>867 Å</td><td>9600</td><td>WIRCam</td><td>0.186</td><td>17AF12</td><td>2017 April 8</td></tr><tr><td>g' (401)</td><td>4873 Å</td><td>1455 Å</td><td>2345</td><td>Megacam</td><td>0.186</td><td>18AF99</td><td>2018 May 23, June 13</td></tr><tr><td>r' (601)</td><td>6282 Å</td><td>1219 Å</td><td>4963</td><td>Megacam</td><td>0.186</td><td>19AF03</td><td>2019 April 3</td></tr><tr><td>i' (702)</td><td>7776 Å</td><td>1508 Å</td><td>1827</td><td>Megacam</td><td>0.186</td><td>11AC08</td><td>2011 March 1</td></tr><tr><td></td><td>K<sub>s</sub></td><td>2.15 μm</td><td>0.33 μm</td><td>880</td><td>WIRCam</td><td>0.307</td><td>13AS03</td><td>2013 February 13</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>13AS03</td><td>2013 February 15, 17; May 3</td></tr></tbody></table>

**Notes.**

same correlation, regardless of whether they contain an active galactic nucleus (AGN), they call into question the relevance of AGN feedback to the relation. Reines & Volonteri (2015) analyze two samples, one of ETG and classical bulges, mostly without active AGNs, and another of LTGs with active AGNs. They find similar slopes (1.4 and 1.0, respectively, i.e., less steep for LTGs), but with an offset of more than 1 order of magnitude at log $M_*/M_\odot \sim 10$. In the same parameter space, Simmons et al. (2017) determine that the slope for a sample of AGNs in disk-dominated, merger-free, galaxies is 1.2, roughly equal to that of the bulge sample in Häring & Rix (2004), and with a small offset of ~0.2 dex at log $M_*/M_\odot = 10$; they hence conclude that mergers are inconsequential for the coevolution of black holes and galaxies, and that secular processes, like *calm* accretion and AGN feedback, are more fundamental for galaxy assembly and black hole growth.

An intriguing correlation, given the extremely disparate scales, is the one between the central black hole mass and the total number of GCs ($N_{GC}$; Burkert & Tremaine 2010; Harris & Harris 2011; Harris et al. 2014). The correlation can be expressed as $N_{GC} \propto M_{*}^{1.02 \pm 0.10}$ and spans over 3 orders of magnitude. Possible causal links have been proposed, for instance, feedback by the jets of AGNs (e.g., Silk & Rees 1998; Fabian 2012) and cannibalization of GCs by black holes (e.g., Capuzzo-Dolcetta & Donnarumma 2001; Capuzzo-Dolcetta & Vicari 2005; Capuzzo-Dolcetta & Mastrobuono-Battisti 2009; Gnedin et al. 2014); as it is roughly linear for ellipticals, it has been argued that it could be due to statistical convergence through merging. On the other hand, GC systems are known to be very good tracers of the galaxy virial mass (e.g., Blakeslee et al. 1997; Spitler & Forbes 2009; Georgiev et al. 2010; Hudson et al. 2014; Harris et al. 2017). This correlation is good

over 7 orders of magnitude in the halo mass, from dwarf galaxies to galaxy clusters, with a strongly declining dispersion with increasing mass, $\delta N_{GC}/N_{GC} \propto M_{vir}^{1/2}$ (Forbes et al. 2018; Burkert & Forbes 2020).

The study of GC systems in spiral galaxies has been hampered by the sparsity of their GCs, compared to ellipticals, and has been mostly limited to edge-on objects, given the difficulty of detecting individual GCs projected on a spiral disk. Until relatively recently, there were only five spiral galaxies with precise measurements of both $N_{GC}$ and $M_*$: the Milky Way (MW, Sbc), M104 (Sa), M81 (Sab), M31 (Sb), and NGC 253 (Sc). Burkert & Tremaine (2010) only included the first four, and readily noticed that, while M31, M81, and M104 fall right on the $N_{GC}-M_*$ correlation for ellipticals, our Galaxy has a black hole that is about 1 order of magnitude lighter than expected from its $N_{GC}$. They also observed that, compared to M1, M81, and M104, the MW has both a later Hubble type and possibly a pseudobulge, and therefore hypothesized that these factors could be related to its noncompliance with the correlation.

We are in the process of studying the $N_{GC}$ versus $M_*$ correlation in all nine spirals with precise black hole measurements within 16 Mpc: NGC 1068, NGC 3368, NGC 4051, NGC 4151, NGC 4258, NGC 4395, NGC 4736, NGC 4826, and NGC 5055, although so far we only have full data sets for NGC 3368, NGC 4258, NGC 4395, NGC 4736, and NGC 4826. The bulge type was not considered when selecting the sample, but with one exception all of them seem to have a pseudobulge (Kormendy et al. 2010; Kormendy & Ho 2013; Kormendy 2013), while NGC 4258, NGC 4826, and NGC 5055 may also have a classical bulge. The single exception, NGC 4395, is a pure disk, bulgeless, spiral (Filippenko & Ho 2003; Kormendy & Ho 2013). For

<footnote><sup>a</sup> The central wavelength between the two points defining the FWMH (http://svo2.cab.inta-csic.es/svo/theory/fps3/index.php?id=CFHT/).</footnote>

<footnote><sup>b</sup> Ibid.</footnote>
<figure><img src="image_4.png" /><figcaption>Figure 1. CFHT *i'*-band images, asinh scale. Top left: NGC 3368; top right: NGC 4395; bottom left: NGC 4736; bottom right: NGC 4826.</figcaption></figure>

<table><caption>**Table 2**
PSF Star Parameters</caption><thead><tr><th rowspan="2">Galaxy</th><th rowspan="2">Filter</th><th colspan="2">FLUX-RADIUS</th><th colspan="2">MAG_AUTO</th><th rowspan="2">N PSF Stars</th></tr><tr><th>Min pixel</th><th>Max pixel</th><th>Min mag</th><th>Max mag</th></tr></thead><tbody><tr><td rowspan="4">NGC 3368</td><td>u*</td><td>2.10</td><td>2.60</td><td>16.0</td><td>23.0</td><td>1998</td></tr><tr><td>g'</td><td>1.60</td><td>2.00</td><td>17.5</td><td>25.5</td><td>3876</td></tr><tr><td>i'</td><td>1.30</td><td>1.60</td><td>17.0</td><td>23.0</td><td>5306</td></tr><tr><td>K<sub>s</sub></td><td>1.10</td><td>1.60</td><td>15.5</td><td>20.0</td><td>1162</td></tr><tr><td rowspan="4">NGC 4395</td><td>u*</td><td>1.80</td><td>2.40</td><td>17.0</td><td>23.0</td><td>2379</td></tr><tr><td>g'</td><td>1.70</td><td>2.20</td><td>17.0</td><td>23.0</td><td>3937</td></tr><tr><td>i'</td><td>1.60</td><td>2.10</td><td>15.0</td><td>21.5</td><td>3741</td></tr><tr><td>K<sub>s</sub></td><td>1.10</td><td>1.60</td><td>16.0</td><td>20.0</td><td>449</td></tr><tr><td rowspan="4">NGC 4736</td><td>u*</td><td>2.00</td><td>2.70</td><td>15.5</td><td>22.0</td><td>1296</td></tr><tr><td>g'</td><td>3.10</td><td>3.70</td><td>16.0</td><td>22.9</td><td>3112</td></tr><tr><td>r'</td><td>3.20</td><td>3.70</td><td>15.5</td><td>22.0</td><td>4302</td></tr><tr><td>i'</td><td>2.50</td><td>2.80</td><td>16.0</td><td>22.0</td><td>5047</td></tr><tr><td rowspan="4">NGC 4826</td><td>u*</td><td>2.50</td><td>3.10</td><td>15.0</td><td>23.0</td><td>2300</td></tr><tr><td>g'</td><td>2.00</td><td>2.40</td><td>16.0</td><td>23.0</td><td>2379</td></tr><tr><td>r'</td><td>3.00</td><td>3.60</td><td>16.0</td><td>22.0</td><td>5115</td></tr><tr><td>i'</td><td>1.80</td><td>2.20</td><td>16.0</td><td>22.0</td><td>4805</td></tr><tr><td></td><td>K<sub>s</sub></td><td>1.10</td><td>1.40</td><td>15.5</td><td>20.5</td><td>519</td></tr></tbody></table>

completeness, we should mention that M31 and M81 have classical bulges, NGC 253 and the MW have pseudobulges, and M104 has both a bulge and a pseudobulge (Kormendy & Ho 2013). Pseudobulges are widely considered the product of secular evolution with few major mergers (e.g., Kormendy & Kennicutt 2004; Athanassoula 2005), although according to, for

example, Sauvaget et al. (2018), they can also be formed by major mergers of gas-rich progenitors in the distant universe.

In this paper, we present new measurements and analyses of the GC systems of the Sab galaxies NGC 3368 (M96), NGC 4736 (M94), and NGC 4826 (M64), and the Sm galaxy NGC 4395. Their surface brightness fluctuation (SBF) distances are $10.4_{-1.0}^{+1.1}$ Mpc for NGC 3368, $5.0 \pm 0.4$ Mpc for NGC 4736, and $7.3 \pm 0.7$ Mpc for NGC 4826 (Tonry et al. 2001; Blakeslee et al. 2010). NGC 4395 is completely devoid of a bulge and hence lacks an SBF measurement; we adopt a Cepheid distance of $4.3 \pm 0.4$ Mpc (Thim et al. 2004). The masses of their central supermassive black holes are $(3.6 \pm 1.1) \times 10^5 M_{\odot}$ for NGC 4395 (Peterson et al. 2005); $(7.5 \pm 1.5) \times 10^6 M_{\odot}$ for NGC 3368; $6.8_{-1.6}^{+1.5} \times 10^6 M_{\odot}$ for NGC 4736; and $(1.6 \pm 0.4) \times 10^6 M_{\odot}$ for NGC 4826 (Kormendy & Ho 2013). Their inclinations to the line of sight are $46.2^{\circ}$ (NGC 3368), $33.7^{\circ}$ (NGC 4395), $35.6^{\circ}$ (NGC 4736), and $57.5^{\circ}$ (NGC 4826; de Vaucouleurs et al. 1991). We take the following position angles (PA; north to east): $5^{\circ}$ (NGC 3368), $147^{\circ}$ (NGC 4395), and $115^{\circ}$ (NGC 4736 and NGC 4826).

In order to identify globular cluster candidates (GCCs) in these galaxies, we apply the $(u^*-i')$ versus $(i' - K_s)$ diagram technique $(u^*i'K_s$, hereafter). It is extremely powerful to isolate, in different regions and according to their stellar populations and star formation histories, foreground Galactic stars, background galaxies, young clusters in the disk, and GCCs. In addition, objects in such separate areas of the plot also differ in their light concentration parameters, at least up to a distance of ~16 Mpc (Muñoz et al. 2014). The efficacy of the procedure has been corroborated by Powalka et al. (2016) in M87, and by González-Lópezlira et al. (2019), with Optical System for Imaging and
<figure><img src="image_5.png" /><figcaption>**Figure 2.** Completeness tests, recovered artificial point sources. Top left: NGC 3368; top right: NGC 4395; bottom left: NGC 4736; bottom right: NGC 4826. Colors indicate points from artificial images that were actually used in the fits, to ensure the samples of all regions were statistically equivalent.</figcaption></figure>

low-Intermediate-Resolution Integrated Spectroscopy (OSIRIS) observations of the GC candidates in the megamaser prototype NGC 4258. The method allows for a very low contamination of the samples from foreground stars, background galaxies, and young stellar clusters, even in disk galaxies that are not completely edge-on, and in the absence of radial velocity measurements.

## 2. Data

All the data for this work were obtained with the Canada-France-Hawaii Telescope (CFHT), the optical images with MegaCam (Boulade et al. 2003), and the *Ks*-band ones with the Wide-field InfraRed Camera (WIRCam; Puget et al. 2004). MegaCam has a field of view (FOV) of 0.96 × 0.94, with a plate scale of 0.′186 pixel⁻¹, while the FOV of the WIRCam is ~21′ × 21′, with a plate scale of 0.′307 pixel⁻¹. Brief descriptions of the detectors' layouts, cameras' performances, and data reduction procedures are given in González-Lópezlira et al. (2017). Table 1 provides a summary of the observations.

Except for NGC 4395, the *g*', *i*', and *r*' data are archival, and were originally secured through programs 11AC08 (PI: G. Harris), and 13AS03 (PI: Zhao-Yu Li). The *u*\* and *Ks*-band images, as well as all the NGC 4395 data, are ours, and were acquired through programs 17AF12, 18AF99 (PI: K. Alamo-Martínez), and 19AF03 (PI: Y. Ordenes-Briceño).

To avoid saturation, individual *Ks* exposures of the galaxies were only 10 s long. For NGC 3368, one image was taken in each of the four quadrants of the WIRCam, before nodding the telescope to obtain a sky exposure 2.5 apart. The other three galaxies were observed in an approximately circular pattern with a radius of ~1.6. Given their large diameters compared to the WIRCam FOV (i.e., R₂₅ = 6.6, 5.6, and 5', respectively, for NGC 4395, NGC 4736, and NGC 4826; de Vaucouleurs et al. 1991), separate (also 10 s long) sky frames were taken, respectively, 2.5 (NGC 4395), 1.5 (NGC 4736) and 3.5 (NGC 4826) away, with the same circular pattern, using the target(T)-sky(S) sequence STTSSTTSS...TTS.

Before combining them into mosaics, the individual optical images were recalibrated with the MegaPipe pipeline (Gwyn 2008), in order to achieve astrometric internal and
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Completeness tests. Top left: NGC 3368; top right: NGC 4395; bottom left: NGC 4736; and bottom right: NGC 4826. Fits (solid lines) to recovered fractions (dots) vs. $K_s$ mag with Equation (2). Colors (red, blue, green, gold) refer to the centermost ellipse, and inner, middle, and external annuli, respectively. Blue dotted lines indicate the 90% and 50% completeness values.</figcaption></figure>

<table><caption>**Table 3**
Completeness Fit Parameters</caption><thead><tr><th>Galaxy</th><th>Region<br>R<sub>25</sub></th><th>m<sub>lim</sub><br>K<sub>s</sub> AB mag</th><th>α<sub>cutoff</sub></th><th>γ</th><th>δ</th></tr></thead><tbody><tr><td rowspan="4">NGC 3368</td><td>0.0–0.5</td><td>22.89 ± 0.09</td><td>2.22 ± 0.71</td><td>0.69 ± 0.05</td><td>0.64 ± 0.06</td></tr><tr><td>0.5–1.0</td><td>22.98 ± 0.03</td><td>2.24 ± 0.20</td><td>0.94 ± 0.20</td><td>0.96 ± 0.20</td></tr><tr><td>1.0–1.4</td><td>22.69 ± 0.05</td><td>2.72 ± 0.83</td><td>0.99 ± 0.83</td><td>1.03 ± 0.83</td></tr><tr><td>1.4–1.7</td><td>22.65 ± 0.02</td><td>3.68 ± 0.66</td><td>0.97 ± 0.66</td><td>1.03 ± 0.66</td></tr><tr><td rowspan="4">NGC 4395</td><td>0.0–0.5</td><td>22.14 ± 0.05</td><td>3.09 ± 1.15</td><td>0.46 ± 0.02</td><td>0.46 ± 0.03</td></tr><tr><td>0.5–1.0</td><td>22.10 ± 0.01</td><td>4.77 ± 0.26</td><td>0.97 ± 0.26</td><td>0.98 ± 0.26</td></tr><tr><td>1.0–1.4</td><td>22.23 ± 0.01</td><td>5.08 ± 0.23</td><td>0.98 ± 0.23</td><td>1.00 ± 0.23</td></tr><tr><td>1.4–1.7</td><td>22.16 ± 0.01</td><td>4.26 ± 0.36</td><td>0.97 ± 0.36</td><td>1.01 ± 0.36</td></tr><tr><td rowspan="4">NGC 4736</td><td>0.0–0.5</td><td>22.52 ± 0.23</td><td>0.90 ± 0.45</td><td>0.50 ± 0.08</td><td>0.62 ± 0.14</td></tr><tr><td>0.5–1.0</td><td>22.63 ± 0.03</td><td>2.72 ± 0.32</td><td>0.95 ± 0.32</td><td>0.92 ± 0.32</td></tr><tr><td>1.0–1.4</td><td>22.73 ± 0.05</td><td>2.36 ± 0.43</td><td>0.98 ± 0.43</td><td>0.98 ± 0.43</td></tr><tr><td>1.4–1.7</td><td>22.73 ± 0.01</td><td>5.01 ± 0.41</td><td>0.99 ± 0.41</td><td>0.98 ± 0.41</td></tr><tr><td rowspan="4">NGC 4826</td><td>0.0–0.5</td><td>21.87 ± 0.11</td><td>1.86 ± 0.65</td><td>0.24 ± 0.01</td><td>0.21 ± 0.02</td></tr><tr><td>0.5–1.0</td><td>22.48 ± 0.05</td><td>2.33 ± 0.19</td><td>0.83 ± 0.19</td><td>0.74 ± 0.19</td></tr><tr><td>1.0–1.4</td><td>22.57 ± 0.04</td><td>3.64 ± 0.98</td><td>1.01 ± 0.98</td><td>0.98 ± 0.98</td></tr><tr><td>1.4–1.7</td><td>22.67 ± 0.02</td><td>3.82 ± 0.68</td><td>0.97 ± 0.68</td><td>1.01 ± 0.68</td></tr></tbody></table>
<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /><figcaption>**Figure 4.** Morphology variations across the *u*\*i\'K_s diagram. Top: NGC 3368; second row: NGC 4395; third row: NGC 4736; bottom: NGC 4826. Indicators of shape in the *i'* band are coded as shown by the color bars: FWHM (left) and 100 × SPREAD\_MODEL (right).</figcaption></figure>

external accuracies of 0.04 and 0.15, respectively, and a
photometric accuracy of 0.03 mag. The Ks-band mosaics were
produced with the WIRwolf pipeline (Gwyn 2014), which sky
subtracts individual images and achieves an internal astrometric

accuracy of 0.1. Both MegaPipe and WIRwolf render images
with photometry in the AB system (Oke 1974), with zero
points (zp) set to 30 mag. Figure 1 shows images of the four
galaxies in the i' band.
<figure><img src="image_15.png" /><figcaption>**Figure 5.** ($u^* - i'$) vs. ($i' - K_s$) colors and structural parameters of sources in and closely around the selection region of NGC 3368. Top: FWHM; bottom: 100 × SPREAD MODEL. Left column: all sources; right column: final sample. The gray contour outlines the GCC selection region. GCCs appear in shades of blue and cyan in both compactness estimators.</figcaption></figure>

<table><caption>**Table 4**
Turnover Magnitudes and GCLF Ranges</caption><thead><tr><th rowspan="2">Filter</th><th rowspan="2">M<sup>0</sup><br>mag</th><th colspan="2">NGC 3368</th><th colspan="2">NGC 4395</th><th colspan="2">NGC 4736</th><th colspan="2">NGC 4826</th></tr><tr><th>m<sup>0</sup><sub>TO</sub><br>mag</th><th>m<sup>0</sup><sub>TO</sub> ± 3σ<br>mag</th><th>m<sup>0</sup><sub>TO</sub><br>mag</th><th>m<sup>0</sup><sub>TO</sub> ± 3σ<br>mag</th><th>m<sup>0</sup><sub>TO</sub><br>mag</th><th>m<sup>0</sup><sub>TO</sub> ± 3σ<br>mag</th><th>m<sup>0</sup><sub>TO</sub><br>mag</th><th>m<sup>0</sup><sub>TO</sub> ± 3σ<br>mag</th></tr></thead><tbody><tr><td>u*</td><td>-5.96</td><td>24.12</td><td>20.52 &lt; m<sup>0</sup><sub>u*</sub> &lt; 27.72</td><td>22.21</td><td>19.51 &lt; m<sup>0</sup><sub>u*</sub> &lt; 24.91</td><td>22.53</td><td>18.93 &lt; m<sup>0</sup><sub>u*</sub> &lt; 26.13</td><td>23.36</td><td>20.06 &lt; m<sup>0</sup><sub>u*</sub> &lt; 26.66</td></tr><tr><td>g'</td><td>-7.20</td><td>22.88</td><td>19.28 &lt; m<sup>0</sup><sub>g'</sub> &lt; 26.48</td><td>20.97</td><td>18.27 &lt; m<sup>0</sup><sub>g'</sub> &lt; 23.67</td><td>21.29</td><td>17.69 &lt; m<sup>0</sup><sub>g'</sub> &lt; 24.89</td><td>22.12</td><td>18.82 &lt; m<sup>0</sup><sub>g'</sub> &lt; 25.42</td></tr><tr><td>r'</td><td>-7.69</td><td>22.40</td><td>18.80 &lt; m<sup>0</sup><sub>r'</sub> &lt; 26.00</td><td>20.48</td><td>17.78 &lt; m<sup>0</sup><sub>r'</sub> &lt; 23.18</td><td>20.80</td><td>17.20 &lt; m<sup>0</sup><sub>r'</sub> &lt; 24.40</td><td>21.63</td><td>18.33 &lt; m<sup>0</sup><sub>r'</sub> &lt; 24.93</td></tr><tr><td>i'</td><td>-7.92</td><td>22.16</td><td>18.56 &lt; m<sup>0</sup><sub>i'</sub> &lt; 25.76</td><td>20.25</td><td>17.55 &lt; m<sup>0</sup><sub>i'</sub> &lt; 22.95</td><td>20.57</td><td>16.97 &lt; m<sup>0</sup><sub>i'</sub> &lt; 24.17</td><td>21.40</td><td>18.10 &lt; m<sup>0</sup><sub>i'</sub> &lt; 24.70</td></tr><tr><td>K<sub>s</sub></td><td>-8.1</td><td>22.0</td><td>19.9 &lt; m<sup>0</sup><sub>K<sub>s</sub></sub> &lt; 25.6</td><td>20.1</td><td>18.5 &lt; m<sup>0</sup><sub>K<sub>s</sub></sub> &lt; 22.8</td><td>20.4</td><td>18.4 &lt; m<sup>0</sup><sub>K<sub>s</sub></sub> &lt; 24.0</td><td>21.2</td><td>19.3 &lt; m<sup>0</sup><sub>K<sub>s</sub></sub> &lt; 24.5</td></tr></tbody></table>

### 3. Detection and Photometry

Source detection and photometric measurements in all the stacked images were carried out with SExtractor (Bertin & Arnouts 1996) and PSFEx (Bertin 2011). The detection was performed on images from which their median-filtered version was subtracted; faint sources are detected more easily in a median-subtracted image. All median images were produced with a 31 × 31 pix² median filter. Conversely, the photometry measurements were made on the original stacked images. PSFEx employs point sources detected in a first pass of SExtractor to build a point-spread function (PSF) model that SExtractor can then apply in a second pass to obtain PSF magnitudes of sources. We chose adequate PSF stars manually, based on their brightness versus compactness, as measured by SExtractor parameters MAG_AUTO (a Kron-like elliptical aperture magnitude; Kron 1980) and FLUX_RADIUS (similar to the effective radius); their values for each filter and galaxy are given

in Table 2. A detailed description of this procedure is presented in González-Lópezlira et al. (2017). The spatial variations of the PSF were modeled with polynomials of degree 3. To create the PSF, the flux of each star was measured in an 18 pixel aperture in all bands (equivalent to 3"/3 in the optical and 5"/5 at $K_s$); such aperture, determined through the growth-curve method for each passband, is large enough to measure the total flux of the stars, but small enough to reduce the likelihood of contamination by extraneous objects.

### 4. Completeness

Completeness tests were only performed on the $K_s$-band mosaics; these are the smallest and shallowest images and, in fact, set our object detection limits. In order to determine the GC detection completeness as a function of the magnitude, 65,000 artificial point sources were generated for each galaxy, based on their respective $K_s$ PSF model, in the
<figure><img src="image_16.png" /><figcaption>**Figure 6.** $(u^* - i')$ vs. $(i' - K_s)$ colors and structural parameters of sources in and closely around the selection region of NGC 4395. Top: FWHM; bottom: 100 × SPREAD MODEL. Left column: all sources; right column: final sample. Symbols as in Figure 5.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>**Figure 7.** $(u^* - i')$ vs. $(i' - K_s)$ colors and structural parameters of sources in and closely around the selection region of NGC 4736. Top: FWHM; bottom: 100 × SPREAD MODEL. Left column: all sources; right column: final sample. Symbols as in Figure 5.</figcaption></figure>

interval 19 mag < $m_K$ < 24 mag, and with a uniform, or box-shaped, magnitude distribution. Due to the WIRCam pixel size,<fnref n="8" /> GCCs are mostly unresolved in the $K_s$-band images. The

artificial objects were only added 500 at a time, to avoid creating artificial crowding; that is, a total of 130 images with simulated sources were produced for each galaxy. The positions of the added sources were random, and assigned without regard to the positions of other artificial objects or real sources.

<footnote n="8">⁸ 0′′307 or ~6 pc, ~7 pc, ~11 pc, and ~14.5 pc at the distances of NGC 4395, NGC 4736, NGC 4826, and NGC 3368, respectively.</footnote>
<figure><img src="image_18.png" /><figcaption>Figure 8. $(u^* - i')$ vs. $(i' - K_s)$ colors and structural parameters of sources in and closely around the selection region of NGC 4826. Top: FWHM; bottom: 100 × SPREAD MODEL. Left column: all sources; right column: final sample. Symbols as in Figure 5.</figcaption></figure>

Artificial sources were then recovered by running SExtractor on each one of the simulated images, with the same parameters used for the original $K_s$ galaxy images, and crossmatching the positions of all detections with the known input coordinates of the added objects. Sources with SExtractor output parameter FLAGS≠0 were eliminated; this operation excludes artificial objects falling on top of other artificial or real sources, and hence discards preferentially added objects in crowded regions. The restriction FLAGS = 0 was also applied in the selection of true sources (see Section 5).

As done previously with NGC 4258 by González-Lópezlira et al. (2017), for all the galaxies we estimated the completeness in four different regions within $1.7 R_{25}$: an ellipse with semimajor axis equal to 0.5 $R_{25}$, and three elliptical annuli from 0.5 to 1.0 $R_{25}$, from 1.0 to 1.4 $R_{25}$, and between 1.4 and 1.7 $R_{25}$. With the exception of the innermost ellipse of NGC 3368, all regions have axis ratios and PA equal to those assumed for the observed disks of the galaxies (respectively, 0.69 and 5° for NGC 3368, 0.82 and 147° for NGC 4395, 0.81 and 115° for NGC 4736, and 0.54 and 115° for NGC 4826); the PA of the central ellipse of NGC 3368 follows the alignment of the surface brightness there, and hence differs from the orientation of the outer isophotes. With the goal of estimating completeness with statistically equivalent samples, for each region we considered a number of added sources inversely proportional to its area; in other words, for the inner ellipses the artificial sources from all 130 images were taken into account, whereas only 43, 34, and 39 were included for the first, second, and third annuli, respectively. On average, for each region we consider ~2000 artificial sources in the cases of NGC 4395 and NGC 4736, and ~1000 for NGC 3368 and NGC 4826. Figure 2 shows all recovered sources in black, and those from the artificial images actually considered in colors. In the innermost

ellipse (within $0.5 R_{25}$), all recovered sources were used; hence, all dots appear colored in both black and red.

In the case of a box-shaped magnitude distribution, the fraction of recovered artificial sources as a function of magnitude is often well described by the Pritchet function (e.g., McLaughlin et al. 1994):

$$f^P(m) = \frac{1}{2} \left[ 1 - \frac{\alpha_{\text{cutoff}}(m - m_{\text{lim}})}{\sqrt{1 + \alpha_{\text{cutoff}}^2(m - m_{\text{lim}})^2}} \right]; \quad (1)$$

$m_{\text{lim}}$ is the magnitude at which completeness is 50%, and $\alpha_{\text{cutoff}}$ determines the steepness of the cutoff. However, in the case of crowded regions, where even at bright magnitudes the recovered fraction is flat but <1, better fits are obtained with a modified Pritchet function:

$$f^{mP}(m) = \frac{1}{2} \left[ \gamma - \delta \frac{\alpha_{\text{cutoff}}(m - m_{\text{lim}})}{\sqrt{1 + \alpha_{\text{cutoff}}^2(m - m_{\text{lim}})^2}} \right]; \quad (2)$$

here, $\gamma$ is the asymptotic value of the fraction at bright magnitudes, and $\delta$ is the fraction at the cutoff.

For each one of the galaxies, the quotient of recovered to added sources as a function of output PSF magnitude was fit with Equation (2), separately for each region. The recovered fractions (dots) and their fits (solid lines) versus $K_s$ mag are displayed in Figure 3. It is quite obvious that the regions within $0.5 R_{25}$ are extremely affected by crowding and confusion due to partially resolved sources. This is true also for NGC 4395, in spite of the absence of a conspicuous lack of recovered sources in the central region. The values of the fit parameters $m_{\text{lim}}$, $\alpha_{\text{cutoff}}$, $\gamma$, and $\delta$ are shown in Table 3.
<figure><img src="image_19.png" /><figcaption>**Figure 9.** Spatial distributions of the GCC samples. Top left: NGC 3368; top right: NGC 4395; bottom left: NGC 4736; bottom right: NGC 4826. The GCCs are shown as green-filled circles. Dark blue ellipse: boundary of areas where source confusion is highest (see text); solid cyan line: R<sub>25</sub>.</figcaption></figure>

<table><caption>**Table 5**
i'-band Shape Parameters of GCCs in NGC 3368</caption><thead><tr><th>Name</th><th>R.A. J2000 deg</th><th>Decl. J2000 deg</th><th>100 × (SPREAD<br>_MODEL)<sub>i'</sub></th><th>FWHM<sub>i'</sub> arcsec</th><th>r<sub>eff,i'</sub> pc</th><th>Shape<sup>a</sup></th><th>Index</th><th>S/N</th><th>χ<sup>2</sup></th></tr></thead><tbody><tr><td>J104539+113944</td><td>161.4148</td><td>11.6624</td><td>0.06</td><td>0.42</td><td>&lt;8.65</td><td>KINGx</td><td>30</td><td>235.8</td><td>7.99</td></tr><tr><td>J104540+120330</td><td>161.4185</td><td>12.0585</td><td>0.04</td><td>0.42</td><td>&lt;9.36</td><td>KINGx</td><td>100</td><td>130.0</td><td>4.82</td></tr><tr><td>J104604+115505</td><td>161.5179</td><td>11.9183</td><td>-0.03</td><td>0.41</td><td>&lt;1.37</td><td>KINGx</td><td>30</td><td>241.4</td><td>13.27</td></tr><tr><td>J104604+113655</td><td>161.5183</td><td>11.6154</td><td>0.05</td><td>0.42</td><td>&lt;8.01</td><td>SERSICx</td><td>2</td><td>74.8</td><td>2.33</td></tr><tr><td>J104609+120658</td><td>161.5413</td><td>12.1161</td><td>-0.04</td><td>0.42</td><td>&lt;3.44</td><td>KINGx</td><td>30</td><td>104.1</td><td>4.63</td></tr><tr><td>J104626+113118</td><td>161.6091</td><td>11.5219</td><td>-0.07</td><td>0.41</td><td>&lt;3.46</td><td>KINGx</td><td>30</td><td>88.9</td><td>3.83</td></tr><tr><td>J104633+120015</td><td>161.6379</td><td>12.0043</td><td>0.02</td><td>0.40</td><td>&lt;3.59</td><td>SERSICx</td><td>2</td><td>65.4</td><td>2.49</td></tr><tr><td>J104635+115918</td><td>161.6478</td><td>11.9886</td><td>0.10</td><td>0.42</td><td>&lt;5.19</td><td>KINGx</td><td>30</td><td>86.1</td><td>2.20</td></tr><tr><td>J104635+114912</td><td>161.6493</td><td>11.8201</td><td>0.40</td><td>0.46</td><td>&lt;1.07</td><td>KINGx</td><td>30</td><td>40.4</td><td>1.87</td></tr><tr><td>J104645+113554</td><td>161.6890</td><td>11.5985</td><td>-0.07</td><td>0.52</td><td>&lt;6.15</td><td>SERSICx</td><td>2</td><td>191.0</td><td>10.03</td></tr><tr><td>J104648+115012</td><td>161.7003</td><td>11.8368</td><td>0.30</td><td>0.46</td><td>&lt;1.68</td><td>KINGx</td><td>100</td><td>61.6</td><td>5.50</td></tr><tr><td>J104651+114819</td><td>161.7134</td><td>11.8053</td><td>0.75</td><td>0.54</td><td>&lt;2.66</td><td>KINGx</td><td>100</td><td>99.6</td><td>2.58</td></tr><tr><td>J104709+114112</td><td>161.7882</td><td>11.6868</td><td>-0.00</td><td>0.43</td><td>&lt;2.31</td><td>SERSICx</td><td>2</td><td>184.2</td><td>7.38</td></tr><tr><td>J104750+113703</td><td>161.9601</td><td>11.6176</td><td>0.01</td><td>0.46</td><td>&lt;6.00</td><td>KINGx</td><td>100</td><td>36.9</td><td>1.83</td></tr><tr><td>J104755+113503</td><td>161.9811</td><td>11.5844</td><td>-0.00</td><td>0.45</td><td>&lt;3.46</td><td>SERSICx</td><td>2</td><td>118.2</td><td>2.78</td></tr></tbody></table>

Note. Table 5 is published in its entirety in the machine-readable format. A portion is shown here for guidance regarding its form and content.

<sup>a</sup> Index denotes concentration for King profiles, exponent for Sérsic profiles.

(This table is available in machine-readable form.)
<table><caption>**Table 6**
$i'$-band Shape Parameters of GCCs in NGC 4395</caption><thead><tr><th rowspan="2">Name</th><th rowspan="2">R.A. J2000<br>deg</th><th rowspan="2">Decl. J2000<br>deg</th><th colspan="4">100 × (SPREAD<br>_MODEL)<sub>i'</sub></th><th rowspan="2">Shape</th><th rowspan="2">Index<sup>a</sup></th><th rowspan="2">S/N</th><th rowspan="2">χ<sup>2</sup></th></tr><tr><th></th><th></th><th>FWHM<sub>i'</sub><br>arcsec</th><th>r<sub>eff,i'</sub><br>pc</th></tr></thead><tbody><tr><td>J122452+332844</td><td>186.2204</td><td>33.4792</td><td>0.08</td><td>0.59</td><td>&lt;3.40</td><td>KINGx</td><td>30</td><td>78.2</td><td>0.57</td></tr><tr><td>J122456+333230</td><td>186.2335</td><td>33.5418</td><td>0.11</td><td>0.60</td><td>&lt;3.39</td><td>SERSICx</td><td>2</td><td>111.8</td><td>0.63</td></tr><tr><td>J122522+332549</td><td>186.3426</td><td>33.4303</td><td>0.12</td><td>0.59</td><td>&lt;2.95</td><td>KINGx</td><td>100</td><td>46.4</td><td>0.48</td></tr><tr><td>J122527+332015</td><td>186.3639</td><td>33.3376</td><td>0.05</td><td>0.59</td><td>&lt;3.19</td><td>KINGx</td><td>100</td><td>87.8</td><td>0.92</td></tr><tr><td>J122529+332536</td><td>186.3734</td><td>33.4268</td><td>0.15</td><td>0.60</td><td>&lt;2.48</td><td>KINGx</td><td>100</td><td>43.6</td><td>0.48</td></tr><tr><td>J122538+332654</td><td>186.4118</td><td>33.4486</td><td>0.49</td><td>0.70</td><td>&lt;6.33</td><td>SERSICx</td><td>2</td><td>28.5</td><td>0.45</td></tr><tr><td>J122541+333109</td><td>186.4210</td><td>33.5194</td><td>0.16</td><td>0.72</td><td>&lt;2.86</td><td>KINGx</td><td>30</td><td>19.8</td><td>1.00</td></tr><tr><td>J122544+333016</td><td>186.4354</td><td>33.5046</td><td>0.16</td><td>0.61</td><td>&lt;2.99</td><td>KINGx</td><td>100</td><td>15.4</td><td>0.50</td></tr><tr><td>J122548+333802</td><td>186.4535</td><td>33.6341</td><td>0.14</td><td>0.59</td><td>&lt;3.09</td><td>KINGx</td><td>30</td><td>26.9</td><td>0.57</td></tr><tr><td>J122558+333154</td><td>186.4917</td><td>33.5318</td><td>-0.13</td><td>0.61</td><td>&lt;1.86</td><td>KINGx</td><td>100</td><td>10.1</td><td>0.51</td></tr></tbody></table>

Note. Table 6 is published in its entirety in the machine-readable format. A portion is shown here for guidance regarding its form and content.

a Index denotes concentration for King profiles, exponent for Sérsic profiles.

(This table is available in machine-readable form.)

<table><caption>**Table 7**
$i'$-band Shape Parameters of GCCs in NGC 4736</caption><thead><tr><th rowspan="2">Name</th><th rowspan="2">R.A. J2000<br>deg</th><th rowspan="2">Decl. J2000<br>deg</th><th colspan="4">100 × (SPREAD<br>_MODEL)<sub>i'</sub></th><th rowspan="2">Shape</th><th rowspan="2">Index<sup>a</sup></th><th rowspan="2">S/N</th><th rowspan="2">χ<sup>2</sup></th></tr><tr><th></th><th></th><th>FWHM<sub>i'</sub><br>arcsec</th><th>r<sub>eff,i'</sub><br>pc</th></tr></thead><tbody><tr><td>J124947+411056</td><td>192.4496</td><td>41.1823</td><td>1.30</td><td>1.13</td><td>8.28<sup>+0.45</sup><sub>-0.19</sub></td><td>KINGx</td><td>30</td><td>70.7</td><td>0.57</td></tr><tr><td>J124951+411538</td><td>192.4633</td><td>41.2606</td><td>0.12</td><td>0.81</td><td>&lt;1.44</td><td>KINGx</td><td>100</td><td>655.0</td><td>2.56</td></tr><tr><td>J125001+411350</td><td>192.5053</td><td>41.2307</td><td>0.17</td><td>0.83</td><td>&lt;3.75</td><td>KINGx</td><td>100</td><td>282.2</td><td>1.65</td></tr><tr><td>J125029+410951</td><td>192.6246</td><td>41.1644</td><td>0.10</td><td>0.84</td><td>&lt;3.09</td><td>KINGx</td><td>100</td><td>83.2</td><td>0.81</td></tr><tr><td>J125031+411039</td><td>192.6314</td><td>41.1777</td><td>0.89</td><td>1.10</td><td>5.82<sup>+0.34</sup><sub>-0.33</sub></td><td>SERSICx</td><td>2</td><td>44.9</td><td>1.06</td></tr><tr><td>J125031+410949</td><td>192.6329</td><td>41.1638</td><td>1.03</td><td>1.18</td><td>5.74<sup>+0.45</sup><sub>-0.46</sub></td><td>KINGx</td><td>30</td><td>29.3</td><td>1.04</td></tr><tr><td>J125033+405708</td><td>192.6415</td><td>40.9525</td><td>0.04</td><td>0.81</td><td>&lt;2.89</td><td>KINGx</td><td>100</td><td>325.5</td><td>1.53</td></tr><tr><td>J125039+410913</td><td>192.6651</td><td>41.1538</td><td>1.05</td><td>1.06</td><td>6.69<sup>+0.16</sup><sub>-0.21</sub></td><td>SERSICx</td><td>2</td><td>61.0</td><td>1.41</td></tr><tr><td>J125042+410345</td><td>192.6786</td><td>41.0625</td><td>-0.01</td><td>0.79</td><td>&lt;4.99</td><td>KINGx</td><td>30</td><td>92.1</td><td>0.95</td></tr><tr><td>J125043+410947</td><td>192.6807</td><td>41.1632</td><td>0.72</td><td>0.94</td><td>3.81<sup>+0.04</sup><sub>-0.09</sub></td><td>KINGx</td><td>100</td><td>241.2</td><td>1.34</td></tr><tr><td>J125045+410950</td><td>192.6902</td><td>41.1639</td><td>0.65</td><td>0.93</td><td>2.89<sup>+0.01</sup><sub>-0.12</sub></td><td>KINGx</td><td>100</td><td>176.8</td><td>1.04</td></tr><tr><td>J125046+410210</td><td>192.6920</td><td>41.0361</td><td>0.72</td><td>0.94</td><td>3.93<sup>+0.07</sup><sub>-0.02</sub></td><td>KINGx</td><td>100</td><td>471.5</td><td>2.18</td></tr><tr><td>J125051+410314</td><td>192.7138</td><td>41.0540</td><td>0.66</td><td>0.96</td><td>2.66<sup>+0.12</sup><sub>-0.06</sub></td><td>KINGx</td><td>100</td><td>140.9</td><td>0.90</td></tr><tr><td>J125051+411341</td><td>192.7148</td><td>41.2282</td><td>0.57</td><td>0.93</td><td>2.54<sup>+0.06</sup><sub>-0.03</sub></td><td>KINGx</td><td>100</td><td>329.6</td><td>1.26</td></tr><tr><td>J125056+410327</td><td>192.7340</td><td>41.0576</td><td>1.18</td><td>1.13</td><td>&lt;7.26</td><td>SERSICx</td><td>2</td><td>58.5</td><td>0.73</td></tr><tr><td>J125059+410949</td><td>192.7500</td><td>41.1637</td><td>1.44</td><td>1.17</td><td>13.05<sup>+0.51</sup><sub>-0.30</sub></td><td>KINGx</td><td>100</td><td>147.9</td><td>1.03</td></tr><tr><td>J125101+410046</td><td>192.7577</td><td>41.0128</td><td>0.29</td><td>0.91</td><td>1.33<sup>+0.41</sup><sub>-0.41</sub></td><td>KINGx</td><td>30</td><td>44.4</td><td>0.88</td></tr><tr><td>J125104+410416</td><td>192.7698</td><td>41.0712</td><td>0.50</td><td>0.92</td><td>3.27<sup>+0.07</sup><sub>-0.08</sub></td><td>SERSICx</td><td>2</td><td>163.1</td><td>1.18</td></tr><tr><td>J125108+410404</td><td>192.7848</td><td>41.0679</td><td>0.69</td><td>0.97</td><td>3.00<sup>+0.35</sup><sub>-0.23</sub></td><td>KINGx</td><td>30</td><td>36.7</td><td>0.77</td></tr><tr><td>J125110+410856</td><td>192.7957</td><td>41.1491</td><td>0.63</td><td>0.94</td><td>3.87<sup>+0.05</sup><sub>-0.09</sub></td><td>KINGx</td><td>30</td><td>229.6</td><td>1.26</td></tr><tr><td>J125120+410710</td><td>192.8362</td><td>41.1197</td><td>1.32</td><td>1.17</td><td>8.97<sup>+0.48</sup><sub>-0.18</sub></td><td>SERSICx</td><td>2</td><td>93.6</td><td>1.03</td></tr><tr><td>J125130+410551</td><td>192.8767</td><td>41.0977</td><td>0.03</td><td>0.84</td><td>&lt;3.24</td><td>KINGx</td><td>100</td><td>90.5</td><td>1.05</td></tr><tr><td>J125131+410849</td><td>192.8828</td><td>41.1472</td><td>0.58</td><td>0.93</td><td>2.42<sup>+0.02</sup><sub>-0.01</sub></td><td>KINGx</td><td>100</td><td>608.9</td><td>1.83</td></tr><tr><td>J125143+410606</td><td>192.9315</td><td>41.1018</td><td>0.90</td><td>1.02</td><td>5.08<sup>+0.22</sup><sub>-0.12</sub></td><td>KINGx</td><td>100</td><td>192.4</td><td>0.96</td></tr><tr><td>J125147+410439</td><td>192.9478</td><td>41.0776</td><td>1.09</td><td>1.08</td><td>8.08<sup>+0.19</sup><sub>-0.38</sub></td><td>KINGx</td><td>100</td><td>147.0</td><td>0.86</td></tr></tbody></table>

Note. Table 7 is published in its entirety in the machine-readable format. A portion is shown here for guidance regarding its form and content.

a Index denotes concentration for King profiles, exponent for Sérsic profiles.

(This table is available in machine-readable form.)

## 5. Selection of GCCs

The main tool used for the selection of GCCs is the $(u^* - i')$ versus $(i' - K_s)$ color-color diagram (Muñoz et al. 2014). The combination of optical and near-infrared data in this parameter space constitutes the most powerful photometric-only method for the selection of a clean sample of GC candidates. It probes

simultaneously the main-sequence turnoff, and the red giant and horizontal branches of stellar populations. In this plane, GCs occupy a region that is distinct from the areas inhabited by background galaxies, on the one hand, and foreground Galactic stars, on the other. Objects in these various regions not only have different stellar populations, but light concentration parameters that roughly distinguish GCs, which appear
<table><caption>**Table 8**
$i'$-band Shape Parameters of GCCs in NGC 4826</caption><thead><tr><th rowspan="2">Name</th><th rowspan="2">R.A. J2000 deg</th><th rowspan="2">Decl. J2000 deg</th><th colspan="2">100 × (SPREAD</th><th rowspan="2">r<sub>eff,i'</sub></th><th rowspan="2">Shape</th><th rowspan="2">Index<sup>a</sup></th><th rowspan="2">S/N</th><th rowspan="2">χ<sup>2</sup></th></tr><tr><th>_MODEL)<sub>i'</sub></th><th>FWHM<sub>i'</sub> arcsec</th></tr></thead><tbody><tr><td>J125549+213423</td><td>193.9550</td><td>21.5733</td><td>0.12</td><td>0.61</td><td>&lt;2.42</td><td>KINGx</td><td>30</td><td>296.5</td><td>4.55</td></tr><tr><td>J125601+214923</td><td>194.0083</td><td>21.8233</td><td>0.48</td><td>0.69</td><td>2.81<sup>+0.11</sup><sub>-0.07</sub></td><td>SERSICx</td><td>2</td><td>136.4</td><td>2.30</td></tr><tr><td>J125612+214638</td><td>194.0522</td><td>21.7773</td><td>0.12</td><td>0.58</td><td>&lt;4.72</td><td>KINGx</td><td>100</td><td>34.1</td><td>1.04</td></tr><tr><td>J125613+214412</td><td>194.0544</td><td>21.7368</td><td>1.13</td><td>0.82</td><td>9.45<sup>+0.13</sup><sub>-0.22</sub></td><td>KINGx</td><td>30</td><td>131.5</td><td>1.28</td></tr><tr><td>J125614+214043</td><td>194.0592</td><td>21.6789</td><td>0.73</td><td>0.71</td><td>4.04<sup>+0.07</sup><sub>-0.13</sub></td><td>KINGx</td><td>100</td><td>136.5</td><td>1.44</td></tr><tr><td>J125615+214645</td><td>194.0648</td><td>21.7794</td><td>0.20</td><td>0.62</td><td>&lt;4.62</td><td>KINGx</td><td>100</td><td>119.5</td><td>1.86</td></tr><tr><td>J125622+215134</td><td>194.0944</td><td>21.8597</td><td>0.15</td><td>0.61</td><td>&lt;2.01</td><td>KINGx</td><td>100</td><td>114.8</td><td>1.44</td></tr><tr><td>J125623+214054</td><td>194.0982</td><td>21.6817</td><td>1.10</td><td>0.78</td><td>7.21<sup>+0.09</sup><sub>-0.03</sub></td><td>KINGx</td><td>30</td><td>188.4</td><td>2.36</td></tr><tr><td>J125625+214427</td><td>194.1082</td><td>21.7408</td><td>0.72</td><td>0.71</td><td>3.37<sup>+0.08</sup><sub>-0.03</sub></td><td>KINGx</td><td>100</td><td>203.9</td><td>1.82</td></tr><tr><td>J125626+213440</td><td>194.1095</td><td>21.5779</td><td>0.10</td><td>0.62</td><td>&lt;1.28</td><td>KINGx</td><td>30</td><td>137.0</td><td>1.33</td></tr><tr><td>J125626+214234</td><td>194.1124</td><td>21.7096</td><td>0.71</td><td>0.71</td><td>3.71<sup>+0.12</sup><sub>-0.05</sub></td><td>KINGx</td><td>100</td><td>173.8</td><td>2.65</td></tr><tr><td>J125628+214937</td><td>194.1207</td><td>21.8272</td><td>1.15</td><td>0.81</td><td>8.80<sup>+0.01</sup><sub>-0.07</sub></td><td>SERSICx</td><td>2</td><td>262.1</td><td>5.35</td></tr><tr><td>J125632+214023</td><td>194.1364</td><td>21.6733</td><td>0.43</td><td>0.67</td><td>1.85<sup>+0.07</sup><sub>-0.08</sub></td><td>KINGx</td><td>100</td><td>80.2</td><td>2.13</td></tr><tr><td>J125633+213919</td><td>194.1416</td><td>21.6554</td><td>0.84</td><td>0.74</td><td>4.88<sup>+0.10</sup><sub>-0.10</sub></td><td>KINGx</td><td>100</td><td>182.8</td><td>1.13</td></tr><tr><td>J125638+214512</td><td>194.1583</td><td>21.7535</td><td>0.01</td><td>0.60</td><td>&lt;5.98</td><td>KINGx</td><td>100</td><td>32.3</td><td>0.76</td></tr><tr><td>J125641+213802</td><td>194.1709</td><td>21.6341</td><td>0.64</td><td>0.70</td><td>3.90<sup>+0.16</sup><sub>-0.09</sub></td><td>KINGx</td><td>30</td><td>82.2</td><td>0.86</td></tr><tr><td>J125641+213641</td><td>194.1734</td><td>21.6115</td><td>0.58</td><td>0.69</td><td>2.86<sup>+0.10</sup><sub>-0.02</sub></td><td>KINGx</td><td>100</td><td>159.9</td><td>1.20</td></tr><tr><td>J125642+213204</td><td>194.1761</td><td>21.5347</td><td>0.52</td><td>0.69</td><td>2.53<sup>+0.10</sup><sub>-0.07</sub></td><td>KINGx</td><td>100</td><td>109.9</td><td>1.00</td></tr><tr><td>J125644+213848</td><td>194.1873</td><td>21.6468</td><td>0.79</td><td>0.73</td><td>4.38<sup>+0.14</sup><sub>-0.05</sub></td><td>KINGx</td><td>100</td><td>185.4</td><td>2.14</td></tr><tr><td>J125646+213754</td><td>194.1954</td><td>21.6317</td><td>0.55</td><td>0.69</td><td>2.70<sup>+0.18</sup><sub>-0.07</sub></td><td>KINGx</td><td>100</td><td>82.2</td><td>1.01</td></tr><tr><td>J125649+214425</td><td>194.2065</td><td>21.7404</td><td>0.81</td><td>0.73</td><td>4.88<sup>+0.07</sup><sub>-0.12</sub></td><td>KINGx</td><td>100</td><td>151.2</td><td>1.52</td></tr><tr><td>J125654+215233</td><td>194.2275</td><td>21.8760</td><td>1.04</td><td>0.77</td><td>8.76<sup>+0.34</sup><sub>-0.30</sub></td><td>KINGx</td><td>100</td><td>109.5</td><td>1.16</td></tr><tr><td>J125655+213319</td><td>194.2323</td><td>21.5554</td><td>0.05</td><td>0.60</td><td>&lt;5.97</td><td>KINGx</td><td>30</td><td>64.2</td><td>1.07</td></tr><tr><td>J125655+214633</td><td>194.2332</td><td>21.7761</td><td>0.97</td><td>0.77</td><td>6.74<sup>+0.20</sup><sub>-0.15</sub></td><td>KINGx</td><td>100</td><td>151.3</td><td>1.02</td></tr><tr><td>J125714+213914</td><td>194.3117</td><td>21.6540</td><td>0.13</td><td>0.62</td><td>&lt;1.44</td><td>KINGx</td><td>30</td><td>256.8</td><td>3.05</td></tr><tr><td>J125717+213702</td><td>194.3225</td><td>21.6173</td><td>0.56</td><td>0.69</td><td>3.60<sup>+0.12</sup><sub>-0.17</sub></td><td>KINGx</td><td>30</td><td>79.0</td><td>0.87</td></tr><tr><td>J125721+213816</td><td>194.3410</td><td>21.6378</td><td>0.98</td><td>0.78</td><td>7.40<sup>+0.18</sup><sub>-0.18</sub></td><td>KINGx</td><td>30</td><td>87.3</td><td>0.87</td></tr><tr><td>J125722+213659</td><td>194.3418</td><td>21.6166</td><td>0.03</td><td>0.61</td><td>&lt;1.14</td><td>KINGx</td><td>30</td><td>208.9</td><td>2.46</td></tr><tr><td>J125723+214212</td><td>194.3472</td><td>21.7036</td><td>0.62</td><td>0.71</td><td>3.37<sup>+0.12</sup><sub>-0.07</sub></td><td>KINGx</td><td>100</td><td>134.4</td><td>1.64</td></tr><tr><td>J125723+213711</td><td>194.3480</td><td>21.6198</td><td>0.80</td><td>0.74</td><td>4.72<sup>+0.14</sup><sub>-0.10</sub></td><td>KINGx</td><td>100</td><td>160.6</td><td>1.27</td></tr></tbody></table>

Note. Table 8 is published in its entirety in the machine-readable format. A portion is shown here for guidance regarding its form and content.

<sup>a</sup> Index denotes concentration for King profiles, exponent for Sérsic profiles.

(This table is available in machine-readable form.)

marginally resolved in the optical, from both point and extended sources.

Figure 4 shows the $u^*i'K_s$ diagrams for all the sources detected in the images of NGC 3368 (top row), NGC 4395 (second row), NGC 4736 (third row), and NGC 4826 (bottom row). All the data have been corrected for Galactic extinction, using the values from Schlaflay & Finkbeiner (2011) given for the Sloan Digital Sky Survey filters by the NASA Extragalactic Database,<fnref n="9" /> respectively, for NGC 3368, $A_u = 0.107$, $A_g = 0.083$, $A_i = 0.043$, $A_{K_s} = 0.005$; for NGC 4395, $A_u = 0.073$, $A_g = 0.057$, $A_i = 0.029$, $A_{K_s} = 0.008$; for NGC 4736, $A_u = 0.075$, $A_g = 0.059$, $A_r = 0.041$, $A_i = 0.030$, $A_{K_s} = 0.005$; and for NGC 4826, $A_u = 0.175$, $A_g = 0.137$, $A_r = 0.095$, $A_i = 0.070$, $A_{K_s} = 0.012$.

The sources are color coded by their light concentration in the $i'$ band, as gauged by the FWHM (left column), and $100×$ the dimensionless SExtractor parameter SPREAD MODEL (right column).<fnref n="10" /> In these panels, reddish-brown sources are extended, blue sources are pointlike, and cyan sources are marginally

resolved. The color limits have been chosen to highlight these differences. Objects in the reddish-brown cloud are mostly galaxies, while those in the blue band are main-sequence stars in our Galaxy.

In between the galaxy cloud and the stellar band, the selection region for GCCs is indicated by the gray contour. The selection region was determined using data from the giant elliptical M87 (Muñoz et al. 2014; Powalka et al. 2016); it has the shape of a drop or pennon, and contains more than 2000 spectroscopically confirmed GCs in that galaxy. The technique has already been applied to the spiral megamaser prototype NGC 4258 (González-Lópezlira et al. 2017), and its effectiveness in spirals assessed by González-Lópezlira et al. (2019). One difference with the observations of M87 and our previous work on NGC 4258 is that a new $u^*$ filter was used for the observations presented in this paper. As a consequence, the $u^*$ luminosity function turnover (LFTO) is slightly fainter, and the GC selection region shifted 0.24 mag to the red in ($u^* - i'$).

The spectroscopic observations of the NGC 4258 GCCs reported by González-Lópezlira et al. (2019) found no false negatives, and a sample contamination of, conservatively, 7/23 or 30%, fully consistent with the 50–100 contaminants found by Powalka et al. (2016) for the GCCs of M87, in a FOV 9 times larger. Like M87 and NGC 4258, the fields of NGC 3368, NGC 4395, NGC 4736, and NGC 4826 lie at high Galactic

<footnote n="9">⁹ The NASA/IPA Extragalactic Database (NED) is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.</footnote>

<footnote n="10">¹⁰ For each object, the SPREAD MODEL value results from the comparison between its best-fitting PSF, and the convolution of such PSF with an exponential disk whose scale length is equal to the FWHM of said PSF (Desai et al. 2012).</footnote>
<figure><img src="image_20.png" /><figcaption>**Figure 10.** Grayscale images of GC candidates, from HST exposures. Top, left to right: J104635+114912 and J104651+114819, in NGC 3368. Bottom: J125039+410913, J125045+410950, and J125131+410849, in NGC 4736.</figcaption></figure>

latitudes of $b = 57°0, b = 81°5, b = 76°0, \text{ and } b = 84°4$, respectively.

González-Lópezlira et al. (2019) also determined that the contaminants could be reduced by setting the light concentration parameters SPREAD MODEL $\le 0.015$ and FWHM $\le 29$ pc (0.′′58 for NGC 3368, 1.′′40 for NGC 4395, 1.′′20 for NGC 4736, and 0.′′82 for NGC 4826). Moreover, we only kept objects within $\pm 3\sigma$ of the expected GC LFTO magnitude in every filter, except at $K_s$, as González-Lópezlira et al. (2019) realized that objects more than $1.7 \times \sigma$ brighter than the turnoff at that wavelength were potential contaminants. Other restrictions were an axis ratio $\ge 0.7$ and an error MAGERR_PSF $< 0.2$ mag, both in the $i'$ band, as well as FLAGS = 0 in all bands. The standard deviation of the GCLF depends on the galaxy luminosity (Jordán et al. 2007); based on their Equation (18), we have assumed 0.9 for NGC 4395, 1.1 for NGC 4826, and 1.2 for NGC 3368 and NGC 4736.<fnref n="11" /> Values of the LFTO in the optical were derived by combining the absolute LFTO magnitude in the g band, $M_g^0 = -7.2$ mag (Jordán et al. 2007), with the (AB) colors given in the MegaCam filter system by (Bruzual & Charlot 2003) models for an SSP with $Z = 0.0004$, an age of 12 Gyr, and a Chabrier initial mass function (IMF; Chabrier 2003). The LFTO in the V band would be $M_V^0 = -7.4$ mag. The LFTO magnitude in the $K_s$ band was taken from Wang et al. (2014). The TO absolute magnitudes, observed LFTO magnitudes, and magnitude ranges of the GCLF are shown in Table 4.

Figures 5–8 (left column) show the $u*i'K_s$ diagram, FWHM (top rows), and 100× structural parameter SPREAD MODEL (bottom rows) of sources in and closely around the GCC selection region (gray contour) for NGC 3368, NGC 4395, NGC 4736, and NGC 4826, respectively. The GCC final samples for the galaxies are displayed in the right column.

The spatial distributions of the GCC samples are shown in Figure 9. The members of the samples are displayed as green circles on the $i'$-band images of NGC 3368 (top left), NGC 4395 (top right), NGC 4736 (bottom left), and NGC 4826 (bottom right). The dark blue ellipses outline the regions where source confusion is highest, inferred from the completeness simulations and the dearth of GCC detections. This boundary is located at 0.375 $R_{25}$ for NGC 3368, 0.25 $R_{25}$ for NGC 4395, and $0.5R_{25}$ for both NGC 4736 and NGC 4826. The cyan circles indicate $R_{25}$.

Given the distances to the galaxies, as well as the resolution of the MegaCam data (1 MegaCam pixel = 0.′′ 186; i.e., $\simeq 3.9, 4.5, 6.6, \text{ and } 9.4$ pc, respectively, for NGC 4395, NGC 4736, NGC 4826, and NGC 3368), we have also been able to calculate the half-light radii, $r_e$, in the $i'$ band of all the candidates. To this end, we used the program ISHAPE (Larsen 1999) in the BAOLAB<fnref n="12" /> software package. ISHAPE measures the size of a compact source by comparing its observed light profile with models generated by convolving different analytical profiles with the image PSF. For data with a signal-to-noise ratio (S/N) $\gtrsim 30$, ISHAPE can measure $r_{\text{eff}}$ reliably down to $\sim 0.1$ the PSF FWHM, or $\sim 1.7$ pc for

<footnote n="11">¹¹ The MW GCLF has $\sigma_V = 1.15 \pm 0.1$ (Jordán et al. 2007), also consistent with their Equation (18).</footnote>

<footnote n="12">¹² http://baolab.astroduo.org</footnote>
<figure><img src="image_21.png" /><figcaption>**Figure 11.** Color distributions of GC systems. Top: NGC 3368 GCCs; second row: NGC 4395; third row: NGC 4736; bottom: NGC 4826. From left to right: $(u^*-g')$, $(u^*-i')$, $(g'-r')$, $(g'-i')$, $(g'-K_s)$, $(r'-i')$.</figcaption></figure>

NGC 4736, 2.3 pc for NGC 4826, 2.4 pc for NGC 3368, and 2.5 pc for NGC 4395; objects smaller than this are effectively unresolved (Larsen 1999; Harris et al. 2009). We fitted all the sources with King (King 1962, 1966) and Sérsic (Sérsic 1963) profiles. For King profiles, we tried fixed concentration indices ($C \equiv r_{\text{tidal}}/r_{\text{core}}$) of 30 and 100; in the case of Sérsic, we chose a fixed exponent of 2.13 For each object, the model providing the fit to the data with the smallest $\chi^2$ residuals was then used to derive the effective radius, by applying the conversion factors between $r_{\text{eff}}$ and FWHM given in the ISHAPE manual. For each galaxy, Tables 5–8 list shape parameters in the $i'$ band: FWHM, $100 \times \text{SPREAD\_MODEL}$, $r_e$, the type and index of the best-fitting profile, the S/N of the data, and the $\chi^2$ of the fit.

We present in Figure 10 a few exposures of GCCs in NGC 3368 and NGC 4736 that we were able to find in the Hubble Space Telescope (HST) Legacy Archive; their visual appearance is consistent with their classification. J104635+114912 was identified in the Advance Camera for Surveys (ACS) frame hst_10433_02_acs_wfc_f555w.fits (filter F555W, proposal GO 10433, PI: B. Madore); J104651+114819, in the Wide Field Camera 3 (WFC3) image hst_13364_07_wfc3_uvis_f555w.fits (F555W, proposal GO 13364, PI: D. Calzetti). All the NGC 4736 images were acquired with the ACS. J125039+410913 and J125045+410950 were identified in the frame hst_10402_09_acs_wfc_f555w_drz.fits (proposal GO 10402, PI: R. Chandar); J125131+410849, in hst_9480_u8_

acs_wfc_f775w_drz.fits (filter F775W, proposal GO/PAR 9480, PI: J. Rhodes).

# 6. Properties of the GC Systems

## 6.1. Color Distribution

The distributions of our final samples of GCCs in the colors $(u^*-g')$, $(u^*-i')$, $(g'-r')$, $(g'-i')$, $(r'-i')$, and $(g'-K_s)$, fit with two heteroscedastic Gaussians, are shown in Figure 11. The colors of the individual candidates, shown in Tables 9–12, have been corrected for foreground extinction in the MW, as already mentioned. The means and dispersions of the Gaussian fits are presented in Table 13.

González-Lópezlira et al. (2017) found that the colors of GCs and GCCs in the MW, M31 and NGC 4258 were remarkably consistent, once internal extinction was taken into account. The same is true for NGC 3368, NGC 4395, NGC 4736, and NGC 4826. Their GCC colors have not been corrected for internal extinction, and the bluer Gaussians fit to their color distributions are bracketed by the values of single Gaussian fits to the GC system of M31, with and without such correction. Both these and the colors of the MW GC system are shown in Table 14.

## 6.2. Luminosity Functions

The $K_s$-band luminosity functions of the final samples of GCCs of the four galaxies are shown in Figure 12. Given the exclusion of the regions close to the centers of the galaxies, i.e., the areas most affected by crowding and confusion, the corrections for incompleteness would be barely significant. The

<footnote n="13">13 According to Turner et al. (2012), based on the measurements of Graham & Spitler (2009) and Seth et al. (2010), a Sérsic parameter of ~2 represents Galactic GCs and nuclear clusters well.</footnote>
<table><caption>Table 9
Colors of GCCs in NGC 3368</caption><thead><tr><th>Name</th><th>R.A. J2000 deg</th><th>Decl. J2000 deg</th><th>g'<sub>0</sub> mag</th><th>Δg'<sub>0</sub> mag</th><th>K<sub>s,0</sub> mag</th><th>ΔK<sub>s,0</sub> mag</th><th>(u* - i')<sub>0</sub> mag</th><th>Δ(u* - i')<sub>0</sub> mag</th><th>(g' - i')<sub>0</sub> mag</th><th>Δ(g' - i')<sub>0</sub> mag</th><th>(i' - K<sub>s</sub>)<sub>0</sub> mag</th><th>Δ(i' - K<sub>s</sub>)<sub>0</sub> mag</th></tr></thead><tbody><tr><td>J104539+113944</td><td>161.4148</td><td>11.6624</td><td>20.493</td><td>0.002</td><td>19.97</td><td>0.03</td><td>1.824</td><td>0.005</td><td>0.668</td><td>0.003</td><td>-0.22</td><td>0.03</td></tr><tr><td>J104540+120330</td><td>161.4185</td><td>12.0585</td><td>21.092</td><td>0.003</td><td>20.76</td><td>0.08</td><td>1.736</td><td>0.008</td><td>0.566</td><td>0.004</td><td>-0.31</td><td>0.08</td></tr><tr><td>J104604+115505</td><td>161.5179</td><td>11.9183</td><td>20.401</td><td>0.002</td><td>19.97</td><td>0.03</td><td>1.823</td><td>0.005</td><td>0.602</td><td>0.003</td><td>-0.25</td><td>0.03</td></tr><tr><td>J104604+113655</td><td>161.5183</td><td>11.6154</td><td>21.950</td><td>0.006</td><td>20.85</td><td>0.08</td><td>2.148</td><td>0.018</td><td>0.811</td><td>0.007</td><td>0.21</td><td>0.08</td></tr><tr><td>J104609+120658</td><td>161.5413</td><td>12.1161</td><td>21.510</td><td>0.004</td><td>20.89</td><td>0.10</td><td>2.023</td><td>0.010</td><td>0.736</td><td>0.005</td><td>-0.19</td><td>0.10</td></tr><tr><td>J104626+113118</td><td>161.6091</td><td>11.5219</td><td>21.837</td><td>0.005</td><td>20.73</td><td>0.13</td><td>2.363</td><td>0.014</td><td>0.900</td><td>0.006</td><td>0.13</td><td>0.13</td></tr><tr><td>J104633+120015</td><td>161.6379</td><td>12.0043</td><td>22.081</td><td>0.007</td><td>21.28</td><td>0.15</td><td>1.917</td><td>0.015</td><td>0.787</td><td>0.008</td><td>-0.06</td><td>0.15</td></tr><tr><td>J104635+115918</td><td>161.6478</td><td>11.9886</td><td>22.025</td><td>0.006</td><td>20.56</td><td>0.04</td><td>2.616</td><td>0.020</td><td>1.026</td><td>0.006</td><td>0.36</td><td>0.04</td></tr><tr><td>J104635+114912</td><td>161.6493</td><td>11.8201</td><td>22.666</td><td>0.011</td><td>21.77</td><td>0.10</td><td>2.132</td><td>0.028</td><td>0.880</td><td>0.012</td><td>-0.06</td><td>0.10</td></tr><tr><td>J104645+113554</td><td>161.6890</td><td>11.5985</td><td>20.774</td><td>0.002</td><td>20.07</td><td>0.02</td><td>2.040</td><td>0.007</td><td>0.714</td><td>0.003</td><td>-0.08</td><td>0.02</td></tr><tr><td>J104648+115012</td><td>161.7003</td><td>11.8368</td><td>22.118</td><td>0.006</td><td>20.70</td><td>0.03</td><td>2.495</td><td>0.021</td><td>0.963</td><td>0.007</td><td>0.38</td><td>0.03</td></tr><tr><td>J104651+114819</td><td>161.7134</td><td>11.8053</td><td>21.527</td><td>0.004</td><td>20.54</td><td>0.02</td><td>2.049</td><td>0.011</td><td>0.828</td><td>0.005</td><td>0.09</td><td>0.02</td></tr><tr><td>J104709+114112</td><td>161.7882</td><td>11.6868</td><td>20.870</td><td>0.003</td><td>20.05</td><td>0.04</td><td>2.023</td><td>0.006</td><td>0.759</td><td>0.003</td><td>-0.02</td><td>0.04</td></tr><tr><td>J104750+113703</td><td>161.9601</td><td>11.6176</td><td>23.451</td><td>0.018</td><td>21.43</td><td>0.11</td><td>2.682</td><td>0.045</td><td>1.539</td><td>0.019</td><td>0.41</td><td>0.11</td></tr><tr><td>J104755+113503</td><td>161.9811</td><td>11.5844</td><td>21.309</td><td>0.004</td><td>20.74</td><td>0.06</td><td>1.914</td><td>0.010</td><td>0.687</td><td>0.005</td><td>-0.19</td><td>0.06</td></tr></tbody></table>

(This table is available in machine-readable form.)
<table><caption>Table 10
Colors of GCCs in NGC 4395</caption><thead><tr><th>Name</th><th>R.A. J2000 deg</th><th>Decl. J2000 deg</th><th>g'<sub>0</sub> mag</th><th>Δg'<sub>0</sub> mag</th><th>K<sub>x,0</sub> mag</th><th>ΔK<sub>x,0</sub> mag</th><th>(u*−i')<sub>0</sub> mag</th><th>Δ (u*−i')<sub>0</sub> mag</th><th>(g'−i')<sub>0</sub> mag</th><th>Δ (g'−i')<sub>0</sub> mag</th><th>(i'−K<sub>s</sub>)<sub>0</sub> mag</th><th>Δ (i'−K<sub>s</sub>)<sub>0</sub> mag</th></tr></thead><tbody><tr><td>J122452+332844</td><td>186.2204</td><td>33.4792</td><td>20.001</td><td>0.004</td><td>19.59</td><td>0.03</td><td>1.802</td><td>0.007</td><td>0.656</td><td>0.006</td><td>−0.30</td><td>0.03</td></tr><tr><td>J122456+333230</td><td>186.2335</td><td>33.5418</td><td>19.580</td><td>0.003</td><td>19.17</td><td>0.02</td><td>1.739</td><td>0.005</td><td>0.654</td><td>0.004</td><td>−0.30</td><td>0.02</td></tr><tr><td>J122522+332549</td><td>186.3426</td><td>33.4303</td><td>20.697</td><td>0.006</td><td>20.08</td><td>0.04</td><td>1.940</td><td>0.012</td><td>0.761</td><td>0.009</td><td>−0.20</td><td>0.04</td></tr><tr><td>J122527+332015</td><td>186.3639</td><td>33.3376</td><td>20.041</td><td>0.004</td><td>19.23</td><td>0.03</td><td>1.877</td><td>0.008</td><td>0.813</td><td>0.005</td><td>−0.05</td><td>0.03</td></tr><tr><td>J122529+332536</td><td>186.3734</td><td>33.4268</td><td>20.734</td><td>0.007</td><td>20.17</td><td>0.04</td><td>1.952</td><td>0.013</td><td>0.730</td><td>0.009</td><td>−0.22</td><td>0.04</td></tr><tr><td>J122538+332654</td><td>186.4118</td><td>33.4486</td><td>21.223</td><td>0.009</td><td>20.71</td><td>0.16</td><td>1.696</td><td>0.016</td><td>0.657</td><td>0.013</td><td>−0.20</td><td>0.16</td></tr><tr><td>J122541+333109</td><td>186.4210</td><td>33.5194</td><td>21.903</td><td>0.016</td><td>20.28</td><td>0.05</td><td>2.709</td><td>0.035</td><td>1.058</td><td>0.020</td><td>0.52</td><td>0.06</td></tr><tr><td>J122544+333016</td><td>186.4354</td><td>33.5046</td><td>23.298</td><td>0.053</td><td>20.12</td><td>0.05</td><td>3.232</td><td>0.069</td><td>2.148</td><td>0.055</td><td>0.98</td><td>0.05</td></tr><tr><td>J122548+333802</td><td>186.4535</td><td>33.6341</td><td>21.255</td><td>0.010</td><td>20.70</td><td>0.08</td><td>1.939</td><td>0.016</td><td>0.738</td><td>0.013</td><td>−0.24</td><td>0.08</td></tr><tr><td>J122558+333154</td><td>186.4917</td><td>33.5318</td><td>23.479</td><td>0.062</td><td>20.88</td><td>0.10</td><td>2.977</td><td>0.079</td><td>1.877</td><td>0.066</td><td>0.67</td><td>0.10</td></tr></tbody></table>

(This table is available in machine-readable form.)
<table><caption>Table 11
Colors of GCCs in NGC 4736</caption><thead><tr><th>Name</th><th>R.A. J2000 deg</th><th>Decl. J2000 deg</th><th>g'<sub>0</sub> mag</th><th>Δg'<sub>0</sub> mag</th><th>K<sub>5,0</sub> mag</th><th>ΔK<sub>5,0</sub> mag</th><th>(u*-i')<sub>0</sub> mag</th><th>Δ (u*-i')<sub>0</sub> mag</th><th>(g' - r')<sub>0</sub> mag</th><th>Δ (g' - r')<sub>0</sub> mag</th><th>(g' - i')<sub>0</sub> mag</th><th>Δ (g' - i')<sub>0</sub> mag</th><th>(i' - K<sub>s</sub>)<sub>0</sub> mag</th><th>Δ (i' - K<sub>s</sub>)<sub>0</sub> mag</th></tr></thead><tbody><tr><td>J124947+411056</td><td>192.4496</td><td>41.1823</td><td>22.850</td><td>0.048</td><td>20.28</td><td>0.05</td><td>3.226</td><td>0.063</td><td>1.166</td><td>0.053</td><td>1.545</td><td>0.060</td><td>0.97</td><td>0.06</td></tr><tr><td>J124951+411538</td><td>192.4633</td><td>41.2606</td><td>19.098</td><td>0.008</td><td>18.57</td><td>0.01</td><td>1.717</td><td>0.010</td><td>0.425</td><td>0.010</td><td>0.667</td><td>0.012</td><td>-0.20</td><td>0.01</td></tr><tr><td>J125001+411350</td><td>192.5053</td><td>41.2307</td><td>20.147</td><td>0.014</td><td>19.71</td><td>0.02</td><td>1.699</td><td>0.017</td><td>0.419</td><td>0.018</td><td>0.661</td><td>0.022</td><td>-0.28</td><td>0.02</td></tr><tr><td>J125029+410951</td><td>192.6246</td><td>41.1644</td><td>21.591</td><td>0.027</td><td>20.95</td><td>0.05</td><td>1.743</td><td>0.032</td><td>0.492</td><td>0.033</td><td>0.737</td><td>0.041</td><td>-0.15</td><td>0.06</td></tr><tr><td>J125031+411039</td><td>192.6314</td><td>41.1777</td><td>22.573</td><td>0.053</td><td>21.28</td><td>0.07</td><td>2.711</td><td>0.076</td><td>0.612</td><td>0.063</td><td>0.850</td><td>0.076</td><td>0.39</td><td>0.09</td></tr><tr><td>J125031+410949</td><td>192.6329</td><td>41.1638</td><td>23.248</td><td>0.075</td><td>21.60</td><td>0.10</td><td>2.607</td><td>0.106</td><td>0.638</td><td>0.089</td><td>1.060</td><td>0.103</td><td>0.54</td><td>0.12</td></tr><tr><td>J125033+405708</td><td>192.6415</td><td>40.9525</td><td>19.946</td><td>0.012</td><td>19.49</td><td>0.01</td><td>1.821</td><td>0.014</td><td>0.399</td><td>0.015</td><td>0.647</td><td>0.019</td><td>-0.25</td><td>0.02</td></tr><tr><td>J125039+410913</td><td>192.6651</td><td>41.1538</td><td>22.044</td><td>0.039</td><td>21.40</td><td>0.09</td><td>1.884</td><td>0.048</td><td>0.482</td><td>0.048</td><td>0.690</td><td>0.060</td><td>-0.10</td><td>0.10</td></tr><tr><td>J125042+410345</td><td>192.6786</td><td>41.0625</td><td>23.082</td><td>0.061</td><td>19.81</td><td>0.02</td><td>3.000</td><td>0.040</td><td>1.320</td><td>0.067</td><td>2.358</td><td>0.068</td><td>0.86</td><td>0.04</td></tr><tr><td>J125043+410947</td><td>192.6807</td><td>41.1632</td><td>20.309</td><td>0.016</td><td>19.89</td><td>0.02</td><td>1.746</td><td>0.019</td><td>0.417</td><td>0.020</td><td>0.647</td><td>0.024</td><td>-0.28</td><td>0.03</td></tr><tr><td>J125045+410950</td><td>192.6902</td><td>41.1639</td><td>20.772</td><td>0.020</td><td>19.92</td><td>0.02</td><td>2.065</td><td>0.022</td><td>0.502</td><td>0.024</td><td>0.784</td><td>0.029</td><td>0.01</td><td>0.03</td></tr><tr><td>J125046+410210</td><td>192.6920</td><td>41.0361</td><td>19.819</td><td>0.014</td><td>18.47</td><td>0.01</td><td>2.688</td><td>0.014</td><td>0.587</td><td>0.016</td><td>0.923</td><td>0.019</td><td>0.37</td><td>0.01</td></tr><tr><td>J125051+410314</td><td>192.7138</td><td>41.0540</td><td>21.023</td><td>0.022</td><td>20.32</td><td>0.03</td><td>2.033</td><td>0.025</td><td>0.466</td><td>0.027</td><td>0.747</td><td>0.033</td><td>-0.10</td><td>0.04</td></tr><tr><td>J125051+411341</td><td>192.7148</td><td>41.2282</td><td>19.920</td><td>0.013</td><td>19.39</td><td>0.01</td><td>1.708</td><td>0.015</td><td>0.399</td><td>0.016</td><td>0.634</td><td>0.019</td><td>-0.16</td><td>0.02</td></tr><tr><td>J125056+410327</td><td>192.7340</td><td>41.0576</td><td>22.302</td><td>0.040</td><td>20.78</td><td>0.05</td><td>2.794</td><td>0.057</td><td>0.582</td><td>0.048</td><td>0.906</td><td>0.058</td><td>0.56</td><td>0.06</td></tr><tr><td>J125059+410949</td><td>192.7500</td><td>41.1637</td><td>21.343</td><td>0.026</td><td>20.56</td><td>0.04</td><td>2.130</td><td>0.030</td><td>0.516</td><td>0.031</td><td>0.745</td><td>0.038</td><td>-0.02</td><td>0.05</td></tr><tr><td>J125101+410046</td><td>192.7577</td><td>41.0128</td><td>22.393</td><td>0.042</td><td>21.26</td><td>0.08</td><td>2.136</td><td>0.050</td><td>0.560</td><td>0.050</td><td>0.844</td><td>0.060</td><td>0.23</td><td>0.09</td></tr><tr><td>J125104+410416</td><td>192.7698</td><td>41.0712</td><td>20.960</td><td>0.023</td><td>19.85</td><td>0.02</td><td>2.321</td><td>0.025</td><td>0.539</td><td>0.028</td><td>0.866</td><td>0.033</td><td>0.19</td><td>0.03</td></tr><tr><td>J125108+410404</td><td>192.7848</td><td>41.0679</td><td>22.459</td><td>0.043</td><td>21.60</td><td>0.11</td><td>1.984</td><td>0.053</td><td>0.523</td><td>0.052</td><td>0.755</td><td>0.063</td><td>0.05</td><td>0.12</td></tr><tr><td>J125110+410856</td><td>192.7957</td><td>41.1491</td><td>20.314</td><td>0.017</td><td>19.81</td><td>0.02</td><td>1.753</td><td>0.020</td><td>0.403</td><td>0.021</td><td>0.646</td><td>0.026</td><td>-0.20</td><td>0.03</td></tr><tr><td>J125120+410710</td><td>192.8362</td><td>41.1197</td><td>21.730</td><td>0.029</td><td>20.51</td><td>0.04</td><td>2.473</td><td>0.037</td><td>0.546</td><td>0.035</td><td>0.790</td><td>0.043</td><td>0.38</td><td>0.05</td></tr><tr><td>J125130+410551</td><td>192.8767</td><td>41.0977</td><td>21.431</td><td>0.025</td><td>20.92</td><td>0.06</td><td>1.714</td><td>0.030</td><td>0.434</td><td>0.031</td><td>0.657</td><td>0.039</td><td>-0.20</td><td>0.07</td></tr><tr><td>J125131+410849</td><td>192.8828</td><td>41.1472</td><td>19.149</td><td>0.009</td><td>18.68</td><td>0.01</td><td>1.743</td><td>0.010</td><td>0.399</td><td>0.011</td><td>0.633</td><td>0.013</td><td>-0.22</td><td>0.01</td></tr><tr><td>J125143+410606</td><td>192.9315</td><td>41.1018</td><td>20.757</td><td>0.018</td><td>20.10</td><td>0.04</td><td>2.027</td><td>0.021</td><td>0.469</td><td>0.022</td><td>0.678</td><td>0.027</td><td>-0.07</td><td>0.04</td></tr><tr><td>J125147+410439</td><td>192.9478</td><td>41.0776</td><td>21.403</td><td>0.026</td><td>20.16</td><td>0.04</td><td>2.570</td><td>0.030</td><td>0.548</td><td>0.031</td><td>0.871</td><td>0.037</td><td>0.32</td><td>0.05</td></tr></tbody></table>

(This table is available in machine-readable form.)
<table><caption>Table 12
Colors of GCCs in NGC 4826</caption><thead><tr><th>Name</th><th>R.A. J2000 deg</th><th>Decl. J2000 deg</th><th>g'<sub>0</sub> mag</th><th>Δg'<sub>0</sub> mag</th><th>K<sub>s,0</sub> mag</th><th>ΔK<sub>s,0</sub> mag</th><th>(u*-i')<sub>0</sub> mag</th><th>Δ (u*-i')<sub>0</sub> mag</th><th>(g'-r')<sub>0</sub> mag</th><th>Δ (g'-r')<sub>0</sub> mag</th><th>(g'-i')<sub>0</sub> mag</th><th>Δ (g'-i')<sub>0</sub> mag</th><th>(i'-K<sub>x</sub>)<sub>0</sub> mag</th><th>Δ (i'-K<sub>x</sub>)<sub>0</sub> mag</th></tr></thead><tbody><tr><td>J125549+213423</td><td>193.9550</td><td>21.5733</td><td>19.982</td><td>0.009</td><td>19.36</td><td>0.03</td><td>2.011</td><td>0.007</td><td>0.424</td><td>0.011</td><td>0.665</td><td>0.011</td><td>-0.17</td><td>0.03</td></tr><tr><td>J125601+214923</td><td>194.0083</td><td>21.8233</td><td>21.238</td><td>0.018</td><td>20.26</td><td>0.03</td><td>1.854</td><td>0.013</td><td>0.811</td><td>0.021</td><td>1.027</td><td>0.021</td><td>-0.17</td><td>0.03</td></tr><tr><td>J125612+214638</td><td>194.0522</td><td>21.7773</td><td>22.550</td><td>0.033</td><td>21.38</td><td>0.09</td><td>2.465</td><td>0.044</td><td>0.484</td><td>0.040</td><td>0.810</td><td>0.040</td><td>0.23</td><td>0.10</td></tr><tr><td>J125613+214412</td><td>194.0544</td><td>21.7368</td><td>22.804</td><td>0.034</td><td>19.36</td><td>0.01</td><td>3.273</td><td>0.027</td><td>1.946</td><td>0.036</td><td>2.331</td><td>0.036</td><td>0.98</td><td>0.02</td></tr><tr><td>J125614+214043</td><td>194.0592</td><td>21.6789</td><td>21.255</td><td>0.016</td><td>20.17</td><td>0.02</td><td>1.983</td><td>0.013</td><td>0.730</td><td>0.019</td><td>0.956</td><td>0.019</td><td>0.01</td><td>0.03</td></tr><tr><td>J125615+214645</td><td>194.0648</td><td>21.7794</td><td>20.949</td><td>0.015</td><td>20.30</td><td>0.03</td><td>1.958</td><td>0.013</td><td>0.349</td><td>0.019</td><td>0.625</td><td>0.019</td><td>-0.10</td><td>0.03</td></tr><tr><td>J125622+215134</td><td>194.0944</td><td>21.8597</td><td>21.335</td><td>0.017</td><td>20.39</td><td>0.05</td><td>2.067</td><td>0.014</td><td>0.716</td><td>0.020</td><td>0.952</td><td>0.020</td><td>-0.14</td><td>0.05</td></tr><tr><td>J125623+214054</td><td>194.0982</td><td>21.6817</td><td>21.091</td><td>0.015</td><td>19.85</td><td>0.02</td><td>1.841</td><td>0.011</td><td>0.972</td><td>0.017</td><td>1.096</td><td>0.018</td><td>0.02</td><td>0.02</td></tr><tr><td>J125625+214427</td><td>194.1082</td><td>21.7408</td><td>20.446</td><td>0.013</td><td>19.72</td><td>0.02</td><td>1.894</td><td>0.010</td><td>0.355</td><td>0.016</td><td>0.638</td><td>0.015</td><td>-0.04</td><td>0.02</td></tr><tr><td>J125626+213440</td><td>194.1095</td><td>21.5779</td><td>20.705</td><td>0.013</td><td>20.34</td><td>0.03</td><td>1.706</td><td>0.011</td><td>0.266</td><td>0.017</td><td>0.516</td><td>0.017</td><td>-0.27</td><td>0.03</td></tr><tr><td>J125626+214234</td><td>194.1124</td><td>21.7096</td><td>20.816</td><td>0.013</td><td>19.95</td><td>0.02</td><td>1.901</td><td>0.011</td><td>0.530</td><td>0.016</td><td>0.851</td><td>0.016</td><td>-0.11</td><td>0.02</td></tr><tr><td>J125628+214937</td><td>194.1207</td><td>21.8272</td><td>20.872</td><td>0.014</td><td>19.38</td><td>0.01</td><td>1.956</td><td>0.011</td><td>0.954</td><td>0.016</td><td>1.198</td><td>0.017</td><td>0.17</td><td>0.02</td></tr><tr><td>J125632+214023</td><td>194.1364</td><td>21.6733</td><td>21.338</td><td>0.018</td><td>20.55</td><td>0.04</td><td>1.850</td><td>0.016</td><td>0.335</td><td>0.023</td><td>0.624</td><td>0.023</td><td>0.04</td><td>0.04</td></tr><tr><td>J125633+213919</td><td>194.1416</td><td>21.6554</td><td>20.733</td><td>0.013</td><td>20.01</td><td>0.02</td><td>1.710</td><td>0.010</td><td>0.538</td><td>0.015</td><td>0.743</td><td>0.016</td><td>-0.15</td><td>0.03</td></tr><tr><td>J125638+214512</td><td>194.1583</td><td>21.7535</td><td>23.490</td><td>0.049</td><td>21.22</td><td>0.08</td><td>2.774</td><td>0.053</td><td>1.230</td><td>0.054</td><td>1.678</td><td>0.054</td><td>0.47</td><td>0.08</td></tr><tr><td>J125641+213802</td><td>194.1709</td><td>21.6341</td><td>21.815</td><td>0.021</td><td>20.74</td><td>0.05</td><td>1.862</td><td>0.016</td><td>0.762</td><td>0.025</td><td>1.020</td><td>0.025</td><td>-0.07</td><td>0.05</td></tr><tr><td>J125641+213641</td><td>194.1734</td><td>21.6115</td><td>20.810</td><td>0.013</td><td>19.93</td><td>0.02</td><td>2.026</td><td>0.011</td><td>0.494</td><td>0.016</td><td>0.760</td><td>0.016</td><td>-0.00</td><td>0.02</td></tr><tr><td>J125642+213204</td><td>194.1761</td><td>21.5347</td><td>21.075</td><td>0.016</td><td>20.35</td><td>0.03</td><td>1.940</td><td>0.014</td><td>0.352</td><td>0.020</td><td>0.612</td><td>0.020</td><td>-0.01</td><td>0.03</td></tr><tr><td>J125644+213848</td><td>194.1873</td><td>21.6468</td><td>20.897</td><td>0.014</td><td>19.90</td><td>0.02</td><td>1.755</td><td>0.010</td><td>0.808</td><td>0.016</td><td>0.979</td><td>0.016</td><td>-0.11</td><td>0.02</td></tr><tr><td>J125646+213754</td><td>194.1954</td><td>21.6317</td><td>21.352</td><td>0.018</td><td>20.72</td><td>0.04</td><td>1.768</td><td>0.016</td><td>0.314</td><td>0.023</td><td>0.562</td><td>0.023</td><td>-0.05</td><td>0.05</td></tr><tr><td>J125649+214425</td><td>194.2065</td><td>21.7404</td><td>21.212</td><td>0.016</td><td>20.01</td><td>0.02</td><td>2.093</td><td>0.012</td><td>0.787</td><td>0.019</td><td>0.993</td><td>0.019</td><td>0.09</td><td>0.02</td></tr><tr><td>J125654+215233</td><td>194.2275</td><td>21.8760</td><td>22.006</td><td>0.026</td><td>19.70</td><td>0.04</td><td>3.167</td><td>0.028</td><td>1.013</td><td>0.029</td><td>1.297</td><td>0.029</td><td>0.88</td><td>0.04</td></tr><tr><td>J125655+213319</td><td>194.2323</td><td>21.5554</td><td>21.993</td><td>0.023</td><td>21.18</td><td>0.06</td><td>1.729</td><td>0.020</td><td>0.707</td><td>0.028</td><td>0.960</td><td>0.028</td><td>-0.27</td><td>0.06</td></tr><tr><td>J125655+214633</td><td>194.2332</td><td>21.7761</td><td>20.895</td><td>0.015</td><td>20.32</td><td>0.03</td><td>1.830</td><td>0.013</td><td>0.391</td><td>0.018</td><td>0.587</td><td>0.018</td><td>-0.14</td><td>0.03</td></tr><tr><td>J125714+213914</td><td>194.3117</td><td>21.6540</td><td>19.931</td><td>0.009</td><td>19.66</td><td>0.02</td><td>1.805</td><td>0.008</td><td>0.271</td><td>0.012</td><td>0.466</td><td>0.012</td><td>-0.32</td><td>0.02</td></tr><tr><td>J125717+213702</td><td>194.3225</td><td>21.6173</td><td>21.816</td><td>0.022</td><td>20.73</td><td>0.04</td><td>1.887</td><td>0.016</td><td>0.789</td><td>0.025</td><td>0.990</td><td>0.026</td><td>-0.03</td><td>0.04</td></tr><tr><td>J125721+213816</td><td>194.3410</td><td>21.6378</td><td>22.215</td><td>0.028</td><td>19.73</td><td>0.02</td><td>3.257</td><td>0.032</td><td>0.998</td><td>0.031</td><td>1.343</td><td>0.031</td><td>1.01</td><td>0.02</td></tr><tr><td>J125722+213659</td><td>194.3418</td><td>21.6166</td><td>20.674</td><td>0.013</td><td>19.80</td><td>0.02</td><td>1.784</td><td>0.009</td><td>0.705</td><td>0.015</td><td>0.961</td><td>0.015</td><td>-0.21</td><td>0.02</td></tr><tr><td>J125723+214212</td><td>194.3472</td><td>21.7036</td><td>20.805</td><td>0.015</td><td>20.36</td><td>0.04</td><td>1.689</td><td>0.012</td><td>0.301</td><td>0.019</td><td>0.528</td><td>0.018</td><td>-0.21</td><td>0.04</td></tr><tr><td>J125723+213711</td><td>194.3480</td><td>21.6198</td><td>20.644</td><td>0.014</td><td>20.18</td><td>0.03</td><td>1.754</td><td>0.011</td><td>0.324</td><td>0.018</td><td>0.493</td><td>0.017</td><td>-0.16</td><td>0.03</td></tr></tbody></table>

(This table is available in machine-readable form.)
<table><caption>**Table 13**
Parameters of Double Gaussian Fits to Color Distributions</caption><thead><tr><th>Color</th><th>Parameter</th><th>NGC 3368</th><th>NGC 4395</th><th>NGC 4736</th><th>NGC 4826</th></tr></thead><tbody><tr><td rowspan="6">(u* - g')<sub>0</sub></td><td>μ<sub>1</sub></td><td>1.23</td><td>1.12</td><td>1.07</td><td>1.08</td></tr><tr><td>σ<sub>1</sub></td><td>0.07</td><td>0.06</td><td>0.03</td><td>0.21</td></tr><tr><td>N<sub>1</sub></td><td>12</td><td>9</td><td>7</td><td>27</td></tr><tr><td>μ<sub>2</sub></td><td>1.53</td><td>1.651</td><td>1.40</td><td>1.83</td></tr><tr><td>σ<sub>2</sub></td><td>0.05</td><td>0.001</td><td>0.31</td><td>0.10</td></tr><tr><td>N<sub>2</sub></td><td>3</td><td>1</td><td>18</td><td>3</td></tr><tr><td rowspan="6">(u* - i')<sub>0</sub></td><td>μ<sub>1</sub></td><td>1.97</td><td>1.85</td><td>1.86</td><td>1.87</td></tr><tr><td>σ<sub>1</sub></td><td>0.13</td><td>0.10</td><td>0.16</td><td>0.11</td></tr><tr><td>N<sub>1</sub></td><td>11</td><td>7</td><td>16</td><td>25</td></tr><tr><td>μ<sub>2</sub></td><td>2.54</td><td>2.97</td><td>2.66</td><td>2.98</td></tr><tr><td>σ<sub>2</sub></td><td>0.12</td><td>0.21</td><td>0.30</td><td>0.32</td></tr><tr><td>N<sub>2</sub></td><td>4</td><td>3</td><td>9</td><td>5</td></tr><tr><td rowspan="6">(g' - r')<sub>0</sub></td><td>μ<sub>1</sub></td><td>...</td><td>...</td><td>0.49</td><td>0.61</td></tr><tr><td>σ<sub>1</sub></td><td>...</td><td>...</td><td>0.07</td><td>0.27</td></tr><tr><td>N<sub>1</sub></td><td>...</td><td>...</td><td>23</td><td>29</td></tr><tr><td>μ<sub>2</sub></td><td>...</td><td>...</td><td>1.24</td><td>1.946</td></tr><tr><td>σ<sub>2</sub></td><td>...</td><td>...</td><td>0.08</td><td>0.001</td></tr><tr><td>N<sub>2</sub></td><td>...</td><td>...</td><td>2</td><td>1</td></tr><tr><td rowspan="6">(g' - i')<sub>0</sub></td><td>μ<sub>1</sub></td><td>0.78</td><td>0.72</td><td>0.75</td><td>0.82</td></tr><tr><td>σ<sub>1</sub></td><td>0.13</td><td>0.06</td><td>0.10</td><td>0.24</td></tr><tr><td>N<sub>1</sub></td><td>14</td><td>7</td><td>23</td><td>28</td></tr><tr><td>μ<sub>2</sub></td><td>1.539</td><td>1.66</td><td>1.72</td><td>1.81</td></tr><tr><td>σ<sub>2</sub></td><td>0.001</td><td>0.49</td><td>0.55</td><td>0.46</td></tr><tr><td>N<sub>2</sub></td><td>1</td><td>3</td><td>2</td><td>2</td></tr><tr><td rowspan="6">(g' - K<sub>s</sub>)<sub>0</sub></td><td>μ<sub>1</sub></td><td>0.63</td><td>0.50</td><td>0.79</td><td>0.71</td></tr><tr><td>σ<sub>1</sub></td><td>0.24</td><td>0.13</td><td>0.38</td><td>0.28</td></tr><tr><td>N<sub>1</sub></td><td>12</td><td>7</td><td>23</td><td>26</td></tr><tr><td>μ<sub>2</sub></td><td>1.28</td><td>2.39</td><td>2.87</td><td>2.45</td></tr><tr><td>σ<sub>2</sub></td><td>0.43</td><td>0.67</td><td>0.35</td><td>0.53</td></tr><tr><td>N<sub>2</sub></td><td>3</td><td>3</td><td>2</td><td>4</td></tr><tr><td rowspan="6">(r' - i')<sub>0</sub></td><td>μ<sub>1</sub></td><td>...</td><td>...</td><td>0.27</td><td>0.24</td></tr><tr><td>σ<sub>1</sub></td><td>...</td><td>...</td><td>0.05</td><td>0.04</td></tr><tr><td>N<sub>1</sub></td><td>...</td><td>...</td><td>24</td><td>24</td></tr><tr><td>μ<sub>2</sub></td><td>...</td><td>...</td><td>1.038</td><td>0.28</td></tr><tr><td>σ<sub>2</sub></td><td>...</td><td>...</td><td>0.001</td><td>0.09</td></tr><tr><td>N<sub>2</sub></td><td>...</td><td>...</td><td>1</td><td>6</td></tr></tbody></table>

solid red lines are Gaussians with the expected characteristics of the luminosity functions: mean = 22.0 mag, σ = 1.2 mag for NGC 3368; mean = 20.1 mag, σ = 0.9 mag for NGC 4395; mean = 20.4 mag, σ = 1.2 mag for NGC 4736; mean = 21.2 mag, and σ = 1.1 mag for NGC 4826. The curves have been scaled such that their integrals are equal to the expected GCCs for each galaxy, respectively, 35, 15, 46, and 69, for NGC 3368, NGC 4395, NGC 4736, and NGC 4826 (see Section 7 and Table 10).

We also take the opportunity here to stress that we do not use the extrapolation over the luminosity function to derive the total number of globular clusters in the system. We perform the completeness and GCLF corrections implicitly, as we explain in the next section.

# 7. Total Number of GCs

## 7.1. Correction for Incomplete Spatial Coverage

Given the small number of clusters detected, and the lack of constraints in the centermost regions of the galaxies due to confusion, here we derive the total number of GCs for each

galaxy through a comparison with the GC system of the MW. The procedure was introduced by Kissler-Patig et al. (1999), who applied it to edge-on spirals; its results are consistent with those from a fit to the radial number density, when both methods can be applied to the same object (Kissler-Patig et al. 1999; Goudfrooij et al. 2003). González-Lópezlira et al. (2017) adapted it for use on any galaxy, regardless of orientation. With this method, the correction for incomplete spatial coverage implicitly takes care of the completeness correction and the extrapolation over the luminosity function.

In brief, the method consists in estimating the number of GCs that one would detect if the MW were at the distance and orientation of the galaxy of interest, and were observed with the same instrument and to the same depth. By comparison, the total number of GCs would be

$$N_{GC} = N_{GC}(\text{MW}) \frac{N_{\text{obs}}}{N_{\text{FOV}}}. \qquad (3)$$

$N_{GC}(\text{MW})$ is the total number of clusters in the MW, including objects invisible to us behind the bulge; $N_{\text{obs}}$ is the number of clusters observed in the target galaxy, and $N_{\text{FOV}}$ is the number
<table><caption>Table 14
Single Gaussian Fits to the Colors of the GC Systems of the MW and M31</caption><thead><tr><th rowspan="2">System</th><th colspan="2">(u* - g')</th><th colspan="2">(u* - g')<sub>0</sub></th><th colspan="2">(u* - i')</th><th colspan="2">(u* - i')<sub>0</sub></th><th colspan="2">(g' - r')</th><th colspan="2">(g' - r')<sub>0</sub></th><th colspan="2">(g' - i')</th><th colspan="2">(g' - i')<sub>0</sub></th><th colspan="2">(g' - K<sub>s</sub>)</th><th colspan="2">(g' - K<sub>s</sub>)<sub>0</sub></th><th colspan="2">(r' - i')</th><th colspan="2">(r' - i')<sub>0</sub></th></tr><tr><th>μ</th><th>σ</th><th>μ</th><th>σ</th><th>μ</th><th>σ</th><th>μ</th><th>σ</th><th>μ</th><th>σ</th><th>μ</th><th>σ</th><th>μ</th><th>σ</th><th>μ</th><th>σ</th><th>μ</th><th>σ</th><th>μ</th><th>σ</th><th>μ</th><th>σ</th></tr></thead><tbody><tr><td>M31</td><td>1.30</td><td>0.26</td><td>1.05</td><td>...</td><td>2.29</td><td>0.53</td><td>1.72</td><td>...</td><td>0.64</td><td>0.17</td><td>0.45</td><td>...</td><td>1.00</td><td>0.28</td><td>0.68</td><td>...</td><td>1.24</td><td>0.61</td><td>0.56</td><td>...</td><td>0.36</td><td>0.12</td><td>0.23</td><td>...</td></tr><tr><td>MW</td><td>...</td><td>...</td><td>1.01</td><td>0.15</td><td>...</td><td>...</td><td>1.67</td><td>0.26</td><td>...</td><td>...</td><td>0.45</td><td>0.09</td><td>...</td><td>...</td><td>0.66</td><td>0.12</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>0.21</td><td>0.03</td></tr></tbody></table>

Note. We remind the reader that colors using the new *u*\* filter are ~0.2 mag redder. The colors of the M31 GCs were transformed by González-Lópezlira et al. (2017) to the previous CFHT system.
<figure><img src="image_22.png" /><figcaption>**Figure 12.** *K*<sub>s</sub>-band luminosity functions of the GCCs. Top left: NGC 3368; top right: NGC 4395; bottom left: NGC 4736; bottom right: NGC 4826. Histograms: number of detected objects; *solid red lines*: expected Gaussian GCLFs (see Table 4 and Section 7).</figcaption></figure>

of objects recovered in the artificial observation of the MW. We take $N_{GC}$ (MW) = 160 ± 10 (Harris et al. 2014).

In order to estimate $N_{FOV}$ we use the catalog by Harris (1996), which provides X, Y, Z coordinates for 144 MW GCs. The origin of this coordinate system is at the position of the Sun; the X-axis points toward the Galactic Center, the Y axis points in the direction of Galactic rotation, and Z is perpendicular to the Galactic plane. We define a new coordinate system, X'YZ, with origin in the Galactic Center, assuming a Galactocentric distance for the Sun $R_0 = 8.34$ kpc (Reid et al. 2014). For galaxies that are not edge-on, we first rotate the MW GC system in 3D by the inclination angle $i$ of the target galaxy (i.e., 46°.2 for NGC 3368, 33.7 for NGC 4395, 35.6 for NGC 4736 and 57.5 for NGC 4826) with respect to either the X' or Y-axis, then project it on the plane of the sky; the rotated pairs ($X'_{rot,X'}$, $Y_{rot,X'}$), ($X'_{rot,Y}$, $Y_{rot,Y}$), where the subscript indicates the Galactic axis of 3D rotation, are directly the projected coordinates. The easiest way to place the projected system on the WIRCam FOV is to then apply a rotation around the line of sight equal to the PA of the target galaxy (5° for NGC 3368, 147° for NGC 4395, and 115° for both NGC 4736 and NGC 4826, always north through east).

To ensure a fair comparison with the MW, we then mask out elliptical regions in the centers of the galaxies. For NGC 4395, NGC 4736, and NGC 4826, they have the same axis ratios [i.e., $\cos(i)$] and PA as the galaxies. Their semimajor axes are equal to, respectively, 98.9, 168.3, and 150, or 0.25 $R_{25}$ for NGC 4395, and 0.5 $R_{25}$ for both NGC 4736 and NGC 4826. For NGC 3368, we exclude an ellipse with an axis ratio 0.69 and $PA = 155^\circ$, like the region in the galaxy with the highest surface brightness, and semimajor axis equal to 85.6, or 0.375 $R_{25}$ (de Vaucouleurs et al. 1991). These are the areas most affected by confusion (see Section 4 and Figures 2 and 3). We also need to set detection limits for these simulated observations. To this end, we combine the real limiting magnitude of the $K_s$ images, with the difference between the $K_s$ and V bands TO magnitudes; the results are $V = 22.5, 21.6, 23.4, \text{and } 23.1$ mag, respectively, for NGC 3368, NGC 4395, NGC 4736, and NGC 4826. Finally, the V mag of each MW cluster is corrected for the Galactic extinction given in the Harris (1996) catalog, and subsequently dimmed by the foreground extinction in the direction of each galaxy, i.e., 0.069 mag (NGC 3368), 0.047 mag (NGC 4395), 0.049 mag (NGC 4736), and 0.113 mag (NGC 4826), respectively.
<figure><img src="image_23.png" /><figcaption>**Figure 13.** MW GC system, at the distance and orientation of studied galaxies, projected coordinates $+X_{\text{proj}}$, $+Y_{\text{proj}}$. Top: NGC 3368; bottom: NGC 4395. Left: 3D rotation about the Galactic X'-axis before projection on the plane of the sky. Right: 3D rotation about Galactic Y-axis. Solid black line: mask; red crosses: sources visible in the WIRCam FOV; yellow crosses: recovered in the simulation, but outside of the WIRCam FOV; black crosses: masked-out GCs.</figcaption></figure>

For every galaxy, there are four possible orientations of the FOV and mask that preserve its alignment; they can be seen as mirror reflections of the projected coordinates ($+X_{\text{proj}}$, $+Y_{\text{proj}}$; $+X_{\text{proj}}$, $-Y_{\text{proj}}$; $-X_{\text{proj}}$, $+Y_{\text{proj}}$; $-X_{\text{proj}}$, $-Y_{\text{proj}}$) with two sets of four pairs, i.e., one for each of the two possible rotation axes).

We show in Figures 13 and 14 the results of the artificial observations of the MW GC system, for the rotation around the X' (left) and Y (right) axes, respectively, and $+X_{\text{proj}}$, $+Y_{\text{proj}}$. Results for NGC 3368 and NGC 4395 are displayed, respectively, in the top and bottom panels of Figure 13, whereas outcomes for NGC 4736 and NGC 4826 are presented in the top and bottom panels of Figure 14. Angular distances in arcsec are measured relative to the centers of the galaxies, with the horizontal axis increasing in the direction of decreasing R.A. The ellipses delineated with the black solid line mark the outer edges of the masks; the red crosses are clusters visible in the WIRCam FOV, while sources that have been masked out are represented by black crosses.

In the case of NGC 3368, for the four realizations rotating around the X'-axis we detect, respectively, 50 ($+X_{\text{proj}}$, $+Y_{\text{proj}}$), 50 ($+X_{\text{proj}}$, $-Y_{\text{proj}}$), 50 ($-X_{\text{proj}}$, $+Y_{\text{proj}}$), and 50 ($-X_{\text{proj}}$, $-Y_{\text{proj}}$) sources; for rotating around the Y-axis, the numbers are 46, 46, 46, and 46. With these numbers, there would be, on average, $48 \pm 2$ simulated clusters visible in NGC 3368, and Equation (3) gives a total $N_{\text{GC}} = 50 \pm 13$. This error is statistical only; it includes errors in the assumed number of total GCs in the MW, Poisson errors in the observed number of GCCs in NGC 3368, and Poisson errors in the number of simulated clusters in the WIRCam FOV. To this error, we add potential systematics. Errors in the distance to NGC 3368 result in uncertainties in the detection limiting magnitude, and in the effective areas of the galaxy covered by the FOV and excluded by the mask. For the given uncertainty in the distance to NGC 3368 ($^{+1.1}_{-1.0}$ Mpc), $N_{\text{GC}}$ would vary by +21/-14 if the random and systematic errors are added in quadrature. Another potential concern is that the MW and NGC 3368 likely have a different number of obscured clusters. To account for this
<figure><img src="image_24.png" /><figcaption>**Figure 14.** MW GC system, at the distance and orientation of studied galaxies, projected coordinates +X<sub>proj</sub>, +Y<sub>proj</sub>. Top: NGC 4736; bottom: NGC 4826. Symbols as in Figure 13.</figcaption></figure>

possibility, we include an additional uncertainty of 25% (±12). We end up with $N_{GC} = 50_{-19}^{+24}$, or $50 \pm 13_{-13}^{+20}$, with the first error statistical and the second, systematic (from distance and differential obscuration).

For NGC 4395, rotations around X' yield 80, 80, 80, 79; for the Y-axis, the results are 73, 71, 75, 71. Therefore, the average simulated clusters visible would be 76 ± 4, and a total $N_{GC} = 21 \pm 5$ from Equation (3). The distance uncertainty of ± 0.4 Mpc results in an additional error of ± 1 in $N_{GC}$. Including a 25% (±6) uncertainty for differential obscuration, the census for NGC 4395 is $N_{GC} = 21 \pm 8$, or $21 \pm 5$ ± 6.

For NGC 4736, we find, respectively, 62, 62, 62, and 61 for rotations around X'; for the Y-axis, the results are 60, 60, 61, and 60. Hence, the average simulated clusters visible would be 61 ± 1, and a total $N_{GC} = 66 \pm 14$ from Equation (3). The distance uncertainty of ± 0.4 Mpc results in an additional error of +6/−3 in $N_{GC}$. Including a 25% (±16) uncertainty for differential obscuration, the tally for NGC 4736 is $N_{GC} = 66_{-21}^{+22}$, or $66 \pm 14_{-16}^{+17}$.

Finally, for NGC 4826, rotations around X' give 49, 49, 50, and 49 detections; for the Y-axis, the results are 48, 47, 47, and 48. Accordingly, the average simulated clusters visible would be 48 ± 1, and a total $N_{GC} = 99 \pm 19$ from Equation (3). The distance uncertainty of ± 0.7 Mpc results in an additional error of +20/−10 in $N_{GC}$. Including a 25% (±25) uncertainty for differential obscuration, the count for NGC 4826 is $N_{GC} = 99_{-33}^{+37}$, or $99 \pm 19_{-21}^{+32}$.

We make a final, downward, correction of 30% to these numbers, based on the percentage contamination found for NGC 4258 by González-Lópezlira et al. (2019), from spectroscopic observations of its GC candidates. Hence, we get $N_{GC} = 35_{-16}^{+20}$ for NGC 3368, $N_{GC} = 15 \pm 7$ for NGC 4395, $N_{GC} = 46 \pm 18$ for NGC 4736, and $N_{GC} = 69_{-28}^{+31}$ for NGC 4826.

The correlation of $N_{GC}$ with virial mass provides an additional sanity check, at least for NGC 4736 and NGC 4826. From their rotation curves (respectively, Jałocha et al. 2008 and Saburova et al. 2009), both galaxies are quite light, with total halo masses ~4 × 10<sup>10</sup> M<sub>☉</sub>; their log $N_{GC}$ ~ 1.7
<figure><img src="image_25.png" /></figure>

**Figure 15.** BCES fits to elliptical galaxies. Top: log *M*, vs. log *N*<sub>GC</sub>; bottom: log *N*<sub>GC</sub> vs. log *M*. Left: no additional scatter; center: additional $\epsilon_y$; right: $\epsilon_y$ and $\epsilon_x$. Solid black lines: best fits; translucent gray lines: range of possible solutions. Solid (red) and open (green) circles represent, respectively, elliptical and lenticular galaxies in the sample of Harris et al. (2014), reclassified as per Sahu et al. (2019b); the blue crosses are the spiral galaxies M 31, M 81, and M 104. Solid blue star: Milky Way. Solid light olive star: NGC 256, with correct number of GCs. Solid purple star: NGC 4258 (González-Lópezlira et al. 2017, 2019); Solid violet, light brown, dark brown, and light blue stars: NGC 3368, NGC 4395, NGC 4736, and NGC 4826, respectively (this work). For NGC 3368, NGC 4395, NGC 4258, NGC 4736, and NGC 4826, random errors of *N*<sub>GC</sub> are shown by small bars, while systematic errors, added in quadrature, are illustrated by the large bars. Errors for the MW are smaller than the blue star.

is fully consistent with the larger dispersion of the correlation at low masses (see Burkert & Forbes 2020, their Figure 1).<fnref n="14" />

**8. Specific Frequency, and the N<sub>GC</sub> versus M. Relation**

From the distance to NGC 3368 and the values of $B_{T,0} = 9.80 \pm 1.5$ mag and $(B-V)_{T,0} = 0.79 \pm 0.01$ given in de Vaucouleurs et al. (1991), we find $M_V = -21.08 \pm 0.36$ mag, and a specific frequency $S_N = N_{GC} \times 10^{0.4 \times [M_V+15]} = 0.13 \pm 0.06$, if we consider random errors only, and $S_N = 0.13 \pm 0.07$, if we include the uncertainty in the number of obscured clusters.<fnref n="15" /> For NGC 4395, de Vaucouleurs et al. (1991) report $B_{T,0} = 10.57 \pm 0.54$ mag and $(B-V)_{T,0} = 0.46 \pm 0.08$ mag; this results in $M_V = -18.06 \pm 0.59$ mag and $S_N = 0.90 \pm 0.55$, with statistical errors only, and $S_N = 0.90 \pm 0.65$ if the uncertainty in the number of obscured clusters is included. For NGC 4736, the values are $B_{T,0} = 8.75 \pm 0.13$ mag and $(B-V)_{T,0} = 0.72 \pm 0.01$ mag, from which $M_V = -20.46 \pm 0.21$ mag, and $S_N = 0.30 \pm 0.10$, with random errors only, and $S_N = 0.30 \pm 0.13$, if we include systematics. For NGC 4826, de

Vaucouleurs et al. (1991) give $B_{T,0} = 8.82 \pm 0.24$ mag and $(B-V)_{T,0} = 0.71 \pm 0.01$ mag; $M_V = -21.21 \pm 0.32$ mag, and $S_N = 0.23 \pm 0.09$ or $S_N = 0.23 \pm 0.11$, respectively, without and with the uncertainty in the number of obscured clusters. For comparison, the Milky Way has $S_N = 0.5 \pm 0.1$ (Ashman & Zepf 1998).

Before placing our four galaxies on the *N*<sub>GC</sub>—*M*. correlation, we redetermine it in the Appendix for the sample in Harris et al. (2014), plus NGC 4258 and the spirals in this paper, albeit with updated galaxy classifications from Sahu et al. (2019b).

Figures 15 and 16, and Table 17 display the Bivariate Correlated Errors and Intrinsic Scatter (BCES, Akritas & Bershady 1996) fits for, respectively, ellipticals and spirals. The black solid lines represent the best fits, and the translucent gray lines illustrate the range of possible solutions. Each gray line corresponds to a realization of the fit, obtained by adding a random variable to each the slope *β* and the intercept *α* of the best fit, drawn from the normal distributions of errors, $\sigma_β$ and $\sigma_α$. Since 1,000 realizations were obtained for each fit, roughly 50 gray lines (5% of the total 1,000) belong to fits separated by $2\sigma$ or more from the best values. In the figures, ellipticals appear as solid red circles and lenticulars as solid dark green ones; the spirals M 31, M 81, and M 104 are the blue crosses. The locations of the MW, NGC 253, NGC 3378, NGC 4258, NGC 4395, NGC 4736, and NGC 4826 are shown as solid stars, respectively, blue, light olive, violet, purple, light brown, dark brown, and light blue. We correct the position of NGC 253, whose number of GC had been read

<footnote n="14">¹⁴ We note here that, from their analysis of the NGC 4736 rotation curve, Jalocha et al. (2008) conclude that it violates the sphericity condition at large radii (i.e., mass ceases to increase with distance). Hence, the galaxy would not have a massive spherical halo and its mass distribution would be best fit with a disk model.</footnote>

<footnote n="15">¹⁵ The systematic error in the distance basically cancels out, because the absolute magnitude of the galaxy also changes.</footnote>
<figure><img src="image_26.png" /><figcaption>**Figure 16.** BCES fits to spiral galaxies. Top: log M. vs. log N<sub>GC</sub>; bottom: log N<sub>GC</sub> vs. log M. Left: no additional scatter; center: additional ϵ<sub>y</sub>; right: ϵ<sub>y</sub> and ϵ<sub>x</sub>. Lines and symbols as in Figure 15.</figcaption></figure>

erroneously by Harris et al. (2014). Indeed, Olsen et al. (2004) report N<sub>GC</sub> = 21, but with a completeness of 0.21, i.e., they really implied N<sub>GC</sub> ~ 100. They also give a specific frequency in the K-band S<sub>N,K</sub> = N<sub>GC</sub> × 10<sup>0.4</sup> × [M<sub>K+18</sub>] = 0.30 ± 0.07, or N<sub>GC</sub> = 92 ± 21. Previously, Blecha (1986) had found N<sub>GC</sub> = 80 ± 40 for NGC 253.

The Figures show M. versus N<sub>GC</sub> in the top row; from left to
right, fits without extra “cosmic” scatter, fits with additional ϵ<sub>y</sub>,
and fits with additional intrinsic scatter in both x and y (see
Appendix). The bottom row illustrates N<sub>GC</sub> versus M., only for
fits with additional ϵ<sub>y</sub>, which are not symmetrical. We find that
the slope of the correlation is roughly 60% steeper for spirals
than for ellipticals (see Table 17).

9. The *M.* versus *M.* Correlation from NGC

In order to investigate whether the discrepant slopes of the M.
versus N<sub>GC</sub> correlations for elliptical and spiral galaxies reflect the
slopes between M. and M*, we derive M* from its correlation with
N<sub>GC</sub>, for the ellipticals and LTGs in our sample. Hudson et al.
(2014) have obtained log M<sub>GC</sub> versus log M* for the 422 galaxies
(248 ellipticals, 93 lenticulars, and 81 spirals and irregulars) in the
Harris et al. (2013) sample, where M<sub>GC</sub> is the total mass of the GC
system of a galaxy. In actuality, N<sub>GC</sub> is the observable, while M<sub>GC</sub>
has the advantage of a smaller sensitivity to undetected faint GCs,
since 99% of the total GC system mass is roughly contained in
the clusters brighter than 1 mag below the GCLF turnover
(González-Lópezlira et al. 2017).<sup>16</sup> Hudson et al. (2014) assume

a relation between total number and total mass of GC log
N<sub>GC</sub> = 0.90 × M<sub>GC</sub> - 4.65. The relations between log M<sub>GC</sub> or
N<sub>GC</sub> and M* are broken power laws, with log M<sub>GC</sub> = 0.53 ×
log M* + 2.00, log M* = 2.11 × log N<sub>GC</sub> + 5.99, for lower
galaxy masses, and M<sub>GC</sub> = 1.60 × log M* - 9.22, log
M* = 0.69 × log N<sub>GC</sub> + 8.96, for higher galaxy masses, with
the inflection point at log M*/M⊙ ~ 10.4, log N<sub>GC</sub> ~ 2.1.

Figure 17 and Table 19 show the BCES fits to M. versus M_\* for, respectively, ellipticals (red-dashed and pink translucent lines) and spirals (black solid and gray translucent lines). Their slopes are, roughly, 1.47 ± 0.16 and 1.22 ± 15, respectively, i.e., the same within the errors, with the best fits as close or closer than those found by Reines & Volonteri (2015), also less steep for spirals than for ellipticals, and with an offset of ~0.2–0.3 dex at log M_\*/M_⊙ = 10. A fit to both ellipticals and spirals together (Figure 18, Table 19) yields a slope of ~1.5 ± 0.15, and a cosmic scatter ϵ ~ 0.4, of the order of half that found by van den Bosch (2016).

10. Discussion and Conclusions

We have now successfully applied the u*i'Ks* diagram GC selection technique (Muñoz et al. 2014) to five spiral galaxies: NGC 4258 (González-Lópezlira et al. 2017), NGC 3368, NGC 4395, NGC 4736, and NGC 4826 (this work). We complement the *u*i'*Ks* plot with GCC structural parameters; this combination of techniques constitutes a very efficient tool to study GC systems of nearby galaxies. The sample of spirals with measurements of both the GC system and the SMBH mass has now been increased to 10, or 100% more than before we embarked on this project. Our full spiral working sample

<footnote n="16">16 The trends of N<sub>GC</sub> with total K-band luminosity, a good tracer of mass, are remarkably similar for all galaxy types.</footnote>
<figure><img src="image_27.png" /><figcaption>**Figure 17.** BCES fits to elliptical and spiral galaxies. Top: log M* vs. log M*; bottom: log M* vs. log M*. Left: no additional scatter; center: additional $\epsilon_y$; right: $\epsilon_y$ and $\epsilon_x$. Dashed red lines: best fits for ellipticals; translucent pink lines: range of possible solutions for ellipticals. Solid black lines: best fits for spirals; translucent gray lines: range of possible solutions for spirals. Symbols as in Figure 15.</figcaption></figure>

comprises all galaxies observable from the northern hemisphere with a direct measurement of their central SMBH mass, and within 16 Mpc, regardless of orientation in the sky, i.e., a total of nine; so far, we have analyzed the five for which we have complete $u^*$, $i'$, and $K_s$ data. We have also taken the opportunity to correct the position of NGC 253 in the M* versus the NGC diagram.

The spiral galaxies for which we have determined NGC, as well as NGC 253, seem to have undergone few major mergers. Like the MW, they all belong to small groups, i.e., Leo I, Canes I, Canes II, and Sculptor. They also have pseudobulges, except for NGC 4395, which is a bulgeless, purely disk galaxy. Additionally, the GC systems of both NGC 4258 and NGC 253 seem to lie in rotating disks (González-Lópezlira et al. 2019; Olsen et al. 2004). Together with simulations (e.g., Kravtsov & Gnedin 2005; Agertz et al. 2009; Kruijssen 2015) and observations of clumpy star-forming disks at $z \sim 2$ (e.g., Cowie et al. 1995; Guo et al. 2015), the discovery of GC disks in the local universe supports the idea that GCs probably formed in disks, and came to populate halos through multiple mergers (e.g., Schweizer 1987; Ashman & Zepf 1992; Côté et al. 1998).

We have investigated the correlation between M* and NGC, for both ellipticals and LTG. We find log M* ∝ (1.01 ± 0.13) log NGC for ellipticals, and log M* ∝ (1.64 ± 0.24) log NGC for LTG, in both cases including cosmic scatter in both variables. Hence, they are not consistent with each other, and the slope of the correlation for LTG, in contrast with that for ellipticals, is not linear. This, together with the likely scarcity of major interactions for LTG, may argue in favor of statistical

convergence through mergers as the cause of the correlation in elliptical galaxies.

On the other hand, we have derived M*, for the ellipticals and LTG in our sample, from its relation with NGC, and measured the correlations with M*. Far from mirroring the discrepant slopes of the M* versus NGC fits, they are quite similar, i.e., M* ∝ (1.48 ± 0.18) log M* for ellipticals, and M* ∝ (1.21 ± 0.16) log M* for LTG, with a small offset of ~0.2-0.3 dex at log M*/M⊙ = 10, in both cases including cosmic scatter in both variables. These results are in line with those obtained by Reines & Volonteri (2015) and Simmons et al. (2017), and argue for a mostly nonmerger driven M* growth, and galaxy black hole coevolution through secular processes, like calm accretion and feedback. (Simmons et al. 2017; Martin et al. 2018; Smethurst et al. 2019).

Researching GC systems and scaling relations in spirals is very important. While these relations in ellipticals seem to be showing the end result of star formation and galaxy assembly, in lower mass galaxies we may be witnessing the fingerprints of the individual steps of the process.

R.A.G.L. acknowledges the financial support of DGAPA, UNAM, project IN108518. R.A.G.L. and L.L.N. acknowledge the support of CONACYT, Mexico, project A1-S-8263. L.L. acknowledges the support of DGAPA PAPIIT grants IN112417 and IN112820, CONACYT-AEM grant 275201, and CONACYT-CF grant 263356. Y.O.-B. acknowledges support from FONDECYT Postdoctoral Fellowship project No. 3210442. We would like to thank the anonymous referee,
<figure><img src="image_28.png" /><figcaption>Figure 18. BCES fits to E+S galaxies. Top: log M. vs. log M*, bottom: log M* vs. log M. Left: no additional scatter; center: additional $\epsilon_y$; right: $\epsilon_y$ and $\epsilon_x$. Lines and symbols as in Figure 15.</figcaption></figure>

for their pertinent criticisms and suggestions, and Daniel Díaz-González, for his help with the routine we used to calculate two-Gaussian fits.

This research has made use of the VizieR catalog access tool, CDS, Strasbourg, France (DOI: 10.26093/cds/vizier). The original description of the VizieR service was published in A&AS 143, 23.

*Facility:* CFHT.

*Software:* DAOPHOT (Stetson 1987, 2011), GALSIM (Rowe et al. 2015), IRAF (Tody 1986, 1993), ISHAPE (Larsen 1999), Matplotlib (Hunter 2007), NumPy (Harris et al. 2020), PSFEx (Bertin 2011), SAOImage (Joye & Mandel 2003), SciPy (Virtanen et al. 2020), SExtractor (Bertin & Arnouts 1996), SuperMongo (Lupton & Monger 1991), TOPCAT (Taylor 2005).

## Appendix

We determine the M. versus N<sub>GC</sub> correlation for the sample in Table 15. We use the galaxy types in Sahu et al. (2019b; Column 3), which are based on the classification grid of Graham (2019). We obtain separate fits for ellipticals (E), lenticulars (L), and spirals (S), with the FITEXY regression routines (Press et al. 1992), as modified by Tremaine et al. (2002) and Novak et al. (2006) to allow for the addition of intrinsic (or cosmic) scatter in the parameters. Summarizing, if data pairs $(x_i, y_i)$ with individual measurement uncertainties

($\sigma_{x,i}$, $\sigma_{y,i}$) are related by the linear equation $y = \alpha + \beta x$, the expression to minimize is

$$ \chi^2 = \sum \frac{y_i - \alpha - \beta(x_i - \langle x \rangle)^2}{(\sigma_{y,i}^2 + \epsilon_y^2) + \beta^2(\sigma_{x,i}^2 + \epsilon_x^2)}, \quad (A1) $$

where $\langle x \rangle \equiv N^{-1}\sum_{i=1}^{N}x_i$ is the sample mean, and $\epsilon_x$ and $\epsilon_y$ represent the additional intrinsic scatter over the formal measurement errors. If additional cosmic scatter indeed exists, as implied by a reduced $\chi^2 > 1$, the epsilons can be increased until $\chi^2 = 1$. We searched for solutions both assuming $\epsilon_x = 0$, with all additional scattering in y, and distributing the potential supplemental scattering between $\epsilon_x$ and $\epsilon_y$. In the absence of other constraints, when epsilons are added simultaneously to the M. and N<sub>GC</sub> values, their squares are kept in the same ratio observed when only $\epsilon_y$ is appended to either variable.

Correlation solutions with the FITEXY routines are shown in Table 16. We also carry out fits with the BCES method by Akritas & Bershady (1996), with results for the bisector line of the forward ($Y|X$) and inverse ($X|Y$) regressions presented in Table 17. The solutions have the form $Y = \alpha + \beta(X - \langle x \rangle)$. To note: lenticular galaxies do show a correlation.

We perform analogous fits to M. versus M*, for E, S, and E +S galaxies. The solutions are listed in Tables 18 and 19.
<table><caption>**Table 15**
Properties of Galaxies Used in the Fits</caption><thead><tr><th>Galaxy</th><th>Type1</th><th>Type2</th><th>d (Mpc)</th><th>N<sub>GC</sub></th><th>Δ N<sub>GC</sub></th><th>log M<sub>☉</sub>/M<sub>☉</sub></th></tr></thead><tbody><tr><td>NGC 221</td><td>E2</td><td></td><td>0.8</td><td>10</td><td></td><td>6.46(+0.08, -0.10)</td></tr><tr><td>NGC 4486A</td><td>E2</td><td>E</td><td>15.6</td><td>21</td><td></td><td>7.15(+0.13, -0.11)</td></tr><tr><td>NGC 821</td><td>E4</td><td>E</td><td>24.1</td><td>320</td><td>40</td><td>8.23(+0.16, -0.25)</td></tr><tr><td>NGC 1332</td><td>S0</td><td>ES</td><td>22.9</td><td>1000</td><td>500</td><td>9.17(+0.06, -0.06)</td></tr><tr><td>NGC 1399</td><td>E1</td><td>E</td><td>20.0</td><td>6625</td><td>1180</td><td>8.69(+0.06, -0.07)</td></tr><tr><td>NGC 3377</td><td>E5</td><td>E</td><td>11.2</td><td>266</td><td>66</td><td>8.25(+0.19, -0.29)</td></tr><tr><td>NGC 3379</td><td>E1</td><td>E</td><td>10.6</td><td>270</td><td>68</td><td>8.04(+0.22, -0.26)</td></tr><tr><td>NGC 3414</td><td>S0</td><td>E</td><td>25.2</td><td>400</td><td>200</td><td>9.40(+0.06, -0.08)</td></tr><tr><td>NGC 3585</td><td>S0</td><td>E</td><td>20.0</td><td>300</td><td>100</td><td>8.51(+0.15, -0.13)</td></tr><tr><td>NGC 3607</td><td>E</td><td>E</td><td>22.8</td><td>600</td><td>200</td><td>8.15(+0.10, -0.15)</td></tr><tr><td>NGC 3608</td><td>E2</td><td>E</td><td>22.9</td><td>450</td><td>200</td><td>8.67(+0.09, -0.10)</td></tr><tr><td>NGC 3842</td><td>E</td><td>E</td><td>98.4</td><td>9850</td><td>3900</td><td>9.99(+0.11, -0.13)</td></tr><tr><td>NGC 4261</td><td>E2</td><td>E</td><td>31.6</td><td>530</td><td>100</td><td>8.71(+0.08, -0.09)</td></tr><tr><td>NGC 4291</td><td>E2</td><td>E</td><td>26.2</td><td>1200</td><td>600</td><td>8.98(+0.10, -0.18)</td></tr><tr><td>NGC 4350</td><td>S0</td><td>EBS</td><td>15.4</td><td>196</td><td>60</td><td>8.74(+0.10, -0.10)</td></tr><tr><td>NGC 4374</td><td>E1</td><td>E</td><td>18.4</td><td>4300</td><td>1200</td><td>8.96(+0.05, -0.04)</td></tr><tr><td>NGC 4472</td><td>E2</td><td>E</td><td>16.3</td><td>7800</td><td>850</td><td>9.26(+0.12, -0.18)</td></tr><tr><td>NGC 4473</td><td>E5</td><td>E</td><td>15.7</td><td>376</td><td>97</td><td>7.95(+0.19, -0.29)</td></tr><tr><td>NGC 4486</td><td>E0</td><td>E</td><td>16.1</td><td>13300</td><td>2000</td><td>9.77(+0.03, -0.03)</td></tr><tr><td>NGC 4552</td><td>E1</td><td>E</td><td>15.3</td><td>1200</td><td>250</td><td>8.68(+0.04, -0.05)</td></tr><tr><td>NGC 4621</td><td>E4</td><td>E</td><td>18.3</td><td>800</td><td>355</td><td>8.60(+0.06, -0.07)</td></tr><tr><td>NGC 4649</td><td>E2</td><td>E</td><td>16.8</td><td>4745</td><td>1100</td><td>9.63(+0.09, -0.11)</td></tr><tr><td>NGC 4697</td><td>E6</td><td>E</td><td>11.7</td><td>229</td><td>50</td><td>8.28(+0.08, -0.10)</td></tr><tr><td>NGC 4889</td><td>E</td><td>E</td><td>103.2</td><td>11000</td><td>1340</td><td>10.32(+0.25, -0.54)</td></tr><tr><td>NGC 5846</td><td>E0</td><td>E</td><td>24.9</td><td>4700</td><td>1200</td><td>9.04(+0.07, -0.09)</td></tr><tr><td>NGC 6086</td><td>E</td><td>E</td><td>132.0</td><td>4584</td><td>1362</td><td>9.56(+0.16, -0.16)</td></tr><tr><td>NGC 7768</td><td>E</td><td>E</td><td>112.8</td><td>3000</td><td>1300</td><td>9.11(+0.15, -0.27)</td></tr><tr><td>IC 1459</td><td>E4</td><td>E</td><td>29.2</td><td>2000</td><td>800</td><td>9.45(+0.14, -0.25)</td></tr><tr><td>IC 4296</td><td>BCG</td><td>E</td><td>50.8</td><td>6400</td><td>1600</td><td>9.13(+0.06, -0.07)</td></tr><tr><td>NGC 5845</td><td>E3</td><td>ES</td><td>25.9</td><td>140</td><td>70</td><td>8.69(+0.12, -0.16)</td></tr><tr><td>NGC 4382</td><td>E2</td><td></td><td>18.4</td><td>1100</td><td>181</td><td>7.81</td></tr><tr><td>A2052</td><td>BCG</td><td></td><td>141.0</td><td>27000</td><td>9000</td><td>9.66</td></tr><tr><td>NGC 4486B</td><td>E1</td><td>E</td><td>16.3</td><td>15</td><td></td><td>9.00</td></tr><tr><td>NGC 5128</td><td>E0p</td><td>S0merg</td><td>3.8</td><td>1300</td><td>300</td><td>7.71(+0.13, -0.19)</td></tr><tr><td>NGC 1023</td><td>SB0</td><td>SB0</td><td>11.4</td><td>221</td><td>100</td><td>7.64(+0.04, -0.04)</td></tr><tr><td>NGC 1316</td><td>E</td><td>SAB0merg</td><td>21.5</td><td>647</td><td>100</td><td>8.24(+0.17, -0.23)</td></tr><tr><td>NGC 2778</td><td>E2</td><td>S0</td><td>22.9</td><td>50</td><td>30</td><td>7.15(+0.30, -0.30)</td></tr><tr><td>NGC 3115</td><td>S0</td><td>S0</td><td>9.7</td><td>550</td><td>150</td><td>8.96(+0.19, -0.15)</td></tr><tr><td>NGC 3384</td><td>SB0</td><td>S0</td><td>11.6</td><td>128</td><td>100</td><td>7.04(+0.16, -0.26)</td></tr><tr><td>NGC 4459</td><td>E2</td><td>S0</td><td>16.1</td><td>218</td><td>28</td><td>7.84(+0.08, -0.08)</td></tr><tr><td>NGC 4564</td><td>S0</td><td>S0</td><td>15.0</td><td>213</td><td>31</td><td>7.92(+0.10, -0.14)</td></tr><tr><td>NGC 5813</td><td>E2</td><td>S0</td><td>32.2</td><td>1650</td><td>400</td><td>8.84(+0.07, -0.07)</td></tr><tr><td>NGC 7332</td><td>S0</td><td>SB0</td><td>23.0</td><td>175</td><td>15</td><td>7.11(+0.17, -0.21)</td></tr><tr><td>NGC 7457</td><td>S0</td><td>S0</td><td>13.2</td><td>178</td><td>75</td><td>7.00(+0.20, -0.40)</td></tr><tr><td>NGC 224</td><td>Sb</td><td>SBb</td><td>0.7</td><td>450</td><td>100</td><td>8.18(+0.20, -0.10)</td></tr><tr><td>NGC 253</td><td>SBc</td><td>SABc</td><td>3.4</td><td>92</td><td>21</td><td>6.70(+0.30, -0.30)</td></tr><tr><td>NGC 3031</td><td>Sb</td><td>SABab</td><td>3.6</td><td>172</td><td>100</td><td>7.84(+0.11, -0.06)</td></tr><tr><td>NGC 3368<sup>a b</sup></td><td></td><td>SABa</td><td>10.4</td><td>35</td><td>18</td><td>6.88(+0.09, -0.09)</td></tr><tr><td>NGC 4258<sup>a c</sup></td><td></td><td>SABb</td><td>7.6</td><td>105</td><td>40</td><td>7.60(+0.01, -0.01)</td></tr><tr><td>NGC 4395<sup>a d</sup></td><td></td><td>SBm</td><td>4.3</td><td>15</td><td>7</td><td>5.56(+0.13, -0.13)</td></tr><tr><td>NGC 4594</td><td>Sa</td><td>Sa</td><td>9.8</td><td>1900</td><td>300</td><td>8.72(+0.30, -0.57)</td></tr><tr><td>NGC 4736<sup>a b</sup></td><td></td><td>SABab</td><td>5.0</td><td>46</td><td>18</td><td>6.83(+0.10, -0.10)</td></tr><tr><td>NGC 4826<sup>a b</sup></td><td></td><td>Sab</td><td>7.3</td><td>69</td><td>30</td><td>6.20(+0.11, -0.11)</td></tr><tr><td>MW</td><td>Sbc</td><td>SBbc</td><td>0.0</td><td>160</td><td>10</td><td>6.61(+0.04, -0.04)</td></tr></tbody></table>

Notes. Galaxy sample from Harris et al. (2014); data from references therein. Column 3: galaxy types from Sahu et al. (2019b), based on the classification grid of Graham (2019).

Galaxies NGC221, NGC4486A, NGC4486B, NGC4382, A2052 (upper limits), NGC5845, NGC5128 (outliers and/or large uncertainties) are excluded from the fits.

<footnote><sup>a</sup> These galaxies were not in the original sample. N<sub>GC</sub> from González-Lópezlira et al. (2017, 2019), this work.</footnote>

<footnote><sup>b</sup> M, from Kormendy & Ho (2013).</footnote>

<footnote><sup>c</sup> M, from Humphreys et al. (2013).</footnote>

<footnote><sup>d</sup> M, from Peterson et al. (2005).</footnote>
<table><caption>**Table 16**
Correlation Solutions with FITEXY</caption><thead><tr><th>Solutions for:</th><th>Sample</th><th>N</th><th>α<br>dex</th><th>β</th><th>⟨x⟩<br>dex</th><th>ε<sub>y</sub><br>dex</th><th>ε<sub>x</sub><br>dex</th><th>χ<sup>2</sup><sub>ν</sub></th><th>rms<br>dex</th></tr></thead><tbody><tr><td rowspan="6">log M<sub>☉</sub> versus log N<sub>GC</sub></td><td rowspan="3">E</td><td rowspan="3">27</td><td>8.871 ± 0.029</td><td>0.915 ± 0.051</td><td>3.2</td><td>0</td><td>0</td><td>6.9</td><td>0.403</td></tr><tr><td>8.963 ± 0.074</td><td>0.771 ± 0.130</td><td>3.2</td><td>0.35</td><td>0</td><td>1.0</td><td>0.378</td></tr><tr><td>8.967 ± 0.080</td><td>0.972 ± 0.158</td><td>3.2</td><td>0.26</td><td>0.27</td><td>1.0</td><td>0.396</td></tr><tr><td rowspan="3">S</td><td rowspan="3">10</td><td>6.455 ± 0.080</td><td>2.394 ± 0.261</td><td>2.1</td><td>0</td><td>0</td><td>6.2</td><td>0.964</td></tr><tr><td>7.086 ± 0.164</td><td>1.515 ± 0.310</td><td>2.1</td><td>0.42</td><td>0</td><td>1.0</td><td>0.444</td></tr><tr><td>7.077 ± 0.170</td><td>1.673 ± 0.329</td><td>2.1</td><td>0.32</td><td>0.17</td><td>1.0</td><td>0.464</td></tr><tr><td rowspan="5">L</td><td rowspan="5">10</td><td>7.802 ± 0.072</td><td>1.617 ± 0.243</td><td>2.4</td><td>0</td><td>0</td><td>2.6</td><td>0.374</td></tr><tr><td>7.767 ± 0.127</td><td>1.617 ± 0.342</td><td>2.4</td><td>0.28</td><td>0</td><td>1.0</td><td>0.372</td></tr><tr><td>7.752 ± 0.133</td><td>1.776 ± 0.388</td><td>2.4</td><td>0.21</td><td>0.12</td><td>1.0</td><td>0.387</td></tr><tr><td>3.232 ± 0.032</td><td>1.093 ± 0.061</td><td>8.9</td><td>0</td><td>0</td><td>6.9</td><td>0.440</td></tr><tr><td>3.138 ± 0.077</td><td>0.815 ± 0.136</td><td>8.9</td><td>0.36</td><td>0</td><td>1.0</td><td>0.378</td></tr><tr><td rowspan="6">log N<sub>GC</sub> versus log M<sub>☉</sub></td><td rowspan="3">E</td><td rowspan="3">27</td><td>3.132 ± 0.082</td><td>1.029 ± 0.166</td><td>8.9</td><td>0.27</td><td>0.26</td><td>1.0</td><td>0.407</td></tr><tr><td>2.334 ± 0.030</td><td>0.418 ± 0.045</td><td>7.1</td><td>0</td><td>0</td><td>6.2</td><td>0.403</td></tr><tr><td>2.083 ± 0.098</td><td>0.534 ± 0.103</td><td>7.1</td><td>0.25</td><td>0</td><td>1.0</td><td>0.273</td></tr><tr><td rowspan="3">S</td><td rowspan="3">10</td><td>2.080 ± 0.101</td><td>0.598 ± 0.118</td><td>7.1</td><td>0.17</td><td>0.32</td><td>1.0</td><td>0.277</td></tr><tr><td>2.398 ± 0.045</td><td>0.618 ± 0.093</td><td>7.8</td><td>0</td><td>0</td><td>2.6</td><td>0.231</td></tr><tr><td>2.434 ± 0.071</td><td>0.509 ± 0.116</td><td>7.8</td><td>0.16</td><td>0</td><td>1.0</td><td>0.213</td></tr><tr><td rowspan="3">L</td><td rowspan="3">10</td><td>2.427 ± 0.073</td><td>0.564 ± 0.123</td><td>7.8</td><td>0.12</td><td>0.21</td><td>1.0</td><td>0.218</td></tr></tbody></table>

<table><caption>**Table 17**
Correlation Solutions with BCES</caption><thead><tr><th>Solutions for:</th><th>Sample</th><th>N</th><th>α<br>dex</th><th>β</th><th>⟨x⟩<br>dex</th><th>ε<sub>y</sub><br>dex</th><th>ε<sub>x</sub><br>dex</th><th>χ<sup>2</sup><sub>ν</sub></th><th>rms<br>dex</th></tr></thead><tbody><tr><td rowspan="6">log M<sub>☉</sub> versus log N<sub>GC</sub></td><td rowspan="3">E</td><td rowspan="3">27</td><td>8.980 ± 0.078</td><td>1.000 ± 0.098</td><td>3.2</td><td>0</td><td>0</td><td>7.8</td><td>0.400</td></tr><tr><td>8.980 ± 0.074</td><td>0.803 ± 0.126</td><td>3.2</td><td>0.35</td><td>0</td><td>1.0</td><td>0.378</td></tr><tr><td>8.992 ± 0.079</td><td>1.010 ± 0.126</td><td>3.2</td><td>0.26</td><td>0.27</td><td>1.0</td><td>0.403</td></tr><tr><td rowspan="3">S</td><td rowspan="3">10</td><td>7.110 ± 0.146</td><td>1.660 ± 0.218</td><td>2.1</td><td>0</td><td>0</td><td>20.9</td><td>0.460</td></tr><tr><td>7.128 ± 0.139</td><td>1.470 ± 0.182</td><td>2.1</td><td>0.42</td><td>0</td><td>1.0</td><td>0.441</td></tr><tr><td>7.118 ± 0.144</td><td>1.640 ± 0.237</td><td>2.1</td><td>0.32</td><td>0.17</td><td>1.0</td><td>0.457</td></tr><tr><td rowspan="5">L</td><td rowspan="5">10</td><td>7.760 ± 0.126</td><td>1.850 ± 0.447</td><td>2.4</td><td>0</td><td>0</td><td>2.7</td><td>0.398</td></tr><tr><td>7.758 ± 0.119</td><td>1.670 ± 0.418</td><td>2.4</td><td>0.28</td><td>0</td><td>1.0</td><td>0.376</td></tr><tr><td>7.750 ± 0.126</td><td>1.850 ± 0.496</td><td>2.4</td><td>0.21</td><td>0.12</td><td>1.0</td><td>0.398</td></tr><tr><td>3.114 ± 0.072</td><td>0.787 ± 0.089</td><td>8.9</td><td>0.36</td><td>0</td><td>1.0</td><td>0.377</td></tr><tr><td>2.063 ± 0.086</td><td>0.532 ± 0.101</td><td>7.1</td><td>0.25</td><td>0</td><td>1.0</td><td>0.272</td></tr><tr><td rowspan="3">E+S</td><td rowspan="3">37</td><td>2.413 ± 0.067</td><td>0.485 ± 0.142</td><td>7.8</td><td>0.16</td><td>0</td><td>1.0</td><td>0.212</td></tr></tbody></table>

<table><caption>**Table 18**
Correlation Solutions with FITEXY for M<sub>☉</sub> and Total Galaxy Mass</caption><thead><tr><th>Solutions for:</th><th>Sample</th><th>N</th><th>α<br>dex</th><th>β</th><th>⟨x⟩<br>dex</th><th>ε<sub>y</sub><br>dex</th><th>ε<sub>x</sub><br>dex</th><th>χ<sup>2</sup><sub>ν</sub></th><th>rms<br>dex</th></tr></thead><tbody><tr><td rowspan="6">log M<sub>☉</sub> versus log M<sub>*</sub></td><td rowspan="3">E</td><td rowspan="3">27</td><td>8.812 ± 0.035</td><td>1.369 ± 0.086</td><td>11.1</td><td>0</td><td>0</td><td>5.5</td><td>0.411</td></tr><tr><td>8.915 ± 0.075</td><td>1.141 ± 0.190</td><td>11.1</td><td>0.34</td><td>0</td><td>1.0</td><td>0.380</td></tr><tr><td>8.906 ± 0.080</td><td>1.416 ± 0.228</td><td>11.1</td><td>0.25</td><td>0.18</td><td>1.0</td><td>0.399</td></tr><tr><td rowspan="3">S</td><td rowspan="3">10</td><td>5.472 ± 0.203</td><td>3.065 ± 0.418</td><td>10.0</td><td>0</td><td>0</td><td>10.0</td><td>2.34</td></tr><tr><td>7.092 ± 0.183</td><td>1.028 ± 0.262</td><td>10.0</td><td>0.51</td><td>0</td><td>1.0</td><td>0.502</td></tr><tr><td>7.077 ± 0.196</td><td>1.238 ± 0.310</td><td>10.0</td><td>0.37</td><td>0.30</td><td>1.0</td><td>0.535</td></tr><tr><td rowspan="5">E+S</td><td rowspan="5">37</td><td>7.865 ± 0.040</td><td>2.425 ± 0.082</td><td>10.8</td><td>0</td><td>0</td><td>8.8</td><td>1.082</td></tr><tr><td>8.425 ± 0.082</td><td>1.390 ± 0.129</td><td>10.8</td><td>0.43</td><td>0</td><td>1.0</td><td>0.475</td></tr><tr><td>8.407 ± 0.085</td><td>1.556 ± 0.146</td><td>10.8</td><td>0.31</td><td>0.20</td><td>1.0</td><td>0.322</td></tr><tr><td>11.224 ± 0.024</td><td>0.730 ± 0.046</td><td>8.9</td><td>0</td><td>0</td><td>5.5</td><td>0.300</td></tr><tr><td>11.153 ± 0.053</td><td>0.567 ± 0.094</td><td>8.9</td><td>0.24</td><td>0</td><td>1.0</td><td>0.263</td></tr><tr><td rowspan="6">log M<sub>*</sub> versus log M<sub>☉</sub></td><td rowspan="3">E</td><td rowspan="3">27</td><td>11.154 ± 0.056</td><td>0.706 ± 0.113</td><td>8.9</td><td>0.18</td><td>0.25</td><td>1.0</td><td>0.282</td></tr><tr><td>10.585 ± 0.027</td><td>0.327 ± 0.045</td><td>7.1</td><td>0</td><td>0</td><td>10.0</td><td>0.763</td></tr><tr><td>10.084 ± 0.150</td><td>0.678 ± 0.168</td><td>7.1</td><td>0.41</td><td>0</td><td>1.0</td><td>0.422</td></tr><tr><td rowspan="3">S</td><td rowspan="3">10</td><td>10.076 ± 0.157</td><td>0.807 ± 0.202</td><td>7.1</td><td>0.30</td><td>0.37</td><td>1.0</td><td>0.432</td></tr><tr><td>11.077 ± 0.016</td><td>0.413 ± 0.014</td><td>8.4</td><td>0</td><td>0</td><td>8.8</td><td>0.446</td></tr><tr><td>10.869 ± 0.053</td><td>0.576 ± 0.054</td><td>8.4</td><td>0.27</td><td>0</td><td>1.0</td><td>0.320</td></tr><tr><td rowspan="3">E+S</td><td rowspan="3">37</td><td>10.861 ± 0.054</td><td>0.643 ± 0.060</td><td>8.4</td><td>0.20</td><td>0.31</td><td>1.0</td><td>0.500</td></tr></tbody></table>
<table><caption>**Table 19**
Correlation Solutions with BCES for *M* and Total Galaxy Mass</caption><thead><tr><th>Solutions for:</th><th>Sample</th><th>N</th><th>α<br>dex</th><th>β</th><th>⟨χ⟩<br>dex</th><th>ε<sub>y</sub><br>dex</th><th>ε<sub>x</sub><br>dex</th><th>χ<sup>2</sup><sub>ν</sub></th><th>rms<br>dex</th></tr></thead><tbody><tr><td rowspan="6">log M<sub>*</sub> versus log M<sub>*</sub></td><td>E</td><td>27</td><td>8.960 ± 0.078</td><td>1.460 ± 0.149</td><td>11.1</td><td>0</td><td>0</td><td>5.5</td><td>0.405</td></tr><tr><td rowspan="3">S</td><td rowspan="3">10</td><td>8.955 ± 0.073</td><td>1.190 ± 0.183</td><td>11.1</td><td>0.34</td><td>0</td><td>1.0</td><td>0.381</td></tr><tr><td>8.952 ± 0.078</td><td>1.480 ± 0.184</td><td>11.1</td><td>0.25</td><td>0.18</td><td>1.0</td><td>0.407</td></tr><tr><td>7.151 ± 0.167</td><td>1.220 ± 0.135</td><td>10.0</td><td>0</td><td>0</td><td>10.0</td><td>0.530</td></tr><tr><td rowspan="5">E+S</td><td rowspan="5">37</td><td>7.090 ± 0.158</td><td>1.000 ± 0.131</td><td>10.0</td><td>0.51</td><td>0</td><td>1.0</td><td>0.501</td></tr><tr><td>7.081 ± 0.166</td><td>1.210 ± 0.163</td><td>10.0</td><td>0.37</td><td>0.30</td><td>1.0</td><td>0.527</td></tr><tr><td>8.390 ± 0.080</td><td>1.500 ± 0.140</td><td>10.8</td><td>0</td><td>0</td><td>8.8</td><td>0.491</td></tr><tr><td>8.469 ± 0.078</td><td>1.380 ± 0.131</td><td>10.8</td><td>0.43</td><td>0</td><td>1.0</td><td>0.475</td></tr><tr><td>8.420 ± 0.080</td><td>1.500 ± 0.153</td><td>10.8</td><td>0.31</td><td>0.20</td><td>1.0</td><td>0.488</td></tr><tr><td rowspan="3">log M<sub>*</sub> versus log M<sub>*</sub></td><td>E</td><td>27</td><td>11.134 ± 0.050</td><td>0.543 ± 0.062</td><td>8.9</td><td>0.24</td><td>0</td><td>1.0</td><td>0.262</td></tr><tr><td>S</td><td>10</td><td>10.042 ± 0.133</td><td>0.681 ± 0.128</td><td>7.1</td><td>0.41</td><td>0</td><td>1.0</td><td>0.420</td></tr><tr><td>E+S</td><td>37</td><td>10.837 ± 0.052</td><td>0.611 ± 0.070</td><td>8.4</td><td>0.27</td><td>0</td><td>1.0</td><td>0.318</td></tr></tbody></table>

ORCID iDs

Rosa A. González-Lópezlira https://orcid.org/0000-0003-1557-4931

Luis Lomelí-Núñez https://orcid.org/0000-0003-2127-2841

Yasna Ordenes-Briceño https://orcid.org/0000-0001-7966-7606

Laurent Loinard https://orcid.org/0000-0002-5635-3345

Stephen Gwyn https://orcid.org/0000-0001-8221-8406

Karla Alamo-Martínez https://orcid.org/0000-0002-5897-7813

Gustavo Bruzual https://orcid.org/0000-0002-6971-5755

Ariane Lançon https://orcid.org/0000-0002-7214-8296

Thomas H. Puzia https://orcid.org/0000-0003-0350-7061

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