Luminosity functions of globular clusters in five nearby spiral galaxies using HST/ACS images Free

ABSTRACT

1 INTRODUCTION

Globular clusters (GCs) are among the oldest objects in the Universe. Their relatively high luminosities (M_V = −5 to −10) and compact sizes (half-light radius of a few parsecs) allow them to be readily detectable in nearby external galaxies (Harris 1996). Their low metallicities (log [Fe/H] ≲ −0.5) and enhancements of α elements (log [O/Fe] ≥ 0.20) suggest that they are formed at very early epochs of galaxy formation (Binney & Merrifield 1998). The GC formation requires highly efficient star formation, usually associated with intense starburst activity (Bastian 2008). Star formation in the spheroids (early-type galaxies, spiral bulges, and haloes) represents one such activity in the early Universe. Interactions and mergers between galaxies provided the next epochs of star formation efficient enough to form massive star clusters such as GCs (Whitmore & Schweizer 1995). These intermediate-age clusters are similar in size and mass as the young massive clusters, also known as Super Star Clusters (SSCs), seen in presently active starburst regions (O’Connell et al. 1995). In this work, we refer to as SSCs all those relatively younger clusters associated to discs of galaxies and reserve the word GCs to describe old clusters associated to spheroids. Because of their early formation, the properties of GC systems in galaxies provide important constraints on models of galaxy formation and evolution (Ashman & Zepf 1998).

A variety of GC system properties that are potentially relevant to cosmological theories of galaxy formation have been identified. These include, colour distribution (Larsen et al. 2001; West et al. 2004), luminosity function (Reed, Harris & Harris 1994; Whitmore et al. 1995), radial density distribution (Bassino, Richtler & Dirsch 2006; Kartha et al. 2014), specific frequency as a function of galaxy type (Harris & van den Bergh 1981; Peng et al. 2008), total number of GCs as a function of supermassive black hole masses (Burkert & Tremaine 2010; Harris & Harris 2011; Harris et al. 2014), and the nature of their size distribution (Kundu & Whitmore 1998; Larsen et al. 2001; Webb, Harris & Sills 2012). These properties have been exhaustively reviewed in Brodie & Strader (2006).

Elliptical galaxies have been the most commonly used targets for the study of GC systems. This is principally because of the relative ease with which GCs can be identified when superposed on a smooth light distribution in these galaxies, as compared to the inhomogeneities inherent to the discs of galaxies. In addition, the identification procedure of GCs in disc galaxies has to take into account possible contamination from reddened young SSCs and intermediate-old (age∼1–10 Gyr) SSCs. Correction of GC magnitudes and colours for the effects of dust in the interstellar medium also becomes more important in spiral galaxies, than in elliptical galaxies.

The most important characteristic of GC systems is the existence of bimodality in their colour distribution (Zepf & Ashman 1993; Gebhardt & Kissler-Patig 1999; Larsen et al. 2001). This bimodality is understood to be due to an underlying bimodal distribution of GC metallicities (Brodie & Strader 2006). Elliptical galaxies with well-determined metallicities confirm the existence of such a bimodal distribution in metallicities (e.g. Cohen, Blakeslee & Ryzhov 1998; Usher et al. 2012). This has led to the division of GC systems into two sub-populations: red and blue, corresponding to metal-rich and metal-poor populations, respectively. These two sub-populations show differences in other properties, such as size and spatial distribution (Kundu & Whitmore 1998; Larsen & Brodie 2000a; Webb et al. 2012), suggesting possibly two independent formation channels of GC systems.

The GC luminosity function (GCLF) is another property that is well established in elliptical galaxies. GCLFs are described by lognormal distributions with M_{0, V} = −7.40 ± 0.25 and σ = 1.40 ± 0.06 (e.g. Reed et al. 1994; Whitmore et al. 1995). The GCLF is often suggested to be a universal function (e.g. Hanes 1977b; Richtler 2003) in elliptical galaxies, and have been used as a standard candle for the determination of distances to their host galaxies (e.g. Richtler 2003). Among spiral galaxies, the lognormal nature of LFs have been firmly established only in the Milky Way (e.g. Harris 1996; Bica et al. 2006) and Andromeda (e.g. Peacock et al. 2010), the only two spiral galaxies where GC system properties have been reasonably well-characterized, with values of M_{0, V} = −7.33, σ = 1.23 (Secker 1992; Reed et al. 1994) and M_{0, V} = −7.6 ± 0.15, σ = 0.82 (Secker 1992; Reed et al. 1994), respectively. Within the errors of measurements, these values are in agreement with the TO found in elliptical galaxies (Ashman, Bird & Zepf 1994). Using the catalogue of Harris (1996) with 143 GCs, Jordán et al. (2007) found M_{0, V} = −7.40 ± 0.10, σ = 1.15 ± 0.10 for MW. Fall & Zhang (2001) reproduced the lognormal form, as well as the TO value of the Galactic GCs by evolving dynamically clusters obeying power-law mass functions under the gravitational potential of the Milky Way. The uniformity in the TO values in spite of GC systems being constituted of two independently formed sub-populations puts strong constraints on the formation scenarios of metal-rich and metal-poor sub-populations.

The total number of GCs in galaxies (N_GC) is another property that strongly constraints the formation scenarios of galaxies. Hanes (1977a) found that N_GC is proportional to the mass of its host galaxy and is independent of its morphology. Harris & van den Bergh (1981) defined the specific frequency, S_N, defined as the number of GCs per absolute magnitude in the V-band, normalized to M_V = −15 mag: S_N|$= {N}_{\text{G}\text{C}}\times 10^{0.4({M}_{V}+15)}$|⁠. They found that S_N of a galaxy is approximately proportional to the total luminosity of the spheroidal component in the galaxy. Recent studies have shown that elliptical galaxies have a higher S_N as compared to that in spiral galaxies (e.g. Peng et al. 2008; Georgiev et al. 2010).

Classical models of formation of elliptical galaxies either by merging of disc galaxies or by the multiphase dissipational collapse have serious short comings to explain all the above-discussed properties of GC systems. For example, the scenario of the formation of ellipticals by mergers of spiral galaxies predicts similar S_N values in ellipticals as compared to spirals. These models require the metal-poor population forming earlier than the metal-rich clusters. On the other hand, under the hierarchical scenario of galaxy formation, metal-rich GC systems formed in-situ in the parent galaxy, which are defined as the highest peaks in density fluctuations, whereas the metal-poor GC systems formed in low-mass haloes and got accreted into host galaxy (Côté, Marzke & West 1998). The predictions from these latter models depend critically on the assumed GC system properties in spiral and dwarf galaxies, which are yet to be well established beyond the Milky Way and Andromeda.

For firmly establishing GC system properties in spiral galaxies, the GC sample should cover a substantial area of the galaxy, reaching limiting magnitudes fainter than the expected TO magnitudes. In addition, it is desirable to have observations in one of the filters blueward of the Balmer jump (∼3650 Å) at least in some fields in order to estimate the contamination of the GC sample by reddened SSCs. The first criterion requires analysis of multiple pointing Hubble Space Telescope (HST) images or ground based images taken with wide-field cameras, whereas the second one requires images deep enough to register V ∼23 mag at distances less than 10 Mpc. The third criterion requires the availability of images in the U-band covering at least for some part of the target galaxies.

The existing works on spiral galaxies do not fulfil all the above three criteria. For example, Chandar, Whitmore & Lee (2004) carried out a study of GCs in five spiral galaxies and Goudfrooij et al. (2003) of seven edge-on disc galaxies, both using HST/WFPC2 fields, but covered relatively small areas in each galaxy. Study by Young, Dowell & Rhode (2012) of two edge-on spirals covered spatially their entire optical extents, but had a limiting magnitude slightly brighter than the expected TO. Other works on spiral galaxies include Santiago-Cortés et al. (2010) and Nantais et al. (2010b) (M81; Sab), Hwang & Lee (2008) (M51; Sbc), Barmby et al. (2006); Simanton et al. (2015) (M101; Scd), Cantiello et al. (2018) (NGC 253; Sc), and González-Lópezlira et al. (2017) (NGC 4258 Sbc). None of these works fulfilled all the three criteria.

At present, multipointing HST data covering a good fraction of the galaxy angular size (see Fig. 1) and observed in multiple filters exist for a number of nearby spiral galaxies. Some of these galaxies are also observed in the F336W filter. A careful analysis of these images would be able to provide catalogues of GCs that are free from contaminating stellar and non-stellar objects, and with a good spatial coverage. In this paper, we analyse five giant spiral galaxies that fulfill all the criteria mentioned above, and are nearer than 10 Mpc.

Figure 1.

Sample of study. Galaxies are shown in F435W filter, with observation footprints superimposed. Cyan-coloured rectangles show the F336W filter footprints. The number in each footprint indicates the visit number within proposal. All galaxies are aligned such that north is up and east to the left. Black ellipse represent R₂₅ for NGC 4258 and M51, and 0.5R₂₅ for M101 and NGC 628. See fig. 1 in Santiago-Cortés et al. (2010) for visualization of footprints in M81.

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In Section 2, we describe the sample of galaxies and the data used. In Section 3, we explain the detection and our criteria for selecting sample of GCs in the selected galaxies. Results of the completeness tests are presented in Section 4. Analysis and discussion of the properties of our GC samples is presented in Section 5. In Section 6, we give concluding remarks.

2 SAMPLE OF SPIRAL GALAXIES AND DATA

With the aim of comparing the properties of GC populations in spiral galaxies with those in elliptical galaxies, we searched for nearby giant spiral galaxies with multiple pointing HST Advanced Camera for Surveys (ACS) images in at least three optical broad-band filters. Galactic GCs typically have half-light radius r_h ≲ 10 pc (Harris 1996). At the spatial resolution of ∼0.1 arcsec (image scale = 0.05 arcsec pixel⁻¹) offered by the ACS, majority of the GCs are more extended than the Point Spread Function (PSF) up to ∼10 Mpc distances. Beyond this distance, GC selection would be heavily affected by incompleteness. Keeping this in mind, we looked for HST images of giant spiral galaxies at distances <10 Mpc. We analysed such data for five galaxies. In Table 1, we list these galaxies along with their basic properties and source of images. All these galaxies have multiple pointing HST/ACS images in F435W (B), F555W (V), and F814W (I) bands, covering a good fraction of their optical extent. In addition, all have at least one pointing in the F336W (U) filter, which allows an estimation of the contamination of our GC catalogues by reddened SSCs.

The Hubble Legacy Archive¹ (HLA) provides images and photometric catalogues obtained with daophot² (Stetson 1987) and SExtractor³ (Bertin & Arnouts 1996). These catalogues have been used by Whitmore et al. (2014) to study the luminosity function of star clusters in selected fields for a sample of 20 spiral and irregular galaxies. As a first step, we used these catalogues to select a sample of GCs. However, we noticed that the adjacent images had vastly different limiting magnitudes in some galaxies. A visual inspection of catalogued sources on the images suggested that the background values used in some images were inappropriate (see Appendix  A). Since we are looking for a complete sample of GCs up to a given limiting magnitude, we decided to make our own catalogues on the downloaded images.

In Fig. 1, we show the images of galaxies in F435W band, with footprints superposed. In Tables 2 and 3, we give logs of observations for four of our galaxies in the optical and F336W filters, respectively. Different columns tabulate pointing IDs, exposure times, zeropoints⁴ (c0) in each filter. We also give the number of stars used for astrometry and RMS error in the coordinates. The fifth galaxy, M81, has been the subject of study previously by our group (Santiago-Cortés et al. 2010), and hence we directly use the GC catalog from that study.

3 SOURCE DETECTION AND CLUSTER SELECTION

We used images in F814W band for detecting sources using SExtarctor. The critical detection parameters used are: detect_minarea = 5 pixel, detect_thresh = 1.4, back_size = 32 pixel and back_filtersize = 3 pixel, where each pixel corresponds to 0.05 arcsec. Using these criteria, typically we obtained several tens of thousands sources in each frame. Elaborate filtering criteria need to be implemented to select GCs from this catalogue.

As discussed in the introduction, making a catalogue of GCs is more challenging in spiral galaxies as compared to elliptical galaxies. This is because, unlike elliptical galaxies, spiral galaxies show a lot of structures at the scale comparable to the size of GCs. These structures lead to a lot of spurious sources in the SExtarctor catalogue. Filtering based on structural parameters (e.g. Mayya et al. 2008), colour (e.g. Fedotov et al. 2011), concentration index (e.g. Whitmore et al. 2014), colour–colour diagrams (e.g. Muñoz et al. 2014; González-Lópezlira et al. 2017) or a combination of these, are the most commonly used methods. In this paper, we used the cluster selection method used in Mayya et al. (2008) and Santiago-Cortés et al. (2010), which consists of using SExtractor-derived structural parameters (fwhm, area, ellipticity) to define a cluster sample, and photometric parameters (colour) to separate young clusters from GCs. The method is described in detail in Sections 3.2 and 3.4, below.

3.1 Astrometric correction of HST images

Before running SExtratctor it was necessary to astrometrize all HLA images. We performed this with the help of GAIA stars using Gaia Data Release 2 (Gaia DR2; Gaia Collaboration 2016, 2018). We used the iraf task ccmap with a second-order polynomial in coordinates to achieve this. Minimum of 10 stars were used in each pointing (5 stars in one pointing of NGC 4258), resulting in mean rms astrometric accuracies of ∼0.095 arcsec (M101), ∼0.014 arcsec (NGC 4258), ∼0.048 arcsec (M51), and ∼0.042 arcsec (NGC 628). We took into account these rms errors to identify and eliminate duplicate sources in the overlap zones between two adjacent frames. In Fig. 2, we zoom in on an image section in M101 to illustrate a typical field before and after astrometric correction. The left-hand image shows the HST coordinate system for this field, whereas the image on the right shows the corrected coordinate system. The circles show the coordinates of GAIA (Gaia DR2) stars in this field of view.

Figure 2.

Illustration of astrometry on the HST image using a section of M101. Left-hand panel: astrometric coordinates on the downloaded image from HLA. Right-hand panel: image after applying our astrometric corrections based on the GAIA DR2 coordinates of the field stars. Three field stars in the displayed FOV are identified with blue circles of 1 arcsec radius. North is up and east to the left in these images.

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3.2 Selection criteria for defining a cluster sample

In this work, we aim to obtain a sample of GCs with properties similar to those in the Milky Way, which are marginally resolved on the HST/ACS images at the distances of sample galaxies. We considered all objects with fwhm>2.4 pixel as GC candidates. This cut-off corresponds to 2.1 pc and 5.7 pc, in the nearest (M81) and farthest (NGC 628) galaxies of the sample. Thus, farther a galaxy is, lesser would be the number of compact objects we would detect. GCs do not show a mass–radius (or equivalently luminosity–radius) relationship (Gieles et al. 2010) and hence this bias is not expected to affect the LF of GCs. GCs are roundish objects, and hence their ellipticity parameter is expected to be close to zero. SExtractor-measured ellipticity even for roundish objects could be as high as 0.3, as it is measured at the isophote corresponding to the detection threshold on the background subtracted image. Another parameter that SExtractor calculates is area, with is the number of pixels enclosed by the isophote where ellipticity is measured. Both the ellipticity and area depend on the threshold used for the detection, and hence a cluster of same magnitude and fwhm can have different values of ellipticity and area, depending on the underlying background.

We have carried out Monte Carlo simulations to understand the behaviour of these parameters for clusters of different fwhm and magnitudes, appropriate to the background and crowding encountered in each galaxy in the F814W band. In Section 4, we describe in detail these simulations. In Fig. 3 (right-hand panel), we show the simulated clusters in area versus fwhm diagram for each of our sample galaxies. Simulations were carried out for a range of magnitudes between 19 and 24 magnitudes, for fixed values of fwhm. As expected, brighter clusters have larger areas at a given fwhm, and the area increases quadratically with fwhm for a cluster of given magnitude. We show the dependence of area with fwhm for objects of 23 mag by the blue solid curve, which is defined by the same equation, AREA = 52.5 − 1.0 FWHM + 0.50 FWHM², for all our sample galaxies. On the left-hand panel, we show all the detected sources in fwhm versus area diagram for our five sample galaxies. The parabola defined by the simulations is shown, which separates the bonafide cluster candidates (that are above the parabola) from contaminating sources (image blemishes, stellar asterisms, image borders etc.), which dominate the number of detected sources at every fwhm. A hard cut in magnitude or area can also eliminate the contaminating objects, but the use of parabola is the most effective way to eliminate these contaminating sources, without missing many genuine clusters. GCs at the distance of sample galaxies are expected to have fwhm close to the observational lower limit of 2.4 pixels. In the top panel of Fig. 4, we show the observed distribution of fwhm for our final GC sample for one of our sample galaxies (M101), which indeed peaks at the first bin. However, we include objects up to fwhm = 10 pixels to account for possible errors in the measurement of fwhm at detection limits. Simulations suggest that even the brightest clusters (F814W = 19) do not occupy an area>500 pixels as long as the fwhm∼5 pixels, and hence we eliminated sources with area>500 pixel.

Figure 3.

Left-hand panel: Selected GCs (red dots) compared to all SExtractor sources (black dots) in area versus fwhm plane for our 5 sample galaxies. GCs have (B − I)₀ > 1.5 mag, 2.4<fwhm/pix<10 and are above the parabola (blue line). Clusters bluer than this limit are SSCs which are identified by blue dots. Black dots above the parabola are extended sources with ellipticities>0.3, and hence do not satisfy all cluster selection criteria. Right-hand panel: area versus fwhm for simulated star clusters. The fwhm of mock clusters are fixed at 2.0 (black), 2.4 (cyan), 3.0 (blue), 4.0 (green), 5.0 (magenta), 6.0 (yellow), 7.0 (orange), and 8.0 (red) pixels. For each fixed fwhm, 100 mock clusters between 19 and 24 magnitudes are generated, which are shown by symbols of different sizes (successively smaller sizes for fainter sources; see the bottom-most right-hand panel for a guide on the symbol size). Most of the clusters with mag >23 lie below the parabola defining the minimum area–fwhm relation, and hence are rejected by our selection criteria.

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Figure 4.

(Top) Distribution of fwhm for the candidate GCs in one of our galaxies (M101). (Bottom) Comparison of the two commonly used discriminators between clusters and stars, CI versus fwhm. Data are consistent with a linear fit (solid line whose equation is given in the top left-hand corner) above the dividing line between clusters and stars (horizontal dashed line at CI = 1.15). Data correspond to M101, which has 45 GCs below the defining line (see the text for details).

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The HLA catalogues include a parameter known as concentration index (CI), defined as the difference between magnitudes measured in 1 and 3 pixel radius apertures. Some studies have made use of this parameter to discriminate between point and extended sources (e.g. Whitmore et al. 2014; Simanton et al. 2015) CI <1.15 for stars. In our study, we have used the fwhm = 2.4 pixel (0.12 arcsec), a direct discriminator between unresolved (stars) and resolved (extended) sources. In the bottom panel of Fig. 4, we show CI against the fwhm for all our clusters for M101. As expected, the two parameters are correlated. The minimum CI (1.07) for our sample clusters is slightly less than 1.15, the value adopted in other studies. Forty-five (∼4 per cent) of our sources would not have been classified as stellar cluster if we had adopted the CI criterion. A visual inspection of these borderline objects suggests they are likely to be clusters, rather than stars. We identify these borderline cases (1.07<CI<1.15) by red dots surrounded by black circles in Fig. 8. In NGC 4258, these include two of the brightest GCs.

3.3 Aperture photometry

3.3.1 Magnitudes, colours, and aperture correction

SExtractor was also used for obtaining photometry in the three bands for all the detected sources. The photometry was carried out in 10 apertures with radii between 1 and 15 pixel (0.05 arcsec to 0.75 arcsec), using the zeropoints (c0) tabulated in Table 2 for each frame. Unlike stars, aperture correction for clusters depend on the cluster size, which is parametrized by the fwhm in SExtractor. The aperture correction is defined as the difference between magnitude at 3 pixel (0.15 arcsec) radius and the magnitude at an infinite aperture (ΔF814W = m_F814W(3 pix)−m_F814W(tot)). Even the most extended clusters (objects with Gaussian fwhm = 9 pixel) contain more than 98 per cent of their total flux within an aperture of 15 pixel radius, because of which we have used the magnitude in an aperture of 15 pixel radius as m_F814W(tot).

We used the results of our experiments with simulated clusters, described later in Section 4, to obtain the correction as a function of measured fwhm in each galaxy. The results are shown in Fig. 5 for M101. A group of horizontally distributed points corresponds to the same input fwhm. The measured fwhm for fainter clusters tends to be systematically larger than the input fwhm, which is the reason for the horizontal spread. The aperture corrections (open circles) obtained for 35 isolated clusters with good photometry (error <0.005 mag in 9 pixel) is also shown in the figure. Both the simulated and observed corrections smoothly increase with the fwhm. For the simulated data, we obtained mean values of measured fwhm and correction for each input fwhm and fitted these mean values by a straight line which is shown by the solid line. The fitted results (the slope m, and the abscissa, b) for all the sample galaxies are given in Table 4.

Figure 5.

Apertures corrections versus FWHM for observed (open circles) and simulated (coloured points) star clusters in M101. The line is the linear fit to the simulated points.

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We applied these corrections to the F814W aperture magnitudes of 3 pixel radius of all cluster candidates to obtain their total magnitudes. Colours (F435W − F814W, F435W − F555W, and F555W − F814W), however are obtained by subtracting magnitudes in the corresponding filters at 3 pixel radius aperture. This procedure ensures that errors on colours are smaller than the aperture corrected magnitudes. The errors on colours were calculated by quadratically summing the magnitude errors in the two bands forming a colour.

3.3.2 Photometric error estimation

Formal errors⁵ on photometric measurements are obtained using the formula: MAGERR = 1.086 × (FLUXERR/FLUX), where |$FLUXERR=\sqrt{\displaystyle \sum _{i\in A} (\sigma _{i}^{2}+\frac{p_{i}}{g_{i}})}$|⁠, with A representing the set of pixels defining the photometric aperture, σ_i, the standard deviation of noise (in ADU) estimated from the local background, p_i the background-subtracted image pixel value, and g_i the effective detector gain in e-/ADU at pixel i. However, small-scale variations in the disc background gives rise to additional errors while carrying out photometry of non-stellar objects such as GCs, that are usually larger than the formal errors. We use the colour–colour diagram (F435W − F555W)₀ versus (F435W − F814W)₀ to estimate the real errors on our colours. In Fig. 6, we illustrate the method adopted for this. In this plot, we show the colours for star clusters in NGC 4258, with the SSPs with Z = 0.001 and 0.019 metallicities from Bruzual & Charlot (2003). The reddening vector for A_V = 4 mag is also shown. The reddening vector and the evolutionary trajectory are parallel in this colour–colour diagram, implying the spread in the (F435W − F555W)₀ colour for a fixed (F435W − F814W)₀ colour (and vice versa) is entirely due to observational errors. We calculated the dispersions in colour for each axis for fixed bins of 0.2 mag width in the other axis. In the figure, we show these dispersions by crosses places at every 0.4 mag. There is a tendency for slightly higher error for the reddest colours. We take into account this dispersion in each colour as an additional source of error while comparing observational colours with model colours.

Figure 6.

Colour–colour diagram showing all SExtractor-detected clusters for one of our sample galaxies (NGC 4258). The SSP evolution between 0 and12 Gyr at two metallicities and the reddening vector for A_V = 4 mag, with arrow heads placed at 1 mag intervals, are shown. Both the evolution and the reddening move the points along the same direction, and hence the spread in either axis around a mean local value (the crosses) is entirely due to observational errors in colours.

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3.4 The sample of GCs

We define GCs as old (age>10 Gyr) metal-poor (Z ≲ 0.001) clusters, having properties similar to that for the sample of Galactic GCs. However, unlike the Galactic GCs, extragalactic GCs cannot be selected by their visual appearance even on the HST images. Our cluster sample contains GCs as well as relatively young clusters, such as SSCs. In Table 5, we list the source detection statistics in each galaxy. The second column contains all SExtractor-defined sources, with the column 3 containing the number of cluster sources. Cluster samples in spiral galaxies contain more SSCs than GCs, and hence quantitative criteria are required to discriminate between GCs and SSCs. Cluster colour is the most useful discriminator for achieving this. For example, metal-poor SSPs (Z ≤ 0.001) predict B − I ≥1.5 mag for populations older than ∼3 Gyr (Bruzual & Charlot 2003).

In Fig. 7, we plot the distribution of (F435W − F814W)₀ colours for all clusters (black histogram) and for clusters brighter than M_F814W = −9 mag (red histogram) in each galaxy. The latter is multiplied by a factor which is indicated in the figure annotation. For the bright cluster sample, four of the five galaxies studied here show a bimodality in the distribution, the exception being M101. The colour that separates the two distributions is nearly the same in all these galaxies, and corresponds to the (F435W − F814W)₀ = 1.5 mag bin. The full cluster sample also shows a minimum in the distribution close to this colour in four of the galaxies. In M101, although the evidence for bimodality is not strong for the bright cluster sample, the total sample indicates bimodality with the saddle point again corresponding to the (F435W − F814W)₀ = 1.5 mag. The blue and red distributions correspond to the SSCs, and GCs, respectively. Based on this, we use (F435W − F814W)₀ = 1.5 mag to separate GCs and SSCs. Column 4 of Table 5 lists the number of clusters classified as GCs using this colour criterion. Coordinates and photometry for each of the selected GCs are given in Table 6. The table in the body of the text contains data only for three brightest objects in each galaxy. The entire table is available in electronic version.

Figure 7.

Colour histogram of all (SSC+GC) cluster candidates. The black line shows the colour distribution over the entire range of magnitudes, whereas the red histogram shows the distribution for bright (M_I ≤ −9) clusters. The latter histogram values are multiplied by a factor indicated in each panel. The vertical line at (F435W − F814)₀ = 1.5 separates SSCs from GCs.

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The red tail of the reddened SSC colours most likely extends beyond the colour cut of (F435W − F814W)₀ = 1.5 mag, and hence colour-selected GC sample in spiral galaxies is expected to have some contamination from the reddened SSCs. The SSC population has a long tail on the red side, which is either due to a spread in reddening, or/and due to a spread in ages of SSCs. In either case, the red tail of SSC distribution has very few clusters beyond (F435W − F814W)₀ >1.5 mag. The estimation of contaminating objects in the GCs samples is discussed in Section 3.5.

In Fig. 8, we plot all candidate clusters in a colour–magnitude diagram (CMD) formed using |$M_{F814W_{0}}$| versus (F435W − F814W)₀, where SSCs and GCs are shown by blue and red points, respectively. The evolutionary loci of clusters for Simple Stellar Population (SSP) models from Bruzual & Charlot (2003) at typical metallicities of SSCs (Z = 0.008∼1/3 solar) and GCs (Z = 0.001) are shown. These models correspond to synthetic clusters of mass = 1 × 10⁶ |$\mathcal {M}_{\odot }$| obeying the Kroupa initial mass function (IMF) between masses 0.1 and 100 |$\mathcal {M}_{\odot }$|⁠. If the GCs are as old as 12 Gyr, the range of magnitudes covered by the GCs corresponds to mass range shown by the dashed vertical line, and the range of colours corresponds to reddening equivalent to A_V = 0 to ∼2 mag.

Figure 8.

|$M_{F814W_{0}}$| versus (F435W − F814W)₀ CMD of all cluster candidates in our sample of galaxies. Candidates having (F435W − F814W)₀ >1.5 mag are GC candidates (red dots), and bluer objects are young disc cluster candidates (blue dots). The evolutionary locus of the SSPs from Bruzual & Charlot (2003) for two metallicities (Z = 0.001, black solid line and Z = 0.008, black dashed line), of mass = 1 × 10⁶ |$\mathcal {M}_{\odot }$| and Kroupa IMF, are shown. Locations corresponding to selected ages (0.1, 0.5, 1, 3, 6, and 12 Gyr) are marked (cyan and magenta triangles in each SSP). The chosen colour cut separates clusters older than 3 Gyr from the younger ones for unreddened SSPs. The reddening vectors with A_V = 1 mag are shown for 3 cluster masses for an SSP of 12 Gyr age and Z = 0.001, typical values expected for GCs. The majority of the GC candidates are in the zone occupied by clusters of mass 1 × 10⁵ to 5 × 10⁶ |$\mathcal {M}_{\odot }$| and A_V between 0 and 1 mag. Encircled red dots correspond to compact GC candidates (1.07 <CI<1.15; see section 3.2 for details) in our sample.

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3.5 Contamination of the GC sample from reddened SSCs

Fig. 8 suggests that the reddened SSC colours overlap with the GC colours. The colour histogram (Fig. 7) also suggests that the distribution of the SSC colours (the bluer peak) most likely has a long tail on the redder side, that overlaps with the GC colours. Thus, contamination to some degree from reddened SSCs is unavoidable when selecting GC samples in spiral galaxies using colour-cuts. We use the subsample of clusters with U-band photometry to estimate the fraction of contaminants in each galaxy.

Use of colour–colour diagrams involving ultraviolet and optical filters is known to break the age-reddening degeneracy (e.g. Georgiev et al. 2006; Bastian et al. 2011; Fedotov et al. 2011). In particular, U − B colour separates clearly clusters younger (SSCs) and older (GCs) than ∼3 Gyr. Keeping this in mind, we searched the HST archives for images in the WFC3/F336W filter. All our sample galaxies have at least one pointing in this filter (see Table 3). For M101, the F336W images had good astrometry. For the fields in other galaxies, we carried out the astrometry following the same procedure as described in Section 3.1.

WFC3/F336W image for M81 is available for only one pointing, as compared to the 29 pointings with the ACS, with only 7 GC candidates (4 per cent) falling in the FoV of the F336W image. The contamination fraction obtained from such a small coverage of the FoV is not expected to be representative. On the other hand, Sloan Digital Sky Survey⁶ (SDSS) image of this galaxy obtained from multiple pointings covers the FoV of all the 29 HST/ACS pointings. The relative nearness of this galaxy allows the detection and photometric analysis of 65 per cent of clusters that occupy the relatively uncrowded fields. We hence used the SDSS u − g colours for estimating the contamination fraction in M81. In column 5 of Table 5, we present the fraction of GC candidates with U-band images, i.e. SDSS-u for M81 and HST/WFC3 F336W for the rest. We performed photometry using the phot task in iraf using the same photometric parameters as for the HST/ACS images.

In Fig. 9, we plot all candidate clusters with F336W coverage in (F336W − F435W)₀ versus (F435W − F814W)₀ colour–colour diagram. For M81, we show the SDSS u − g colours (in the AB system) in the ordinate. The evolutionary loci of clusters in this diagram for theoretical SSPs from Bruzual & Charlot (2003) of different metallicities are shown. The U − B colours of reddened young (<10 Myr) clusters are distinctly different from that of clusters older than ∼3 Gyr, which allows us to break the age-reddening degeneracy. Thus reddened young SSCs (contaminants) would lie below the SSP locus for age>3 Gyr. In other words, for a redder (F435W − F814W₀ > 1.5) cluster to be considered a genuine GC, its U − B colour, after taking into account photometric errors, should correspond to a location above the SSP locus in the figure. As illustrated in Fig. 6, the real errors in photometry are larger than the formal error bars, which limits the use of the colours for a precise determination of age. Nevertheless, the photometric quality is good enough to separate reddened SSCs from GCs. In the last column of Table 5, we give the fraction of contaminants in our GC samples. The values lie between 14 and 35 per cent in the sample galaxies.

Figure 9.

The U-selected cluster candidates in (u − g)₀ versus (F435W − F814W)₀ diagram for M81 and (F336W − F435W)₀ versus (F435W − F814W)₀ diagram for the rest of the sample galaxies. Candidates having (F435W − F814W)₀ >1.5 mag are GC candidates (red dots), and bluer objects are young disc SSC candidates (blue dots). The evolutionary loci of SSPs from Bruzual & Charlot (2003) for different metallicities using Kroupa IMF are shown by solid curves of different colours, following the colour notation shown in each panel. The bluest colour that a classical GC can have (Z = 0.0004 and age 12 Gyr) is marked by a solid triangle. The reddening vector with A_V = 1 mag is shown. The reddened young SSCs that occupy the GC colours are contaminants, which are identified by red dots surrounded by circles of cyan colour.

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In Fig. 10, we explore whether contaminant fraction in our GC samples depends on the colour and magnitude of the GCs. We carry out this analysis in bins of 0.5 mag in colours and magnitudes. In order to avoid fluctuations caused due to small number statistics in some of the bins, we plot only those values for which the number of contaminants in any bin was more than the Poisson error in that bin, taken as the square root of the total number of GC candidates in that bin. For the rest of the bins, we plot the global values. In general, all galaxies have higher contaminant fraction for (F435W − F814W)₀ >2.2 mag, with as much as 50 per cent of the GCs of (F435W − F814W)₀ = 2.5 mag being contaminants (reddened young SSCs) in M101 and M81. None of the galaxies show any significant dependence of the contaminating fraction with magnitude. We hence use the global values of the contaminant fraction to correct the LF obtained from our entire GC sample in Section 5 for all galaxies.

Figure 10.

The fraction of contaminants (reddened young SSCs) in our GC samples as a function of colour (left-hand panel) and magnitude (right-hand panel) for our five sample galaxies. The vertical dashed-line in the left-hand figure corresponds to the reddest colours reached by SSPs for unreddened GCs. See the text for details.

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3.6 Comparison of our GC catalogues with those in the literature

In four of our five sample galaxies, there exists a previous catalogue of GCs. We reiterate that none of these catalogues are as complete as our catalogues in terms of spatial and magnitude coverages, as well as in the estimation of contamination fraction from reddened SSCs. We here compare our catalogues, obtained using uniform selection criteria, with the catalogues from other authors, using different selection criteria.

3.6.1 M81

Nantais et al. (2010b) reported a sample of 233 GC candidates in M81, that had made use of data from HST/ACS and SDSS. They used an FWHM>3 ACS pixel (0.15 arcsec) as the main discriminator. We find that 107 of our 154 GCs are present in the catalogue of Nantais et al. (2010b). Most of the remaining 49 GCs in our sample have 2.4<FWHM<3 pixel, which is the main reason for their exclusion in Nantais et al. (2010b). Lower number of GCs in our sample as compared to that of Nantais et al. (2010b) is due to the more stringent filtering that we imposed in the selection of GCs.

3.6.2 M101

Similarly, using data from the HST/ACS, Simanton et al. (2015) reported a sample of 326 star clusters in M101. The selection was made using the concentration index and a colour cut. Their sample includes extended objects, and hence they used a magnitude cut of M_V ≤ −6.5 to define GCs, resulting in a sample of 98 GC candidates. We find that 48 are present in their sample of GC candidates. Reasons for us missing 50 of their objects are that 25 of these have ELLIPTICITY>0.3, 19 do not meet the AREA criterion and the rest do not meet our FWHM criterion.

3.6.3 NGC 4258

González-Lópezlira et al. (2017) reported a sample of 39 GCs in NGC 4258 using near-infrared (NIR) data from CFHT (Canada–France–Hawaii Telescope) over a large FoV (1° × 1°), but based on seeing-limited (∼0.7 arcsec) data set. The selection of the GCs was carried out using the colour–colour diagram u*i′K_s ((i′ − K_s) versus (u* − i′)) (Muñoz et al. 2014). In comparison, our catalogue using HST/ACS images contains 226 GCs over an FoV of ∼12.3 arcmin × 17.2 arcmin. From a spectroscopic follow-up of the objects, González-Lópezlira et al. (2019) concluded that the selection based on colour–colour diagram has between 10 and30 per cent contaminants (e.g. Muñoz et al. 2014; González-Lópezlira et al. 2019). Our FoV includes 29 objects of González-Lópezlira et al. (2017), of which 23 are in our catalogue. Out of the six missing objects in our sample, two are confirmed to be GCs using spectroscopic data by González-Lópezlira et al. (2019), another two are dwarf galaxies, with the remaining one being a foreground star. Reason for the two of their GCs to be absent in our sample is that they do not satisfy our selection criteria.

3.6.4 M 51

Star clusters in M51 were catalogued by Hwang & Lee (2008) using HST/ACS images. They used the SExtractor parameters stellarity, FWHM, and ellipticity for star cluster selection. They created two subsamples, one with 2.4<FWHM<20 and the other with 2.4<FWHM<40 pixel, resulting in a catalogue of 8400 stellar cluster candidates. If we applied their colour discriminator ((B − V) >0.5 and (V − I) >0.8) in their catalogue we obtained a sub-catalogue of 224 red clusters, 214 of which have FWHM<10 ACS ACS pixels. Only 85 of these objects are in our catalogue of 223 GCs. We searched our master SExtractor output catalogue to find out the reasons for we missing 139 of their objects, and found that 85 of these have ELLIPTICITY>0.3, 15 do not meet the AREA criterion, and the rest do not meet our FWHM criterion.

3.6.5 NGC 628

The last galaxy of our sample, NGC 628, has also been a target for cluster searches using HST images by Ryon et al. (2017). However, they reported only young and intermediate-age clusters, and no GCs.

4 COMPLETENESS CORRECTIONS

We aim to study GC luminosity functions in our sample galaxies. In order to do that, we need to take into account possible sources of incompleteness in our catalogues. Two principal sources of incompleteness in our study are: (i) incompleteness in magnitude and (ii) incompleteness in radial coverage even with multiple HST pointings. In this section, we describe the method we have followed to correct for these observational limitations and obtain a final GC luminosity function.

4.1 Monte Carlo cluster simulations

We generated mock clusters using the iraf/daophot tasks addstars and mkobjects. A cluster is defined by an intensity profile that follows a Gaussian function of a given fwhm and a total magnitude, with fwhm taking values of 2.0, 2.4, 3.0, 4.0, 5.0, 6.0, 7.0, and 8.0 pixels, and magnitudes varying between 19 and 24 magnitudes at interval of 0.5 mag. For a fixed fwhm, 1100 clusters were generated, 100 for each simulated magnitude.

Coordinates of these sources were randomly selected and were inserted on to an observed HST image. The faintest object that can be detected in an observation under uniform background conditions defines the detection limit of that observation. In real observations, the background is often non-uniform, and each non-point source has a different size. Further, crowding of objects in an image can lead to non-detection of objects that are brighter than the detection limit. Hence, for each galaxy, we chose HST images corresponding to two FoV, representing zones of (i) low background and low crowding, and (ii) high background and high crowding. The former simulates the conditions typical of clusters in the external parts of galaxies, whereas the latter represents the characteristics of clusters in the bulge and spiral arms. For M81, which has as many as 29 pointings, simulations were carried out on an additional frame containing the bulge and nucleus (R09; see fig. 1 in Santiago-Cortés et al. 2010, for the footprint of M81). The results of these latter simulations were used exclusively in the analysis of radial density distribution of clusters in the inner part of this galaxy. The same object detection and selection criteria (Section 3.2) we had used for real objects were applied on the mock-object added frames. In Fig. 11, we zoom-in on a randomly selected region of M101, before (left-hand panel) and after (right-hand panel) inserting mock sources. In the image the positions of the mock sources, which cover a range of magnitudes, are indicated by blue circles.

Figure 11.

A randomly selected region of M101 before adding mock sources (left-hand panel) and after adding them (right-hand panel); sources have different magnitudes. All blue circular regions have 1 arcsec radius. North up, east left.

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We have also used these simulations to establish criteria to select cluster candidates from all sources catalogued by the SExtractor, and apply fwhm-dependent aperture corrections, described in Section 3.3. We used the results of the simulations for low background and low crowding for this purpose.

4.2 Completeness corrections: magnitude

For a proper counting of a population, it is necessary to know completeness factor as a function of object magnitude. We used the results of our simulation to determine the completeness factors. This factor is expected to depend on the fwhm.

In the top panel of Fig. 4, we plot the distribution of fwhm, which peaks at fwhm<3 pixel. Hence, we calculate the completeness factors for mock clusters of input fwhm = 3 pixel. The completeness factor is defined as the ratio of the number of recovered objects (N_out) to the inserted objects (N_in) at each inserted magnitude.

Figure 12.

Completeness correction curves in the F814W band for our sample galaxies in low (dotted line passing through circles) and high (dashed line passing through triangles) background regions. The mean of these two curves is shown by the solid line. The identification codes of high and low background frames used in these simulations are shown in parenthesis.

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4.3 Completeness corrections: radial distribution

While the images obtained from HST observations offer the best spatial resolution, they do not cover the whole extent of galaxies even with the multiple pointings. Thus, outer halo GCs are often missing in catalogues selected from HST images. The following analysis was carried out to correct for the absence of GCs beyond the galaxy’s disc.

Figure 13.

Radial distribution of surface number density of GCs from our data (solid circles) are fitted with Sérsic profile (solid line). Catalogued GCs beyond the spatial coverage of the HST images are shown by the empty circles (M81 and NGC 4258, only). Observed number densities in these two galaxies are consistent with the extrapolation of the fitted function. The vertical dashed lines show the best-fitting values of R_e before (black solid circles) and after (magenta solid circles) incompleteness correction.

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The number density obtained wide-field ground-based surveys underestimates the number of GCs inside R_e by more than an order of magnitude in both the galaxies with such data. In NGC 4258, the slope of our fit in the external part agrees with the observed number densities from wide-field survey, with the absolute values marginally below our predictions. On the other hand, number densities obtained from wide-field survey in M81 remain constant over a large radial range, which are likely due to some selection biases in the survey. On the other hand, the wide-field survey suggests an excess of GCs in the external parts of this galaxy as compared to our predicted values. This excess could be due to contamination from foreground stars and unbound intergalactic GCs in the M81 group (see e.g. Jang et al. 2012; Ma et al. 2017).

Two of the most well-studied spiral galaxies, the Milky Way and M31, have n = 1.9 and R_e = 4.41 kpc and n = 1.6 and R_e = 4.59 kpc (Battistini et al. 1993), respectively. In comparison, for elliptical galaxies the calculated values are larger, e.g. NGC 720 (E5): n = 4.16 ± 1.21, R_e = 13.7 ± 2.2 kpc; NGC 1023 (S0): n = 3.15 ± 2.85, R_e = 3.30 ± 0.9 kpc; NGC 2768 (E): n = 3.09 ± 0.68, R_e = 10.6 ± 1.8 kpc (Kartha et al. 2014). The n and R_e for our sample galaxies are in the range of expected values in spiral galaxies. The n values are <1 in four of our galaxies, suggesting flatter distribution in the inner parts of our galaxies, as compared to the Milky Way and M31.

5 GLOBULAR CLUSTER LUMINOSITY FUNCTIONS (GCLFS)

Having obtained a sample of GCs in five spiral galaxies, we now analyse the properties of the GC systems in these galaxies. All magnitudes and colours have been corrected for the foreground Galactic extinction using the A_V values given in Table 1, and the Cardelli, Clayton & Mathis (1989) reddening curve. We start our analysis with the colour distribution.

5.1 Colour distribution

For comparing colours of our GCs with those in the MW, we transformed all our photometry into the Johnson–Cousins photometric system using the transformation equation (B1) and the corresponding coefficients in Table B1 in Appendix  B, which were taken from Sirianni et al. (2005).

In Fig. 14, we show the distributions of (B − I)₀, (B − V)₀ and (V − I)₀ colours of GC systems in our sample galaxies, where the sub-index 0 stands for Galactic reddening-corrected colours, using the A_V values in Table 1. For comparison, we also plot the colour histograms of the GCs in the Milky Way using the data from Harris (1996). The black and blue histograms correspond to the observed and dereddened colours, respectively. In Table 9, we list the mean and mode of the distributions of the three colours (B − I)₀, (B − V)₀, and (V − I)₀ for our sample as well as for the MW sample from Harris (1996). We use only 97 Galactic GCs which had integrated colours available in Harris (1996). For comparison, we list the colour of an SSP of 13 Gyr with Z = 0.001, the typical metallicity of old GCs, in the last row. The reddening-corrected colours of MW GCs agree within 0.1 mag with these SSP colours.

Figure 14.

Colour distributions of GCs of our galaxies compared to that in the MW (bottom-most panels). The distributions of (B − I)₀ colour after correcting for contaminating fractions are shown by magenta histograms. The mean value for each distribution is shown by a vertical dashed line. The colour histograms after dereddening the colours by the reddening reported for each GC for the MW GCs are shown in blue.

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