Astron. Nachr. / AN 325, No. 2, 84–87 (2004) / DOI 10.1002/asna.200310180

Stellar kinematics in the centers of globular clusters

J. GERSSEN

Department of Physics, University of Durham, South Road, Durham, UK

Received 09 September 2003; accepted 23 October 2003; published online 6 February 2004

Abstract. The high central stellar densities in globular clusters provide a unique environment to study the fundamentaldynamical process of two-body relaxation. This process is the main driver of the dynamical evolution in the center of aglobular cluster and has a profound effect on the structure of the cluster and on its stellar environment. We have obtainedstellar absorption line spectra with STIS to measure the radial velocities of individual stars in the crowded center of theglobular cluster M15. These data increase the number of stars with known radial velocities within the central arcsec by afactor of about three and significantly improve the constraints on the mass distribution in M15. The data provide the mostdetailed look of the central structure of any globular cluster and show that there is a compact dark central mass component.Similar studies using ground based facilities can be efficiently performed by employing Integral Field Units. We have starteda project to better constrain the central mass density in the globular cluster M3 using the GMOS-IFU on Gemini North. Thedata will also allow us to better understand the central rotation which is neither explained nor predicted by any globularcluster model.

Key words: globular clusters: kinematics and dynamics – globular clusters: individual (M3, M15)

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1. Introduction

Globular clusters are among the oldest stellar systems in theuniverse. Several dynamical processes take place in thesesystems on time scales shorter than the Hubble time. Unlikegalaxies, globular clusters provide a unique environment tostudy two-body relaxation which plays a fundamental role inthe evolution of these systems. This relaxation process leadsto equipartition of energy and massive stars will thereforeend up orbiting closer to the cluster potential center thanless massive stars as shown by numerous theoretical studies(e.g. Meylan & Heggie 1997 for a review). This segregationof mass builds up a large mass density in the cluster center.A large fraction of this mass will be dark because the mostmassive stars will have evolved into stellar remnants (neutronstars and white dwarfs) over the lifetime of the cluster. Massdoes therefore not follow light in the center of a globularcluster. To pin down the most fundamental parameter of acluster center, its mass density, requires stellar kinematics.

The high central stellar densities have a profound effecton the stellar environment in these systems. For instance,near the center of M15, which has one of the largest knowncentral densities, two millisecond pulsars and a double X-raysource have been found. Numerical work suggests that the

Correspondence to: Joris.Gerssen@durham.ac.uk

high incidence of stellar collisions and mergers (PortegiesZwart & McMillan 2002) may even lead to the formationof an intermediate mass (∼ 1000M�) black hole (IMBH).However, even in M15 with the best kinematical data that iscurrently available (Gerssen et al. 2002, 2003) the signatureof an IMBH cannot be confirmed (nor can it be excluded).

In galaxies, stellar kinematics are usually derived fromintegrated light spectra. But in globular clusters the fewbrightest stars in an aperture will dominate the integratedlight, complicating the interpretation of the results. Stellarmotions can also be derived from images obtained overa sufficiently long time line. Such proper motion studieshave the added benefit that they provide two of the threecomponents of stellar motion. However, in the very crowdedcentral regions of globular clusters the method is difficultto apply. The most straightforward method to constrain thecentral masses in globular clusters is therefore to determinethe radial velocities of individual stars.

Accurate mass modeling needs to incorporate the kine-matics of faint stars to improve the statistics. With the adventof multi-object spectrographs on large aperture telescopes ithas become feasible to efficiently augment existing data sets.One of the most surprising results to emerge from the datathat have been assembled is that globular clusters apparentlyshow central rotation (e.g. Gebhardt et al. 1997). Two-bodyrelaxation tends to drive angular momentum away from the

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J. Gerssen: Stellar kinematics in the centers of globular clusters 85

Fig. 1. Schematic diagram of the central 2.5 by 2.5 arcsec of M15.All stars in the WFPC2 catalog that are brighter than V = 20 areshown. Overplotted are the slit and pixel positions of the HST /STISobservations to an accuracy of better than 0.01 arcsec. Note that fourslits were observed with on-chip spatial binning.

cluster center and the origin of the observed central rotationis at present not well understood. From an observational pointof view this phenomenon can be efficiently explored using In-tegral Field Units. We have started a pilot study to derive theradial velocities in the center of the globular cluster M3 usingthe GMOS-IFU.

2. M15 (NGC 7078)

The remarkably high stellar density in the center of M15 hasprompted numerous studies to explore this region in moredetail. The high central density leads to significant blendingof light from neighboring stars. With seeing limited observa-tions from the ground it is therefore difficult to unambigu-ously measure the radial velocities of individual stars in thevery center of M15. To counter this problem, we have usedthe STIS spectrograph on HST to obtain spectra of individ-ual stars in the center of M15 using the highest spatial resolu-tion that is currently attainable. These data minimize blend-ing, but cannot completely remove it. However, from WFPC2photometry we were able to quantify the blending and subse-quently correct for it.

2.1. Observations

Long-slit stellar absorption line spectra of the center ofM15 were obtained using the Space Telescope ImagingSpectrograph. In order to map a two-dimensional region withthe one-dimensional STIS, we placed the slit at 18 adjacentpositions as shown schematically in fig. 1. The slit width is

Fig. 2. Comparisons between the STIS data and model predictions.The top two panels show the results for a model with a constantmass-to-light ratio. The bottom panels are for a model in which themass-to-light profile based on the Fokker-Planck models of Dull etal. (2003) have been used. Models with a central black hole rang-ing from 0 to 10 × 103M� are shown in the right panels. A non-parametric estimate of the projected RMS velocity profile is over-plotted with the heavy line (heavy dashed lines are 68% confidenceregions). The left panels show the likelihood (λ) of each model giventhe data. The best-fit models (minimum λ) have a MBH of 3500 M�and 1700 M� respectively. The dotted lines indicate the 1σ and 2σconfidence levels.

0.1 arcsec and the observations therefore cover the centraltwo arcsec of M15.

All spectra were centered around the Mgb absorptionline feature and have a velocity scale of 16 km s−1 per pixel.The expected central velocity dispersion in M15 is ∼ 12 kms−1. Several intricate corrections for the motion of HSTand the exact location of each star with respect to slit weretherefore necessary (van der Marel et al. 2002) since bothcan introduce errors that are as large as the expected centralvelocity dispersion. The radial velocities were derived bycross-correlating the STIS spectra with Kurucz model tem-plates. In the end we were able to reliably measure the radialvelocities for 64 stars in the STIS data. Within the centralarcsec the STIS data triple the number of stars with measuredradial velocities. About one third of the STIS stars alreadyhave a ground based measurement of the radial velocity. Acomparison between the two velocity sets shows that theSTIS velocities are accurate in a systematic sense to about 2.5km s−1. The residuals between the STIS data and the groundbased data show no trends with either stellar magnitude orcolor. The mean residual velocity is 0.2 km s−1.

The central velocity dispersion in M15 derived from theSTIS data is 14 km s−1 which is somewhat higher than thepreviously published ground based values of about ∼ 12km s−1 (e.g. Gebhardt et al. 2000). Rather than to use this

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value directly, we use a model approach to constrain the cen-tral mass density in M15. In order to compare the modelsto the data over the largest range in radii possible, we com-bine the STIS data with a compilation of ground based veloc-ities (Gebhardt et al. 2000). The combined data set consistsof 1797 stars covering radii from 0.3 to 1000 arcsec.

2.2. Models

Stellar velocity profiles are estimated from the discrete dataset using a non-parametric technique. The projected RMS(v2 + σ2 averaged over rings on the sky) velocity profile andits 1σ uncertainties are shown in the right panels of fig. 2.These profiles allow a visual comparison between the dataand the models. The actual quantitative comparison betweenthe models and the data is made by calculating the likelihoodof each model given all 1797 measured radial velocities. Todetermine the mass distribution in M15 we assume that thecluster is spherical and that it is in hydrostatic equilibrium.Such a system obeys the Jeans equation (Binney & Tremaine1987). In order to solve this equation for velocities werequire the mass density and the gravitational potential. Weobtain the luminosity density by deprojecting a combinationof the surface brightness profiles published by Trager et al.(1995) and Guhathakurta et al. (1996) and transform this intoa mass density by assuming either a constant mass-to-lightratio (Υ) or an Υ profile based on Fokker-Planck models.The gravitational potential is obtained from the mass densityusing Poisson’s equation. The contribution of a possiblecentral point mass MBH is added to the potential. With boththe mass density and the gravitational potential determinedwe can solve the Jeans equation for velocities and project theresults along the line of sight.

The first set of isotropic models that we calculate haveΥ independent of radius. The top left panel in fig. 2. showsthe likelihood values as a function of point mass MBH. Thebest-fitting mass-to-light ratio is fairly independent of MBH,Υ = 1.6 ± 0.1. The best-fit MBH = (3.2 ± 2.2) × 103 M�.To quantify the effects of uncertainties in the cluster position(about 0.2 arcsec) on the mass MBH we repeated thelikelihood analysis with the M15 center shifted to differentpositions by several tenths of arcsec. The resulting changesin MBH are insignificant, less than 10 percent.

While a constant mass-to-light profile model is a usefulbenchmark, it is an over-simplification in the cores ofglobular clusters. Globular cluster evolution is driven bytwo-body relaxation. The lack of a constant density core inM15 suggests that this cluster has undergone core collapse asa result of this process. A natural consequence of two-bodyrelaxation is mass segregation. In an attempt to reachequipartition, heavy stars and dark stellar remnants sinkto the center of cluster, which causes a central increase inΥ(r). This boosts the predicted velocities close to the center,which may obviate the need to invoke a central black holein the models. Our second set of models therefore uses avarying mass-to-light profile for M15. This profile is derivedfrom detailed Fokker-Planck models (Dull et al. 2003). Thebottom two panels of fig. 2 show that models without a

Fig. 3. Schematic diagram showing the central 10 by 10 arcsec ofM3. All stars that are brighter than V = 20 are shown. The size of astar corresponds to its magnitude. The stellar positions and magni-tudes were derived from an archival WFPC2 image. The overplotted40 by 25 hexagonal apertures of the GMOS Integral Field Unit coverthe central 7 by 5 arcsec.

black hole are found to be statistically acceptable (within1σ) although inclusion of an intermediate-mass BH, withMBH = 1.7+2.7

−1.7 × 103 M�, still provides a marginally betterfit to the data (although not a statistically significant one).

An important shortcoming of the Dull et al. model is thatit assumes that all neutron stars that are formed in the clus-ter are retained. However, the observed distribution of pulsarkick velocities indicates that the retention factor should be nomore than 10 percent. The models therefore only provide anupper limit on the concentration of dark remnants in M15. N-body models constructed by Baumgardt et al. (2003) are ableto fit the M15 data with and without the inclusion of neutronstars. But these models cannot definitely rule out the presenceof a central IMBH in the M15 data.

3. M3 (NGC 5272)

The STIS observations of M15 described in the previoussection essentially emulate Integral Field Spectroscopy. Atrue Integral Field Unit (IFU) is much more time efficientsince it can map the stellar velocities in a single point-ing. Alternative observational strategies to measure radialvelocities in globular cluster centers include Fabry-Perottechniques and fiber spectroscopy. However, the former aredifficult to perform/analyze and generally have fairly poorvelocity resolution while the latter suffers from the inabilityto position fibers arbitrarily close.

We have started a project (Gemini North, semester2003B, band 1) to measure the radial velocities of stars inthe center of the globular cluster M3 using the GMOS-IFU

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J. Gerssen: Stellar kinematics in the centers of globular clusters 87

Fig. 4. Kinematical profiles derived from a set of ∼ 400 radial ve-locities obtained for the globular cluster M3. The velocity dispersionand velocity profiles are derived in azimuthally averaged radial bins(top and center panels respectively.) The dotted lines are the one-sigma uncertainties. The bottom panel shows the ratio of the veloc-ity to the velocity dispersion. The large increase observed toward thecenter is unexplained (nor predicted) by existing models of globularclusters.

spectrograph. The central stellar density of this cluster iswell matched to the spatial resolution and to the 5” x 7”field-of-view of the GMOS-IFU (see fig. 3). The GMOS-IFU (Allington-Smith et al. 2002) uses a system of 25 by 40lensed fibers to reformat the field into two long-slits. Unlikemany other IFUs, the spectral resolution of the GMOS-IFU(R ∼ 5000) is sufficient to study the internal kinematics ofstellar sytems. Additional advantages of an IFU include theelimination of a non-uniform spatial coverage (cf the M15STIS data). And, more importantly, a high relative velocityaccuracy can be achieved since problems due to for instanceflexure are similar for all apertures and therefore cancel out.The object-to-object velocities in the center of M3 are the rel-evant quantities to build a model, not the absolute velocitiesof the central stars.

The GMOS-IFU velocities will be combined with a set ofsome 400 stellar velocities that cover the large scale kinemat-ics in M3. These velocities were derived using the RutgersFabry-Perot etalons on the CFHT and are necessary to con-strained the mass profile of M3 at all radii. Non-parametricvelocity profiles derived from this data set are shown infig. 4. The increase in rotational velocity cannot be under-stood in terms of two-body relaxation since this process leadsto an isotropic velocity distribution. A possible explanationinvokes a central point mass which can induce tangentialanisotropy in the velocity distribution of the surrounding stars(Young 1980).

4. Summary

The HST /STIS data of M15 that we obtained provide themost detailed view of the central structure of any globularcluster to date. The data show that there in a dark centralmass concentration in M15 but it is not uniquely establishedwhether this is due to a central black hole or to normal masssegregation. It is interesting to note that independent evidenceis emerging for central black holes in other globular clusters.Gebhardt et al. (2002) recently found dynamical evidencefor an IMBH in the globular cluster G1. The relaxation timesin this cluster are longer than in M15 and it is therefore moredifficult to explain the G1 data in terms of mass segregation.

Further progress will require both more advanced mod-eling, and more and larger data sets. On the theoretical sidemore realistic evolutionary models that include neutron starescape are desirable. In addition, such models also need toaddress the issue of central rotation which now appears tobe a very common feature of globular clusters. IFU spec-troscopy may be the ideal tool to observationally probe thecentral stellar kinematics in globular clusters. With such in-struments the stellar kinematics in the central few arcsec ofa Galactic globular cluster can be measured using a singlepointing. This approach not only avoids the time consumingobservations required by other methods but it also returns ve-locities with very high object-to-object velocity accuracies.We have started a pilot project to explore the feasibility ofsuch an approach using the GMOS-IFU targeted at the cen-tral region of M3.

The author acknowledges support from the EURO3D Re-search Training Network, funded by the European Commis-sion under contract No. HPRN-CT-2002-00305.

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