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Mapping the galaxy NGC 4486 (M87) through its Globular Cluster System

As shown in previous works, globular clusters can be used to trace the overall structure of the diffuse stellar populations in early type galaxies if the number of clusters per unit stellar mass depends on metallicity. In this paper we further test this assumption in the galaxy NGC 4486 (M 87), by combining several data sources. The results show that globular clusters allow the mapping of the galaxy in terms of the surface brightness profile, integrated colour gradient, chemical abundance, and mass to luminosity ratios up to 1000 arcsec (or 80.4 kpc) from its centre (i.e. some 10 effective radii). The analysis indicates the presence of a dominant high metallicity bulge associated with the red globulars, whose ellipticity increases outwards, and of a more flattened low metallicity halo connected with the blue globulars. The chemical abundance gradient of the composite stellar population is remarkably similar to that inferred from X ray observations of hot gas. The mass-metallicity spectrum of the stellar population can, in principle, be understood in terms of inhomogeneous enrichment models. In turn, the distribution of the bluest GCs, and lowest metallicity halo stars, has an intriguing similarity with that of dark matter, a feature shared with NGC 1399. Also, in these two galaxies, the number of blue GCs per dark mass unit is identical within the errors, \approx 1.0(\pm0.3) \times 10^{-9} . The total stellar mass derived for NGC 4486 is 6.8(\pm1.1) \times 10^{11} M\odot with a baryonic mass fraction fb = 0.08(\pm 0.01).

quences of that idea were discussed in Forte, Vega & Faifer (2009) (hereafter FVF09) who performed an analysis of 69 galaxies within the Virgo ACS (see Ferrarese et al. 2004;Peng et al. 2008).
FVF09 also find that globular cluster systems (GCS) in Virgo galaxies with stellar masses below M * ≈ 10 11 M⊙, lie on plane defined (in a 3-D logarithmic space) by GC formation efficiency (number of GCs per unit stellar mass), total stellar mass and projected stellar mass density. NGC 4486, and other bright Virgo ellipticals, lie well outside this plane, probably reflecting the effects of past merger events.
In this paper we revise the case of NGC 4486 (M 87), taking advantage of a number of photometric works (Tamura et al. 2006;Harris 2009;Jordán et al. 2009) that, combined, allow an analysis on an angular scale of ≈ 1000 arcsec.
An important assumption of the analysis is that GCs and field stars are mostly coeval or formed within a narrow period of time. Arguments in support of this hypothesis can be found, for example, in Spitler (2010) and references therein. In particular, a direct estimate of the age of the halo of the galaxy NGC 3923, as well as of its associated GCs, was presented by Norris et al. (2008) using Gemini MOS spectra and Lick indices. These results also indicate and old age (about 12 Gyr) for both stars and GCs (see Beasley et al. 2008 for the case of NGC 5128).
More arguments in favour of old ages and multi-metallicity spectra for the dominant stellar populations in elliptical galaxies, stand on the analysis of their integrated colours as discussed in Schombert & Rakos (2009).
Several papers, on the other side, deal with the surface brightness profile of NGC 4486. In this work we adopt the blue band (Johnson system) surface brightness profile presented by Caon et al. (1990). All these works denote the existence of a flattened cD halo (already detected by Arp & Bertola 1971), traced to very low luminosity levels in Mihos et al. (2005). More recently, Rudick et al. (2010) find that the (B − V ) colour gradient of the galaxy has a logarithmic dependence along the semi major axis over an angular range of (at least) 1000 arcsec (i.e., approximately, ten effective radii). This corresponds to 80.1 kpc for a distance modulus (V o − Mv) = 31.1, or 16.5 Mpc, (Tonry et al. 2001), adopted in this work .
The paper is organized as follows: Section 2 presents an improved version of the GC integrated colours vs. metallicity relation given in FFG07 and the connection between chemical abundance Z (in solar units hereafter) and the cluster integrated colours, including an attempt to model the so called "blue tilt". Section 3 explains the assumed link between GCs and field stars. Section 4 describes the fit of the GC colour histograms within the inner 300 arcsec along the galaxy semi major axis, aiming at determining the number of clusters belonging to the blue or red sub-population as well as their respective chemical scale-lengths. A discussion of the large angular scale features of the galaxy, including the shape of the surface brightness profile, colour gradient, stellar metallicity function and stellar mass to luminosity ratios is given in Section 5. The inferred halo, bulge and total stellar masses, and a comparison with the dark matter content is presented in Section 6. Finally, the GCs formation efficiencies for both the blue and red GCs and the conclusions of this paper, are included in Section 7 and 8, respectively.

THE GLOBULAR CLUSTERS COLOUR DISTRIBUTION.
In their analysis of the GCS systems associated with Virgo ellipticals, Peng et al. (2006) present non parametric fits of the CG colour histograms. In this paper we adopt a different approach, that seeks the determination of the chemical abundance scales as well as the fraction of clusters in each population, on the basis of a Monte Carlo simulation. As discussed in FFG07, the simplest function that links the chemical abundance Z with the integrated (C − T1)o colours through the empirical calibration, and within the inherent statistical noise of the GC counts, is where Zi is a pedestal abundance and Zs is the characteristic abundance scale length of each GC sub-population. The modelling of the GCs colour bimodality, is then similar to that given in FFG07. First, a "seed" globular is randomly generated with a given Z governed by the Zsparameter. The synthetic integrated colours were in turn obtained from the empirical colour metallicity calibration and adding Gaussian observational errors. A colour excess E(B − V ) = 0.02 from Schlegel et al. (1998), that transforms to E(C − T1) = 0.04, was also added to the intrinsic (C − T1)o colours in order to match the FFG07 photometry. T1 magnitudes were also generated for each cluster adopting a GC Gaussian luminosity function with a turn over at T1 = 23.2 and characterized by a dispersion σ(T1) = 1.60 mag. A detailed discussion of the behaviour of this parameter for the Virgo ACS galaxies is given in Villegas et al. (2010).
The shape of the empirical colour-metallicity relation requires a GC bimodal metallicity distribution in order to match the observed colour bimodality defined in terms of the so called blue and red GCs (for which we adopt upper chemical abundance values Z = Z⊙ and Z = 3.5Z⊙, respectively). Previous, and more recent arguments, in favour of bimodal GC metallicity distributions can be found, for example, in Alves-Brito et al. (2011) (however, see Yoon et al. 2011 for a different interpretation of the colour bimodality).
FFG07 presented an empirical colour-metallicity relation based on 100 MW GCs with (C − T1) Washington sytem colours and 98 extragalactic GCs with (g ′ − i ′ ) colours in the (modified) Gunn system. In turn, Moyano Loyola, Faifer & Forte (2010) derived an improved version of that calibration: obtained by observing a reference field in NGC 4486 with Gemini/MOS (Forte et al. in preparation) with GC candidates observed in both photometric systems. In turn, from FFG07 and Jordán et al.
Other colour-colour relations used in this work are: derived from observations of galactic globulars (see, also Forbes & Forte 2001) and can be used to transform the relation given in eq. 2 to other colours. A similar calibration based on 40 MW GCs, and presented in Sinnott et al. (2011), shows very good agreement with ours in the range defined between [F e/H] −2.5 and −0.5. At higher metallicities, their calibration (that includes 3 MW GCs, compared with 26 GCs that define eq. 2) becomes steeper and leads to (C − T1) colours redder by 0.15 mag at [F e/H] = 0.0.
An analysis of the colour residuals from our adopted calibration as a function of the GC ages, determined from colour magnitude diagrams for the MW GCs, or from Lick indices for the extragalactic globulars, reveals no systematic trends. The empirical calibration, then, corresponds to the mean age of the MW GCs, that we assume as 12 Gyr.
For any other age τ (in Gyr) the colour transforms to: where the term d(C − T1)/dτ can be approximated, for ages between 8 and 15 Gyr, as: derived from the single stellar population models by Bruzual & Charlot (2003 The GCs colour magnitude diagram for NGC 4486 shows the so called "blue tilt" (Peng et al. 2009, and references therein), a feature explained in FFG07 as an increase of the Zi parameter with the GC brightness and mass. Alternative views about the interpretation of the blue tilt, and the role of chemical pre and/or self enrichment, are given in Strader & Smith (2008) and Bailin & Harris (2009).
A linear relation between colours and GC magnitudes was adopted in FFG07 to describe the tilt. However, a new analysis rather suggests a non linear trend (see, also, the colour magnitude diagrams presented by Harris 2009): where (C − T1)t and T1 are (reddening corrected) colours and magnitudes that define the tilt shape. At a given T1, the (C − T1)t colour leads to a metallicity defined through the empirical colourmetallicity relation, [F e/H]t, and then to a [Z/H]t from the Mendel et al. relation: In this paper, we attempt modelling the chemical variation associated with the tilt by defining: where Zoi is a fit parameter (the lowest chemical abundance for a given GC sample), and ∆Z is given by: This procedure leads to values that range from ∆Z = 0.06 at T1 = 19.0 mag, corresponding to the brightest objects, to ∆Z = 0.0 at T1 = 23.2 mag, the turn-over of the GCs integrated luminosity function, where the tilt seems to disappear.

THE GLOBULAR CLUSTERS-FIELD STARS CONNECTION.
As shown in several papers, the metallicity distributions of GCs and resolved field stars are noticeably different, e.g., Durrell et al. (2001) in M 31 or Rejkuba et al. (2011) in NGC 5128. The tentative link between these systems, explored in FFG07 and FFG09, comes from the fact that both the number N of GCs per unit stellar mass (e.g., Miller & Lotz 2007) and the metallicity of a galaxy (Tremonti et al. 2004) can be approximated as power laws of the stellar galaxy mass. Combining these relations, and adding an explicit dependence with chemical abundance, leads to: This equation connects dN (Z), derived from the GC colour histograms, to an (assumed coeval) diffuse stellar mass element dM * (Z), whose mass to luminosity ratio and colour solely depend on chemical abundance.
Then, the knowledge of the projected GC areal density at a given galactocentric radius, allows the fit of the colour and surface brightness of the galaxy by iterating the δ and γ parameters, and integrating in the chemical abundance domain covered by the GCs. Eq. 16 imply that the integrated colours, composite (M/L) ratios and mean chemical abundances (mass or luminosity weighted) are governed by δ since this parameter regulates the relative masses of stars associated to GC with different chemical abundances.
As in FF07 and FVF09, the B luminosity associated with M * (Z), was obtained from: which gives a good approximation to the mass to B luminosity ratios, given by Worthey (1994) for a Salpeter stellar mass function. An idea about the uncertainty of this relation comes from a comparison with other models. For example, the Maraston (2004) models show an agreement within 10 per cent with Worthey's although, at the lowest chemical abundance, this last author gives ratios ≈ 24 per cent larger. Other source of uncertainty is connected with the assumed stellar mass function. The adoption of a Chabrier (2003) function leads to stellar masses systematically smaller by a factor of 0.55.

NGC 4486: THE INNER 300 ARCSEC (24.1 KPC).
In this section we discuss the inner 300 arcsec along the semi major axis of the galaxy, where the photometric works by Jordán et al. (2009) and FFG07 give a complete areal coverage for objects brighter than the GCs turn-over. At this magnitude level we estimate a background contamination of about one object per sq. arcmin, which agrees with the value given by Harris (2009), after taking into account the slightly different limiting magnitude in both works. For this region in particular, the total expected background contamination should be below 5 per cent, then minimizing the effects of these objects on the colour histograms of the GC candidates. In contrast with FFG07, where single scale parameters ZSB and ZSR were adopted to characterize either the blue or the red GC population, we performed distinct fits within elliptical annuli (30 arcsec wide) following the ellipticity variation of the galaxy halo in an attempt to detect chemical abundance gradients.
An analysis of all the colour histograms shows a small asymmetry in the sense that GCs to the NE of the semi major axis of the galaxy seem slightly redder (by ≈ 0.015 in (C − T1)) than those to the SW of that axis, and may indicate differential reddening. Besides, the three outermost annuli show a bump at (C − T1) ≈ 0.95 (see the Appendix).
The nature of these objects (around fifty in total) remains unclear although we noticed that they appear mostly to the NE of the galaxy major semiaxis and without any obvious concentration towards the centre of the galaxy. As a tentative explanation, they might be foreground MW stars connected with the so called "Virgo over-density" (see, for example, Lee et al. 2010).
The GC colour histograms were fit by iterating the Zoi and Zs parameters as well as the number of clusters of each sub-population and minimizing the "quality fit" parameter defined by Côté (1998). These values are listed in Table 1. Typical errors of the ZSB and ZSR parameters are ± 0.005 and ± 0.05 respectively. The observed and model GC colour distributions are displayed in the Appendix, both in discrete bins and smoothed histograms.
The GC colour histograms corresponding to regions defined between a = 0 to 90 arcsec and a = 90 to 300 arcsec are depicted in Figures 1 and 2 . These diagrams also display the composite model colour histograms obtained by combining the individual fits listed in Table 1. This table shows a decrease of the GCs chemical scales ZSB and ZSR along the semi major axis of the galaxy, and also a difference in the sense that red GCs require higher values of the initial abundances Zoi, compared to those of the blue GCs.
The ∆Z component of the Zi parameter (Section 2) was also included in the colour modelling of the red GCs. However, their large chemical abundance scale length, compared with the ∆Z parameter, makes the tilt effect practically undetectable for these clusters.
The (B − R) colour gradient of the galaxy and the mean integrated colours of the whole cluster population are shown in Fig. 3. This last gradient is steeper than that of the galaxy, an effect noted for example, by Liu et al. (2010). We stress that both gradients are sensitive to eventual chemical gradients but, while the first one reflects the luminosity weighted contribution of the different diffuse stellar populations, the GC gradient is sensitive to the changing ratio in number of blue to red clusters along the galaxy major axis.
The galaxy gradient in the last figure is based on the BVRI data discussed by Michard (2000). This author determined the sky level in each photometric band through an iterative procedure that led to consistent "nice logarithmic gradients" .
Transforming the Michard's colour gradients to (B − R), through the colour-colour relations given in section 2, leads to a mean gradient: The δ parameter that fits the (B − R) colour of the galaxy within each annular region was determined using the GCs parameters listed in Table 1. In turn, the γ parameter was obtained in such a way that the model B magnitude agreed with that obtained by integrating the Caon et al. (1990) profile within the inner and outer boundaries of each annulus.
The run of the δ and γ parameters along semi major axis of the galaxy are displayed in Fig. 4 and Fig. 5 respectively. The first one shows a mean value of 1.80 with an rms of ±0.05. In contrast, γ rises in a monotonic way until reaching a value of about 0.55 × 10 −8 at a ≈ 250 arcsec . This trend indicates an increasing number of GCs per diffuse stellar mass, and may be explained as the result of dynamical destruction/erosion effects, which become less important with increasing galactocentric radius (see, for example, Capuzzo-Dolcetta & Mastrobuono-Battisti 2009 and references therein). Table 1 also includes the mean chemical abundance (number weighted) for the blue and red GCs , and the mean chemical abundance (mass and luminosity weighted) of the inferred composite stellar population. Linear least square fits to the blue GC abundances (with a in arcsec) yield: and for the red GCs: in turn, for the galaxy (mass weighted): The gradient fits corresponding to the GCs and to the galaxy (B luminosity weighted), are depicted in Figure 6.
Excluding the [Z/H] value of the innermost blue clusters, the gradients of both GC sub-populations seem rather similar. However, taking into account the uncertainties of the derived coefficients, we cannot dismiss a lower or even null colour gradient for the blue GCs.
To within the uncertainties, our result is in very good agreement with Harris (2009) who finds galactocentric slopes of −0.12(±0.02) and −0.17(±0.03) for the blue and red GCs respectively.
The significance of the [Z/H] value corresponding to the blue GCs in the innermost annulus would deserve further analysis since, if confirmed by other means (e.g. spectroscopy), would imply an enhanced chemical enrichment process, probably at the very early stages of the formation of the galaxy. Figure 6 also shows another particular feature: the abundance residuals from the linear fits seem to occur in phase for both the blue and red GCs along the semi major axis of the galaxy. A possible explanation to this effect would be differential interstellar reddening affecting the colours from which metallicities are derived. Such a kind of GC colour fluctuations are in fact seen in Fig. 3 (but not on the galaxy colours, as they come from a linear fit to the data in Michard's work).
In turn, Fig. 7 shows the (mass weighted) mean chemical abundance of the stellar population along the semi major axis of the galaxy, as well as the Fe abundances determined by Gastaldello & Molendi (2002)   shifted upwards by 0.18 in ordinates). Stars and hot gas behave in a remarkably similar fashion suggesting a strong coupling. The effects of changing the adopted age (12 Gyr) of the system on the chemical abundances, and following the prescription described in Section 2, are also shown in Fig. 7. As an example, the vertical bars correspond to an increase/decrease of 1.5 Gyr, leading to abundances that decrease/increase within a range of −0.05 to The assumption of an older age would not have an impact on the overall gradient while a younger age would lead to an even shallower gradient. The stellar mass statistics inferred from eq. 16, corresponding to δ = 1.80, and convolved with a Gaussian kernel (σ = 0.1), is shown in Fig. 8 for two different ranges along the semi major axis: within one effective radius (≈ 100 arcsec or 8 kpc); Caon et al. 1990 and within one to three times that value.
These distributions show a broad high abundance component with a peak that shifts towards smaller values with increasing galactocentric radius while the presence of a low metallicity tail, reaching [Z/H] ≈ −2.0, becomes more prominent.
Our inferred stellar mass-chemical abundance distribution has a strong similarity with the MDFs of resolved stars in NGC 5128 (Rejkuba et al. 2005;Rejkuba et al. 2011). From their analysis, these authors conclude that the bulk of the stars in NGC 5128 are 11 to 12 Gyr old and exhibit a range in chemical abundance that spans from (Z/Z⊙)≈ 0.007 to 2.8.
The comparison, however, assumes that our stellar mass statistics is reflected as a number statistic (resolved stars), a valid reasoning only if the stellar mass function does not depends strongly on metallicity.
The detection of stellar haloes with low metallicity in resolved galaxies has been reported, for example, in NGC 3379 (Harris et al. 2007) and in NGC 4486 itself. In this galaxy Bird et al. (2010) find a low metallicity tail, using HST observations. However, the limiting magnitude in this last work prevents a reliable assessment of the upper end of the metallicity distribution.
The presence of an extended stellar halo with low metallicity in NGC 4486 is also coherent with the detection of stars with ages older than 10 Gyr and metallicities below [F e/H] ≈ −1.0, at large distances from the dominant Virgo galaxies (Williams et al. 2007).

LARGE SCALE FEATURES: UP TO 1000 ARCSEC (80.4 KPC) ALONG THE GALAXY SEMI MAJOR AXIS.
An extension of the previous discussion to a larger angular scale can be performed by combining the GC areal densities from Harris (2009) and the (B − V ) colour gradient of the galaxy presented by Rudick et al. (2010). We start modelling the spatial distribution of the GC subpopulations, and then look for the δ and γ that provide the best fit to both the large scale colour gradient and of the galaxy profile brightness. Those parameters, in turn, will allow the determination of the chemical abundance distribution and (M/L) ratios for field stars, as well as of the total stellar mass.

Areal densities.
A usual approach in the literature is the adoption of r 1/4 or of power laws in order to fit the GC areal densities as a function, for example, of galactocentric radius. Both Tamura et al. (2006) and Harris (2009) present this kind of analysis. Alternatively, the combination of their data with those given by Jordán et al. (2009) and FFG07, and taking into account the slightly different magnitude limits in these works, shows that Sérsic (1968) profiles can provide adequate fits even including the central regions of the galaxy, where GCs display core-like density profiles.
As a first step, we found the Sérsic parameters (scale length rs and n index) that fit the density profiles along the galactocentric radius (i.e. within circular annuli) for both GC populations. However, as already noted by McLaughlin, Harris & Hanes (1994) the GC system rather follows the galaxy flattening.
Taking this feature into account, we generated a model areal distribution which, in the case of the red GCs, follows the ellipticity of the galaxy halo (ǫ = 0.03 at a = 5 arcsec to ǫ = 0.35 at a = 500 arcsec). For the blue GCs we set a constant ellipticity (ǫ = 0.40). This last procedure seems justified since, in the outer regions, both the galaxy and the blue GC population exhibit a similar ellipticity (see fig 4. in Tamura et al. 2006). Comparable values of the ellipticities of the red and blue GC distributions have been presented in the extensive work by Strader et al. (2011).
The galactocentric (wavy lines) and semi major axis (continuous line) density runs of the models are shown in Fig. 9 for the blue GCs (rs = 43 arcsec, n = 2.20, central density= 170 clusters per sq. arcmin) and in Fig. 10 for the red GCs (rs = 13.5 arcsec, n = 2.35, central density = 350 clusters per sq. arcmin). These diagrams also display the uncertainties of the profiles as a result of the adopted background and GC counting statistics.

(B-R) Colours.
In order to fit the integrated colours of the galaxy we followed the approach described in paragraph 3, adopting the GC areal density profile models to determine the number of blue and red GCs along the semi major axis (previous subsection).
In turn, the variation of the GC chemical abundance scales within 300 arcsec were approximated through linear relations: for the red GCs, which are compatible with the abundance gradient derived from   both GC sub-populations). As a first approach these gradients were extrapolated outwards a = 300 arcsec. The (B − R) colour gradients are displayed in Fig. 11, where large open dots represent the best fit model corresponding to δ = 1.70, while the straight line is the (transformed) Rudick et al. (2010) colour gradient.
The δ parameter, in this case, is about 6 percent smaller than that derived in Section 4. The difference arises because the colour gradient from Rudick et al., ∆(B − R)/∆log(a) = −0.14, is slightly steeper than that derived from the Michard (2000) data for the innermost regions. Fig. 11 also includes the colour gradients of the halo and bulge stars, both governed by the metallicity gradients discussed in Section 4. Although these gradients are rather similar, the shape of the colour-metallicity relation leads to a shallower colour slope for the halo, a behaviour shared by the blue GCs, and also found in other galaxies (e.g Forbes et al. 2011or Faifer et al. 2011. As an important result, Fig. 11 indicates that most of the colour gradient of the galaxy arises from the luminosity weighted composition of the halo and the bulge, whose relative contributions change along the semi major axis. The metallicity gradients of each sub-population seem to play a relatively minor role regarding the composite stellar colour gradient. For example, adopting null colour gradients outwards a = 300 arcsec, yields (B − R) colours that are only 0.015 mag redder at a = 1000 arcsec.
Finally, as seen in Fig. 11, the model integrated colours keep within ±0.01 mag from the observed ones and do not seem to require a significant variation of the stellar age, as reported in the photometric study by Liu et al. (2005).

The NGC 4486 Brightness profile.
The Caon et al. (1990) B profile adopted in this work, and shown in Fig. 12, is in good agreement with previous ones (e.g. the E-W profile by de Vaucouleurs & Nieto 1978, or the photographic work by Carter & Dixon 1978), as can be seen in the comparison presented by Liu et al. (2005).
A single Sérsic profile fit gives n = 10 ± 2, for a galactocentric range that covers from a = 20 arcsec to a = 1000 arcsec. The residuals, displayed in Fig. 13, correspond to an overall rms = ±0.07 mag. The innermost region of the galaxy was not included to avoid the complex structure connected with the NGC 4486 jet as well as seeing effects. A similar fit, transforming the Caon et al. (1990)  Alternatively, we used GCs as "brightness tracers". In this case, each "diffuse" stellar mass element (eq. 16) was spatially distributed following the description given in subsection 5.1 and, after adopting γ = 0.55 × 10 −8 and δ = 1.70, transformed to B luminosity to generate a bidimensional image of the galaxy. This image was analysed with the IRAF package to obtain the model surface brightness profile. The variation of the model ellipticity along the semi major axis of the galaxy is compared with the observed one in Fig. 14.
The brightness residuals obtained by comparing the observed and model profiles, also depicted in Fig. 13, are very similar to those arising from the Sérsic profile outwards a = 250 arcsec.
The systematic trend of these residuals towards the centre of the galaxy, is consistent with the behaviour of the γ parameter shown in Fig. 5, and with the possible destruction of GCs by dynamical effects. Reconciling the observed brightness profile with that traced by the GCs, imply that we currently observe 85 per cent and 60 per cent of the original blue and red GC populations, respectively.
We stress that the completeness factors of the photometric works by FFG07 and Jordán et al. (2009) are higher than 90 percent for GC candidates brighter than the turn over of the GC luminosity function, then ruling out that this trend could be eventually caused by instrumental or galaxy background effects.
Our two components (halo and bulge) fit has some similarities with the approach presented by Seigar, Graham & Jerjen (2007) who found that the brightness profiles of five cD galaxies are better represented by combining two Sérsic profiles with different n indices and scale lengths. In particular, they noticed the common presence of outer exponential haloes (n = 1.0). This result, in a first approximation, is not in conflict with ours since, forcing n = 1.0 leaves brightness residuals smaller than ±0.05 mag for the halo component, within a range of a = 250 arcsec to a = 1000 arcsec. Fig. 12 also suggests that the brightness of the extended halo should equal the bulge brightness at a ≈ 1300 arcsec (104 kpc) and that, presumably, would become dominant outwards. This result is consistent, but better constrained than that in FFG07, mainly due to a more reliable definition of the colour gradient of the galaxy on an extended angular scale.

A comparison between the chemical abundance of globular clusters and field stars.
The chemical abundance distribution function for the blue GCs and halo stars, as well as for the red GCs and bulge stars, within a = 1000 arcsec (80.4 kpc), are depicted in Fig. 15 and Fig. 16. These  diagrams show mean stellar abundances about 1.6 times (0.2 dex) larger than those of the GCs. Preliminary interpretations of these mass-chemical abundance spectra can be made along the usual pathways, i.e., assuming that Z is a "clock" as in simple models or, alternatively, that chemical abundance is rather a volume "sampler" as in the inhomogeneous enrichment models.
A search of the literature shows that the inferred MDF of the bulge stars is rather similar to the "push" model put forward by Schombert & Rakos (2009). These authors artificially modify the output of an infall model, by reducing the low metallicity end of the stellar population, in an attempt to asses the impact on the integrated model colours of elliptical galaxies and to avoid the "infamous G-dwarf problem" .
They also reject the simplest chemical evolution scenarios and, at the same time, point out the similarity of their tentative approach with the results from inhomogeneous enrichment models (Oey 2000) which also provide a better representation of the high metallicity drop-off of the MDFs.
The abundance distributions in the inhomogeneous enrichment models are the result of star formation in different events that eventually overlap, and are are characterized by the product n.Q, where n is the number of stellar generations and Q is a filling factor that measures the relative volumes of enriched and primordial gas.
In particular we note the similarity of the MDFs presented in this work and those depicted in Oey's figures 2 and 3, corresponding to the halo and bulge of the MW, which require low and high n.Q values respectively. It is tempting to connect these results with the fact that, the γ and δ parameters derived in previous sections, imply that ≈ 50 percent of the blue GCs form associated with diffuse stellar masses below 10 7 M⊙, and with masses below 12 × 10 7 M⊙ in the case of the red GCs.
Another intriguing result is suggested by Oey's fig 1 (panel  c).That diagram shows the decoupling of the MDFs characterizing the very early stellar generations from the composite one at the end of the whole star forming process. In this scenario, the first stellar generations still reflect the so called "metal production function" f (Z), that is assumed to be a power law (decreasing with Z) governed by SNe enrichment. In our analysis, GCs follow a comparable trend (although with an exponential dependence) and could be in fact mapping such f (Z) if their formation is restricted to the initial stellar generations. In either case, the landscape seems coherent with Spitler (2010), who argues in favour of an intense formation of bulge-GCs followed by an era of stellar bulge growth and little cluster production.

Stellar mass to luminosity ratio.
The dependence of the mass to B luminosity ratio with chemical abundance adopted in this work (eq. 17) was used to determine integrated ratios for galaxies in the Virgo cluster (FFV09). The ratios inferred in that work are in perfect agreement with those reported by Napolitano, Romanowsy & Tortora (2010) through a completely different approach.
Using the same dependence, the chemical gradients described before, and adopting δ = 1.70 (subsection 5.2), we derived the mass to luminosity ratios for the B and V bands (within elliptical annuli 30 arcsec wide in a) for the composite stellar population, i.e., including both halo and bulge stars, that are plotted in Fig. 17 and correspond to an overall integrated ratio (M/L)B = 8.3.
Most  Fig. 17 is comparable to (M/L)V = 6.3 ± 0.8, given in the first paper, but significantly lower than the range (M/L)V = 8.2 to 9.1 reported in the second work.

STELLAR AND DARK MATTER MASSES.
The halo, bulge and total (projected) cumulative masses are shown in Fig. 18. These curves were obtained by combining the Caon et al. photometry and the (M/L)B ratios discussed in the previous section within a = 1000 arcsec. Outwards, where the stellar mass contributes with only ≈ 10 percent of the total, we assumed constant ratios set by the outermost (M/L)B value. Using kinematic data of planetary nebula, Doherty et al. (2009), determine the "edge" of the NGC 4486 halo to be at ≈2000 arcsec (164.8 kpc), which is the adopted upper galactocentric limit in Fig. 18. Within this galactocentric radius we obtain a total stellar mass of 6.8(±1.1) × 10 11 M⊙. This mass is consistent the Sérsic index nV vs-stellar mass relation derived by D'Onofrio et al (2011) (see their fig. 1, upper left panel) in an analysis of the connection between the shape of early type galaxies and their stellar populations.
Our estimate of the mass uncertainty, about ± 15 percent, comes from errors of ± 0.05, and ± 0.10, for the γ and δ parameters, respectively, and of ± 0.25 mag for the integrated blue magnitude of the galaxy (B =9.50). Fig. 18 indicates that the halo and the bulge make different contributions to the total stellar mass (14 per cent and 86 per cent, respectively) and also that these subsystems have very distinct spa- tial distributions characterized by half mass projected radii of 110 and 350 arcsec (8 and 28 kpc, respectively). A similitude between the projected blue GCs areal densit given by FFG07 and that of dark matter in NGC 1399 (from Richtler et al. 2004), was pointed out in Forte, Faifer & Geisler (2005), and still holds after the recent and improved analysis by Schuberth et al. (2010) (see their models a10 and b10). The same comparison can be performed for NGC 4486 using the results presented by Thomas (2009) andMurphy, Gebhardt &Adams (2011).
In this case, and even though the total enclosed mass derived by those authors are in good agreement (2 to 3 × 10 13 M⊙ within 160.8 kpc), their inferred spatial distributions for dark matter are significantly different. Under the assumption of a logarithmic potential to represent the dark halo, those works obtain core radii in the range from 164 arcsec to 414 arcsec.
The corresponding dark matter volumetric density profiles (eq. 3 in Gebhardt & Thomas 2009), once projected on the sky and given on a pseudo magnitude scale arbitrarily shifted in ordinates, are displayed in Fig. 19. As the outer spatial limit of the dark matter halo is not well constrained we adopted two tentative values in order to asses the impact on the projected profile. The lower curves correspond to a cut off radius of 2500 arcsec, i.e., 25 per cent larger than that given by Doherty et al. (2009), while the upper curve corresponds to twice that radius.
This figure also shows the inferred surface brightness profile of the stellar population with a chemical abundance lower than (Z/Z⊙) = 0.025. These astars are connected with GCs bluer than the "blue peak" (at ≈ (C − T1) = 1.25) of the cluster colour distributions.
A meaningful comparison closer to the centre of the galaxy (i.e. within 250 arcsec) becomes blurred by dynamical erosion on the blue GCs, used as tracers of the stellar component, and would require a rigurous assessment of these effects. Even though dark matter and very low metallicity stars display rather similar projected distributions, a comparison between their spatial distributions still remains somewhat ambiguous due to the uncertain cut off radius of the halo. On one side, adopting the Doherty et al. (2009) value, would suggest that these stars in fact "map" the dark halo. Alternatively, doubling that cut off radius, leads to a somewhat shallower distribution for dark matter. In fact, Strader et al. (2011) do not find evidence for a transition in the inner halo to a potential dominated by the Virgo cluster.
A shallower distribution of the dark matter is predicted by the Abadi, Navarro & Steinmetz (2006) models for isolated galaxies, where an extended halo develops by accretion of stars shed from early merging sub-units, in an hierarchical galaxy formation scenario. A further and rigorous comparison, however, should take into account the distinct environmental situation of NGC 4486 as a central galaxy in the Virgo cluster.
The results discussed in this subsection also allow an estimate of the baryon fraction (f b ) in NGC 4486, which we restrict to a galactocentric radius of 80.4 kpc aiming at avoiding the inherent uncertainties that become more important at larger radii. The total baryonic mass, within that boundary, and in the form of stars, is 6.8 × 10 11 M⊙, while the hot gas amounts to 2.0 × 10 11 M⊙, from Fabricant & Gorenstein (1983) (and after correcting the distance adopted by these authors, d = 15 Mpc, to ours). On the other side, the total enclosed mass in both Gebhardt & Thomas (2009) and Murphy, Gebhardt & Adams (2011) is close to 10 13 M⊙, then yielding a fraction f b = 0.08. This value is well below the cosmic baryon fraction (0.17). However, combined with the circular velocities (715 to 800 km/s) given in these last two works, it falls close, and within the dispersion, of the baryonic fraction-vs-circular relation presented by Dai et al. (2010) (see their figure 4).

GLOBULAR CLUSTER FORMATION EFFICIENCY.
The estimated number of blue and red globulars within a = 2000 arcsec, assuming a fully Gaussian GC integrated luminosity function, (12200± 1500 and 4600± 1000) corresponds to an specific Sn frequency close to 14 ± 1.5 and is consistent with the already known nature of NGC 4486 as an archetype "high Sn system". The number of GCs, and the halo and bulge masses discussed in Section 6, yield the intrinsic GCs formation efficiency for each subsystem in terms of the associated halo mass log(tB) = 2.15, or bulge mass, log(tR) = 0.90 (both given in 10 −9 units). These values are shown in Fig. 20 and compared with the locus corresponding to GCS in Virgo galaxies, derived from a re-discussion of the FVF09 data. In this last work, we note, the definition of GC formation efficiency is that given by Zepf & Ashman (1993), i.e., in terms of the total stellar mass of the galaxy (see also Rhode, Zepf & Santos 2005). Fig. 20 also shows the MW GC formation efficiencies, after adopting the halo and bulge masses from the discussion presented by Boley et al. (2009), and a number of 110 halo and 35 bulge GCs (Mackey & van den Bergh 2005;Bica et al. 2006). The MW clusters also show a much higher formation efficiency for the halo GCs, and compare well with the Virgo GCS locus which, in principle, seems dominated by galaxies that have suffered minor merging events. Even though the GC formation efficiencies presented in this work depend on the assumed connection between the number of GCs and the diffuse stellar mass (Section 3), those of the MW GCs come from a completely independent approach.
The reason behind the strong difference in the formation efficiency of halo and bulge globulars is not clear. However, a distinctive feature between both systems, besides metallicity, seems to be the mean density of the associated stellar populations. A first esti-mate of these densities, using the half mass radii and stellar masses given in the previous subsection, indicates a mean bulge stellar density an order of magnitude higher than in the halo.
In an speculative way, this suggests that the erosion of potential GC formation sites by field stars may be more important in the bulge environment then leading to a lower cluster formation efficiency.
In turn, Fig. 20 indicates that dry merging might have provided both the halo stellar mass and the high number of blue GCs in NGC 4486 through some 300 galaxies with indicative masses of ≈ 30 × 10 7 M⊙.
Within this frame, and as a tentative approach, we created a "composite" galaxy using the Jordán et al. (2009) data corresponding to ten Virgo galaxies with more than fifty blue GCs each.
The total population of the composite galaxy includes 916 GC candidates brighter than the NGC 4486 GCs turn-over magnitude (g = 23.87 mag;Villegas et al. 2010).
From the analysis of this data set we emphasize: a) The composite GCs colour-magnitude diagram shows a blue tilt similar to the tilt observed for the blue GCs in NGC 4486. b) A fit similar to those given in Table 1, leads to GC chemical scale lengths of ZSB = 0.015 and ZSR = 0.55. c) The blue GCs chemical scale parameter, ZSB, is comparable to that expected for the blue GCs in the outer regions of NGC 4486. d) The red GC colours can be adequately fit by a single ZSR parameter even though they are the result of composing galaxies that exhibit a large range in their individual parameters (0.12 to 0.90).
These results give support to the idea that the blue tilt is a generalized feature in most Virgo galaxies and could be detected even after eventual merging processes.
Although the accretion of low mass galaxies might have provided an important fraction of the NGC 4486 halo mass, as suggested in the naive approach by Forte, Martinez & Muzzio (1982), the presence of a metallicity gradient for the blue GCs rather indicates that dissipative collapse has also played a role.
On the other side, dry merging alone cannot explain the characteristics of the red GCs-bulge in NGC 4486 since the inferred ZSR parameters in this galaxy reach values that are as twice as those of the individual galaxies with comparable tR in Fig. 20. The result commented in item d is also interesting in the sense that eventual multiple mergers will not yield detectable effects on the (almost always) bimodal colour distributions.

CONCLUSIONS
The distribution of the integrated GC colours in NGC 4486 is compatible with the presence of two different (blue and red) populations both following an exponential decay (in number) with increasing chemical abundance Z. The chemical scale lengths, however, are very different, being much smaller for the blue GC family. Both GC chemical scales have negative gradients with increasing galactocentric radius. In turn, the composite mass weighted chemical gradient obtained for the composite stellar population is compara- ble to that derived through X ray observations of hot gas, indicating a strong connection between stars and the interstellar medium. The main idea behind the GCs-field stars connection adopted in this work is that the metallicity of a given cluster is a proxy to the mass of the associated diffuse stellar population where it is born and which, through pre-enrichment (see Bailin & Harris 2009), determines the cluster metallicity itself. Furthermore, metallicity may be indicative of the mean stellar density of the environment, a factor possibly governing the GCs formation efficiency.
The approach allows, by combining both the halo and bulge components, the reconstruction of the galaxy profile brightness and of the negative integrated colour gradient over an angular scale of, at least, 1000 arcsec (≈ 80 kpc). Given the multi-metallicity nature of the stellar population, SSP models are not adequate for a proper understanding of integrated colours in terms of chemical abundance (for a detailed discussion on this subject see Schombert & Rakos 2009).
The chemical abundance distribution inferred in this work for the stellar population is similar to those observed in resolved galaxies and exhibits similarities with the predictions given by heterogeneous enrichment models as discussed by Oey (2000).
In particular, the halo/bulge systems can be identified as formed in low/high density environments typified by small/large number of stellar generations and different filling factors. A comparison of our Fig. 15 and 16 with figs. 2 and 3 in Oey's work, appeals for a further, more quantitative exploration.
If GCs appear at the very beginning of the star forming process their own chemical distribution may be reflecting the original "metal production function" and this would also imply larger mean ages than that of the field stars. In agreement with this, Spitler (2010) suggests that metal rich GCs should be older by about 1 Gyr compared with the average age of the bulge.
The GC formation efficiency for each (halo, bulge) system shows that the NGC 4486 system clearly deviates from those corresponding to other Virgo galaxies with masses smaller that 10 11 M⊙.
Although both the NGC 4486 stellar halo mass, and the large number of blue globulars, could be reached by accreting low mass galaxies, the presence of a chemical abundance gradient rather suggests that accretion might have coexisted with the in-situ formation of indigenous blue GCs (see Harris 2009 for a similar conclusion). A description of the mechanisms that may play a simultaneous role in the formation of galaxy haloes is given, for example, in the model analysis by Murante et al. (2007).
We also stress that the eventual accretion of an external population of blue clusters, through numerous small mergers, would not affect the detectability of the chemical or colour gradient of the indigenous blue GCs or of the blue tilt (as shown in Section 7). Alternatively, but not in necessary disagreement, Kissler-Patig & Gebhardt (1998) argue that, their detection of rotation for the blue GCs, is possibly the fingerprint of an important single past merger.
On the other side, pure dry merging cannot explain the red GC-bulge population since the chemical scale parameter of the plausible progenitor galaxies is much smaller than that in the central region of NGC 4486. Both dissipative collapse and/or wet merging leading to high star forming efficiencies and chemical enrichment seem required. The low central surface brightness, as well as the shallow chemical gradient in NGC 4486 are compatible with merging processes (e.g. Kim, Shin & Jin 2010). This is also suggested by the position of the galaxy in the Sérsic n index-vs-central brightness relation "normal" ellipticals (see Graham & Guzmán 2003 for a comprehensive discussion). A scenario were GC formation is in fact entirely merger-driven is given in Muratov & Gnedin (2010).
The spatial distribution of the halo stars with the lowest chemical abundance is remarkably similar to that inferred for dark matter. This coincidence was already noticed in the case of NGC 1399 (Forte, Faifer & Geisler 2005). This last galaxy and NGC 4486 seem to have a very similar baryonic mass (see Jones et al. 1997) and also a comparable number of red GCs. However, they differ both in the number of blue GCs and dark mass content by the same factor, which is ≈ 3 larger in NGC 4486 . Besides, a re discussion of the photometric data presented in FFG07 and of the dark matter content presented by Schuberth et al. (2010) for NGC 1399, also indicates a remarkably similar number of blue GCs per dark mass unit, ≈ 1.0(±0.3) × 10 −9 in both galaxies.
All these features add to the discussion of the possible origins of GCs, and in particular of the blue clusters, in connection with primordial dark matter sub-haloes (e.g. Santos 2003;Mashchenko & Sills 2005;Bekki et al. 2008;Boley et al. 2009).
Further arguments about the connection between GCs and dark matter come from the very large scale study by Lee et al. (2010), who report the detection of "intracluster" GCs whose projected spatial distribution resembles those of dwarf galaxies and dark matter on very large angular scales. The change in the slope of the GC areal density profile in their work, at ≈ 40 arcmin (193 kpc) from the centre of NGC 4486, is close to the "edge" of the galaxy halo as determined by Doherty et al. (2009) (but see Strader et al. 2011 for a different conclusion).
The analysis presented in this work strongly support the idea that GCs appear along the main star forming events in early type galaxies and can be used as tracers of the dominant stellar populations. The "two phases" process, as suggested by Forbes, Brodie & Grillmair (1997), seems an adequate scenario to explain the overall features of GCs and associated stars. The mean-ing of "phase", however, may require further clarification in terms of the existence of a temporal sequence (i.e. halo globulars appear prior to to bulge globulars as suggested by the very different chemical abundances ?), environmental differences (underlying in the inhomogeneous enrichment models) and, eventually, about how both factors combine in the overall landscape of galaxy formation.