Spectroscopy of NGC 4258 globular cluster candidates: membership confirmation and kinematics

TL;DR

This study confirms globular cluster candidates in NGC 4258 using spectroscopy, validating a new selection method and revealing their kinematic association with the galaxy’s HI disk, which enhances understanding of galaxy-GC relationships.

Contribution

It introduces and validates the uiks-method for selecting globular clusters in spiral galaxies, improving accuracy and understanding of their kinematics.

Findings

70% of candidates confirmed as GCs

GCs are mostly metal-poor

GCs co-rotate with the HI disk

Abstract

We present multi-object spectroscopic observations of 23 globular cluster candidates (GCCs) in the prototypical megamaser galaxy NGC 4258, carried out with the OSIRIS instrument at the 10.4 m Gran Telescopio Canarias. The candidates have been selected based on the ($u^*\ -\ i^\prime$) versus ($i^\prime\ -\ K_s$) diagram, in the first application of the uiks-method to a spiral galaxy. In the spectroscopy presented here, 70% of the candidates are confirmed as globular clusters. Our results validate the efficiency of the uiks-method in the sparser GC systems of spirals, and given the downward correction to the total number of GCs, the agreement of the galaxy with the correlations between black hole mass, and total number and mass of GCs is actually improved. We find that the GCs, mostly metal-poor, co-rotate with the HI disk, even at large galactocentric distances.

Tables

Table 1. Table 1 Summary of Photometric Observations

Filter	${\lambda }_{\mathrm{cen}}^a$	FWHMb	Exposure	Depth	$m_0^{\mathrm{TO}}$
			s	AB mag	AB mag
$u^{\ast }$	3793 Å	654 Å	13360	26.0	23.1
$g^{\prime }$	4872 Å	1434 Å	10400	26.5	22.2
$r^{\prime }$	6276 Å	1219 Å	3500	25.4	21.7
$i^{\prime }$	7615 Å	1571 Å	8080	25.7	21.5
$K_s$	2.15 $\mu m$	0.33 $\mu m$	200	21.5	21.3

Table 2. Table 2 Target velocity fit parameters, HST image information, and probable object types.

Name	RA J2000	DEC J2000	SNR	$V_{\mathrm{proj}}$	$\Delta V_{\mathrm{proj}}$	$r$-value	Template	Range	$V_{\mathrm{HI},\mathrm{proj}}$	$\Delta V_{\mathrm{HI},\mathrm{proj}}$	HST image	FWHM	FWHM PSF	Object type
	deg	deg		km s-1	km s-1			$\AA$	km s-1	km s-1		$″$	$″$
Confirmed GC candidates
GLL J121851+471400	184.7166	47.2335	28	324.0	72.6	4.92	fglotemp	4400–7100	378.5	14.9	hst_11570_97_acs_wfc_f555w	0.160	0.100	GC
GLL J121852+472201	184.7205	47.3672	11	779.4	82.3	2.58	fglotemp	4100–7198	573.4	36.8	hst_11570_86_acs_wfc_f555w	0.130	0.105	GC
GLL J121854+472318	184.7266	47.3885	31	496.9	57.4	5.35	fglotemp	4100–7198	555.1	23.1	hst_11570_91_acs_wfc_f555w	0.195	0.100	GC
GLL J121856+471411	184.7345	47.2366	12	315.9	51.7	3.67	fs2temp	4000–7198	364.0	21.1	hst_11570_97_acs_wfc_f555w	0.165	0.105	GC
GLL J121857+472330	184.7384	47.3918	23	338.7	48.3	8.78	fglotemp	4100–7198	528.2	8.7	hst_11570_91_acs_wfc_f555w	0.155	0.105	GC
GLL J121859+472107	184.7500	47.3520	52	662.2	69.6	6.00	fglotemp	3720–7100	514.3	25.8	hst_11570_86_acs_wfc_f555w	0.150	0.100	GC
J121901+471859a	184.7553	47.3166	9	577.3	49.4	4.31	fs2temp	4000–7000	449.5	44.3	hst_11570_88_acs_wfc_f555w	0.105	0.100	GC
GLL J121901+471905	184.7565	47.3183	15	260.1	68.7	3.71	fglotemp	4100–7000	448.4	43.8	hst_11570_88_acs_wfc_f555w	0.155	0.095	GC
GLL J121902+472048	184.7585	47.3469	33	383.8	52.4	5.44	fglotemp	4000–6950	488.6	22.9	hst_11570_86_acs_wfc_f555w	0.175	0.095	GC
GLL J121902+472125	184.7622	47.3572	23	608.3	23.6	9.82	fglotemp	4000–6850	488.8	11.8	hst_11570_99_acs_wfc_f555w	0.125	0.090	GC
GLL J121902+472043	184.7624	47.3453	35	625.8	31.4	7.78	fglotemp	4000–6850	477.0	9.0	hst_11570_88_acs_wfc_f555w	0.155	0.100	GC
GLL J121908+471355	184.7847	47.2322	27	257.9	47.5	5.86	fglotemp	4000–7400	322.2	31.3	hst_11570_96_acs_wfc_f555w	0.140	0.100	GC
GLL J121925+471228	184.8578	47.2079	36	282.0	39.0	7.03	fglotemp	4200–7198	289.0	14.2	hst_11570_94_acs_wfc_f555w	0.165	0.100	GC
GLL J121928+471152b	184.8685	47.1978	17	505.5	72.8	4.19	fglotemp	4300–7198	290.8	14.2	hst_11570_94_acs_wfc_f555w	0.200	0.100	GC
GLL J121929+471215	184.8711	47.2042	54	219.5	17.1	14.02	fglotemp	4250–7198	298.9	16.3	hst_11570_94_acs_wfc_f555w	0.150	0.100	GC
GLL J121934+471316	184.8944	47.2212	21	401.2	66.6	4.03	fglotemp	3720–7198	344.7	6.0	hst_10399_50_acs_wfc_f606w	0.170	0.080	GC
Rejected GC candidates
GLL J121852+471313	184.7187	47.2204	12	-209.3	47.9	5.66	eltemp	4100–7198	368.1	15.3	hst_11570_97_acs_wfc_f555w	0.105	0.100	star
GLL J121854+472144c	184.7261	47.3625	8	543.6	53.7	4.69	fm32temp	4100–7198	564.3	32.6	hst_11570_90_acs_wfc_f555w	0.155	0.090	dwarf gal/GC
GLL J121854+472245	184.7278	47.3792	53	-199.3	14.6	18.59	fm32temp	4000–7100	558.8	25.4	hst_11570_91_acs_wfc_f555w	0.095	0.10	star
GLL J121903+472613b	184.7654	47.4372	20	470.2	158.1	1.64	fglotemp	4300–5500d	512.6	7.7	no images			dwarf gal/GC
GLL J121905+472422	184.7744	47.4063	86	750.7	49.7	5.42	fm32temp	4100–6600	498.4	6.1	hst_11570_91_acs_wfc_f555w	0.285	0.100	dwarf gal/GC
GLL J121909+471335	184.7909	47.2265	12	400.3	101.4	2.43	eltemp	4300–5500e	309.4	34.5	hst_11570_96_acs_wfc_f555w	0.160	0.100	dwarf gal/GC
GLL J121910+471343	184.7931	47.2287	23	172.2	104.9	4.34	fglotemp	4000–7200	308.9	37.1	hst_11570_96_acs_wfc_f555w	0.250	0.100	dwarf gal/GC
Confirmed non-candidates
J121853+472136	184.7219	47.3600	21	853.5	36.2	8.05	fn7331temp	4100–7198	578.3	45.7	hst_11570_90_acs_wfc_f555w	0.235	0.100	dwarf gal (?)
J121907+472113	184.7795	47.3538	19	43004.9	31.1	7.90	eltemp	4000–6500	472.4	15.6	hst_11570_99_acs_wfc_f555w	0.240	0.090	gal
J121924+471306	184.8518	47.2185	12	12576.2	19.8	5.66	femtemp97	4100–7198	300.1	12.6	hst_11570_94_acs_wfc_f555w	0.115	0.100	gal
J121849+471357	184.7042	47.2325	2	38418.3	46.6	3.26	femtemp97	3720–7198	386.2	14.6	hst_11570_97_acs_wfc_f555w	0.100	0.100	gal (?)
J121853+471330	184.7232	47.2250	19	329.3	16.4	10.32	femtemp97	3720–7198	366.4	16.2	hst_11570_97_acs_wfc_f555w	0.117	0.100	HII reg
J121854+472235	184.725	47.3764	24	618.8	13.9	12.74	femtemp97	3720–7198	564.4	25.3	hst_11570_91_acs_wfc_f555w	0.100	0.100	HII reg
J121854+471324	184.7284	47.2235	18	10015.5	99.5	2.67	eltemp	4100–7198	363.2	17.0	hst_11570_97_acs_wfc_f555w	0.115	0.100	gal
J121856+471342	184.7374	47.2286	12	380.4	16.0	10.70	femtemp97	3720–7198	356.8	20.8	hst_11570_90_acs_wfc_f555w	0.120	0.090	HII reg
J121920+471332	184.8365	47.2256	12	104927e					302.8	12.2	hst_11570_94_acs_wfc_f555w	0.310	0.100	gal
J121930+471254	184.8786	47.2152	3	43234.8	51.8	2.17	femtemp97	4000–7198	321.3	11.1	hst_11570_94_acs_wfc_f555w	0.267	0.100	gal (?)

Table 3. Table 3 Observation Log

Run/Field	Principal Investigator	Date	Position angle	Slit Width	Grism	Exp. time	Airmass	Seeing	Night	Standard star
			$°$	$″$		s		$″$
2017A-NS1	R. González-Lópezlira	2017-05-24	270	1.0	R1000B	3$\times$1325	1.42	$0\stackrel{\prime \prime }{.}7$	Dark, clear	Ross 640
2017A-EW4	R. González-Lópezlira	2017-05-30	0	1.0	R1000B	2$\times$1325	1.24	$0\stackrel{\prime \prime }{.}8$	Gray, clouds	GD153
2017A-EW4	R. González-Lópezlira	2017-05-31	0	1.0	R1000B	1325	1.39	$0\stackrel{\prime \prime }{.}8$	Gray, clouds	GD153

Table 4. Table 4 Fits to GC and HI projected velocities

System	Amplitude	Phase	Systemic velocity
	km s-1	$°$	km s-1
HI	146.1 $\pm$ 0.2	121.6 $\pm$ 0.1	445.6 $\pm$ 0.2
GCs	127.9 $\pm$ 60.9	122.1 $\pm$ 45.9	443.1 $\pm$ 50.9
GCs+dwarfs	168.1 $\pm$ 66.0	132.3 $\pm$ 31.2	467.7 $\pm$ 44.5

Full text

1. Introduction

It has become commonplace to state that globular clusters (GC) are powerful signposts of the structure, dynamics, and star formation and assemblage histories of their host galaxies. Not only are they compact and bright, and hence traceable to large distances; they do correlate with global properties and other components of their hosts, such as their luminosity (e.g., Peng et al., 2008; Georgiev et al., 2010); light concentration and stellar velocity dispersion (Harris et al., 2013); total stellar mass and bulge light (Rhode, 2012), and total halo (Spitler & Forbes, 2009; Harris et al., 2017) and central supermassive black hole masses (e.g., Sadoun & Colin, 2012; Burkert & Tremaine, 2010; Harris & Harris, 2011; Harris et al., 2014). However, until now, studies of GC systems have focused on early type galaxies, given their significantly larger number of GCs, and the ease of their identification in the absence of a dusty, stellar disk, composed of partially resolved, bright sources.

Although understandable, given the obvious difficulties, the scarcity of studies of late-type galaxies constitutes a real obstacle to actually using GC systems as probes of galaxy formation and evolution, for several reasons, as expressed already a couple of decades ago (e.g., Kissler-Patig et al., 1999). Firstly, we do not really know how typical the GC system of our Galaxy is, and yet it is the standard to which all other systems are compared. More importantly, perhaps, while there seems to be a consensus that elliptical galaxies, and hence their GC systems, form through mergers, there is now mounting observational (e.g., Förster Schreiber et al., 2009; Tacconi et al., 2013; Dessauges-Zavadsky et al., 2015; Patrício et al., 2018) and theoretical (e.g., Dekel et al., 2009; Kruijssen, 2015) evidence that massive stellar clusters form at $z\geqslant 2$ by the fragmentation of gaseous disks, rotating but turbulent, suffering intense, cold gas accretion flows. Globular clusters would be the relics of this star formation epoch, and low mass spirals may still contain relatively undisturbed primeval systems, given their slightly lower major ($M_{\rm sat}/M_{\rm primary}\geqslant$ 1:4) merger rates (Rodriguez-Gomez et al., 2015).

Motivated originally to explore the correlation between total number of GCs, $N_{\rm GC}$, and central black hole mass, $M_{\bullet}$ (e.g., Burkert & Tremaine, 2010; Harris & Harris, 2011) in spiral galaxies, we have embarked on a campaign to observe 9 northern galaxies closer than 16 Mpc, with good measurements of their central black hole masses. The first analyzed target was the megamaser prototype NGC 4258 (M 106). It is the largest member of the Canes II group, populated mostly by late-type spirals and irregular galaxies. Thanks to a circumnuclear maser disk, NGC 4258 has the most precise extragalactic $M_{\bullet}$ measurement. It also follows several correlations established for elliptical galaxies, like those between $M_{\bullet}$, and bulge luminosity and mass, respectively (Läsker et al., 2016).

Using the $u^{*}i^{\prime}K_{s}$ photometric method (Muñoz et al., 2014), described below in Section 2, González-Lópezlira et al. (2017) selected a sample of GC candidates (GCCs) in NGC 4258 and determined that it likewise falls on the $N_{\rm GC}$ versus $M_{\bullet}$ correlation. Interestingly, the projected spatial distribution of the González-Lópezlira et al. sample appears disky, and aligned with the galaxy, although their colors rule out that they are young clusters in the stellar disk (see González-Lópezlira et al. 2017 and Section 2 below). The $u^{*}i^{\prime}K_{s}$ is possibly the most efficient photometric method to select GCCs in elliptical galaxies. This paper analyzes spectra of the GCC sample of NGC 4258, with two main goals: quantify the efficiency of the $u^{*}i^{\prime}K_{s}$ method for the study of the much sparser GC systems of spirals, and investigate the kinematics of the NGC 4258 GCs. The paper is organized as follows: Section 2 recapitulates the sample selection process carried out in González-Lópezlira et al. (2017); Section 3 presents the spectroscopic observations, their reduction, and the determination of the line-of-sight velocities of the candidates; in Section 4 we derive the kinematics of the system; the metallicity of the composite spectra of the whole sample is estimated in Section 5; the efficiency of the $u^{*}i^{\prime}K_{s}$ method is analyzed in Section 6; finally, the discussion and conclusions are presented in Section 7.

2. GCC sample

González-Lópezlira et al. (2017) defined a sample of 39 GCCs in NGC 4258, from Canada-France-Hawaii Telescope (CFHT) optical ($u^{*}$, $g^{\prime}$, $r^{\prime}$, $i^{\prime}$) and near-infrared ($K_{s}$) data, both archival and proprietary. Potential candidates had photometric errors smaller than 0.2 mag in the $i^{\prime}$-band, and were within $\pm$ 3.6 mag of the expected GC luminosity (LF) function turnover (LFTO) magnitude in every filter. Also, they were neither saturated, nor blended or close to bright neighbors. These latter requirements against crowding eliminated all sources within an elliptical region centered on NGC 4258, with semi-major axis = 3$\farcm$5, or 0.37 $R_{25}$, axis ratio = cos(67$\arcdeg$), and the same position angle (P.A.) as the galaxy, of $=150\arcdeg$ (de Vaucouleurs et al., 1991). Table 1 gives a summary of the photometric observations, including exposure times, depths, and expected location of the LFTO. Given the significantly shorter exposure time, all the analysis by González-Lópezlira et al. was limited by the $K_{s}$-band image; the GCLF was complete to $\sim$ 20.5 AB mag in this wavelength (González-Lópezlira et al., 2017).

Our main selection tool was the ($u^{*}\ -\ i^{\prime}$) versus ($i^{\prime}\ -\ K_{s}$) color-color diagram (Muñoz et al., 2014); this was the first application of the $u^{*}i^{\prime}K_{s}$ technique to a spiral galaxy. The GCC selection region in this diagram was determined from the area that contains the highest density (more than 2000) of spectroscopically confirmed GCs in M 87 (Muñoz et al., 2014; Powalka et al., 2016). The region has approximately the shape of a drop or pennon, and appears drawn in brown in Figure 1. Crucially, it is well separated from the loci occupied by background galaxies, foreground Galactic stars, and young stellar clusters in the disk of spiral galaxies. To further decrease the probability of contamination by background galaxies, as well as by dwarf galaxies in NGC 4258 itself, only sources with $i^{\prime}$-band FWHM $\leqslant 0\farcs 84$ (31 pc at a distance of 7.6 Mpc) and SExtractor (Bertin & Arnouts, 1996) light concentration parameter SPREAD_MODEL $\leqslant$ 0.017 were kept.111 The SPREAD_MODEL value for each object results from the comparison between its best fitting point-spread-function (PSF), and the convolution of such PSF with an exponential disk with scale length FWHMPSF/16, where FWHMPSF is the full width at half max of the same PSF (Desai et al., 2012). Half-light radii of the objects, measured by fitting King profiles to their radial light distributions with the program ishape (Larsen, 1999), were all smaller than 6 pc.

A couple of GCCs in the spectroscopic sample come from a previous, unpublished, photometric sample of 38 objects (the published and unpublished samples share 30 sources in common). In this case, the selection region in the $u^{*}i^{\prime}K_{s}$ diagram was the ellipse centered at ($u^{*}$ - $i^{\prime}$) $=2.25$, ($i^{\prime}$ - $K_{s}$) $=0.35$, with semi-major and semi-minor axes 1.25 mag and 0.345 mag, respectively, and rotated 39$\arcdeg$ counterclockwise from the ($u^{*}$ - $i^{\prime}$) axis. This elliptical region contains the pennon, was delimited based on Bruzual & Charlot (2003, hereafter BC03) model single stellar populations (SSPs), and is drawn, with a dotted orange line, in Figure 1. The figure also shows two lines, short-dashed cyan and long-dashed red, that represent zero age main sequences with, respectively, $Z=0.008$ and $Z=0.02$. They trace a band of Galactic field stars that brushes the orange ellipse near ($u^{*}$ - $i^{\prime}$) $\sim$ 1.8, ($i^{\prime}$ - $K_{s}$) $\sim$ -0.4. In view of potential contamination from these objects, the unpublished sample also had minimum size bounds in the $i^{\prime}$ filter (FWHM = $0\farcs 65$, SPREAD_MODEL = 0.002). These minimum size bounds, however, would have eliminated GCs with $r_{e}<$ 4.7 pc, or about half the total in the MW.

GCCs in either of the photometric samples are identified with the acronym GLL (“Globular Luis Lomelí”) before their equinox J2000.0 equatorial coordinates. The spectroscopic sample, enumerated in Table 2, includes GLL GCCs, objects in either of the color-color selection regions that did not fulfill the light concentration requirements, and random objects in the observed fields as additional controls. The two latter classes of objects are listed by their equinox J2000.0 equatorial coordinates, with no preceding acronym.

[FIGURE:]

3. Spectroscopic observations

The dataset used in this work was obtained with the Optical System for Imaging and low-Intermediate-Resolution Integrated Spectroscopy (OSIRIS), in multi-object spectroscopy (MOS) mode, at the Nasmyth-B focus of the Gran Telescopio Canarias (GTC).222 Gran Telescopio Canarias is a Spanish initiative with the participation of Mexico and the University of Florida, USA, and is installed at the Roque de los Muchachos Observatory in the island of La Palma. This work is based on the proposal GTC17-9AMEX, using Mexican share of the GTC time. OSIRIS has two mosaicked Marconi CCD44-82 detectors, with a $9\farcs 4$ gap between them. Each detector has 2048$\times$4096 pixels, whose physical size is 15$\mu$m on the side, for a scale of $0\farcs 127$ on the sky. In standard observing modes, however, pixels are binned 2$\times$2, for an effective spatial scale of $0\farcs 254$. We observed with the R1000B grism, whose wavelength range goes from $\sim$3700 Å to 7500 Å. The slit width of 1″ yielded a resolution of 5.51 Å. OSIRIS offers a maximum field-of-view (FOV) of $7.5^{\prime}\times 6.0^{\prime}$ for slitlet placement. However, we used only a FOV of $7.5^{\prime}\times 3.0^{\prime}$ in each of our two pointings in order to ensure the coverage of the complete spectral range of 3700 Å–7500 Å for all observed targets.

The dataset consists of spectra in two fields, located, respectively, north (NS1) and south (EW4) of the minor axis of NGC 4258. The NS1 field was oriented N-S, with the dispersion axis running E-W; conversely, the EW4 field was oriented E-W, with the dispersion axis along the N-S direction. Their centers were, respectively, RA = 12h18m52.10s, Dec=+47$\arcdeg 19\arcmin 51\farcs 8$, (J2000.0) for field NS1, and RA=12h19m27.17s, Dec=+47$\arcdeg 13\arcmin 16\farcs 4$ (J2000.0) for field EW4.

Spectra were obtained for slightly over 50% of the GCC sample defined by González-Lópezlira et al. (2017). The positions of the science slits in each field are shown as yellow boxes, over grayscales of the CFHT $r^{\prime}$ image of the galaxy, in Figure 2. For illustration purposes, all slits have been drawn with the same size; in actuality, slitlets had varying lengths, so as to not overlap, and included object-free regions to allow for the subtraction of sky spectra. Observations of reference stars for astrometry were also carried out (positions not shown).

Each field was observed for a total of 3975 s, divided in 3 exposures of 1325 s to facilitate cosmic ray cleaning. Standard stars, arc lamps, bias, and flat-field frames were also obtained for each pointing. Field NS1 was secured on 2017 May 24, i.e., a clear, dark night; field EW4 was observed during 2017 May 30 and 31, which were gray nights with some cloud cover. Consequently, while the average signal-to-noise ratio (SNR) of the sources in field NS1 is $\sim$ 29, for those in field EW4 it is only $\sim$ 19, as gauged by the routine DER_SNR.333Stoehr, F., ST-ECF Newsletter, Issue # 42, www.stecf.org/software/ASTROsoft/DER_SNR/. A summary of the spectroscopic observations is given in Table 3.

3.1. Data reduction

The reduction of the spectroscopic data was performed with GTCMOS,444 http://www.inaoep.mx/$\sim$ydm/gtcmos/gtcmos.html an ad hoc pipeline based on IRAF555 IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. (Tody, 1986, 1993) tasks. The reduction procedure has been described at length by Gómez-González et al. (2016), but we give a brief summary here.

The pipeline tiles the two OSIRIS CCDs and corrects for geometrical distortions. All tiled bias frames in an observing block are combined into a master bias image with a median algorithm; the master bias is then subtracted from all the images in the block. All images of each target are then combined, also with a median algorithm, a procedure that cleans cosmic rays from the final frames. Arc spectra are also tiled and combined into a single arc image, which is used for wavelength calibration. The pipeline also corrects the curvature of the slit images in the spatial direction and obtains independent dispersion solutions for each slitlet, using a spline3 function of order 2. Final rms errors are better than 0.5 ${\rm\AA}$. The best solution for each slitlet is used to create a wavelength calibrated 2-D image, with the spectral axis linearly resampled to a dispersion of 2.1 ${\rm\AA}$ pixel*-1*. The dispersion-corrected spectra are also shifted linearly, in order to force the centroid of the [OI]$\lambda$5577 sky line in every spectrum to lie at its rest wavelength.

Standard star spectra are reduced individually in a similar fashion. Once spectra are extracted, sensitivity tables between the flux and count rate at all available spectral bands are obtained with the IRAF task standard. Atmospheric extinction corrections are performed, for both standard stars and targets, by combining the extinction curve for the observatory with the registered airmasses of the observations.

The IRAF task apall was used for the extraction of the spectra of individual targets from the wavelength- and flux-calibrated 2-D images. The background (sky plus underlying galaxy) spectrum was also subtracted during the extraction procedure. For all the targets the continuum is well registered so as to enable in-situ tracing. The width of the extraction window is kept between 4–6 pixels (1–1.5″), which has been found to maximize the SNR of the extracted spectrum. Most of the slitlets were long enough to include object-free pixels for the extraction of the background spectrum. In a few cases, where this was not possible, background zones were selected from slitlets that were spatially closest to the object.

The sky plus underlying galaxy background is as bright or, very often, brighter than the object within the extraction window. Furthermore, sky noise increases monotonically towards the blue, i.e., almost by a factor of two between 5000 Å to 4000 Å. Thus, the SNR of the extracted spectrum, especially blueward of 5000 Å, is mainly governed by the photon noise of the background spectrum. We considered only those parts of each spectrum where the SNR pixel*-1* (of 2.1 Å width) is above at least 10. In Table 2 we give the SNR, again as estimated by the routine DER_SNR, as well as the useful wavelength range for each spectrum.

3.2. Line of sight velocities

Projected heliocentric velocities of the GCCs and other targets were determined with the Fourier cross-correlation method implemented in the xcsao task of the rvsao package (Kurtz & Mink, 1998), within IRAF. For comparison with our spectra, we used some of the templates provided by the Smithsonian Astrophysical Observatory (SAO; http://tdc-www.harvard.edu/software/rvsao/Templates/). We employed the two templates derived from M 31 GCs (called fglotemp and fs2temp); a synthetic galaxy emission line spectrum (femtemp97) that provides a good match to HII regions; four galaxy templates, i.e., a composite spiral galaxy template, a composite elliptical galaxy template, one derived from M 32 and one produced from NGC 7331 (respectively, sptemp, eltemp, fm32temp, fn7331temp). All templates were resampled to the resolution of the spectra obtained with OSIRIS/GTC and reduced with GTCMOS. The goodness of fit is gauged through the $r$-value, also provided by the xcsao task for each comparison; the higher the $r$-value, the better the fit. The sky region, between 5500 ${\rm\AA}$ and 5650 ${\rm\AA}$, was always excluded from the fits, as were the edges of the spectra in the cases where they looked noisy.

For an object to be considered a GC, the highest $r$-value should occur for the M 31 GC templates in the whole observed spectral window, and the derived heliocentric velocity had to lie in the expected range of objects in NGC 4258, i.e., between $\sim$ 300 km s*-1* and $\sim$ 750 km s*-1*. Objects that had a good match in the same velocity range with the template femtemp97 are likely HII regions. All other objects were considered either as foreground stars (velocity less than the minimum allowed, and FWHM similar to the PSF FWHM –see Table 2, columns 13 and 14), dwarf satellite galaxies (velocity in the range), or background galaxies (velocity larger than the maximum allowed).

The classification of all objects was further visually confirmed through the inspection of Hubble Space Telescope (HST) archival images, as NGC 4258 has one of the largest Hubble Legacy Archive (HLA)666https://hla.stsci.edu. data collections available (Fig. 3, left panel777The graphic was produced using the HLA site, with the footprints superimposed on a Digitized Sky Survey (DSS; http://archive.stsci.edu/dss/) image.). All the frames used in this work were acquired with the Advanced Camera for Surveys (ACS); their footprints are illustrated in golden yellow, in the right panel of Fig. 3, superimposed on the CFHT $i^{\prime}$-band data of NGC 4258. Except in one case, the images were obtained through the F555W filter and proceed from proposal GO 11570 (P.I. A. Riess). For GLL J121934+471316, we used an F606W image from proposal GO 10399 (P.I. L.J. Greenhill); no HST image was found for GLL J121903+472613. Via this comparison with ACS data, for example, we assessed that GLL J121854+472245 is likely a star; we also rejected GLL J121910+471343, given its very elongated aspect, in spite of having a best match with a GC spectral template. Confirmed and rejected GCC candidates are shown as, respectively, green triangles and red circles in Figure 1.

For each observed source, together with its name and J2000 coordinates, Table 2 lists its projected velocity $V_{\rm proj}$ and error $\Delta V_{\rm proj}$; the $r$-value of the cross-correlation; the velocity template with the best fit; the spectral range over which the cross-correlation was performed; the projected velocity of the HI gas at the position of the source $V_{\rm HI,proj}$ and its error $\Delta V_{\rm HI,proj}$ (see below, Section 4); the archival HST image inspected; the FWHM of the object; the FWHM of the point-spread-function (PSF) of the image; the probable object type. The table has three sections: confirmed candidates; rejected candidates; confirmed non-candidates. Among the rejected candidates, given their spectra and projected velocities, GLL J121854+472144, GLL J121903+472613, GLL J121905+472422, GLL J121909+471335, and GLL J121910+471343 are consistent with being satellite dwarf galaxies of NGC 4258. The first three objects in the latter section (confirmed non-candidates) were within the elliptical selection region in the $u^{*}i^{\prime}K_{s}$ diagram described in Section 2, i.e., their colors resemble those of GCs. J121907+472113 had been discarded mainly on account of its angular size, and indeed it is a spiral galaxy at $z=0.14$. J121924+471306 was blended in the CFHT data and has a small axis ratio (0.5); it appears to be a galaxy at $z=0.04$, with emission lines in its spectrum. J121853+472136, however, although blended in the CFHT data and with a small axis ratio (0.6), could be associated with NGC 4258, given its spectrum and projected velocity. The remaining non-candidates were observed only as a consistency check because they fell on the two fields targeted with the GTC.

Figure 4 shows, for each confirmed candidate, its spectrum in observed wavelength and HST image. For most objects, the spectra are presented in two windows, one shortward of 5450 $\AA$, and one showing the H$\alpha$ region. Spectra have been smoothed with a boxcar of size 5 pixels. The most characteristic spectral lines of old stellar populations or HII regions are indicated.888 We note here that lines are not conspicuous in either GLL J121856+471411 or GLL J121901+471859; however, the SNRs of their spectra are not high enough to confidently eliminate them from the list of confirmed candidates on this basis.

Spectra and images of rejected candidates and confirmed non-candidates are presented, respectively, in Figure 5 and Figure 6.

The spectrum and image of one object within each category are given in the main body of the text; all three figures are continued in the Appendix.

4. Rotation and velocity dispersion

The projected spatial distribution of the GCC sample determined in González-Lópezlira et al. (2017, their Figure 10) suggests a disk. We can now investigate the kinematics of the system, and whether there is evidence of rotation.

Figure 7 shows the projected line-of-sight (LOS) velocities of the confirmed GCCs versus their projected distances from the center of the galaxy; there is no correlation between these two parameters (correlation coefficient of -0.33). Figure 8, on the other hand, overplots the highly probable GCCs (filled circles, confirmed GCCs in Table 2) on the NGC 4258 HI velocity field map from the Westerbork Synthesis Radio Telescope (WSRT) Hydrogen Accretion in LOcal GAlaxieS (HALOGAS) survey (Heald et al., 2011). LOS velocity is coded by color, as indicated in the side-bar, and the same scale is used for both the HI and the GCCs. This graphic shows that the GCCs south of the rotation axis are approaching us, while most of the ones in the observed northern field are receding.

Finally, Figure 9 displays the measured LOS projected velocities versus azimuthal angle, measured counterclockwise from North, for the confirmed GCCs (solid green triangles), rejected candidates that could be satellite galaxies of NGC 4258 (solid red circles), rejected candidates that appear to be foreground stars (solid blue squares), and one non-candidate that could also be an object associated with NGC 4258 (empty red circle). Our GTC objects are overplotted on the NGC 4258 projected HI gas heliocentric velocities (gray curve) in the elliptical annulus with center at RA=12h18m57.505s, Dec=+47$\arcdeg 18\arcmin 4\farcs 3$; position angle PA = 150$\arcdeg$; axis ratio $b/a$ = 0.389 (i.e., cos 67$\fdg$1),999 The inclination $i$ is, actually, 68$\fdg$3, from cos${}^{2}i=[(b/a)^{2}-q_{0}^{2}]/[1-q_{0}^{2}]$, with $q_{0}=$ 0.13 (Giovanelli et al., 1994).

and inner and outer semi-major axes, respectively, 6$\arcmin$ and 12$\arcmin$ (13.3 and 26.5 kpc at the distance of NGC 4258). The projection parameters of the galaxy have been taken from de Vaucouleurs et al. (1991). The HALOGAS moment-1 pixels are 4$\arcsec$ on the side, but the actual resolution is 30$\arcsec$. Given the data quality and depth, the map is reliable to a column density level of $N_{\rm HI}=2\times\ 10^{19}$ atom cm*-2*, at which it has been clipped. Sinusoidal unweighted fits to the projected GC and HI velocities are shown with, respectively, a solid green and a dashed black lines.

Table 4 lists the amplitude, phase, and systemic velocity of the fits. While the amplitude is slightly smaller for the GCs,101010We note that the sinusoidal fit to the HI data does not reach the maximum projected velocity of $\sim$ 203 km s*-1*. the phases and systemic velocities are virtually identical for the two systems. Moreover, the uncertainty-corrected velocity dispersion of the GC system, $\sigma_{\rm GC}$, goes down from 162.1 km s*-1* to 119.8 km s*-1* when the HI velocity at its projected position is subtracted from each one of the clusters, and to 99.5 km s*-1* when the value of the fit to the GC projected velocities is used instead.111111The average uncertainty of the fit, 88.5 km s*-1*, was estimated by means of a Monte Carlo simulation, i.e., we performed 50,000 realizations of the fit around the values of the amplitude, phase, and systemic velocity in Table 4, to probe their Gaussian uncertainties.

In order to estimate the probability of detecting actual rotation from a sample as small as 16 objects, we simulated various cluster systems with different structure and kinematics, and examined which one better matched the observations. The radial distribution of the clusters was chosen to reproduce that of the Milky Way GC system. Specifically, we used the Galactocentric radii in Harris 1996 (2010 edition), and fitted them with a Lorentzian profile.121212${\mathscr{L}}(r)=h/\pi[1+(r/\gamma)^{2}]$, where $\gamma=$ 5.72 kpc, and $h$ is a normalization factor that depends on the number of clusters. This function provides a very good fit to the data, far superior to a Gaussian or a power-law distribution. For the angular distribution, we considered first a system with spherical symmetry, mimicking a spherical halo, and, as a second possibility, a thin disk. Finally, for the kinematics, we worked with two options. Firstly, a rotating system with a flat rotation curve with $V_{\rm max}=220$ km s*-1* beyond a radius of 1.5 kpc, and a solid body rotation within that radius; superposed on this organized rotation, we added a random component with a dispersion of 10 km s*-1* in each of the three directions. The second velocity choice was a random distribution, also with $V_{\rm max}=220$ km s*-1*. In all cases, we included errors on the simulated radial velocities of 20 to 80 km s*-1*, consistent with the observational errors of the actual data. Summarizing, then, we had three different types of simulations: a random halo, a rotating halo, and a rotating disk.

We ran each kind of simulation 200 times. For every run, we extracted positions on the plane of the sky and radial velocities (i.e., projected along the line of sight), and selected the same number of clusters as in the observations (i.e., 16), restricted to the two areas where the actual spectroscopic data were obtained (see right panel of Figure 3). We then fitted the simulated velocities as a function of position angle with a sinusoid, as we did with the real observations. The fits to the observed HI and GC data presented in Figure 9, above, agree with each other to about an rms of 13 km s*-1*.131313This is the rms of the difference between the two fits, calculated in 1$\arcdeg$ bins. We consider that a fit to one realization of the simulations is consistent with the data if it agrees to better than 3$\sigma$ (defined in the same way as the quoted rms) with the HI fit. We find that this occurs for 51% of the simulations of a rotating disk, for 24% of the realizations for a rotating halo, and only 1% of the time for a halo with randomly distributed velocities (see Figure 10). This exercise indicates that the measured velocities are incompatible with a non-rotating system, and significantly more compatible with a rotating disk than with a rotating spherical system.

Hence, we conclude that there is strong evidence of rotation among the confirmed GC candidates of NGC 4258, and adopt a value of $\sigma_{\rm GC}=110\pm$ 10 km s*-1* (average of the two previous estimates) for the galaxy. We also observe that probable satellite galaxies seem to share the rotation of the GC system. If we include them in the fit to the projected GC velocities the amplitude actually increases, while remaining consistent with the measurement for GCs only, as shown in Table 4. Finally, if these objects are included in the calculation of the velocity dispersion, we get $\sigma=120\pm 9$ km s*-1*, consistent with the measurement without them.

We can now compare the measured rotation-corrected velocity dispersion of the GC system to the expected $\sigma_{\rm GC}$ from the correlation with the central supermassive black hole mass ($M_{\bullet}$) derived by Sadoun & Colin (2012). These authors find log ($M_{\bullet}$) $=\alpha+\beta$ log ($\sigma_{\rm GC}/200$ km s*-1*), with $\alpha=8.63\pm 0.09$ and $\beta=3.76\pm 0.52$. Taking $M_{\bullet}=(4.00\pm 0.09)\times 10^{7}M_{\odot}$ (Humphreys et al., 2013) and propagating the errors in both the correlation coefficients and the $M_{\bullet}$ measurement, the expected velocity dispersion is $\sigma_{\rm GC}=107\pm 13$ km s*-1*, which is in excellent agreement with the value of 110$\pm$10 km s*-1* derived by us.

5. Metallicity

As a result of the generally low SNR, we did not attempt to estimate the ages and metallicities of the GC candidates from their individual spectra. Instead, we stacked the spectra of all the confirmed GC candidates into a single spectrum, and hence derived a mean age and metallicity for the GC population. To this end, we used the Penalized Pixel-Fitting algorithm (pPXF; Cappellari & Emsellem, 2004), which extracts stellar population properties by fitting a linear combination of different templates to an observed spectrum in pixel space. The available templates are 182 solar-scaled isochrones with a Salpeter IMF; initial masses from 0.15 $M_{\odot}$ to 7$M_{\odot}$; a range of metallicity -2.3 $<$ [M/H] $<$ 0.2; a helium fraction of $Y=0.23+2.25Z$; and ages between 1 and 17 Gyr. The isochrones also incorporate the thermally pulsing AGB regime to the point of complete envelope ejection (Girardi et al., 2000).

Before stacking, each individual GCC spectrum was multiplied by a mask with a value of zero in noisy regions and one otherwise;141414Noisy regions are those also excluded from the Fourier cross-correlation for the radial velocity estimate. the coadded spectrum was divided by the sum of the masks, then normalized to a maximum value of 1. The resulting spectrum, in rest wavelength, is shown in Figure 11; in view of the improved SNR ($\sim$ 80) with respect to the individual GCC spectra, we did not apply additional smoothing.

Given the lack of a perfect flux calibration along the full spectral range, we carried out separate fits in windows 200$\AA$ wide around the Mg $b$ triplet and H${\alpha}$, respectively, a metallicity-sensitive indicator and a widely used age-sensitive feature. For each region, a first pPXF fit was performed in order to estimate the noise factor, i.e., such that multiplied by the noise one would obtain a reduced $\chi^{2}$ ($\chi^{2}$ per degree of freedom) = 1. No polynomial (either multiplicative nor additive) was included in the fit, since the continuum shape contains important information about the population (Wolf et al., 2007; Cappellari & Emsellem, 2004). Subsequently, a second iteration of the fit was done with the previously obtained noise factor, and with linear regularization (smoothing) of the weights in the age and metallicity axes; both the continuum and the absorption features were fit, assuming constant noise per pixel. Milky Way foreground extinction was not considered, given its very low value of $A_{V}=0.04$ (Schlafly & Finkbeiner, 2011) in the line of sight towards NGC 4258.

In Figures 12 and 13, we show the best fit for the two spectral regions, and their corresponding mass fraction distributions as a function of age and metallicity. The values above the top panels are mass-weighted metallicity [M/H] and age, respectively. We note that the mass fraction distribution with metallicity is quite different for the two spectral windows. In the case of the Mg$b$ index, it is very extended, and goes from 1/20 solar to supersolar; almost half (44%) of the mass has [M/H] $>$ -1.2. For H$\alpha$, the mass distribution is significantly narrower in [M/H]. However, the mass-weighted mean metallicities are very similar for both ranges. While there are limitations of the data and the models (the resolution can modify absortion features, calibration of wavelength and continuum, fraction of blue stragglers, among others) and we cannot set strong contraints on the age or the metallicity, we can certainly conclude that the recovered populations are old ($\sim$ 11 Gyr) and metal-poor ($<[M/H]>\sim$ -1.2).

6. Photometric method validation and the $N_{\rm GC}$ versus $M_{\bullet}$ correlation

Our spectroscopic observations of about half the total sample of NGC 4258 GCCs show 16 confirmed candidates, 10 confirmed non-candidates, and 7 rejected candidates, i.e., no false negatives and a sample contamination of 30%. The 7 contaminants are fully consistent with the results of Powalka et al. (2016), who found, with the $u^{*}i^{\prime}K_{s}$ technique, between 50 and 100 contaminants among the GCCs of M87, in a FOV 9 times larger. Both M 87 and NGC 4258 lie at high Galactic latitudes (respectively, $b=74\fdg 5$ and $b=68\fdg 8$), and indeed the Besançon model of Galactic structure (Robin & Creze, 1986) predicts an almost equal number of foreground stars in their lines of sight (355 versus 329 brighter than apparent $u$ = 20 mag within one square degree). The number of background galaxies, on the other hand, should be about the same, within a few times the Poisson error (e.g., Ellis & Bland-Hawthorn, 2007).

The left panel in Figure 14 displays the distributions of galactocentric projected distances of both confirmed (dashed green line) and rejected (solid red line) candidates; the latter lie on average slightly further away than most confirmed GCCs, so crowding and background light should not be important contributing factors to contamination. Figure 15 shows the FWHM (top left), SPREAD_MODEL($\times$ 100; top right), axis ratios (middle left), $K_{s}$ magnitude values (middle right), ($u^{*}$ - $i^{\prime}$) (bottom left), and ($i^{\prime}$ - $K_{s}$) (bottom right) colors of the confirmed (green bars) and rejected (red bars) candidates. GLL J121905+472422 has both the largest FWHM and SPREAD_MODEL, and the bluest ($u^{*}$ - $i^{\prime}$) and ($i^{\prime}$ - $K_{s}$) colors; together with GLL J121854+472245, it is also among the 3 brightest objects in the $K_{s}$-band. GLL J121910+471343 has the second largest SPREAD_MODEL value, whereas GLL J121903+472613 holds the second bluest ($u^{*}$ - $i^{\prime}$) and ($i^{\prime}$ - $K_{s}$) colors. GLL J121854+472144 has an axis ratio of 0.63, which is clearly smaller than the minimum observed axis ratio of 0.7 for the GCs in both the MW (White & Shawl, 1987) and M 31 (Lupton, 1989). The inclusion of GLL J121854+472144 in our sample was definitely an oversight, since we had actually measured the axis ratios of our candidates with galfit (Peng et al., 2010). Given the shallowness of our near-infrared data of NGC 4258, we hesitate at this point to propose moving the faint cut in $K_{s}$ to a brighter limit. However, a histogram of the $K_{s}$ magnitudes of the confirmed and rejected candidates (Figure 14, right panel) indicates they do have different distributions, and the middle right panel of Figure 15 shows that 3 rejected candidates cluster around $K_{s}$ = 21.4; only one confirmed GCC is fainter. Of the 3 very faint rejected candidates, GLL J121909+471335 alone does not stand out as a near-outlier in any other gauge (GLL J121903+472613 is quite blue and GLL J121854+472144 has a small axis ratio). Finally, GLL J121852+471313 is the singular unremarkable source in every one of the inspected parameters.

We could easily depurate the sample of 5 (out of 7) spurious candidates, while losing solely one confirmed GC, by slightly changing the limits of our selection parameters in future works. As indicated by the dashed lines, we would suggest using SPREAD_MODEL $\leqslant$ 0.015, axis ratio $\geqslant$ 0.7, LFTO - 2 (or LFTO - 1.7 $\sigma_{\rm LFTO}$) $\leqslant$ MAG_AUTO151515Kron-like (Kron, 1980) elliptical aperture magnitude measured by SExtractor. $\leqslant$ LFTO + 3 $\sigma_{\rm LFTO}$, FWHM $\leqslant$ 29 pc, ($u^{*}$ - $i^{\prime}$) $\lesssim$ 1.54, ($i^{\prime}$ - $K_{s}$) $\lesssim$ -0.11.

From their final sample of 39 GC candidates, and considering two (5%) contaminants, González-Lópezlira et al. (2017) extrapolated to a total of $N_{\rm GC}$ = 144$\pm$31${}^{+38}_{-36}$ for NGC 4258, with the first error statistical and the second, systematic. These numbers were obtained following the procedure introduced by Kissler-Patig et al. (1999). The method, based on a comparison with the GC system of the MW, simultaneously accounts for photometric incompleteness, extrapolation over the luminosity function, and incomplete spatial coverage. The total number of clusters in a galaxy, $N_{\rm GC}$, is equal to the number of MW clusters, multiplied by the ratio of the observed GCCs to the numbers that would have been detected in the MW if our Galaxy were observed at the distance and with the orientation of the galaxy of interest, with the same instrument and to the same depth.

Here, applying the 30% contamination correction to the total number, total mass, and specific frequency derived by González-Lópezlira et al. (2017) for the GC system of NGC 4258, we arrive at $N_{\rm GC}=105\pm 26\pm 31$, log $M_{\rm GC}=7.5\pm 0.1\pm 0.1$, $S_{N}=0.3\pm 0.1$ (random uncertainty only). After the contamination correction, NGC 4258 is in even closer agreement than estimated by González-Lópezlira et al. (2017) with the scaling relations between GC system parameters and $M_{\bullet}$ derived for elliptical galaxies.161616 The relations can be written as log $N_{\rm GC}=(-5.78\pm 0.85)+(1.02\pm 0.10)$ log $M_{\bullet}/M_{\odot}$, and log $M_{\rm GC}=(-1.40\pm 0.79)+(1.15\pm 0.09)$ log $M_{\bullet}/M_{\odot}$. For the mass of the central black hole of NGC 4258, these correspond to $N_{\rm GC}=$ 100 and log $M_{\rm GC}=$ 7.3.

7. Discussion and conclusions

Using multi-object spectroscopy, we have investigated both the validity of the $u^{*}i^{\prime}K_{s}$ method plus light concentration parameters to select GCC samples in spiral galaxies, and the kinematics of the GC system of the megamaser prototype NGC 4258.

Regarding the $u^{*}i^{\prime}K_{s}$ method, we have confirmed that it works very efficiently for spirals, with the only, expected, limitation that the fractional contamination will be slightly higher than for ellipticals, given the sparser GC systems of disk galaxies. In our working case there were no false negatives, and the absolute number of contaminants in the sample was consistent with the Galactic latitude of the observed field and the cosmic variance of background galaxies. We suggest here a few distance-independent refinements to the limits on the light-concentration parameters and magnitude values used for the sample selection that should help reduce contamination by 30% – 50%.

Once corrected for contamination, NGC 4258 falls right on the $N_{\rm GC}$ and $M_{\rm GC}$ (total mass of the GC system) versus $M_{\bullet}$ relations followed by elliptical galaxies, within significantly less than one sigma.

We have also determined that the GC system seems to actually have a disky configuration, and to be rotating with a projected maximum velocity of 128 km s*-1*, in phase with the HI disk. This merits further investigation, for example, through a full dynamical modeling. In a few GC systems for which rotation has been measured, it is most common for the metal-rich population (MRP) with small real or projected galactocentric distances. For example, in the MW,171717 https://ned.ipac.caltech.edu/level5/Harris2/Harris1.html. the MRP ([Fe/H] = -0.6) within 9 kpc from the Galaxy center has an average rotation velocity $V_{\rm rot,MRP}$ = 116$\pm$24 km s*-1* ($\sim$ 50% of disk rotation; Reid et al. 2014), and a ratio $V_{\rm rot,MRP}/\sigma_{\rm LOS,MRP}$ = 1.4$\pm$0.3, where $\sigma_{\rm LOS}$ is the line-of-sight velocity dispersion. However, the metal-poor population (MPP, [Fe/H] = -1.6) is pressure-supported, with an average $V_{\rm rot,MPP}$ = 31$\pm$26 km s*-1*, $V_{\rm rot,MPP}/\sigma_{\rm LOS,MPP}$ = 0.3$\pm$0.3 between 0 and 12 kpc.

On the other hand, in M 81 (Nantais & Huchra, 2010) the MRP ([Fe/H] $>$ -1.06) lies mostly within 4 kpc from the center and has $V_{\rm rot,MRP}$ = 122$\pm$18 km s*-1* ($\sim$ 60% of disk rotation, Faber & Gallagher 1979), $V_{\rm rot,MRP}/\sigma_{\rm LOS,MRP}$ = 1., whereas the MPP ([Fe/H] $<$ -1.06) reaches beyond 8 kpc and is, once again, pressure supported, with $V_{\rm rot,MPP}$ = 67$\pm$ 38 km s*-1*, $V_{\rm rot,MPP}/\sigma_{\rm LOS,MPP}$ = 0.5. In M 31, Lee et al. (2008) find that the MRP ([Fe/H] = -0.6) rotates within 3 kpc with an average $V_{\rm rot,MRP}$ = 221$\pm$35 km s*-1* ($\sim$ 95% of disk rotation, Faber & Gallagher 1979), $V_{\rm rot,MRP}/\sigma_{\rm LOS,MRP}$ = 1.9 $\pm$ 0.3. In addition, Perrett et al. (2002) notice that the MRP of M 31 is not flattened, hence bulge-like; that its rotation axis is tilted 5$\arcdeg$–10$\arcdeg$ with respect to the minor axis of M 31; and that its velocity dispersion is quite similar to the bulge’s. Beyond 3 kpc, there is no evidence of rotation for the metal-rich clusters. The MPP in M 31 rotates with basically the same speed as the MRP, $V_{\rm rot,MPP}$ = 217$\pm$ 33 km s*-1*, to a projected distance of 5 kpc, albeit with a slightly larger velocity dispersion, i.e., $V_{\rm rot,MPP}/\sigma_{\rm LOS,MPP}$ = 1.6$\pm$0.5. Further away than 5 kpc, the MPP in M 31 is pressure supported, with $V_{\rm rot,MPP}/\sigma_{\rm LOS,MPP}$ = 0.7 $\pm$ 0.7.

The GC system of NGC 4258 is different. It does not have strong signs of bimodality (González-Lópezlira et al., 2017); its members seem to have low metallicity, around $Z=$ 0.001 ([Fe/H] $\sim$ -1.2); its spatial distribution seems flattened; and its projected rotation velocity of 128 km s*-1* is $\sim$ 65% of the projected HI disk rotation velocity, up to a projected distance of more than 17 kpc. Assuming that the GC system has an intrinsic anisotropy similar to the HI disk, and that the viewing angle is the same, the deprojected velocity would be $V_{\rm rot}\sim$ 140 km s*-1*, and $V_{\rm rot}/\sigma_{\rm GC}$ = 1.3; without deprojection, $V/\sigma$ = 1.2.

These characteristics evoke the clumpy, gaseous, high pressure, disks at $z\geqslant$ 2 that constitute nowadays the more favored environment for GC formation (e.g. Agertz et al., 2009; Kruijssen, 2015). These disks rotate, but are highly turbulent, with $V/\sigma\sim$ 1, and their existence is supported by strong observational evidence (e.g., Förster Schreiber et al., 2009; Wisnioski et al., 2015; Harrison et al., 2017; Turner et al., 2017; Dessauges-Zavadsky & Adamo, 2018).

Beyond validating the $u^{*}i^{\prime}K_{s}$ plus light-concentration parameters method for the identification of GCCs in spirals, the present work highlights the importance of studying GC systems and scaling relations in spirals. 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, and hence fundamental clues to the understanding of galaxy formation.

R.A.G.L. & L.L. acknowledge the financial support of DGAPA, UNAM (respectively, projects IN108518 and IN112417), and of CONACyT, Mexico. We sincerely thank the anonymous referee for the very constructive and insightful comments. Based on observations made with the NASA/ESA Hubble Space Telescope, and obtained from the Hubble Legacy Archive, which is a collaboration between the Space Telescope Science Institute (STScI/NASA), the Space Telescope European Coordinating Facility (ST-ECF/ESA) and the Canadian Astronomy Data Centre (CADC/NRC/CSA).