---
abstract: 'This paper is the third in the series of papers on M81 globular clusters.  In this paper, we present spatial and metal abundance properties of 95 M81 globular clusters, which comprise nearly half of all the M81 globular cluster system.  These globular clusters are divided into two M81 metallicity groups by a KMM test.  Our results show that, the metal-rich clusters did not demonstrate a centrally concentrated spatial distribution as ones in M31, and metal-poor clusters tend to be less spatially concentrated.  In other words, the distribution of the metal-rich clusters in M81 is not very similar to that of M31.  Most of the metal-rich clusters distribute at projected radii of 4-8 kpc.  It is also noted that the metal-rich clusters distribute within the inner 20 kpc, and the metal-poor ones do out to radii of $\sim 40$ kpc.  Like our Galaxy and M31, the metallicity distribution of globular clusters in M81 along galactocentric radius suggests that some dissipation occurred during the formation of the globular cluster system, i.e. smooth, pressure-supported collapse models of galaxies are unlikely to produce such radial distribution of metallicity presented in this paper.  There is not evident correlation between globular cluster luminosity and metallicity in M81 globular clusters.  The overwhelming conclusion of this paper seems to be that a more complete and thorough cluster search is needed in M81.' 
author:
- 'Jun Ma, David Burstein, Zhou Fan, Xu Zhou, Jiansheng Chen, Zhaoji Jiang, Zhenyu Wu and Jianghua Wu'
title: Metal Abundance Properties of M81 Globular Cluster System
---

Introduction
============

An understanding of galaxy formation and evolution is one of the principal goals of modern astrophysics.  Globular clusters are fossils of the earliest stages of galaxy formation and evolution.  They are bright, easily recognized packages containing a stellar population with a homogeneous abundance and age.  So, their integrated properties of location, abundance, and kinematics provide valuable clues to the nature and duration of galaxy formation [@bh00]. 

The metallicity distribution of globular clusters is of particular importance in deepening our knowledge of the dynamical and chemical evolution of the parent galaxies.  For example, the globular clusters of many elliptical galaxies show multi-modal metallicity distributions, suggesting that multiple star formation episodes occurred in these elliptical galaxies in the past [@zepf93; @bh00].  Great progress has been made in the past decade in our understanding of globular cluster systems of galaxies, especially the discovery that many galaxies possess two or more distinct subpopulations of globular clusters [e.g., @west04 and references therein].  Based on the data from $Hubble$ $Space$ $Telescope$ ($HST$) archive, @Gebhardt99, @larsen01 and @kw01 presented that many large galaxies possess two or more subpopulations of globular clusters that have quite different chemical compositions.  Recently, @peng06 presented the color distributions of globular cluster systems for 100 early-type galaxies observed in the Virgo Cluster Survey with the Advanced Camera for Surveys (ACS) on the $HST$, and found that, on average, galaxies at all luminosities in their study appear to have bimodal or asymmetric GC color/metallicity distributions.  The presence of color-bimodality indicates that there have been at least two major star-forming mechanisms in the histories of galaxies. 

@patr99 presented a metallicity distribution of 133 Galactic globular clusters that apparently shows two peaks (i.e., two distinct metal-poor and metal-rich globular cluster populations).  A double-Gaussian can best fit these two subpopulations, the mean metallicity values are $-1.59$ and $-0.55$ dex, respectively.  Using the data for 247 globular clusters in M31, @bh00 studied the metallicity distribution, which is asymmetric, implying the possibility of bimodality.  Then they applied a KMM algorithm showing that the metallicity distribution is really bimodal.  @perrett02 confirmed the conclusions of @bh00.  @ma05 showed that the intrinsic $B$ and $V$ colors and metallicities of 94 M81 globular clusters are bimodal, with metallicity peaks at $\rm
{[Fe/H]}\approx -1.45$ and $-0.53$, similar to what we find for the Milky Way and M31 globular clusters. 

M81 is one of the nearest Sa/Sb-type spiral outside the Local Group, very similar to M31, and roughly as massive as the Milky Way.  So, beyond the Local Group, it is a good candidate for reaching a detailed study of spiral galaxy globular cluster system for comparison to the Milky Way and M31 system.  @bh91 derived spectroscopic metallicities for eight globular clusters in M81 and presented the sample mean of $\rm [Fe/H]=-1.46\pm0.31$. @pbh95 obtained low signal-to-noise spectra of 82 candidates, 25 of which were confirmed as $bona$ $fide$ M81 globular clusters.  They derived the mean metallicity to be $\rm
[Fe/H]=-1.48\pm0.19$ both from the weighted mean of the individual metallicities, and directly from the composite spectrum of the 25 confirmed globular clusters.  To maximize the success rate of the globular cluster candidate list for the ongoing spectroscopic observations, @pr95 used an extensive database that included photometric, astrometric, and morphological information on 3774 objects covering over a $>50~\rm{arcmin}$ diameter field centered on M81 to reveal 70 globular cluster candidates. 

@sbkhp02 presented moderate-resolution spectroscopy for 16 globular cluster candidates from the list in @pr95, and confirmed these 16 candidates as $bona$ $fide$ globular clusters.  They also obtained metallicities for 15 of the 16 globular clusters.  From their results, @sbkhp02 concluded that the M81 globular cluster system is very similar to the Milky Way and M31 systems, both chemically and kinematically. 

With the superior resolution of the $HST$, M81 is close enough for its clusters to be easily resolved on the basis of image structure [@cft01].  Thus, using the $B$, $V$, and $I$ bands of $HST$ Wide Field Planetary Camera 2 (WFPC2), @cft01 imaged eight fields covering a total area of $\sim 40~\rm{arcmin}^{2}$, and detected 114 compact star clusters in M81, 59 of which are globular clusters.  Based on the estimated intrinsic colors, @cwl04 found that the M81 globular cluster system has an extended metallicity distribution, which argues the presence of both metal-rich and metal-poor globular clusters.  @ma05 then confirmed this conclusion. 

The outline of the paper is as follows.  In § 2 we provide some statistical relationships.  The summary is presented in § 3. 

Properties of Globular Clusters in M81
======================================

Sample of globular clusters
---------------------------

In the first paper of our series, @ma05 studied the distributions of intrinsic $B$ and $V$ colors and metallicities of 95 M81 globular clusters which are from @pbh95, @cft01 and @sbkhp02.  This cluster sample includes nearly half of the M81 total globular cluster population.  About the M81 total globular cluster population, @pr95 estimated it to be $210\pm30$ by the $BVR$ photometric, astrometric, and image structure study of the M81 field; @cft01 indicated the total number of globular clusters in M81 to be $211\pm29$ using globular cluster estimates in various annular bins and correcting for incompleteness.  It is difficult to detect and confirm globular clusters beyond the Local Group before $HST$ appears.  In fact, even in the Local Group, it is also not easy to detect and confirm globular clusters.  For example, the total number of globular clusters in M31 was estimated to be $460\pm70$ by @bh01, the largest number of globular clusters used to study the metal abundance properties of the M31 globular clusters includes 301 clusters collected by @perrett02, a little more than half of the total number.  Beyond the Local Group, the globular cluster sample in M81 collected by @ma05 includes the largest number of globular clusters comparing to the total globular clusters in the host galaxy. 

In the second paper of our series, @ma06 presented the spectral energy distributions of 42 M81 globular clusters selected from @ma05 in 13 intermediate-band filters from 4000 to 10000[Å]{}, using the CCD images of M81 observed as part of the Beijing-Arizona-Taiwan-Connecticut (hereafter BATC) multicolor survey of the sky, and confirmed the conclusions of @sbkhp02 that, M81 contains clusters as young as a few Gyrs, which were also observed in both M31 and M33.  In this paper, we will study the spatial and metal abundance properties of the M81 globular clusters using the sample globular clusters of @ma05.  Figure 1 is the image of M81 in filter BATC07 (5785[Å]{}) of BATC multicolor survey of the sky, the circles indicate the positions of the sample clusters. 

As mentioned above, @ma05 studied the distributions of intrinsic $B$ and $V$ colors and metallicities of these 95 M81 globular clusters, and first found that the abundance distribution of the globular cluster system is consistent with a bimodal distribution with peaks at $\rm {[Fe/H]}\approx -1.45$ and $-0.53$ based on the KMM algorithm of @abz94.  It is true that, the appearance of the histogram can be ambiguous and misleading with binned data, however, the KMM algorithm of @abz94 is a robust method of analysis without relying on binning methods [see @perrett02].  KMM mixture modelling works under the assumption that the sample data are independently drawn from a parent population that comprises a mixture of $N$ Gaussian distributions.  @ma05 presented that, for M81 globular clusters, the posteriori probabilities of group membership returned by the KMM algorithm assigned 74 clusters to the metal-poor population and 20 to the metal-rich population distribution[^1]. 

Spatial distribution
--------------------

Figure 2 shows the projected spatial distributions of the metal-poor and metal-rich globular clusters in M81.  The distance modulus for M81 is adopted to be 27.8 [@fwm94; @cft01].  We adopted the inclination and position angles to be $59^{\circ}$ and $157^{\circ}$ of M81 as @cft01 did, respectively.  When the line of intersection (i.e. the major axis of the image) between the galactic plane and tangent plane is taken as the polar axis, it is easily proved that:

$$r=\rho\sqrt{1+\tan^2 \gamma\sin^2\theta}$$

and $$\tan\phi=\frac{\tan\theta}{\cos\gamma},$$ where $r$ and $\phi$ are the polar co-ordinates in the galactic plane, and $\rho$ and $\theta$ are the corresponding co-ordinates in the tangent plane, and $\gamma$ is the inclination angle of the galactic disk.  Using formula (1), we can obtain the distances of our sample clusters from the center of M81, which are listed in Table 1.  In Table 1, we also listed the metallicities of the sample clusters from @ma05.  From Figure 2, it is clear that the metal-rich globular clusters in M81 are not as centrally concentrated as the metal-rich globular clusters of M31 are [@hbk91; @perrett02].  Figure 3 presents the histogram for the metal-poor and metal-rich globular clusters in M81.  It shows that most of the metal-rich clusters distribute at projected radii of 4-8 kpc.  It is also noted that the metal-rich clusters distribute within the inner 20 kpc, and the metal-poor ones do out to radii of $\sim 40$ kpc.  In the Milky Way, the metal-rich GCs reveal significant rotations and have historically been associated with the thick-disk system [@zinn85; @taft89]; however, other works [@fw82; @minniti95; @patr99; @forbes01] suggested that metal-rich GCs within $\sim 5$ kpc of the Milky Way Galactic center are better associated with the bulge and bar.  In M31, @ew88 showed that the metal-rich clusters constitute a more highly flatted system than the metal-poor ones, and appear to have disklike kinematics; @hbk91 showed that the metal-rich GCs are preferentially close to the galaxy center.  At the same time, @hbk91 showed that the distinction between the rotation of the metal-rich and metal-poor clusters is most apparent in the inner 2 kpc.  So, @hbk91 concluded that the rich-metal clusters in M31 appear to form a central rotating disk system.  With the largest sample of 321 velocities, @perrett02 provided a more comprehensive investigation on the kinematics of the M31 cluster system.  @perrett02 showed that, the metal-rich globular clusters of M31 appear to constitute a distinct kinematic subsystem that demonstrates a centrally spatial distribution with a high rotation amplitude, but does not appear significantly flattened, which is consistent with a bulge population.  It is of interests to mention that, @sbkhp02 performed a maximum-likelihood kinematic analysis on 166 M31 clusters of @bh00 and found that the most significant difference between the rotation of the metal-rich and metal-poor clusters occurs at intermediate projected galactocentric radii.  Especially, @sbkhp02 presented a potential thick-disk population among M31’s metal-rich globular clusters.  For M81 globular clusters, @sbkhp02 performed a kinematic analysis of the velocities of 44 M81 globular clusters, and strongly suggested that the metal-rich clusters are rotating in the same sense as the gas in the disk of M81.  @sbkhp02 concluded that, although their cluster sample is not large enough to make a direct comparison between metal-rich and metal-poor clusters in specific radius ranges, the conclusion with M81’s metal-rich clusters at intermediate projected radii being associated with a thick disk in M81 is correct.  It is true that, from Figure 3, most of metal-rich clusters distribute at projected radii of 4-8 kpc.  So, at least, we can conclude that most of the metal-rich clusters in our sample are not associated with a bulge cluster system of M81; they may associate with a thick disk in M81 as indicated by @sbkhp02.  The sample clusters of this paper include all the sample clusters of @sbkhp02.  But, except for the sample clusters of @sbkhp02, the other clusters have no published radial velocity estimates.  So, obviously, more kinematic and metallicity data are needed for globular clusters in M81 to determine if the inner metal-rich GCs have kinematic properties that are consistent with the bulge and the metal-rich GCs at projected radii of 4-8 kpc are associated with a thick disk in M81. 

Metallicity gradient
--------------------

The presence or absence of a radial trend in globular cluster metallicities is an important test of galaxy formation theory [@bh00].  If a galaxy forms as a consequence of a monolithic dissipative and rapid collapse of a single massive, nearly-spherical spinning gas cloud in which the enrichment timescale is shorter than the collapse time, the halo stars and globular clusters should show large-scale metallicity gradients [@eggen62; @bh00]; however, @sz78 presented a chaotic scheme in the early evolution of a galaxy, in which loosely bound pre-enriched fragments merge with the main body of the proto-galaxy over a significant period, so there should be homogeneous metallicity distribution.  For the Milky Way, @taft89 showed some evidence that metallicity gradients with both distance from the Galactic plane and distance from the Galactic center were present in the disk cluster system.  For M31, there are some inconsistent conclusions, such as @van69 showed that there is little or no evidence for a correlation between metallicity and projected radius, but most of his clusters were inside $50{\arcmin}$; however, some authors [see e.g. @hsv82; @sha88; @hbk91; @perrett02] presented that there is evidence for a weak but measurable metallicity gradient as a function of projected radius.  @bh00 confirmed the latter result based on their large sample of spectral metallicity and color-derived metallicity.  Figure 4 plots the metallicity of the M81 globular clusters as a function of galactocentric radius, in which black circles indicate the clusters with spectroscopic metallicities with uncertainties smaller than 1.0 dex.  Clearly, the dominant feature of this diagram is the scatter in metallity at any radius.  At the same time, our sample clusters are mainly distributed in the inner 10 kpc.  So, it is difficult to determine the metallicity gradient.  It is true that, smooth, pressure-supported collapse models of galaxies are unlikely to produce a result like this.  However, in order to present a quantitative conclusion, we made least-squares fits: the total sample of globular clusters does not have a significant metallicity gradient ($-0.009\pm0.009$ dex $\rm kpc^{-1}$), and the clusters with spectroscopic metallicities with uncertainties smaller than 1.0 dex have a marginally significant gradient ($-0.018\pm0.01$ dex $\rm kpc^{-1}$).  This result is in agreement with @kong00, who obtained metallicity maps of M81 field by comparing simple stellar population synthesis models of BC96 [@bc96] with the integrated photometric measurements of the BATC photometric system, and did not find, within their errors, any obvious metallicity gradient from the central region to the bulge and disk of M81.  But, we should emphasize that, in the least-squares fits of this paper, the metal-rich clusters seem to act an important part in determining the metallicity gradient.  From Figure 4, we can also see the decrease in the “upper envelope" of metallicity reported by @hbk91 and @bh00 for M31 globular clusters.  In fact, we do a least-squares fits for the metal-poor clusters of M81, the metallicity gradient is $-0.006\pm0.006$ dex $\rm kpc^{-1}$. This metallicity gradient may not have any statistical meanings.  It is clear that, the small sample of rich-metal clusters in M81 cannot present any firm conclusion about metallicity gradient. 

Metallicity versus absolute magnitude
-------------------------------------

The correlation between cluster mass (or luminosity) and metallicity is important in globular cluster formation theory.  It is generally believed that, if self-enrichment is important in globular clusters, the most massive clusters could retain their metal-enriched supernova ejecta, so the metal abundance should increase with cluster mass; the opposite is true if cooling from metals determines the temperature in the cluster-forming clouds [@bh00].  The self-enrichment of GCs has been in detail studied in some aspects [see detail from @sbsb06].  However, it is interesting of mentioning the model of globular cluster self-enrichment developed by @pj99.  In this model, cold and dense clouds embedded in the hot protogalactic medium are assumed to be the progenitors of galactic halo globular clusters.  Based on this model, @pg01 presented that the most metal-rich proto-globular clusters are the least massive ones. 

For M31 globular clusters, @hbk91 first presented the metallicity versus apparent magnitude for 150 M31 clusters, and did not find any trend of metallicity with luminosity; then, @bh00 showed metallicity versus dereddened apparent magnitude using a large cluster sample including 247 objects, and confirmed the conclusion of @hbk91. 

Figure 5 shows metallicity versus absolute magnitude for M81 globular clusters, in which black circles indicate the clusters with spectroscopic metallicities with uncertainties smaller than 1.0 dex.  The metallicity and absolute magnitudes for the sample clusters are from @ma05.  It is true that there is not obvious trend of metallicity with luminosity as M31 GCs do.  Least-squares fits show no evidence for a relationship between luminosity and metallicity in M81 clusters. 

As we know, $HST$ provides a unique tool for studying globular clusters in extragalaxies.  Recently, based on the ACS on the $HST$, @harris06 and @sbsb06 found that, in giant ellipticals such as M87, NGC4649 and NGC7094, luminous blue GCs (i.e. metal-poor GCs) reveal a trend of having redder colors, such that more massive GCs are more red (metal-rich).  This trend is referred to as a ‘blue tilt’ [also see @strader06].  This ‘blue tilt’ was interpreted as a result of self-enrichment [@sbsb06].  @sbsb06 speculatively suggested that these GCs once possessed dark matter halos.  @spitler06 subsequently found that this ‘blue tilt’ is also true in the Sombrero spiral galaxy (NGC4594) and may extend to less luminous GCs with a somewhat shallower slope that was derived by @harris06 and @sbsb06.  As @spitler06 pointed out that, the Sombrero provides the first example of this trend in a spiral galaxy and in a galaxy found in a low-density galaxy environment.  However, in these ACS studies, the metal-rich (red) GCs did not show this corresponding trend [also see @bekki07].  Based on high-resolution cosmological simulation with globular clusters, @bekki07 investigated formation processes and physical properties of globular cluster system in galaxies, and found that, luminous metal-poor clusters would emerge a correlation between luminosity and metallicity if they originated from nuclei of low-mass galaxies at high $z$. In fact, in the simulations of @bekki07, the ‘simulated blue tilts’ emerge from the assumption that luminous metal-poor clusters originate from stellar galactic nuclei of the more massive nucleated galaxies with a luminosity-metallicity relation.  So, it is evident that, in @bekki07, galaxies which experienced more accretion/merging events of nucleated low-mass galaxies are more likely to show a blue tilt [see details from @bekki07]. 

Summary
=======

In this paper we present spatial and metal abundance properties of 95 M81 globular clusters, which are collected by @ma05.  This cluster sample includes nearly half of the M81 total globular cluster population, is the largest one comparing to the total globular clusters of the host galaxy beyond the Local Group.  Our conclusions are as follows:

1\. The metal-rich clusters did not demonstrate a centrally concentrated spatial distribution as ones in M31, and metal-poor clusters tend to be less spatially concentrated.  Most of metal-rich clusters distribute at projected radii of 4-8 kpc.  We can conclude that most of the metal-rich clusters in our sample are not associated with a bulge cluster system of M81; they may associate with a thick disk in M81 as indicated by @sbkhp02. 

2\. The globular clusters in M81 have a small radial metallicity gradient like M31 and our Galaxy, suggesting that some dissipation occurred during the formation of the globular cluster system. 

3\. There is not obvious trend of metallicity with luminosity in M81 globular clusters. 

We are indebted to the referee for his/her thoughtful comments and insightful suggestions that improved this paper greatly.  This work has been supported by the Chinese National Natural Science Foundation Nos 10473012, 10573020, 10633020, 10673012 and 10603006; and by National Basic Research Program of China (973 Program) No.  2007CB815403. 

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[^1]: Since the globular cluster 96 of @cft01 has very high $(B-V)_0$ ($(B-V)_0=1.778$), and the metallicity obtained using the color-metallicity correlation is too rich (0.95 dex), @ma05 do not include it when performing the KMM test.