Indication for an intermediate-mass black hole in the globular cluster NGC 5286 from kinematics
A. Feldmeier, N. Lützgendorf, N. Neumayer, M. Kissler-Patig, K. Gebhardt, H. Baumgardt, E. Noyola, P. T. de Zeeuw, B. Jalali
AAstronomy & Astrophysics manuscript no. ngc5286˙final c (cid:13)
ESO 2018November 1, 2018
Indication for an intermediate-mass black hole in the globularcluster NGC 5286 from kinematics
A. Feldmeier , N. L¨utzgendorf , N. Neumayer , M. Kissler-Patig , , K. Gebhardt , H. Baumgardt , E. Noyola , P. T.de Zeeuw , , and B. Jalali European Southern Observatory (ESO), Karl-Schwarzschild-Straße 2, 85748 Garching, Germanye-mail: [email protected] Gemini Observatory, 670 N. A’ohoku Place, Hilo, Hawaii, 96720, USA Astronomy Department, University of Texas at Austin, Austin, TX 78712, USA School of Mathematics and Physics, University of Queensland, Brisbane, QLD 4072, Australia Instituto de Astronomia, Universidad Nacional Autonoma de Mexico (UNAM), A.P. 70-264, 04510 Mexico Sterrewacht Leiden, Leiden University, Postbus 9513, 2300 RA Leiden, The Netherlands I. Physikalisches Institut, Universit¨at zu K¨oln, Z¨ulpicher Str. 77, 50937 K¨oln, GermanyReceived xxxxxxxx xx, xxxx; accepted xxxxxxx xx, xxxx
ABSTRACT
Context.
Intermediate-mass black holes (IMBHs) fill the gap between stellar-mass black holes and supermassive black holes(SMBHs). The existence of the latter is widely accepted, but there are only few detections of intermediate-mass black holes (10 - 10 M (cid:12) ) so far. Simulations have shown that intermediate-mass black holes may form in dense star clusters, and therefore may stillbe present in these smaller stellar systems. Also, extrapolating the M • - σ scaling relation to lower masses predicts intermediate-massblack holes in systems with σ ∼
10 - 20 km / s such as globular clusters. Aims.
We investigate the Galactic globular cluster NGC 5286 for indications of a central intermediate-mass black hole using spectro-scopic data from VLT / FLAMES (cid:63) , velocity measurements from the Rutgers Fabry Perot (RFP) at CTIO, and photometric data fromHST / ACS.
Methods.
We compute the photometric center, a surface brightness profile, and a velocity-dispersion profile. We run analytic sphericaland axisymmetric Jeans models with di ff erent central black-hole masses, anisotropy, mass-to-light ratio, and inclination. Further, wecompare the data to a grid of N -body simulations without tidal field. Additionally, we use one N -body simulation to check the resultsof the spherical Jeans models for the total cluster mass. Results.
Both the Jeans models and the N -body simulations favor the presence of a central black hole in NGC 5286 and our detec-tion is at the 1- to 1.5- σ level. From the spherical Jeans models we obtain a best fit with black-hole mass M • = (1.5 ± · M (cid:12) .The error is the 68% confidence limit from Monte Carlo simulations. Axisymmetric models give a consistent result. The best fitting N -body model is found with a black hole of 0.9% of the total cluster mass (4.38 ± · M (cid:12) , which results in an IMBH mass ofM • = (3.9 ± · M (cid:12) . Jeans models give values for the total cluster mass that are lower by up to 34% due to a lower value of M / L.Our test of the Jeans models with N -body simulation data shows that the discrepancy in the total cluster mass has two reasons: Theinfluence of a radially varying M / L profile, and underestimation of the velocity dispersion as the measurements are limited to brightstars, which have lower velocities than fainter stars. We conclude that detection of IMBHs in Galactic globular clusters remains achallenging task unless their mass fractions are above those found for SMBHs in nearby galaxies.
Key words.
Black hole physics – globular clusters: individual: (NGC 5286) – stars: kinematics and dynamics
1. Introduction
The existence of supermassive black holes (SMBHs) is widelyaccepted. Mass estimates come either from kinematic measure-ments, or from X-ray and radio luminosities, which assumecertain accretion rates. However, the formation and growth ofSMBHs is not well understood, although it is somehow linkedto the evolution of the environment. The mass of a central blackhole is correlated to the mass of the bulge M b of its host system(e.g. H¨aring & Rix 2004), and to the stellar velocity dispersion σ of the bulge (e.g. Gebhardt et al. 2000a; Ferrarese & Merritt2000; G¨ultekin et al. 2009). Systems with higher M b and higher σ contain more massive central black holes. This suggests a con- (cid:63) Based on observations collected at the European Organisationfor Astronomical Research in the Southern Hemisphere, Chile(085.D-0928) nection between the formation and evolution of central blackholes and their host systems.There are several detections of quasars at a redshift higherthan 6 (e.g. Fan et al. 2001; Willott et al. 2010; Mortlock et al.2011). The masses for the central black holes as inferred fromthe luminosity are of the order of ∼ M (cid:12) . These high massescannot be explained by accretion onto a stellar-mass black hole,as not enough time has elapsed at z ∼
6: the accretion rates wouldgreatly exceed the Eddington limit. In order to build a blackhole of 10 M (cid:12) at z ∼
6, the black-hole seed requires a mass of10 -10 M (cid:12) , as shown by Volonteri (2010). Black holes in thismass range are called intermediate-mass black holes (IMBHs)and must have formed in the young universe.There are theories for the formation of IMBHs fromPopulation III stars (Madau & Rees 2001; Bromm & Loeb2003), gas-dynamical processes (Loeb & Rasio 1994), and fromstellar-dynamical instabilities in star clusters (Ebisuzaki et al. a r X i v : . [ a s t r o - ph . GA ] A p r . Feldmeier et al.: Indication for an intermediate-mass black hole in the globular cluster NGC 5286 from kinematics ∼ yr, Ebisuzaki et al. 2001). In a dense core the mas-sive stars undergo runaway stellar mergers. After several col-lisions, a very massive star (VMS) with >
100 M (cid:12) forms andgrows quickly (Portegies Zwart et al. 1999). Yungelson et al.(2008) used an evolutionary code to compute the mass loss forVMSs of initial solar metallicity ( Z = ff erent metallicities, and found that low-metallicitystars with Z = ff er less mass loss. Their final mass is bya factor of ∼ − Z = M (cid:12) .The central black hole continues accreting nearby stars, until thereservoir of massive stars is exhausted.If a cluster is not dense enough, stellar evolution is fasterthan mass segregation. Massive stars evolve to stellar remnantsbefore reaching the center. Miller & Hamilton (2002) proposedthat successive mergers of stellar remnants and accretion canform an IMBH in a globular cluster. Recent models examinedthe retention fraction of stellar black holes in star clusters andmerger rates due to gravitational radiation and found di ff erentresults. The retention fraction for black holes binaries is only1% to 5% according to Moody & Sigurdsson (2009). Miller &Davies (2012) found that nearly all black holes are kicked outduring mergers. On the other hand, Morscher et al. (2013) cameto the result that less than 50% of the black holes are dynamicallyejected, and the total merger rate is ∼ M • - σ scaling relationholds down to the low-mass end, globular clusters, which havevelocity dispersions of ∼
10 - 20 km / s, are a possible environ-ment for intermediate-mass black holes.Noyola et al. (2008) found kinematic signatures for a blackhole of (4.0 + . − . ) · M (cid:12) in ω Centauri from the radial veloc-ity dispersion and isotropic Jeans models. Their result was chal-lenged by van der Marel & Anderson (2010), who used HSTproper motion measurements and determined an upper limitof 1.8 · M (cid:12) . The groups used di ff erent center coordinates,which is probably one of the main reasons for this discrepancy.With the kinematic center from Noyola et al. (2010), Jalali et al.(2012) performed direct N -body simulations and found a centralIMBH with ∼ · M (cid:12) , which is consistent with the sphericalisotropic models of Noyola et al. (2010). Another good candi-date with kinematic measurements is NGC 6388. L¨utzgendorfet al. (2011) used integral field unit data and Jeans models to de-termine a black-hole mass of (1.7 ± · M (cid:12) . The most mas-sive globular cluster in M31, G1, shows kinematic signatures(Gebhardt et al. 2005) as well as X-ray (Pooley & Rappaport2006) and radio emission (Ulvestad et al. 2007), all consis- tent with an IMBH of ∼ · M (cid:12) . Miller-Jones et al. (2012)confirmed the detection of X-ray emission but detected no ra-dio emission in G1. They concluded that the detected emissioncomes more likely from a low-mass X-ray binary (LMXB) witha stellar-mass black hole than from an IMBH.Recent studies found no significant radio sources in the cen-ter of ω Centauri (Lu & Kong 2011) and NGC 6388 (Csehet al. 2010). However, mass estimates from upper limits on radioemission require assumptions on the gas properties and accretionmodel. Pepe & Pellizza (2013) showed that the accretion rate inglobular clusters depends on the mass of the cluster and its veloc-ity dispersion. Further, Perna et al. (2003) found that the widelyused Bondi-Hoyle accretion rate (Bondi & Hoyle 1944) is anupper limit of the true mass accretion, which can be lower byseveral orders of magnitude. The fraction of the Bondi accretionrate at which accretion occurs is highly uncertain (Maccarone2004).There are further examples for black holes in extragalac-tic globular clusters. Zepf et al. (2008) measured broad emis-sion lines in the globular cluster RZ 2109 in the Virgo ellipticalgalaxy NGC 4472 and conclude that, in combination with themeasured X-ray luminosity, this can be explained by the pres-ence of a ∼
10 M (cid:12) black hole. A globular cluster in NGC 1399shows broad emission lines and X-ray emission that can be mod-eled with the tidal disruption of a horizontal branch star by amassive (50 −
100 M (cid:12) ) black hole (Clausen et al. 2012).Baumgardt et al. (2005) performed N -body simulations andascertain that globular clusters with an IMBH have a rather largecore, and a shallow cusp in the surface brightness profile. Thevelocity-dispersion profile rises towards the center, but this isdi ffi cult to detect if only the brightest stars of a cluster are ob-served. Noyola & Gebhardt (2006) obtained a surface brightnessprofile of NGC 5286 that shows a shallow cusp, and for this rea-son we set out to search for kinematic evidence for an IMBH.NGC 5286 is in the halo of the Milky Way at a distance ofabout 11.7 kpc (Harris 1996). Table 1 lists some properties of thiscluster. Milone et al. (2012) found some foreground stars in theregion of NGC 5286. The fairly bright (m V = (cid:48) from the center of NGC 5286. Zorotovic et al. (2009) comparedthe CMD of NGC 5286 with M3 and found that NGC 5286 isabout (1.7 ± (cid:48)(cid:48) , as de-scribed in Section 4. For the outer part of the profile we use a dataset obtained from the Rutgers Fabry Perot, and we investigate itfor indications of rotation. Section 5 and Section 6 introduce theresults of the Jeans models and N -body simulations, which are
2. Feldmeier et al.: Indication for an intermediate-mass black hole in the globular cluster NGC 5286 from kinematics
Table 1.
Properties of the globular cluster NGC 5286.References: Go10 = Goldsbury et al. (2010), Ha10 = Harris(1996, 2010 edition), Zi80 = Zinn (1980), Zo10 = Zorotovicet al. (2010), Wh87 = White & Shawl (1987)
Parameter Value ReferenceRA α (J2000) 13h 46m 26.81s Go10DEC δ (J2000) -51 ◦ (cid:48) (cid:48)(cid:48) Go10Galactic longitude l 311.6142 ◦ Go10Galactic latitude b + ◦ Go10Distance from the sun 11.7 kpc Ha10Distance from the Galactic center 8.9 kpc Ha10Foreground reddening E(B − V) 0.24 Zi80Absolute visual magnitude M V -8.74 Ha10Metallicity [Fe / H] -1.67 Zo10Projected ellipticity (cid:15) = − (b / a) 0.12 Wh87Heliocentric radial velocity v r (57.4 ± / s Ha10Central velocity dispersion σ c (8.1 ± / s Ha10Concentration c = log( r t / r c ) 1.41 Ha10Core radius r c (cid:48)(cid:48) Ha10Half-light radius r h (cid:48)(cid:48) Ha10 compared to the data. We summarize and discuss our results inSection 7.
2. Photometry
The photometric data for NGC 5286 was obtained from theHubble Space Telescope (HST) archive. Observations weremade with the Advanced Camera for Surveys (ACS) in theWide Field Channel (WFC) with a pixel scale of 0.05 (cid:48)(cid:48) / pixel.NGC 5286 is one of 65 observed clusters, being part of the“ACS Survey of Globular Cluster” project (Sarajedini et al.2007). The data were reduced by the “ACS Survey of GlobularCluster”-team as described in Sarajedini et al. (2007) andAnderson et al. (2008), and they also produced a star cat-alog, which provides a nearly complete list of all stars inthe central 2 (cid:48) of the cluster, with information on position,V- and I-band photometry, and some data quality parame-ters for each star. The list for NGC 5286 contains 210,729stars and was retrieved from the “ACS Survey of GalacticGlobular Clusters” database, whereas the HST reference im-age hlsp acsggct hst acs-wfc ngc5286 f606w v2 img.fits in theV-band was downloaded from the HST-Archive. It is essential to have precise center coordinates, as the centerinfluences the shape of the surface brightness profile and of thevelocity-dispersion profile. Using the wrong center usually re-sults in a shallower inner surface brightness profile, and this in-fluences the outcome of our models.The center of NGC 5286 was already determined byNoyola & Gebhardt (2006) and Goldsbury et al. (2010). WithHST / WFPC2 data from the F555W filter (V-band) Noyola &Gebhardt (2006) minimize the standard deviation of star countsin eight segments of a circle. Goldsbury et al. (2010) search forthe most symmetric point by counting stars in circular segmentsand fit ellipses to isodensity contours, using the same star catalogas we do. The center coordinates in right ascension α and dec-lination δ are shown in Table 2 relative to our reference image.We apply three approaches for the center determination. Table 2.
Center coordinates (J2000)
Center determination α δ
Error(h:m:s) ( ◦ : (cid:48) : (cid:48)(cid:48) ) ( (cid:48)(cid:48) )Noyola & Gebhardt (2006) 13:46:26.844 -51:22:28.55 0.5Goldsbury et al. (2010) 13:46:26.831 -51:22:27.81 0.1Star counts 13:46:26.834 -51:22:27.94 0.3Cumulative distribution 13:46:26.844 -51:22:27.88 0.4Isodensity contours 13:46:26.846 -51:22:27.98 0.4 The first method is similar to the so-called “Pie-sliceContours” method described by Goldsbury et al. (2010) andL¨utzgendorf et al. (2011). It uses star counts in opposing wedges.In a second approach we create a cumulative radial distribu-tion of the stars, as described by McLaughlin et al. (2006) andL¨utzgendorf et al. (2011). The crucial point of the center de-termination is to decide in which magnitude interval we countthe stars, i.e. where we make the magnitude cut. This problemarises from the star catalog construction. In the vicinity of brightstars it is not possible to detect fainter stars, and the star list istherefore incomplete. The resulting holes in the apparent stellardistribution become a problem as we count the stars, and oppos-ing wedges seem to be asymmetric. It is therefore important touse only stars brighter than a certain magnitude. In addition, themagnitude cut must not be too low, as then there would not beenough stars for a statistically meaningful result and the sam-ple sizes would no longer be useful. The uncertainty from themagnitude cut is about 10 times larger than the uncertainty fromthe number of wedges. Therefore, we use a combination of thedi ff erent parameters and weight the results with the respectiveerrors. This is done for the simple star count method as wellas for the cumulative radial distribution method. The numberof wedges we use are between 4 and 16, and we determine themedian and standard deviation σ med of the resulting center co-ordinates. We apply this method to magnitude cuts of 19, 20,21, 22, and 23, and weight the resulting center coordinate withthe respective standard deviation σ med to determine a center, andcalculate the standard deviation σ cut of the weighted center. Asa result we obtain center coordinates from the star count and thecumulative radial distribution method and use σ cut as a measurefor the uncertainties.Alternatively, we determine the center with an approachthat is based on the “Density Contour” method as described inGoldsbury et al. (2010). The center is found by creating isoden-sity contours and fitting ellipses to the contours. At first we cre-ate a grid of 200 (cid:48)(cid:48) x 200 (cid:48)(cid:48) with a grid point every 2 (cid:48)(cid:48) , and weuse the center determined by Noyola & Gebhardt (2006) as ourgrid center. Assuming the center determined in Goldsbury et al.(2010) as the grid center changes the result by less than 0.04 (cid:48)(cid:48) .At every grid point we apply a circle with a radius of 500 pixel(25 (cid:48)(cid:48) ), find the stars inside the circle, and determine the densityinside the circle around the grid point. Large radii of the circleresult in smooth contour plots, but if the radius is too large, itreaches the edge of our star field. A contour plot is created witheight contour levels, and four ellipses are fit to the contours. Theinnermost and the outer three contours were ignored as they canbe either biased by shot noise, or be incomplete. For the remain-ing four contours the center of the ellipse fit is determined, andthe median is adopted as the new center, with the standard devi-ation of the ellipse centers as estimated uncertainty. Again, thechoice of a magnitude cut a ff ects the outcome of the center co-ordinates. Excluding faint stars smoothens the distribution, as
3. Feldmeier et al.: Indication for an intermediate-mass black hole in the globular cluster NGC 5286 from kinematics
Fig. 1.
Finding chart for the di ff erent center coordinates with un-certainties. Noyola & Gebhardt (2006): cross, Goldsbury et al.(2010): plus sign, star count method: square, cumulative stellardistribution: diamond, isodensity contours: circle point. The un-derlying image is a synthetic I-band image (see Section 4.1).fainter stars are not likely to be found in the vicinity of brightstars, and create under-dense regions around bright stars. Thisincompleteness is larger in the center of the cluster, as there aremore bright stars. The di ff erence of the center position is up to3 (cid:48)(cid:48) for magnitude cuts at 15 and 29. We combine the isodensitymethod for five magnitude cuts from 19 to 23. The di ff erencein the center determination for these magnitude cuts is less than0.8 (cid:48)(cid:48) , and the result therefore more robust. We calculate an error-weighted average, which is adopted as the new center. The stan-dard deviation is our estimated error, and the results are listed inTable 2.Figure 1 illustrates all centers from our methods with respec-tive errors plotted on top of a synthetic I-band ACS image (seeSection 4.1). They all lie within their error ranges, and all ofthem overlap within their errors with the uncertainty of the cen-ter derived by Noyola & Gebhardt (2006), and with the centerof Goldsbury et al. (2010). This is not unexpected, as we usethe same star catalog as Goldsbury et al. (2010) and similar ap-proaches to determine the center. As Goldsbury et al. (2010) re-port, the center derived with the isodensity contour method ismore reliable over a wide range of density distributions. The starcount methods rely on the symmetry of the cluster, and dependmore on sample size and cluster size, so we adopt the centercalculated with the isodensity contour method. By means of theHST reference image we find the final position in pixel, rightascension α , and declination δ :( x c , y c ) = (2934 . , . ± (7 . , .
88) pixel (1) α =
13 : 46 : 26 . , ∆ α = . (cid:48)(cid:48) (J2000) (2) δ = −
51 : 22 : 27 . , ∆ δ = . (cid:48)(cid:48) (3)As the distance of NGC 5286 is about 11.7 kpc, the uncertaintyof the center determination is only ∼ The next step of the photometric analysis is to calculate the sur-face brightness profile. In the literature there are already surfacebrightness profiles of NGC 5286, one of them is from Noyola &Gebhardt (2006), the other is from Trager et al. (1995). Noyola & -0.5 0.0 0.5 1.0 1.5 2.0 2.5log r (arcsec)242220181614 V ( m a g / a r c s e c ) Fig. 2.
Comparison of the four surface brightness profiles usedfor later analysis: Our combined profile (black asterisks), thesmoothed profile obtained from a fit with Chebychev polynomi-als (red plus signs), the profile from Noyola & Gebhardt (2006)(cyan diamonds), and the Trager et al. (1995) profile (green tri-angles, Chebychev fit on photometric points). The dotted verticalline denotes the core radius of 16.8 (cid:48)(cid:48) (Harris 1996).Gebhardt (2006) use integrated light measurements, whereas ourmethod is based on star counts in combination with integratedlight measurement as described in L¨utzgendorf et al. (2011). Weuse the HST reference image and star catalog in the V-band, andour center as determined in Section 2.1 via isodensity contours.A combination of integrated light measurement and star countsmakes sure that the surface brightness profile is complete androbust. Since the star catalog does not contain every faint star,using only star count measurements would neglect the light con-tribution from faint stars. But their contribution to the light istaken into account in integrated light measurements. To use onlyintegrated light causes problems in the determination of the sur-face brightness at the center. Bright stars produce shot noise andthe resulting profile is sensitive to the choice of the bins. Thise ff ect is weaker with star counts, and therefore we combine bothmethods, to make our profile more robust.For the star counts we apply circular bins around the center,sum the fluxes of all stars with 14 < m V <
19, and divide by thearea of each bin. The integrated light measurement is appliedfor fainter stars with m V ≥
19, and the brighter stars are maskedout in the reference image using a circular mask with a radiusof 0.25 (cid:48)(cid:48) (5 HST pixels). We use the same circular bins for bothmethods and use the bi-weight to determine the distribution ofpixel counts, and sum the fluxes of both methods.To obtain a photometric calibration we scale the outer partof our profile to the profile from Trager et al. (1995), using theirChebychev fit, and extend it with the outer points of this profile.In Figure 2 our adopted surface brightness profile is indicated byasterisks and compared to the profiles from Noyola & Gebhardt2006 (diamonds), and from Trager et al. 1995 (triangles). TheTrager et al. (1995) profile is fainter and flat towards the center.This profile was derived from from ground based images, andthe inner region of the cluster is not as well spatially resolvedas with data from space. Our profile is the brightest, but due tothe method and the data we use, the inner points of the profilehave a high uncertainty, which comes from the Poisson statis-tics of the number of stars in each bin. The exact values of ourprofile are listed in Table 3. However, for later analysis we also
4. Feldmeier et al.: Indication for an intermediate-mass black hole in the globular cluster NGC 5286 from kinematics
Table 3.
The combined surface brightness profile in the V-band. ∆ V l and ∆ V h are the low and high values of the errors. log r V ∆ V l ∆ V h [arcsec] (cid:104) mag / arcsec (cid:105) (cid:104) mag / arcsec (cid:105) (cid:104) mag / arcsec (cid:105) − .
40 14 .
83 1 .
34 0 . − .
19 14 .
63 0 .
65 0 . .
00 15 .
22 0 .
36 0 . .
18 15 .
87 0 .
26 0 . .
48 15 .
90 0 .
08 0 . .
65 16 .
12 0 .
06 0 . .
88 16 .
26 0 .
03 0 . .
00 16 .
37 0 .
03 0 . .
10 16 .
58 0 .
03 0 . .
18 16 .
68 0 .
02 0 . .
30 17 .
06 0 .
01 0 . .
40 17 .
41 0 .
01 0 . .
48 17 .
79 0 .
01 0 . .
60 18 .
20 0 .
01 0 . .
70 18 .
80 0 .
01 0 . .
78 19 .
32 0 .
01 0 . .
85 19 .
72 0 .
01 0 . .
90 19 .
97 0 .
01 0 . .
95 20 .
11 0 .
01 0 . .
00 20 .
46 0 .
01 0 . .
07 21 .
08 0 .
01 0 . .
09 21 .
22 0 .
01 0 . .
17 21 .
88 0 .
01 0 . .
21 22 .
15 0 .
01 0 . .
31 23 .
03 0 .
01 0 . .
37 23 .
48 0 .
01 0 . .
40 23 .
78 0 .
01 0 . .
51 24 .
77 0 .
01 0 . use a smoothed profile. This is obtained by fitting Chebychevpolynomials to our derived profile, as indicated by plus signs inFigure 2. We further check whether the di ff erence to the surfacebrightness profile from Noyola & Gebhardt (2006) comes fromthe di ff erent center position or the di ff erent methods. So we com-pute a profile with our method, but using the Noyola & Gebhardt(2006) center. At large radii the results for the di ff erent centersare very similar, but in the central part the di ff erence becomeslarger, but not more than 0.35 mag / arcsec . The error bars areso large that it is di ffi cult to say whether the choice of center in-fluences the shape of the profile. But the two surface brightnessprofiles with the distinct centers both tend to be higher than theNoyola & Gebhardt (2006) profile. So the di ff erence with theirprofile seems to come mostly from the di ff erent methods used tocompute the surface brightness, and not from the di ff erent cen-ters.
3. Spectroscopy
The spectroscopic data were obtained during two nights with theGIRAFFE spectrograph of the FLAMES instrument (Pasquiniet al. 2002) on 2010-05-05 and 2010-05-06 at the Very LargeTelescope (VLT). Observations were made in ARGUS modewith 1:1 magnification scale, providing a total coverage of11.5 (cid:48)(cid:48) x 7.3 (cid:48)(cid:48) , and a sampling of 0.52 (cid:48)(cid:48) per microlens. We used thelow resolution grating LR8, which covers the wavelength rangefrom 8206 to 9400 Å and has a resolving power R ≈ Fig. 3.
The positions of the ARGUS pointings are indicated asrectangles. The circle indicates the core radius of Harris (1996),which is 16.8 (cid:48)(cid:48) . The underlying image is the synthetic I-bandimage from the HST star catalog (see Section 4.1).triplet lines, which are known to be well suited for kinematicanalysis. Old stars, like those present in globular clusters, showstrong features from these lines. We obtained pointings of thecluster’s center and of adjacent regions around the core radius,every pointing has three exposures of 600 s each. Figure 3 illus-trates the arrangement of the pointings.
Data reduction includes removing cosmic rays, pipeline reduc-tions, and sky subtraction. We follow the procedure largelydeveloped in L¨utzgendorf et al. (2011), except for a changein the order of the steps. At the beginning, we use the
Laplacian Cosmic Ray Identification L.A.Cosmic written by vanDokkum (2001) to remove cosmic rays from the raw images.The GIRAFFE pipeline, programmed by ESO, consists of fiverecipes: In a first step, gimasterbias creates a masterbias and abad pixel map from a set of raw bias frames. The recipe gimas-terdark corrects every raw dark frame for the bias, and createsa masterdark using the median.
Gimasterflat creates a master-flat, which contains information on pixel-to-pixel variations andfiber-to-fiber transmissions. This recipe also locates the positionand width of the spectra on the CCD from the flat-field lamp im-ages. It detects and traces the fibers on the masterflat and recordsthe location and width of the detected spectra. The recipe gi-wavecalibration uses a ThAr arc lamp calibration frame to com-pute the dispersion solution and the setup specific slit geome-try table. The spectrum from the ThAr lamp frame is extractedusing the fiber localization (provided by gimasterflat ). The fi-nal pipeline recipe is giscience , which applies the calibrationsproduced by the other recipes to the cosmic ray removed objectframes. As a result we obtain bias corrected, dark subtracted, flatfielded, extracted and wavelength calibrated spectra, which arealso corrected for fiber-to-fiber transmission and pixel-to-pixelvariations. The next step of data reduction is sky subtraction.
5. Feldmeier et al.: Indication for an intermediate-mass black hole in the globular cluster NGC 5286 from kinematics (a) (b) (c)
10 20 30 40 50 60arcsec10203040506070 a r c s e c -20-15-10-505101520 Fig. 4. (a) The synthetic image cut to the ARGUS pointings, (b) the reconstructed ARGUS image, and (c) the velocity map. Colorsare as indicated by the color bar in units of km / s. The blue spaxels of the velocity map indicate approaching stars, the red spaxels arereceding stars. White spaxels mean that within this spaxel no spectrum was found that could be used to determine the fit parameters.North is right, East is up.Mike Irwin developed a program, which is described in Battagliaet al. (2008), and our program is based on this approach. It splitsthe sky spectra in continuum and sky lines, and subtracts bothfrom the object spectra. We also normalize our spectra. As weare solely interested in the kinematic extraction from the spec-tra, we do not perform flux calibration.
4. Kinematics
The spectroscopic data contain information on the central kine-matics of NGC 5286, and a velocity-dispersion profile is essen-tial for our models. This section describes the construction of avelocity map, and of a velocity-dispersion profile. For the innerpart of NGC 5286 we use the FLAMES data, for the outer partwe use data from the Rutgers Fabry Perot (RFP).
We match the reconstructed images of ARGUS produced by the giscience recipe to a synthetic image in the I-band, constructedfrom the photometric star catalog. Thus we identify which regionthe FLAMES data cover exactly with respect to the photometriccenter. We use the synthetic image since there is an overexposedregion in the HST V-band image, so that the program does notadjust the north-eastern ARGUS images properly. At first, theangle between the synthetic image and each ARGUS pointing isevaluated, and the synthetic image is rotated by this angle. Thenthe synthetic image is blurred by convolving the image with thepoint spread function that is obtained from a Gaussian functionwith σ = (cid:48)(cid:48) , roughly corresponding to the seeing during thespectroscopic observations. We then cross correlate the ARGUSpointings with the respective blurred synthetic image. This pro-cedure is done iteratively, until the o ff set between the ARGUSand synthetic images is smaller than 0.1 ARGUS pixel, which isachieved after four iterations at most. So, every spectrum is cor-related to a certain coordinate, and we obtain an area that covers69 x 70 spaxels. Figure 4 is an illustration of (a) the syntheticimage, cut to match the combination of ARGUS pointings, (b)the reconstructed ARGUS pointings, and (c) the velocity map,the colors denote di ff erent values as indicated by the color bars.Every spectrum is a sum of individual stellar spectra,weighted by the luminosities of the stars. To extract the velocityand velocity dispersion from the integrated spectrum one needs a Fig. 5.
Color-magnitude diagram from the photometric HST starcatalog of stars with low uncertainty in photometry. The starsymbols denote the stars used for the template spectrum, dia-monds denote stars that contribute more than 70% of the light toa spaxel.spectral template. To find a good template we use the photomet-ric star catalog with information on the positions of the stars. Thenumber of stars that contribute to one spaxel, and the fraction oflight coming from a certain star in the spaxel, are calculated.So we can identify stars that dominate a single spaxel. Figure5 shows the color-magnitude diagram from the HST catalog,where stars that dominate a spaxel by at least 70% are marked asblue diamonds. The star symbols denote seven stars, which con-tribute at least 84% of the light in one spaxel and are fainter thanm V =
15. According to their position on the CMD, these stars aremost probably cluster members. Those stars’ spectra were com-bined to a master template spectrum. We found the spectral lines
6. Feldmeier et al.: Indication for an intermediate-mass black hole in the globular cluster NGC 5286 from kinematics of brighter stars are less Gaussian, possibly due to saturation,and therefore not suitable as template spectra.We use the penalized pixel-fitting ( pPXF ) program devel-oped by Cappellari & Emsellem (2004) to derive a velocity andvelocity dispersion for each spaxel. As we have three exposuresfor every pointing and some pointings overlap, there can be sev-eral spectra for one spaxel. Therefore these spectra are identified,and sigma clipping is applied about the median of the data set forevery spaxel, and we use the mean of the spectra for further anal-ysis. It is possible that only one or a few bright stars dominate thelight in their environment. Therefore we check in which spaxeleither a single star contributes more than 70% of the light, or lessthan five stars contribute to one spaxel. 578 spaxels of 3237 area ff ected by shot noise. Those spaxels are excluded from furtheranalysis. To determine the velocity-dispersion profile, we follow the pro-cedure described in L¨utzgendorf et al. (2012b) and construct cir-cular bins around the center of the cluster. We choose sevenindependent, non-overlapping circular bins. A higher numberof bins results in low signal-to-noise. The spaxels that are af-fected by shot noise are excluded. We check di ff erent combi-nations of minimum star number and light contribution, anddi ff erent angular bins, but the overall shape of the kinematicprofile does not change much. In each circular bin the spec-tra are combined and we apply the pPXF method to computethe moments of the line-of-sight velocity distribution (LOSVD).As we combine all the spectra around the center in circularbins, we obtain the mean velocity of the circular bin (cid:104) V (cid:105) bin , and V rms = (cid:113) V rot + σ , with the rotational velocity V rot and the ve-locity dispersion σ . V rms is required for the models, and we willrefer to the V rms profile as velocity-dispersion profile. However,the Gauss-Hermite moments, which are the output of the pPXF program, need to be corrected as described in van der Marel &Franx (1993). Depending on the number of fitted Gauss-Hermitemoments, we obtain di ff erent results. We fit the first two ( V , σ ),four ( V , σ, h , h ), or six ( V , σ, h , h , h , h ) moments.As alternative approach we calculate the velocity-dispersionprofile with a non-parametric fit (see Gebhardt et al. 2000b;Pinkney et al. 2003). The observed cluster spectrum is decon-volved using the template spectrum. Deconvolution is done us-ing a maximum penalized likelihood (MPL) method, and oneobtains a non-parametric LOSVD. For the fitting procedure, thefirst step is to choose an initial velocity profile in bins. This pro-file is convolved with the template to obtain a cluster spectrum,which then is used to calculate the residuals to the observed spec-trum. The parameters for the LOSVD are varied to obtain thebest fit.The error for V rms comes from Monte Carlo simulations, andis an estimate for the amount of shot noise. For every bin thekinematics are calculated in 1,000 realizations. The shot noiseerror is the sigma-clipped standard deviation of these 1,000 ve-locity dispersions. The uncertainties for the other moments ofthe LOSVD and for V rms of the pPXF method are obtained fromMonte Carlo simulations on the spectra. As recommended inCappellari & Emsellem (2004), we repeat the measurement pro-cess for a large number of di ff erent realizations of the data. Thisis done by adding noise to the original binned cluster spectra.After 100 realizations we use the standard deviation of the kine-matic parameters as the corresponding uncertainties. -0.5 0.0 0.5 1.0 1.5 2.0log r (arcsec)68101214 V R M S ( k m / s ) M2M4M6NONPARRFP Data
Fig. 6.
Velocity-dispersion profiles with error bars. Di ff erentsymbols indicate di ff erent methods of calculation. M2, M4, andM6 are the profiles computed with pPXF , fitting only the first2, 4, or 6 moments, respectively. The squares denote the pro-file calculated with the nonparametric method. The triangles arefrom outer kinematic data, and the dotted vertical line denotesthe core radius at 16.8 (cid:48)(cid:48) (Harris 1996).Figure 6 illustrates the outcome of the di ff erent meth-ods. M2 is the pPXF velocity-dispersion profile when onlythe first two parameters ( V , σ ) are fitted, M4 when four pa-rameters ( V , σ, h , h ) are fitted, and M6 when six parameters( V , σ, h , h , h , h ) are fitted. The velocity dispersion values cal-culated with the non-parametric method lie in between M2 andM4, and the shape of the velocity-dispersion profiles are all quitesimilar, but the absolute values computed with pPXF are verysensitive to the number of calculated moments. Therefore weuse the non-parametric profile for further analysis. It is remark-able that the di ff erence between M2, M4, and M6 is less than 1km / s for the innermost bin, but up to 3 km / s for the other bins.We tried to shift the template spectrum by the template veloc-ity, or use another template spectrum, but the discrepancy in thevelocity dispersion remains. Table 4 records the results of theinner kinematic measurements with the non-parametric method.The first column denotes the radii of the bins. The followingcolumns list the kinematic parameters, which are the velocitiesof each bin (cid:104) V (cid:105) bin in the cluster reference frame relative to thetemplate spectrum, and the second moment V rms with respectiveerrors in units of km / s. The signal-to-noise ratio S / N is higherthan 112 except for the outermost bin, where S / N = V r , temp results in (56.9 ± / s, and the velocity of all combined spectra relative toit is V r , cluster = (2.4 ± / s. So the heliocentric velocity ofthe cluster V r = V r , temp + V r , cluster = (59.3 ± / s. This isin agreement with the value from Harris (1996), V r = (57.4 ± / s.
7. Feldmeier et al.: Indication for an intermediate-mass black hole in the globular cluster NGC 5286 from kinematics
Table 4.
The kinematics of NGC 5286 obtained from FLAMESand RFP data. For the FLAMES data, (cid:104) V (cid:105) bin is the velocity rela-tive to the template velocity. FLAMES DATA r (cid:104) V (cid:105) bin ∆ (cid:104) V (cid:105) bin V rms ∆ V rms S / N [ arcsec ] [ km / s ] [ km / s ] [ km / s ] [ km / s ]0 .
52 2 . . . . .
56 4 . . . . .
12 2 . . . . .
46 2 . . . . .
06 2 . . . . .
48 2 . . . . .
54 2 . . . . r (cid:104) V (cid:105) bin ∆ (cid:104) V (cid:105) bin V rms ∆ V rms Number [ arcsec ] [ km / s ] [ km / s ] [ km / s ] [ km / s ] o f stars .
50 59 . . . . .
00 57 . . . . In addition to spectroscopic data in the center we use a seconddata set for larger radii, i.e. up to r ∼ (cid:48)(cid:48) . The data were ob-tained with the 4-m Victor M. Blanco Telescope at the CerroTololo Inter-American Observatory (CTIO). Observations weremade from 1994-05-31 to 1994-06-03, with the Rutgers FabryPerot (RFP). The used methods of observation and data reduc-tion are similar to those described in Gebhardt et al. (1997) forM15. The data set for NGC 5286 contains 1,165 velocities ofindividual stars with errors, flux, and information about their po-sition relative to a center in arcsec. With an RFP image of thepointing, the HST image, and the iraf recipes daofind , ccmap ,and xyxymatch , we transform the coordinates to the world coor-dinate system (WCS).To determine the velocity dispersion we draw circular binsaround the center and use only stars with low error in veloc-ity and with a high flux. This is done to make sure that onlystars with a well-determined velocity are used for further analy-sis. Crowding in the cluster’s center is known to cause problemsin the determination of velocity. Background light contaminatesthe measurements for fainter stars, and this biases the velocitiesof the stars to the mean velocity of the cluster. Therefore, the ve-locities obtained from Fabry-Perot measurements are often toolow. We use only stars in the outer part of the cluster, where thecrowding e ff ect is less relevant. With the maximum likelihoodmethod introduced by Pryor & Meylan (1993) we calculate thevelocity dispersion V rms and mean velocity (cid:104) V (cid:105) bin . The obtainedvalues are listed in Table 4. The last column displays the num-ber of stars that were used to determine V rms for each bin. Bothvalues of (cid:104) V (cid:105) bin are in agreement with the heliocentric velocityof the cluster from Harris (1996), V r = (57.4 ± / s.We also compute the e ff ective velocity dispersion σ e , as de-fined in G¨ultekin et al. (2009) σ e = (cid:82) R e V rms I ( r ) dr (cid:82) R e I ( r ) dr , (4)where R e is the e ff ective radius or half-light radius (43.8 (cid:48)(cid:48) , Harris1996), I(r) is the surface brightness profile, and V rms is the V ( k m / s ) Fig. 7.
The mean radial velocities with error bars of stars at adistance r ≥ (cid:48)(cid:48) plotted versus position angle φ for 6 segmentsfrom RFP data. The solid line is the fit to the data.velocity-dispersion profile. We obtain σ e = (9.3 ± / s, thisis higher than the central velocity dispersion of (8.1 ± / sfrom Harris (1996), but the values agree within their uncertaintylimits. Some globular clusters are known to rotate, for example ω Centauri and 47 Tucanae (Meylan & Mayor 1986). As NGC5286 is not totally spherical and has an ellipticity (cid:15) = ω Centauri ( (cid:15) = (cid:15) = (cid:48)(cid:48) . The meanvelocity of the stars in these areas is determined with the maxi-mum likelihood method. In Figure 7 the mean radial velocity Vof the stars in the segments is plotted against the position angle φ . For six segments there are more than 85 stars in each bin, for18 segments at least 20 stars. We fit the function ff = A sin( φ + ψ ) + V r , (5)with the parameters amplitude A , phase angle ψ , and heliocen-tric cluster velocity V r to the data points for all segment numbersfrom 6 to 18. The best-fit parameters are averaged, and we ob-tain for the mean heliocentric velocity V r = (58.3 ± / s,and for the amplitude A = (2.3 ± / s. The phase ψ is(-0.01 ± ± ◦ , measured positive from north to east. White & Shawl(1987) found the orientation of the major axis at θ = ◦ .The spectroscopic FLAMES data is used to investigate in-dications of rotation in the inner part of the cluster. In somesegments the spectra have low signal-to-noise and therefore themean radial velocities have large error bars of up to more than3 km / s. For the sine fit we use only segments with a signal-to-noise higher than 40. However, the result for the phase angle ψ depends highly on the number of fitted segments, and thereforewe find no significant indication for rotation in the inner 25.5 (cid:48)(cid:48) ofNGC 5286.
5. Jeans models
Jeans models provide an analytical approach to fit kinematics ofthe globular cluster NGC 5286, and we use an
IDL routine devel-
8. Feldmeier et al.: Indication for an intermediate-mass black hole in the globular cluster NGC 5286 from kinematics M BH = 1.5e+03, M/L = 1.07, χ = 1.89, β = 0.10 -0.5 0.0 0.5 1.0 1.5log r (arcsec)681012 V R M S ( k m / s ) BH (10 M SUN )5101520 χ Fig. 8. Di ff erent spherical Jeans models fitted to our combinedsurface brightness profile for fixed anisotropy β = ff er-ent black-hole masses, the thick black line indicates the best fit.The lower panel shows the χ values as a function of black-holemass, and the dashed line denotes ∆ χ =
1. The best fit with χ = • = (1 . + . − . ) · M (cid:12) .oped by Cappellari (2008). In order to solve the Jeans equations,the mass density (cid:37) is required as an input. We use the surfacebrightness profile for NGC 5286 derived in Section 2.2, and de-project it to obtain the luminosity density j of the cluster, whichis related to the mass density (cid:37) by the mass-to-light ratio (M / L).The surface brightness profile is deprojected using the Multi-Gaussian expansion (MGE) method, developed by Emsellemet al. (1994), using the
IDL routine written by Cappellari (2002).With the MGE formalism there are Jeans equations for every sin-gle Gaussian component, and after solving the equations, we ob-tain the second velocity moment v los (R) along the line-of-sight.The results are fitted to the observed velocity-dispersion datapoints, as computed in Sections 4.2 and 4.3. It is possible to varythe values of anisotropy β = − σ θ /σ R and M / L for every in-dividual MGE Gaussian. The velocity-dispersion profile can bescaled to the observations by adjusting M / L. Therefore all mod-els meet in one point at which the model is scaled.
The simplest model is a spherical Jeans model. We considerdi ff erent values of anisotropy β , and di ff erent surface bright-ness profiles. The profiles used are the Chebychev fit fromTrager et al. 1995, Noyola & Gebhardt 2006, our derived pro-file from a combination of star counts and integrated light mea-surements (see Table 3, combined profile), and the profile from afit of Chebychev polynomials to the combined profile to make itsmooth (smooth profile). The best fits are obtained with our com-bined profile. For each profile we test di ff erent values of constantanisotropy β in the interval of [-0.2, 0.3] over the entire clusterradius. We fit a global M / L, and the best fit is obtained with ra-dial anisotropy β = • = · M (cid:12) , and constant M / L = / L are in solar units of M (cid:12) / L V , (cid:12) ). The outcomeis shown in Figure 8. For the other profiles the best fit valuesare listed in Table 5 with errors from the ∆ χ = tot comes onlyfrom the uncertainty in M / L. The value from Harris (1996) forthe integrated V-band magnitude is 7.34, this corresponds to atotal luminosity L tot of 2.40 · L (cid:12) . The Trager et al. (1995)profile has too low resolution at the center and is therefore notas suitable for our analysis as the other profiles.We also assume a radial shape of anisotropy β ∝ r, withisotropy in the very center of the cluster, and rising anisotropytowards the outskirts. At the outermost Gaussian the anisotropy β out is highest. This approach is justified as the relaxation time isshort in the cluster’s center (t relax ≈ · yr, Harris 1996), andhigher at larger radii (at the half-mass radius t relax ≈ · yr,Harris 1996). L¨utzgendorf et al. (2011) ran an N -body simula-tion of a globular cluster with initial anisotropy and showed thatit becomes more isotropic after few relaxation times. Assumingan age of 11.7 · yr (Rakos & Schombert 2005), NGC 5286is already 46 relaxation times old in its center, and about 9relaxation times at the half-mass radius. Therefore the clustershould be isotropic in the central part at least. In this case, thefits have similar values of χ and obtain similar results for allvalues of β out at a given surface brightness profile. Our com-bined profile finds values for the black-hole mass in the rangeof (1.9 − · M (cid:12) and M / L = − β .Figure 9 is a contour plot of χ as a function of β and M • fromthe combined surface brightness profile. For these models weuse a constant and global M / L = / L, since we are interested in showing the influenceof β and M • on the quality of the fit. If M / L is fitted, it usuallyhas a value around 1.1 anyway. In the case of radially varyinganisotropy the abscissa denotes the value of β out , the anisotropyin the outermost part of the cluster. The value of χ is labeledon the contours. For constant β the area with the best models issmaller than for β ∝ r , where fits over a large range of β are ofsimilar goodness. We conclude that anisotropy in the outer partof the cluster has no big e ff ect on the resulting black-hole massin Jeans models as expected, but the central value of anisotropyis crucial.From the ∆ χ = / L and M • we also run Monte Carlo simulations. In 1,000runs we vary the shape of the combined surface brightness pro-file to estimate the e ff ect on the outcome of the Jeans models.We change only the six innermost points of the profile, as theyhave the largest uncertainties and are crucial to determine themass of a central black hole. This is done for β in the rangeof −
9. Feldmeier et al.: Indication for an intermediate-mass black hole in the globular cluster NGC 5286 from kinematics
Table 5.
The spherical Jeans model best-fit values with constant M / L. surface brightness profile β M / L M • M tot L tot χ constant (cid:2) M (cid:12) / L V , (cid:12) (cid:3) (cid:104) M (cid:12) (cid:105) (cid:104) M (cid:12) (cid:105) (cid:104) L (cid:12) (cid:105) combined profile 0 .
10 1 . ± .
03 1 . + . − . . ± .
10 2 . + . − . . .
05 1 . + . − . . + . − . . ± .
12 2 . + . − . . .
10 1 . + . − . . + . − . . ± .
12 2 . + . − . . .
15 1 . + . − . . + . − . . + . − . .
51 2 . -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 β M B H ( M S U N ) M/L = 1.1, β = const . . . . . . . . . . . . . . . . . . . . . . . . . . . . -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 β M B H ( M S U N ) M/L = 1.1, β = β (r) . . . . . . . . . . . . . . . . . Fig. 9. χ contours describing the agreement between the data and spherical Jeans models of the combined profile with constantmass-to-light ratio M / L = χ . Left: β = const., right: β ∝ r. In the case of radiallyvarying anisotropy the abscissa denotes the value of β out , the maximum anisotropy in the outermost part of the cluster. -0.2 -0.1 0.0 0.1 0.2 β M / L V β M B H Fig. 10.
The result of Monte Carlo simulations on the surface brightness profile. After 1000 realizations for every value of constant β the dots denote the median values, the contours are the 68% (dotted line) and 95% (dash-dotted line) confidence limits. The leftpanel displays the mass-to-light ratio M / L V , the right panel is the black-hole mass.the uncertainties δ M / L V = δ M • = · M (cid:12) . Fora confidence limit of 95% we find δ M / L V = δ M • = · M (cid:12) . By varying both, the surface brightness profile andthe velocity-dispersion profile, we run another Monte Carlo sim-ulation and find higher uncertainties of δ M / L V = δ M • = · M (cid:12) for the 68% confidence limit, and δ M / L V = δ M • = · M (cid:12) with 95% confidence. The di ff erence of theuncertainties by varying both profiles or only the surface bright-ness profile give information on the contribution from the dif-ferent profiles. The uncertainty of M / L seems to come mostlyfrom the uncertainty of the kinematic profile, and the influenceon the black-hole mass is also dominated by the kinematic pro-
10. Feldmeier et al.: Indication for an intermediate-mass black hole in the globular cluster NGC 5286 from kinematics file. Nevertheless, one must not underestimate the importance ofthe shape of the surface brightness profile. The ∆ χ = β , and the 68% and 95% confidence limits are the light grey andgrey shaded contours. The uncertainty of M / L is plotted in theleft panel, M • is plotted in the right panel.All our results come from Jeans models in which we neglectthe PSF e ff ects as described in Appendix A of Cappellari (2008).To test the importance of this e ff ects we run spherical Jeans mod-els and convolve the model velocity dispersion with the instru-mental PSF before fitting to the observed data points. We usethe combined surface brightness profile and constant values ofanisotropy. With a seeing of 0.6 (cid:48)(cid:48) and a pixel scale of 0.52 (cid:48)(cid:48) / pixelthe values for black-hole mass, total cluster mass, and mass-tolight ratio decrease by less than 0.4%. As the convolution is timeconsuming but has no big e ff ect on the result, we disregard it inall further Jeans models. N -body simulations of globular clusters usually result in mass-to-light ratios that vary with radius. This is expected from masssegregation of the stars, as more massive stars, in particular darkremnants, wander to the center of the cluster, and low-mass starsto the outskirts. We want to investigate the e ff ect of a varyingM / L profile on the Jeans models, and therefore calculate it from N -body simulations, and use it as input to the Jeans models. Theprofile is displayed in Figure 11, it comes from the best fit ofa grid of N -body simulations, not including the e ff ect of a tidalfield (see Section 6.1), to our profile from a combination of starcounts and integrated light. This profile is scaled to the velocity-dispersion profile in the Jeans models to obtain absolute valuesfor M / L in the V-band. We use only the combined profile, as itgives the best fit for constant M / L, and this profile was also usedto determine the shape of the M / L profile.With a constant value of β =
0, the best-fit black-hole massis (2.0 + . − . ) · M (cid:12) with χ = / Lis ∼ β = + . − . ) · M (cid:12) , M tot = (4.1 ± · M (cid:12) and χ = / L, theyyield similar masses for a central black hole. The higher clus-ter mass comes from the M / L profile, which has higher valuesof M / L at small radii, where our surface brightness profile hasthe largest error bars. It also rises towards the outskirts, but ourvelocity-dispersion measurements extend only to 75 (cid:48)(cid:48) . Thereforethe variable M / L profile adds mass to the cluster without havinga big e ff ect on the outcome of the Jeans models for M • . The axisymmetric model requires the 2D surface brightness pro-file, which we obtain with the
MGE fit sectors IDL packagewritten by Cappellari (2002). We use the HST image and three2MASS images in the J-band, which were combined to one im-age using the tool
Montage . The routine find galaxy.pro mea-sures the ellipticity (cid:15) = − b / a from a two dimensional image.One parameter of find galaxy.pro is the fraction of image pixelsthat are used to measure the outcome. We use di ff erent fractions M / L Fig. 11.
Mass-to-light ratio as a function of radius, calculatedfrom the best fitting N -body model.(0.1, 0.15, 0.2, 0.25, and 0.3), and compute the mean values forellipticity, which is 0.12 ± ± (cid:15) = sectors photometry.pro determines a 2D surface brightness profile from the HST and2MASS images. The 2MASS photometry is matched to theHST flux in the range from 2 (cid:48)(cid:48) to 100 (cid:48)(cid:48) , and scaled to theHST flux. The HST measurements are further used for thecentral part of the cluster up to 60 (cid:48)(cid:48) , the 2MASS photometryfor the outer part (13 (cid:48)(cid:48) − (cid:48)(cid:48) ). The photometry is then scaledto the Trager et al. (1995) profile at 25 (cid:48)(cid:48) − (cid:48)(cid:48) . The routine MGE fit sectors.pro fits a 2D MGE model to the measurements,and to every Gaussian of the fit there is an axial ratio 0 ≤ q k ≤ tot = · L (cid:12) . Varying therange where the photometry is scaled to Trager et al. (1995) in-troduces an uncertainty of 9 · L (cid:12) .Axisymmetric Jeans models have an additional input pa-rameter, the inclination angle i , which is the angle betweenthe rotation axis and the line-of-sight. An inclination angle i = ◦ means the cluster is seen edge-on, and i = ◦ correspondsto face-on. But in the face-on case we would probably see noindication of rotation, as we do in the outer part of the cluster,and the ellipticity (cid:15) would be zero. We run axisymmetric Jeansmodels for i = ◦ , 67 ◦ , and 90 ◦ , and constant β in the intervalof [-0.2, 0.3]. M / L is assumed to be constant and fitted in everymodel.The best fits at every value of i are listed in Table 6. Allerrors are from the ∆ χ = tot comesfrom the uncertainty in M / L and L tot . At lower inclination weobtain better fits, and in contrast to spherical Jeans models, thebest fit is at tangential anisotropy ( β = − i the isotropic case fits best. But all models obtain similar resultsfor M / L, M • , and M tot , which agree within their uncertainties,and are also consistent with the results from the spherical Jeansmodels. N -body simulations N -body simulations In addition to Jeans models we use a grid of N -body modelsand fit the models to the data of NGC 5286. The simulations
11. Feldmeier et al.: Indication for an intermediate-mass black hole in the globular cluster NGC 5286 from kinematics
Table 6.
The axisymmetric Jeans model best-fit values. i β M / L M • M tot L tot χ [ ◦ ] constant (cid:2) M (cid:12) / L V , (cid:12) (cid:3) (cid:104) M (cid:12) (cid:105) (cid:104) M (cid:12) (cid:105) (cid:104) L (cid:12) (cid:105) − .
10 1 . + . − . . + . − . . ± .
13 2 . ± .
09 1 . .
00 1 . + . − . . + . − . . ± .
13 2 . ± .
09 1 . .
00 1 . + . − . . + . − . . ± .
13 2 . ± .
09 1 . are described in McNamara et al. (2012). All simulations usethe code NBODY6 (Aarseth 2003) and start from King (1962)models with a Kroupa (2001) initial mass function between 0.1and 100 M (cid:12) . The stars evolve according to the stellar evolutionmodel of Hurley et al. (2000). The simulations run for 12 Gyrand we use 10 snapshots with a 50 Myr interval in between, start-ing at 11 Gyr. We overlay the snapshots for comparison with thedata. The cluster is then scaled up to NGC 5286 using the scal-ing as described by Jalali et al. (2012). To obtain smooth surfacebrightness and velocity-dispersion profiles from the simulationswe use the infinite projection method of Mashchenko & Sills(2005), which averages the stellar positions over all possible ro-tations of the cluster relative to the observer.Simulations cover a three-dimensional grid with di ff erentvalues of black-hole mass, concentration c = log( r t / t c ), and ini-tial half mass radius R Hi , and we search within this grid to obtainthe model which best fits the observational data. The simula-tions are run without an external tidal field, so cluster evolutionis driven by two-body relaxation and stellar evolution. For thefit to the N -body model we use our combined surface brightnessprofile, as it also results in the lowest χ with spherical Jeansmodels. The error bars in the outskirt of the profile are less than1%, which gives too much weight on the fit of the surface den-sity. Therefore we use the approach of McLaughlin & van derMarel (2005) to estimate the error σ i of the Trager et al. (1995)profile from the relative weights of each data point ( ω i ) and aconstant σ µ , with σ i = σ µ /ω i . The weights were estimated byTrager et al. (1995), and McLaughlin & van der Marel (2005)give the value of σ µ = ∼ (cid:48)(cid:48) .The best fitting models for no IMBH, an IMBH with 1%,and with 2% of the total cluster mass are displayed in Figure 12.The surface density is shown in the left panel, and the velocitydispersion in the right panel. We convolved the model profiles totake the e ff ects of seeing and pixel size into account. The changeof the model profile is small except for the center where R < (cid:48)(cid:48) ,beyond our data points. All models have similar results for thesurface brightness at radii R > (cid:48)(cid:48) and di ff er only at the center.Regarding only the surface brightness profile, the 2% IMBHmodel fits better than the 1% IMBH or the no-IMBH model.However, the velocity-dispersion profile of the 2% IMBH modelrises too much in the center of the cluster, and does not fit theinnermost data point. The 1% model also rises towards the cen-ter, but not as much. The best overall fit contains an IMBH withM • / M tot = χ = χ red = tot = (4.38 ± · M (cid:12) , therefore theIMBH has M • = (3.9 ± · M (cid:12) . The best-fitting no-IMBHmodel has M tot = · M (cid:12) with χ = χ contour lines as a function of the startparameters of the simulations for a 1% IMBH model. The lowest χ for the surface density are at a region of models which start ata concentration of about c = hi is not much constrained. For the velocitydispersion (panel b), best fits are in a narrow band going fromR Hi = Hi = χ , considering the fit to both profiles (panel c) comesfrom a region around c = Hi = χ red = N -bodysimulation In order to test whether Jeans models give reliable results for thetotal cluster mass, we use the N -body simulation which is clos-est to the best-fitting one and analyze it in more detail in thissection. This simulation started with an IMBH mass of 1%, ahalf-mass radius is R Hi = c = · M (cid:12) .We compute the surface brightness and velocity-dispersion pro-files for this simulation and perform a spherical Jeans analy-sis with these profiles. To compute the velocity dispersion wemake three perpendicular projections and compute a velocity-dispersion profile for each projection with the method of Pryor& Meylan (1993). The three projections are averaged to a finalvelocity-dispersion profile. We also vary the limiting magnitudeof stars that contribute to the velocity-dispersion profile. Fainterstars tend to be at larger radii due to mass segregation, and there-fore increase the velocity-dispersion profile there. Computingthe profile with brighter stars only underestimates the velocitydispersion at large radii, and the profile, which rises to the cen-ter, is too steep. Radial anisotropy also steepens the velocity-dispersion profile.We run Jeans models with constant M / L and the radiallyvarying M / L profile from the simulation, and di ff erent constantvalues of β . The limiting magnitude was chosen to be eitherm V =
19, 20, 22, 24, 26, 28, or 30. The influence of varying thelimiting magnitudes, the anisotropy parameter β , and the M / Lprofile on the total cluster mass is shown in Figure 14. The ex-tracted velocity dispersion rises as a function of limiting mag-nitude. This results in a rise of total cluster mass as a functionof limiting magnitude. We run these tests with Jeans models ofconstant M / L as well as for radially varying M / L and find thesame behavior for both. However, the recovered M tot is system-atically lower for constant M / L, as constant M / L underestimatesthe cluster mass at large radii. Also the value of β influences thetotal cluster mass M tot found by the Jeans models. Tangentialanisotropy results in higher M tot than radial anisotropy. The ra-dially varying M / L profile at a magnitude cut of m V =
26 and β =
12. Feldmeier et al.: Indication for an intermediate-mass black hole in the globular cluster NGC 5286 from kinematics
Fig. 12.
Best fitting N -body model without tidal field and with outer kinematic data. The surface density is plotted on the left panel,the velocity dispersion on the right panel. The di ff erent colors denote the best models for a black hole with 1% of the cluster mass(red), 2% of the cluster mass (green), and for no black hole (blue). The data points are denoted as black symbols. Fig. 13. χ contour lines as function of start parameters King concentration c and initial half-mass radius R Hi for the surface density(a), velocity dispersion (b), and both profiles combined (c). The red star indicates the best fit.obtains M tot = · M (cid:12) , which is almost perfectly matchingthe input value of 4.94 · M (cid:12) . As our spectral observations donot contain such faint stars, our measured velocity dispersion forNGC 5286 is probably also too low. This can be the reason whythe Jeans models obtain a lower total cluster mass than the N -body simulation, even after taking the radially varying M / L intoaccount.
7. Conclusions
Using photometric and kinematic data, we modeled the glob-ular cluster NGC 5286 and found indications for the presenceof a central black hole. Our photometric data set consists of anACS / HST image, and the star catalog constructed by Andersonet al. (2008) from ACS / HST observations. We used these to de-termine the photometric center with three di ff erent methods andconfirmed the results of Goldsbury et al. (2010). Further, we pro- duced a surface brightness profile from a combination of starcounts and integrated light measurements. We used two kine-matic data sets, for the inner part of the cluster up to ∼ (cid:48)(cid:48) wehave ground based spectroscopic data from the integral field unitARGUS at the VLT. This data set was reduced and used to pro-duce a velocity map, and a velocity-dispersion profile. The sec-ond data set was obtained with the Rutgers Fabry Perot at theCTIO and contains velocity measurements of single stars. Weused the outer part up to a radius of ∼ (cid:48)(cid:48) to complement ourvelocity-dispersion profile. Examining both data sets for indi-cation of rotation, we found rotation only in the region beyond25 (cid:48)(cid:48) with a rotation velocity of (2.3 ± / s and a rotationaxis consistent with the minor axis of the cluster.With the information provided by the surface brightness pro-file we ran Jeans models and compared the results for the veloc-ity dispersion to our profile. χ statistics were used to find thebest fit. For the spherical models we used our surface bright-ness profile as well as the profiles from Trager et al. (1995),and Noyola & Gebhardt (2006). With di ff erent central black-
13. Feldmeier et al.: Indication for an intermediate-mass black hole in the globular cluster NGC 5286 from kinematics constant M/L
20 22 24 26 28 30m V M t o t -0.2-0.10.00.1 β = 0.2input value radially varying M/L
20 22 24 26 28 30m V M t o t Fig. 14.
Total cluster mass M tot in M (cid:12) from spherical Jeans models, performed on the profiles of an N -body simulation. For thesurface brightness profile we use di ff erent limiting magnitudes m V , thus changing the number of stars contributing to the profile.Left panel: constant M / L. Right panel: radially varying M / L profile. The solid black line is the input value of M tot in the simulation.hole mass and anisotropy behavior the outcome of the modelwas scaled to our velocity-dispersion profile to determine thevalue of a constant mass-to-light ratio. Further, we used an M / Lprofile computed from N -body simulations as input. As a sec-ond approach we computed a two-dimensional surface bright-ness profile from the ACS / HST image and 2MASS images andran axisymmetric Jeans models with di ff erent black-hole masses,anisotropy, and inclination. We also fit the surface brightnessprofile and the velocity-dispersion profile from a grid of N -body models without tidal field to our data. All our models re-quire a central black hole for their best fit. Jeans models find abest fitting black-hole mass of about (1.5 ± · M (cid:12) , whileN-body modes require a black hole of 0.9% of the total clus-ter mass, corresponding to M • = (3.9 ± · M (cid:12) . The errorsare the 68% confidence limits. The models also provide the to-tal mass of the cluster, and the ratio of the black-hole massto the total cluster mass is lower for Jeans models, M • / M tot ≈ − N -body simulations obtain a total cluster massM tot = (4.38 ± · M (cid:12) . The total cluster mass of spheri-cal Jeans models is up to 34% lower, depending on the valueof M / L. For constant M / L we obtain a value of 1.07 M / L V andM tot = (2.89 ± · M (cid:12) , but with the varying M / L pro-file from N -body simulations the cluster mass is higher (M tot = (4.1 ± · M (cid:12) ). The value of M / L from our Jeans models with constant M / Lis about 1.07 M (cid:12) / L V , (cid:12) . Both spherical and axisymmetric Jeansmodels find similar values. The surface brightness profiles fromNoyola & Gebhardt (2006) and Trager et al. (1995) result inhigher values of 1.11 M (cid:12) / L V , (cid:12) and 1.22 M (cid:12) / L V , (cid:12) , respectively.This is probably due to the lower value of total luminosity withthese profiles (see Table 5). The integrated V-band magnitudeof Harris (1996) is 7.34, corresponding to a total luminosity of 2.7 · L (cid:12) . This value is in good agreement with the total lumi-nosity from our profiles.Pryor & Meylan (1993) found a value of M / L = (cid:12) / L V , (cid:12) from integrated light measurements and isotropic King mod-els. McLaughlin & van der Marel (2005) used the Trageret al. (1995) profile and data from Harris (1996) to computeM / L ratios. They used a population-synthesis model (M / L = (1.87 ± (cid:12) / L V , (cid:12) ) and dynamical models to fit M / L (Kingfit: 0.99 + . − . , Wilson fit: 0.94 + . − . , and Power-law fit: 0.91 + . − . in solar units, respectively), and obtained overall lowervalues than Pryor & Meylan (1993), in better agreement withour Jeans model with constant M / L of ∼ (cid:12) / L V , (cid:12) . Maraston(2005) also calculated M / L ratios from evolutionary populationsynthesis models. The results of the Sloan Digital Sky Survey(SDSS) r-band filter at 622 nm can be compared to our valuesof M / L V in the V-band at 606 nm. With the Kroupa (2001) ini-tial mass function, a metallicity of [Z / H] = − .
35 and an age of11 −
12 Gyr, their model gives higher values of M / L = − / L profile from N -body simulations has a global valueof M / L V of about (1.75 ± (cid:12) / L V , (cid:12) after scaling to thevelocity-dispersion profile, which is in rough agreement with theM / L ratio of the population synthesis models.The di ff erences in the total cluster mass between our mod-els can be explained by the influence of the M / L profile.With the M / L profile from N -body simulations as input toour spherical Jeans models in Section 5.2 we obtain a highercluster mass of M tot = (4.1 ± · M (cid:12) , in better agreementwith the value found from the N -body simulations of M tot = (4.38 ± · M (cid:12) . Also the Jeans models that we ran on theprofiles of an N -body simulations in Section 6.2 confirm theinfluence of a radially varying M / L profile on the total clustermass. In the range of 2 (cid:48)(cid:48) < r < (cid:48)(cid:48) the M / L profile is lower thanaverage. The extra mass, compared to a constant M / L, is mostlyat larger radii. Since we have no velocity measurements for r > (cid:48)(cid:48) , the additional mass at large radii does not significantlyinfluence our velocity-dispersion measurements. A rise in M / L
14. Feldmeier et al.: Indication for an intermediate-mass black hole in the globular cluster NGC 5286 from kinematics towards the outer cluster parts could also explain why the dy-namical M / L values of McLaughlin & van der Marel (2005)are smaller than the population synthesis ones. This stressesthe importance of obtaining velocity-dispersion measurementsin the outer cluster parts when trying to determine the total clus-ter mass. Furthermore, the velocity-dispersion measurements arebased on bright stars. Those stars are more massive than average,but have lower velocities. This underestimates the velocity dis-persion and the total cluster mass, as we showed in Section 6.2.For the determination of a central black-hole mass, the valueof the anisotropy β is important. Anisotropy in the outer partof the cluster does not change the result much, but a radialanisotropy in the center can easily be misinterpreted as a cen-tral black hole, whereas unknown tangential anisotropy resultsin an underestimation of the black-hole mass. Assuming ra-dial anisotropy of β = N -body simulations. L¨utzgendorf et al. (2011)ran a simulation of a highly anisotropic cluster and showed thatthe central part of a cluster becomes isotropic after a few relax-ation times. As NGC 5286 is already 9 relaxation times old atits half-mass radius, we expect not much anisotropy ( | β | < N -body models, but both indicate a blackhole with less than 1% of the total cluster mass. This upper limitis higher than the black hole mass fraction usually measured forgalaxies. H¨aring & Rix (2004) found that the fraction of a centralmassive dark object in nearby galaxies is around 0.14% ± σ detections for an IMBH, so the no-black-holecase cannot be excluded. A central black hole should not bemore massive than 6.0 · M (cid:12) , as for N -body simulations thisis where ∆ χ =
5. Jeans models find an upper limit of M • = · M (cid:12) with 95% confidence level from Monte Carlo simu-lations. But independent of the method we use, all our methodsprefer the case with an IMBH over the no-black-hole case. Theresult from N -body simulations is M • = (3.9 ± · M (cid:12) , fromJeans models the black-hole mass is about 50% lower.Our modeling shows that the derived uncertainties for thekinematic profile are too high to precisely constrain the black-hole mass and anisotropy. In the innermost bin the uncertaintyis more than 2.2 km / s, which is 24% of the measured value.However, these high error bars are realistic, as the determina-tion of the velocity dispersion currently shows some ambigu-ity. We used two di ff erent methods and varied the parametersof the pPXF method. Thus we found scatter of up to 3 km / s.Further investigation of this inconsistency is therefore neededto obtain better constrained results. Alternatively, observationswith higher spectral resolution or of individual stars could alsoclear up this issue. NGC 5286 is an interesting case for dynamical modelingand could host an intermediate-mass black hole. Our researchgroup has IFU data for six more globular clusters in the south-ern hemisphere (L¨utzgendorf et al. 2012a). These data are usedto constrain possible IMBHs inside these clusters. This infor-mation can be used to decide which other clusters should beexamined, also in the northern hemisphere. Located betweengalaxies and globular clusters, at σ e ∼
15 - 70 km / s, are systemslike dwarf galaxies, which could also contain intermediate-massblack holes. Assessing the fraction of globular clusters and stel-lar systems with intermediate-mass black hole, the masses of theblack holes and their environments, will help us to understandnot only the dynamical processes in these stellar systems, butmaybe also the formation of supermassive black holes. Acknowledgements.
We thank the anonymous referee for her / ffi ce, Computation TechnologiesProject, under Cooperative Agreement Number NCC5-626 between NASAand the California Institute of Technology. Montage is maintained by theNASA / IPAC Infrared Science Archive.
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