Kinematic signature of an intermediate-mass black hole in the globular cluster NGC 6388
N. Lützgendorf, M. Kissler-Patig, E. Noyola, B. Jalali, P. T. de Zeeuw, K. Gebhardt, H. Baumgardt
aa r X i v : . [ a s t r o - ph . GA ] J u l Astronomy&Astrophysicsmanuscript no. luetzgendorf˙2011 c (cid:13)
ESO 2018July 2, 2018
Kinematic signature of an intermediate-mass black hole in theglobular cluster NGC 6388. ⋆ N. L ¨utzgendorf , M. Kissler-Patig , E. Noyola , , B. Jalali , P. T. de Zeeuw , , K. Gebhardt , and H. Baumgardt European Southern Observatory (ESO), Karl-Schwarzschild-Strasse 2, 85748 Garching, Germanye-mail: [email protected] Max-Planck-Institut f¨ur Extraterrestrische Physik, 85748 Garching, Germany University Observatory, Ludwig Maximilians University, Munich D-81679, Germany Sterrewacht Leiden, Leiden University, Postbus 9513, 2300 RA Leiden, The Netherlands Astronomy Department, University of Texas at Austin, Austin, TX 78712, USA School of Mathematics and Physics, University of Queensland, Brisbane, QLD 4072, AustraliaReceived Febrary 1, 2011; accepted July 20, 2011
ABSTRACT
Context.
Intermediate-mass black holes (IMBHs) are of interest in a wide range of astrophysical fields. In particular, the possibil-ity of finding them at the centers of globular clusters has recently drawn attention. IMBHs became detectable since the quality ofobservational data sets, particularly those obtained with HST and with high resolution ground based spectrographs, advanced to thepoint where it is possible to measure velocity dispersions at a spatial resolution comparable to the size of the gravitational sphere ofinfluence for plausible IMBH masses.
Aims.
We present results from ground based VLT / FLAMES spectroscopy in combination with HST data for the globular cluster NGC6388. The aim of this work is to probe whether this massive cluster hosts an intermediate-mass black hole at its center and to comparethe results with the expected value predicted by the M • − σ scaling relation. Methods.
The spectroscopic data, containing integral field unit measurements, provide kinematic signatures in the center of the clusterwhile the photometric data give information of the stellar density. Together, these data sets are compared to dynamical models andpresent evidence of an additional compact dark mass at the center: a black hole.
Results.
Using analytical Jeans models in combination with various Monte Carlo simulations to estimate the errors, we derive (with68% confidence limits) a best fit black-hole mass of (17 ± × M ⊙ and a global mass-to-light ratio of M / L V = (1 . ± . M ⊙ / L ⊙ . Key words. black hole physics – globular cluster: individual (NGC 6388) – stars: kinematics and dynamics
1. Introduction
For a long time, only two mass ranges of black holes wereknown. On the one hand, we have stellar mass black holes,which are remnants of massive stars, and can be observedin binary systems. On the other hand, there are supermassiveblack holes at the centers of galaxies, some of them accret-ing at their Eddington limit and producing the brightest objectsknown (quasars). It has been demonstrated that supermassiveblack holes show a tight correlation between their mass andthe velocity dispersion of the galaxy in which they reside (e.g.Ferrarese & Merritt 2000; Gebhardt et al. 2000; G¨ultekin et al.2009). Extrapolating this relation to the lower velocity disper-sions of globular clusters, with σ ∼ −
20 km s − , predictscentral black holes in these objects with masses of 10 − M ⊙ .Due to the small amount of gas and dust in globular clusters,the accretion e ffi ciency of a potential black hole at the centeris expected to be low. Therefore, the detection of IMBHs at thecenters of globular clusters through X-ray and radio emissionsis challenging (Miller & Hamilton 2002; Maccarone & Servillat2008). Nevertheless, there is another way to detect IMBHs inglobular clusters: exploring the kinematics of these systemsin the central regions. This method, proposed forty years ago ⋆ Based on observations collected at the European Organization forAstronomical Research in the Southern Hemisphere, Chile (083.D-0444). (Bahcall & Wolf 1976; Wyller 1970), has long been limited bythe quality of observational datasets, since it requires veloc-ity dispersion measurements at a spatial resolution comparableto the size of the gravitational sphere of influence for plausi-ble IMBH masses (1 − ′′ for large Galactic globular clusters).However, with existence of the Hubble Space Telescope (HST)and with high spatial resolution ground based integral-field spec-trographs, the search for IMBHs was revitalized.Gebhardt et al. (1997, 2000) and Gerssen et al. (2002)claimed the detection of a black hole of (3 . ± . × M ⊙ in the globular cluster M15 from photometric and kinematicobservations. After more investigations this cluster no longerappears as a strong IMBH candidate (e.g. Dull et al. 1997;Baumgardt et al. 2003, 2005; van den Bosch et al. 2006), butnew detections of IMBH candidates in other clusters followed.Gebhardt et al. (2002, 2005) used the velocity dispersion mea-sured from integrated light near the center of the M31 clusterG1 to argue for the presence of a (1 . ± . × M ⊙ darkmass at the cluster center. The possible presence of an IMBHin G1 gained further credence with the detection of weak X-rayand radio emission from the cluster center (Pooley & Rappaport2006; Kong 2007; Ulvestad et al. 2007). Also, the globular clus-ter ω Centauri (NGC 5139) has been proposed to host a blackhole at its center (Noyola et al. 2008, 2010). The authors mea-sured the velocity-dispersion profile with an integral field unitand used orbit based dynamical models to analyze the data.
N. L¨utzgendorf et al.: Kinematic signature of an intermediate-mass black hole in the globular cluster NGC 6388.
Anderson & van der Marel (2010) studied the same object usingproper motions from HST images. They found less compellingevidence for a central black hole, but more importantly, theyfound a location for the center that di ff ers from previous mea-surements. Both G1 and ω Centauri have been suggested to bestripped nuclei of dwarf galaxies (Freeman 1993; Meylan et al.2001) and therefore may not be the best representatives of glob-ular clusters. The key motivation of this work is to probe moreglobular clusters for the presence of IMBHs.Further evidence for the existence of IMBHs is the discov-ery of ultra luminous X-ray sources at non-nuclear locationsin starburst galaxies (e.g. Fabbiano 1989; Colbert & Mushotzky1999; Matsumoto et al. 2001; Fabbiano et al. 2001). The bright-est of these compact objects (with L ∼ erg s − ) implymasses larger than 10 M ⊙ assuming accretion at the Eddingtonlimit. Several realistic formation scenarios of black holes inglobular clusters have been developed. The two main forma-tion theories are: a) IMBHs would be Population III stellarremnants (Madau & Rees 2001), or b) they would form in arunaway merging of young stars in su ffi ciently dense clusters(Portegies Zwart et al. 2004; G¨urkan et al. 2004; Freitag et al.2006). In addition Miller & Hamilton (2002) presented scenar-ios for the capture of clusters by their host galaxies and accretionin the galactic disk in order to explain the observed bright X-raysources.Our goal in this paper is to study the globular cluster NGC6388. This cluster is located 11 . ∼ . × M ⊙ it belongs to the mostmassive clusters in the Milky Way. In addition, its high centralvelocity dispersion of 18 . − (Pryor & Meylan 1993), andassuming a black-hole mass correlation with velocity dispersion,make NGC 6388 a good candidate for detecting an intermediate-mass black hole. Besides the kinematic properties, the photomet-ric characteristics are also quite interesting. Noyola & Gebhardt(2006, hereafter NG06) found a shallow cusp in the central re-gion of the surface brightness profile of NGC 6388. N-body sim-ulations showed that this is expected for a cluster hosting anintermediate-mass black hole (Baumgardt et al. 2005). For thatreason, Lanzoni et al. (2007) investigated the projected densityprofile and the central surface brightness profile with a combina-tion of HST high-resolution and ground-based wide-field obser-vations. They found the observed profiles are well reproduced bya multimass, isotropic, spherical King model, with an added cen-tral black hole with a mass of ∼ . × M ⊙ . Also, the work ofMiocchi (2007) suggests the presence of an intermediate-massblack hole in NGC 6388 as a possible explanation for the ex-tended horizontal branch.Another interesting fact about NGC 6388 is that it appears tocontain multiple stellar populations (e.g. Yoon et al. 2000; Piotto2008). This fact makes the scenario of merging clusters plausi-ble, leading to potentially complicated dynamics in the center.Recently, X-ray observations for NGC 6388 showed no signifi-cant signatures for an accreting IMBH (Cseh et al. 2010). But asalready mentioned, this does not rule out a quiescent black hole.In summary, this cluster was chosen as it presents many interest-ing features. We measured the kinematics of the central regions,allowing us to probe the result of Lanzoni et al. (2007) with adi ff erent method, taking the kinematic properties as well as thephotometric properties into account.The basic approach of this work is to first study the lightdistribution of the cluster. Photometric analysis, such as the de- Table 1.
Properties of the globular cluster NGC 6388 fromthe references: NG = Noyola & Gebhardt (2006), H = Harris(1996), M = Moretti et al. (2009), L = Lanzoni et al. (2007) andPM = Pryor & Meylan (1993).
Parameter Value ReferenceRA (J200) 17h 36m 17s NGDEC (J200) − ◦ ′ ′′ NGGalactic Longitude l 345 .
56 HGalactic Latitude b − .
74 HDistance from the Sun R SUN . r c . ′′ LCentral Concentration c 1 . r . ± . / s HCentral Velocity Dispersion σ . / s PMAge (11 . ± .
5) Gyr MMetallicity [Fe / H] − . .
38 MAbsolute Visual Magnitude M Vt − .
42 mag H termination of the cluster center and the measurement of a sur-face brightness profile, is described in section 2. De-projectingthis profile gives an estimation of the gravitational potential pro-duced by the visible mass. The next step is to study the dynamicsof the cluster. Section 3 gives an overlook of the FLAMES obser-vations and data reduction and section 4 describes the analysisof the spectroscopic data. With the resulting velocity-dispersionprofile, it is possible to estimate the actual dynamical mass. Thenext step is to compare the data to dynamical Jeans models (sec-tion 5). These models take the light profile and predict a velocity-dispersion profile, which is scaled to the data in order to obtainthe mass-to-light ratio. This is done for models containing dif-ferent black-hole masses until the best fit to the observed profileis found. In section 6 we summarize our results, list our conclu-sions and give an outlook for further studies.
2. Photometry
The photometric data, retrieved from the archive, were ob-tained with the Advanced Camera of Surveys (ACS) of theHubble Space Telescope (HST) in the Wide-Field Channel (un-der the HST program SNAP-9821, PI: B.J. Pritzl) betweenOctober 2003 and June 2004. This data set is composed of sixB (F435W), V (F555W) and I (F814W) images with exposuretimes of 11, 7 and 3s, respectively. It gives a complete cover-age of the central region of the cluster out to a radius of 110 ′′ .The data were calibrated, geometrically corrected and dither-combined as retrieved from the European HST-Archive (ST-ECF, Space Telescope European Coordinating Facility ). The CMD was obtained using the programs daophot II , allstars and allframes by P. Stetson, applied to our HST image. For a de-tailed documentation of these routines see Stetson (1987). These Based on observations made with the NASA / ESA HubbleSpace Telescope, and obtained from the Hubble Legacy Archive,which is a collaboration between the Space Telescope ScienceInstitute (STScI / NASA), the Space Telescope European CoordinatingFacility (ST-ECF / ESA) and the Canadian Astronomy Data Centre(CADC / NRC / CSA).. L¨utzgendorf et al.: Kinematic signature of an intermediate-mass black hole in the globular cluster NGC 6388. 3 programs were especially developed for photometry in crowdedfields and therefore ideally suited for the analysis of globularclusters. The routines find , phot and psf identify the stars, per-form aperture photometry and compute the average point spreadfunction (PSF) over the image, respectively.Once the PSF has been defined, the next step is to group theneighboring stars to apply the multiple-profile-fitting routine si-multaneously by the task allstars . Afterwards, the find task isapplied again to find, in the star-subtracted image, stars whichwere not found in the first run. The entire procedure was per-formed on the V- and I-band images independently. As a nextstep the programs daomaster and allframes were used to com-bine both images and to create the final catalog containing allstars, their positions and magnitudes in the two bands. At theend, we calibrated the final catalog to the Johnson magnitudesystem by following the steps described in Sirianni et al. (2005).In order to get better quality at the faint end of the CMD,one final step was applied to the catalog. The program separa-tion (Bruntt et al. 2003) computes a separation index for everystar in a catalog. This index is calculated by, first, evaluating alocal surface brightness at the position of a given star. Second,the local surface brightness is compared to the sum of the surfacebrightnesses produced by the PSF of all the other stars in the fieldat the position of the centroid of that star. The ratio of these twosurface brightness values expressed in magnitudes determinesthe separation index. Thus, the stars could be selected consider-ing background-light contamination and not only by magnitude.Figure 1 shows the final CMD of stars with a separation index ≥ Using the star catalog generated with daophot , the center ofthe cluster can be determined. Precise knowledge of the clus-ter center is important since the shape of the surface bright-ness and the angular averaged line-of-sight velocity distribu-tion (LOSVD) profiles depend on the position of that cen-ter. Using the wrong center typically produces a shallower in-ner profile. For example determining the center for ω Centauriis not trivial (Noyola & Gebhardt 2006; Noyola et al. 2010;Anderson & van der Marel 2010). Fortunately, NGC 6388 is notas extended and has a steeper light profile than ω Centauri sothat the center is easier to determine. NG06 determined the cen-ter of this cluster to be at α =
17 : 36 : 17 . , δ = −
44 :44 : 07 .
83 ( J . ′′ , by minimizingthe standard deviation of star counts in eight segments of a cir-cle. In view of the discrepancies about the center location for ω Centauri, we decided to recompute the center of NGC 6388 andto evaluate how precisely the center can be determined. NG06’scenter on our I-band image was used as a first guess for the fol-lowing methods to determine the center in the ACS images, i.e.our reference frame for the spectroscopy.The first method is a simple star count as described inMcLaughlin et al. (2006). The catalog generated with daophot (see section 2.1) contains 88,406 stars. In a field of 4 ′′ × ′′ a gridof trial centers was created, using a grid spacing of 2 ACS pixels(0 . ′′ ). Around each trial center a circle of 300 pixels (15 ′′ ) wasconsidered and divided into 16 wedges as shown in Figure 2. Thestars in each wedge were counted and compared to the oppositewedge. The di ff erences in the total number of stars between twoopposing wedges were summed for all 8 wedge pairs. The coor-dinates that minimized the di ff erence defined a first guess of the m I Fig. 1.
The color-magnitude diagram of NGC 6388. Overplottedare the brightest stars identified in the ARGUS field of view (redcircles), and the template star used (star symbol).center of the cluster. This center was refined as described in thenext sections. We compared our result to the center obtained byNG06. The two centers are only 0 . ′′ apart and thus coincidewithin the error bars of 0 . ′′ (as determined by NG06 performingartificial image tests).The second method that we used is also described inMcLaughlin et al. (2006). Instead of comparing the total num-ber in pairs of opposite wedges, a cumulative radial distributionfor each wedge in 4 bins was generated. This time 8 wedges wereused instead of 16 to avoid too large stochastic errors due to in-su ffi cient numbers of stars in each bin. The bins were placedat equidistant radii. Again the absolute value of the integrateddi ff erence between the radial distributions in any two opposingwedges was calculated and the minimum used to determine thenew center of the cluster. The so derived center lies within 0 . ′′ of the one derived with the previous method and within 0 . ′′ ofNG06’s location.We present a last method in which the light of the stars in-stead of their number, is considered. Similar to the first method,16 wedges without any radial bins were generated, but this timenot the stars were counted but the luminosities of the stars weresummed up in each wedge. In order to avoid a bias by the con-tamination of a few bright stars, only stars from the lower gi-ant branch and the horizontal branch (between m V =
15 and m V =
19) were used. This approach reproduces NG06’s centerwithin the error bars (0 . ′′ ) as well. The method is illustrated inFigure 2. Shown are the grid of trial centers, the 16 wedges weapplied to each of them, and the final contour plot. N. L¨utzgendorf et al.: Kinematic signature of an intermediate-mass black hole in the globular cluster NGC 6388.
TRIAL CENTERS METHOD RESULT E N Fig. 2.
The method to determine the globular cluster center. From left to right: a zoom into our HST / ACS image of NGC 6388(used to derive the CMD and luminosity profile for the cluster) with the over-layed grid of trial centers. Around each trial center,di ff erential stellar counts and stellar luminosity were computed in two opposite wedges extending 15” in radius [middle panel]. Aminimization of the residuals, as shown in the contour plot [right panel] determines the center to within 0 . ′′ . The distances betweenthe contours vary between 40 - 70 stars for the star count methods.For the subsequent analysis, we used the center derived fromour ACS catalog. To estimate the error of our center determina-tion we took the scatter from the three di ff erent methods as wellas an additional test where only eight wedges where used. Forthese eight wedges we repeated the routine by only using thecardinal wedges and the semi-cardinal wedges separately. Forthis dataset (HST J8ON08OYQ, also used as position referencecoordinates) we derived a final position of the center of:( x c , y c ) = (2075 . , . ± (3 . , .
1) pixel (1) α =
17 : 36 : 17 . , ∆ α = . ′′ (J2000) (2) δ = −
44 : 43 : 57 . , ∆ δ = . ′′ (3)All the derived centers lie within a few tenths of an arcsecond( ∼ − pc) radius. However, it must be considered that all themethods are using the same catalog derived by DAOPHOT. Thiscatalog most likely su ff ers from incompleteness since the brightstars are covering the fainter stars underneath. This could biasthe center towards the bright stars even if they are excluded inthe counts. Our center agrees within the error bars with the onedetermined in NG06 on WFPC2 images. It also coincides withthe center found by Lanzoni et al. (2007) which, according tothem, lies ∼ . ′′ northwest of the NG06 center and thereforcloser to ours. The last step of the photometric analysis was to obtain the sur-face brightness profile. This is required as an input for the Jeansmodels described in the following section. To obtain the profile,a simple method of star counts in combination with an integratedlight measurement from the ACS image was applied. The fluxesof all stars brighter than m V =
18 were summed in radial bins ofequal width (50 pix) around the center and divided by the areaof each bin. Since there are no stars in the gap between the twoACS CCD chips this area was subtracted from each a ff ected bin. In addition, the integrated light for stars fainter than m V = m V <
18. After trying di ff erent methods to derive the “average”of the distribution of counts, we applied a simple average thattakes into account the faintest pixels i.e. stars. At the end, theflux per pixel was transformed back into magnitude per squarearcseconds and added to the star counts profile.We compared our profile with Trager et al. (1995),Lanzoni et al. (2007) and NG06. The latter was derived by mea-suring the integrated light using a bi-weight estimator whileLanzoni et al. (2007) derived their points by taking the averageof the counts per pixel in each bin. We were able to reproduce theshape in the outer regions, but due to the method and data that weused our profile in the innermost region has a high uncertainty.The errors on our profile were obtained by Poisson statistics ofthe number of stars in each bin. With a linear fit inside the coreradius ( ∼ ′′ ) we derived a logarithmic slope of β = . ± . β corresponds to µ V ∼ log r β with the surface brightness µ V ), which results in a slope of the surface luminosity density I ( r ) ∝ r α of α = − . ± .
08. This value is steeper (but con-sistent within the errors) than the slope of α = − . ± . α = − . ± . ff set in our profile. The factthat we used all the light in the image, including the backgroundlight could also shift the profile to higher magnitudes than theintrinsic brightness. For that reason, we scaled our profile tothe outer parts of the profile by Trager et al. (1995). This profilewas obtained with photometrically calibrated data and providesa good reference for the absolute values of the profile. The finalresult of the surface brightness profile is shown in Figure 3. . L¨utzgendorf et al.: Kinematic signature of an intermediate-mass black hole in the globular cluster NGC 6388. 5 Table 2.
The derived surface brightness profile in the V-band. ∆ V h and ∆ V l are the high and low values of the errors, respec-tively. log r V ∆ V l ∆ V h [arcsec] [mag / arcsec ] [mag / arcsec ] [mag / arcsec ]- 0.40 14.00 0.52 0.35- 0.12 14.53 0.52 0.350.18 14.31 0.21 0.180.40 14.74 0.16 0.140.60 14.78 0.10 0.090.81 15.18 0.07 0.071.06 15.62 0.05 0.051.22 16.21 0.05 0.051.33 16.68 0.06 0.061.42 17.18 0.07 0.071.50 17.50 0.07 0.071.56 17.91 0.08 0.071.62 18.20 0.08 0.081.67 18.54 0.09 0.091.71 18.74 0.10 0.091.75 18.80 0.09 0.091.79 19.17 0.11 0.101.82 19.33 0.11 0.101.85 19.61 0.13 0.111.88 19.44 0.10 0.10 -0.5 0.0 0.5 1.0 1.5 2.0log r (arcsec)2019181716151413 V ( m a g / a r c s e c ) Fig. 3.
The surface brightness profile of NGC 6388. The profileshows a clear cusp for the inner 10 arcseconds. Also shown is theMGE fit (solid line) which was used to parametrize our profile(see section 8.)
3. Spectroscopy
The spectroscopic data were observed with the GIRAFFE spec-trograph of the FLAMES (Fiber Large Array Multi ElementSpectrograph) instrument at the Very Large Telescope (VLT)in ARGUS (Large Integral Field Unit) and IFU (Integral FieldUnit) mode. The set contains spectra from the center (ARGUS)and the outer regions (IFU) for the globular cluster NGC 6388.The observations were performed during two nights (2009-06-14 / . ′′ , 14 ×
22 pixel array) and pointed to
10 " A B C E N Fig. 4.
The positions of the three ARGUS pointings (A, B andC) reconstructed on the HST / ACS image.three di ff erent positions (exposure times of the pointings: A:3 ×
480 s + × × × ∼
850 nm) which is a strong feature in thespectra. The expected velocity dispersions lie in the range 5-20 km s − and need to be measured with an accuracy of 1-2km s − . This implied using a spectral resolution around 10000,available in the low spectral resolution mode set-up LR8 (820 −
940 nm , R = We reduced the spectroscopic data with the GIRAFFE pipelineprogrammed by the European Southern Observatory (ESO).This pipeline consists of five recipes which are briefly describedbelow.First, a master bias frame was created by the recipe gimas-terbias from a set of raw bias frames. Next, a master dark wasproduced by the recipe gimasterdark which corrected each in-put dark frame for the bias and scaled it to an exposure timeof 1 second. The recipe gimasterflat was responsible for the de-tection of the spectra on a fiber flat-field image for a given fibersetup.
Gimasterflat located the fibers, determined the parametersof the fiber profile by fitting an analytical model of this profile tothe flat-field data and created an extracted flat-field image. Thisimage was later used to apply corrections for pixel-to-pixel vari-ations and fiber-to-fiber transmission.The pipeline recipe giwavecalibration computed a disper-sion solution and a slit geometry table for the fiber setup in use.This was done by extracting the spectra from the bias correctedThAr lamp frame, using the fiber localization (obtained throughthe flat-field), selecting the calibration lines from the line cata-log, and predicting the positions of the ThAr lines on the detec-tor using an existing dispersion solution as an initial guess. Thequality of the calibration was checked in two ways. The first onewas by measuring the centroid of one dominating sky emissionline in all 14 sky spectra and the second was a cross-correlationin Fourier-space of all sky spectra.Both methods did not show any systematic shift of the spec-tra and resulted in an RMS of 0 .
03 Å, which corresponds to avelocity of 1 km s − . The last recipe, giscience combined all cal-ibrations and extracted the final science spectra. A simple sumalong the slit was applied as extraction method. The input obser-vations were averaged and created a reduced science frame, theextracted and rebinned spectra frame. At the end, the recipe alsoproduced a reconstructed image of the respective field of viewof the IFU and the ARGUS observations. N. L¨utzgendorf et al.: Kinematic signature of an intermediate-mass black hole in the globular cluster NGC 6388. N o r m a li z e d F l u x Fig. 5.
Combined spectra of the first, third and sixth bin over-plotted by their best fit (red line). Due to the binning, the spectrashow a high signal-to-noise ratio.The most important parts of our reduction are the sky sub-traction and an accurate wavelength calibration to avoid arti-ficial line broadenings due to incorrect line subtractions. Theprogram we used was developed by Mike Irwin and describedin Battaglia et al. (2008). To subtract the sky, the program firstcombined all (14) sky fibers using a 3-sigma clipping algorithmand computed an average sky spectrum. Using a combinationof median and boxcar, it then split the continuum and the sky-line components in order to create a sky-line template mask. Forthe object spectra, the same method of splitting the continuumfrom the lines was applied. In the process, the sky-lines weremasked out to get a more accurate definition of the continuum.Afterwards, the sky-line mask and the line-only object spectrawere compared to find the optimum scale factor for the sky spec-trum in order to subtract the sky-lines from the object spectra.The continuum was added back to the object spectra and the skycontinuum subtracted by the same scaling factor as obtained forthe lines (assuming that lines and continuum have the same scal-ing factor).After applying the sky subtraction program, the last step inthe reduction of the data was to remove the cosmic rays from thespectra. This was done using the program LA-Cosmic developedby van Dokkum (2001) and based on a Laplacian edge detection.In order to avoid bright stars dominating the averaged spectrawhen they were combined, we applied a simple normalizationby fitting a spline to the continuum and dividing by it.For the small IFUs, we applied the same reduction stepsas for the large integral-field unit, except for the cosmic rayremoval, since LA-Cosmic did not give a satisfying result.However, we were able to average all exposures applying asigma clipping method in order to remove the cosmic rays, dueto the fact that these pointings were not dithered.
4. Kinematics
This section describes how we created a velocity map in orderto check for rotation or other peculiar kinematic signals and howwe derived a velocity-dispersion profile. This profile is then usedto fit analytic models, described in the next section.
The reconstructed images of the three ARGUS pointings werematched to the HST image. With this information, the pointingswere stitched together and each spectrum correlated to one posi-tion in the field of view. The resulting catalog of spectra and theircoordinates allowed us to combine spectra in di ff erent bins. Thecombined pointing contains 24 ×
29 spaxels.For each spaxel, the penalized pixel-fitting (pPXF) programdeveloped by Cappellari & Emsellem (2004) was used to derivethe kinematics in that region. Figure 6 shows a) the field of viewof the three pointings on the HST image, b) the field convolvedwith a Gaussian and resampled to the resolution of the ARGUSarray and c) the reconstructed and combined ARGUS image.The corresponding velocity map is shown in Figure 7. For ev-ery ARGUS pointing, a velocity map was derived before com-bining. The C pointing is a bit more noisy due to the fact thatit only had one exposure. To check for systematic wavelengtho ff sets we compared the derived velocities of the di ff erent point-ings and exposures at overlapping spaxels. We found o ff sets ofup to 1 km s . − We checked for systematic wavelength o ff setsbetween the pointings by cross-correlating their averaged skyspectra. The rms of the shifts measures 0.006 pixel (0.0018 Å)which corresponds to a velocity shift of ∼ . − We con-clude that the velocity o ff sets are not due to uncertainties in thewavelength calibration and do not cause problems for our furtheranalysis. Instead, the o ff sets are explained as follows:i) Di ff erent pointings were dithered about half an ARGUSspaxel. This means that in every pointing a slightly di ff erentcombination of stars contributes to the di ff erent spaxel, whichcould cause a di ff erent velocity measurement. ii) Errors in thereconstruction of the pointing positions could also cause veloc-ity o ff sets between two positions. If the spaxels do not point atthe exact same position we measure, similar to point i), di ff er-ent velocities. iii) Not all pointings had the same exposure time.This causes di ff erent signal-to-noise ratios for di ff erent point-ings. This could also explain some variations in the velocitymeasurements with the pPXF routine. Note that for the veloc-ity dispersion measurements, we grouped the individual spectrain large annuli. For that reason, the position o ff sets do not causea problem for the further analysis as the “error” in position isnot propagated into the velocity dispersion measurement as asystematic shift.We used a star from the central pointing (pointing A) as avelocity template. This has the advantage that it went throughthe same instrumental set-up as well as the same reduction stepsas all other spectra and therefore the same sampling and wave-length calibration. The green circle in the HST image in Figure6 (left panel) and the blue star in the color magnitude diagram(Figure 1) marks the star which was used. We also identified thebrightest stars form the pointing in the CMD to make sure thatthe template and other dominating stars are not foreground stars(see Figure 1). In order to derive an absolute velocity scale, theline shifts of the templates were measured by fitting a Gaussianto each line and deriving the centroid. This was compared withthe values of the Calcium Triplet in a rest frame and the average . L¨utzgendorf et al.: Kinematic signature of an intermediate-mass black hole in the globular cluster NGC 6388. 7 HST IMAGE E N HST BLURRED AND RESAMPLED ARGUS RECONSTRUCTED
Fig. 6.
The ARGUS field of view: the HST image is shown on the left. The red circle marks the center, the green one the templatestar which was used. The same image but convolved with a Gaussian and resampled to the 0.3 pixel scale of the ARGUS array[center]. Compared to the actual reconstructed ARGUS pointing [right], it is clear that they are pointing to the same region.
Km/s
VELOCITY MAP
Fig. 7.
The velocity map of NGC 6388. As shown on the velocity scale, the blue spaxels indicate approaching velocities and the redones receding. The white stars mark the spaxels which we excluded from the velocity dispersion measurement as they might su ff erfrom shot noise. Also shown are the first three velocity dispersion bins to help visualize the binning method.shift was calculated. We then corrected the radial velocity for theheliocentric reference frame. An obvious feature of the velocity map in Figure 7 is the brightblue spot in the middle left of the pointing which seems to dom-inate the blue (approaching) part of the map. We investigatedwhether we see a real rotation around the center or just one or afew bright stars with a peculiar velocity dominating their envi- ronment and with their light contaminating neighboring spaxels.Therefore, we tested the influence of each star on the adjacentspaxels. This allowed us to test if the derived velocity disper-sion is representative of the entire population at a given radius orwhether it is biased by a low number of stars, i.e. dominated byshot noise.To perform this test, we considered our photometric cata-log (described in section 2) for the field of view covered bythe ARGUS pointings. At every position of a star in the cata-log, a two dimensional Gaussian was modeled with a standard
N. L¨utzgendorf et al.: Kinematic signature of an intermediate-mass black hole in the globular cluster NGC 6388.
Table 3.
The four moments of the velocity distribution of NGC6388. log r V V
RMS h h / s] [km / s] − . − . ± . . ± . − . ± . − . ± . . − . ± . . ± . − . ± . − . ± . . − . ± . . ± . − . ± . − . ± . .
56 2 . ± . . ± . − . ± . − . ± . .
65 6 . ± . . ± . − . ± . − . ± . .
78 4 . ± . . ± . − . ± . − . ± . .
04 3 . ± . . ± . − . ± . − . ± . .
26 6 . ± . . ± . − . ± . − . ± . deviation set to the seeing of the ground based observations(FWHM = . ′′ ) and scaled to the total flux of the star. Thenext step was to measure the absolute amount and fraction oflight that each star contributes to the surrounding spaxels. Aftercomputing these values for every star in the pointing, we hadthe following information for each spaxel: a) how many starscontribute to the light of that spaxel, and b) which fraction of thetotal light is contributed by each star, i.e. we determined whetherthe spectrum in a given spaxel was dominated by one or a fewstars. The test showed that most of the spaxels contained mean-ingful contributions by more than 10 stars. Some spaxels, how-ever, were dominated by a single star contributing more than 50% to the spaxel’s light. For this reason, the contribution in per-cent of the brightest star was also derived by the program. Wefound out that the blue area in the left side of the velocity map ofFigure 7 is not due to a single star. In fact this area in the velocitymap corresponds to a group of at least 10 stars moving with 10 -40 km s − with respect to the cluster systemic velocity. To derive a radial velocity-dispersion profile for the stellar pop-ulation of NGC 6388 it is necessary to bin the spectra accord-ingly. We divided the pointing into six independent angular bins,each of them with the same width of three ARGUS spaxels(0 . ′′ , .
04 pc). To check the e ff ect of the distribution of the binson the final result, we tried di ff erent combinations of bins and bindistances as well as overlapping bins. We found no change in theglobal shape of the profile when using di ff erent bins. Thereforethe choice of the bins was not critical, but in order to make anaccurate error estimation, independent bins are more useful.In each bin, all spectra of all exposures where combined witha sigma clipping algorithm to remove any remaining cosmicrays. Velocity and velocity-dispersion profiles were computedusing the pPXF method applied to the binned spectra. The ve-locity map in Figure 7 shows the dynamics in the cluster center.A rotation-like or a shearing signature is visible, but it seemsto be a very local phenomenon (within 3 ′′ , .
15 pc). In earlierattempts, we split the pointing in two halves (tilted line in fig-ure 7) in order check for consistency and symmetry on bothsides. The velocity dispersion was then derived separately forthe binned spectra on each side. Both sides show a rise in thevelocity-dispersion profile but di ff er in their shape and absolutevalues from each other. However, treating both sides separatelywould not properly take into account a possible rotation at thecenter and therefore not exactly represent the observed data. Wedecided to use the total radial profile over the 360 degree binsand measure the second moment V RMS = q V + σ , with the rotation velocity V rot and the velocity dispersion σ . The reasonwhy we chose to analyze V RMS instead of σ is twofold. First, theJeans models require the V RMS rather than the pure velocity dis-persion as an input. Second, the broadening of the line we mea-sured represents V
RMS and not σ . The velocity dispersion can beobtained by subtracting the rotation velocity from this quantity.Determining the rotation is di ffi cult due to the large shot noiseintroduced by the small number of spatial elements in the cen-tral region. The second moment, however, is robustly measuredsince we average over all angles. For simplicity we refer to theV RMS profile as the velocity-dispersion profile in our study.In addition to the central pointings, we derived kinematicsfor regions further out using the small IFU measurements, whichwere scattered at larger radii around the cluster. Unfortunately,the surface brightness of the cluster drops quickly with radiusresulting in a low signal-to-noise ratio for the IFUs most distantfrom the center. These could therefore not be used for furtheranalysis. Only the two innermost positions showed reasonablesignal, so that these two pointings could be used as two separateddata points at 11 ′′ and 18 ′′ radius, respectively. The disadvantageof the small IFU fields (20 spaxels for a total field-of-view of3 ′′ × ′′ ) is that these values are very a ff ected by shot noise sinceonly a few stars fall into the small field-of-view. Consequently,these points show larger errors than the rest of the profile.Further, we estimated the radial velocity of the cluster inthe heliocentric reference frame. We combined all spectra in thepointing and measured the velocity relative to the velocity of thetemplate. This value was then corrected for the motion of thetemplate and the heliocentric velocity and results in a value ofV r = (80 . ± .
5) km s − which is in good agreement with thevalue from Harris (1996) V r = (81 . ± .
2) km s − .We ran Monte Carlo simulations to estimate the error onV RMS due to shot noise. From the routine described in section4.2, we knew exactly how many stars are contributing ( nStars )and how many spaxels are summed ( nSpax ) in each bin. We tookall stars detected in each bin and their corresponding magnitude.Each of the stars was then assigned a velocity chosen from aGaussian velocity distribution with a fixed dispersion. We usedour template spectrum and created nSpax spaxel by averaging nStars flux weighted and velocity shifted spectra. The result-ing spaxels were then normalized, combined and the kinematicsmeasured with pPXF (as for the original data). After 1000 real-izations for each bin, we obtained the shot noise errors from thespread of the measured velocity dispersions. For the outer IFUpointings, we extrapolated the surface density to larger radii andperformed the same Monte Carlo simulations as for the innerpointing, with random magnitudes drawn from the magnitudedistribution in this region. The errors for the velocity and thehigher moments were derived by applying Monte Carlo simula-tions to the spectrum itself. This was done by repeating the mea-surement for 100 di ff erent realizations of data by adding noise tothe original spectra. (see Cappellari & Emsellem 2004, section3.4)The resulting profile is displayed in Figure 8. The plot showsthe second moment of the velocity distribution V RMS . Except forthe innermost point, a clear rise of the profile towards the centeris visible. The highest point reaches more than 25 km s − beforeit drops quickly below 20 km s − at larger radii. In table 3 we listthe results of the kinematic measurements. The first column liststhe radii of the bins. The following columns show the centralvelocities of each bin in the reference frame of the cluster, thesecond moment V RMS as well as higher velocity moments h3 andh4. It is conspicuous that all h4 moments tend to have negative . L¨utzgendorf et al.: Kinematic signature of an intermediate-mass black hole in the globular cluster NGC 6388. 9 values. This hints at a lack of radial orbits in the central regionof the globular cluster.For general purposes we also determined the e ff ective veloc-ity dispersion σ e as described in G¨ultekin et al. (2009). This isdefined by: σ e = R R e V I(r) dr R R e I ( r ) dr (4)Where R e stands for the half light radius ( ∼ ′′ ) and I ( r ) thesurface brightness profile. We extrapolated our kinematic data tothe half light radius since our furthest out data point only reachesa radius of 18 ′′ . This results in an e ff ective velocity dispersion of σ e = (18 . ± .
3) km s − which is in perfect agreement with thevalue derived by Pryor & Meylan (1993) listed in table 1.
5. Dynamical models
The main goal of this work is to compare the derived kinematicsand light profile with a set of simple analytical models in orderto test whether NGC 6388 is likely to host an intermediate-massblack hole in its center. We used Jeans models as implementedand described in Cappellari (2008).
The first input for the Jeans models is the surface brightness pro-file in order to estimate the 3-D density distribution in the clus-ter. Given the fact that the density can only be observed in a pro-jected way, the profiles have to be deprojected. One way of doingthis is by applying the multi-Gaussian expansion (MGE) methoddeveloped by Emsellem et al. (1994). The basic approach of thismethod is to parametrize the projected surface brightness with asum of Gaussians since the deprojection of a Gaussian functionresults again in a Gaussian.To apply this parametrization and to compare results of theJeans equation to our data, we used the Jeans Anisotropic MGE(JAM) dynamical models for stellar kinematics of spherical andaxisymmetric galaxies, as well as the multi-Gaussian expansionimplementation developed by Cappellari (2002, 2008). The IDLroutines provided by M. Cappellari enable the modeling of thesurface brightness profile and fitting the observed velocity dataand the mass-to-light ratio at the same time. We used our surfacebrightness profile in combination with a spherical model withdi ff erent values of anisotropy and constant M / L V setups alongthe radius of the cluster.In Figure 8, we plot the isotropic model data comparison forour velocity-dispersion profile. The JAM program does not ac-tually fit the model to the data but rather calculates the shape ofthe second moment curve from the surface brightness profile, de-convolves the profile with the PSF of the IFU observations, andthen scales it to an average value of the kinematic data in orderto derive the M / L V . This explains why all trial models meet inone point. The thick black line marks the model with the lowest χ value and therefore the best fit.With the given surface brightness profile and without a cen-tral black hole, the models predict a drop in velocity disper-sion towards the central region. As a final result, we used the χ statistics of the fit to estimate an error. This results in: M • = (18 ± × M ⊙ and M / L V = (1 . ± . M ⊙ / L ⊙ . Figure 9 shows Available at http: // purl.org / cappellari / idl the contour plot of χ as a function of black-hole mass and mass-to-light ratio over a grid of isotropic models (black points). Thecontours represent ∆ χ = . , . , . . , ,
95 and 99 percent for 1 degree of free-dom (marginalized). This implies that for an isotropic model andthis specific surface brightness profile the models predict a blackhole of at least M • = × M ⊙ with a confidence of 99 percent.We also tested whether anisotropic Jeans models would re-sult in a significantly better fit. To do this, we repeated the modelfitting with β , χ for a ris-ing β down to χ = .
21 for β = . M • = . × M ⊙ . However, this requires a very highanisotropy of β = − V θ / V = . In section 2.3 we introduced the di ff erent surface brightness pro-files for NGC 6388. The Trager et al. (1995) profile contains themost data points and extends to large radii ( ∼ ′ ). However, theinner regions (important for our dynamical purposes) are not aswell sampled by the ground based observations used by Trageret al. The profile by NG06 was derived by measuring integratedlight on a WFPC2 image using a bi-weight estimator and coversthe inner regions of the cluster very well. To calibrate the profilesto the correct absolute values NG06 also adjusted it to the Trageret al. profile. The third profile was obtained by Lanzoni et al.(2007) by computing the average of the counts per pixel in eachbin of their ACS / HRC images. Since it was not clear in the pa-per how they calibrated their photometry, this profile was alsoshifted (by a small amount of 0 .
09 mag) to overlap with theTrager et al. profile. As a test, we used each of these profilesas an input for the Jeans models and found similar black-holemasses varying from M • = (25 ± × M ⊙ for the Trager et al.(1995) profile to M • = (11 ± × M ⊙ for the Lanzoni et al.(2007) data. The result from the profile provided by NG06 isidentical to the fit of our profile in black-hole mass and slightlylower in the mass-to-light ratio ( M / L V = (1 . ± . M ⊙ / L ⊙ ).Again we find the lowest χ value (and therefore the best fit)for an anisotropic model of β = .
5. In this case the observationscan be explained without any black hole for all profiles. As men-tioned in the previous section this rather unlikely configurationwill be discussed in more detail in the next subsection.From our studies of the surface brightness profiles, we seethat they yield similar, but not identical results. The shape ofthe SB profile predicts the shape of the velocity-dispersion pro-file. Therefore, it is crucial to test the e ff ect of variation of thesurface brightness profile in the inner regions. To perform this,we run Monte Carlo simulations on the six innermost pointsof the profile. We used 1000 runs and a range of β between − . .
5. The results are displayed in figure 10. The blackpoints mark the mean value of the derived black-hole masses.The shaded contours represent the 68 ,
90 and 95 percent confi-dence limits. The mean black-hole mass decreases at higher β values since a radial anisotropy can mimic the e ff ect of a cen-tral black hole. Nevertheless, for an isotropic case, we have ablack hole detection within a mass range of 17 + − × M ⊙ anda global mass-to-light ratio of M / L V = . + . − . M ⊙ / L ⊙ (errorsare the 68 percent confidence limits). We derived the total error(resulting from kinematic and photometric data) by again, run-ning Monte Carlo simulations and varying both, the velocity- V R M S ( k m / s ) M BH = 0 M BH = 44 x 10 M SUN BH ( 10 M SUN )510152025 χ Fig. 8. Di ff erent isotropic ( β = / L is fitted to the databy scaling the profile to the data points. The final values are obtained by finding the minimum of χ while varying the black-holemass: β = . , M BH = . × M ⊙ , M / L V = . , χ min = .
89. The plot on the left panel shows the models together with thedata and the best fit. Labeled are also the black holes masses of the two enclosing models. The solid black line marks the best fit.The right panel shows the χ values of every model as well as the ∆ χ = BH (10 M SUN )1.01.21.41.61.82.02.22.4 M / L Fig. 9.
The contours of the χ as a function of black-holemass and mass-to-light ratio. Each point represents a particu-lar isotropic model. The plotted contours are ∆ χ = . , . , . . , ,
95 and 99 percent.dispersion profile and the surface brightness profile at the sametime. As a final result for the uncertainties of our method we de-rived δ M • = × M ⊙ , δ M / L V = . M ⊙ / L ⊙ . This shows,that a significant percentage of the error ( ∼ In the previous sections we have shown, that the strong signif-icance for a black hole with isotropic models vanishes whenusing anisotropic models. The anisotropic Jeans models showa better fit for a model with much lower black-hole masses orwithout a black hole requiring an anisotropy of β = . β = . ff erent col-ors represent di ff erent areas in the cluster. Important for ourcase are the kinematics inside the half-light radius (curves with <
50% light / mass enclosed in figure 11). The system relaxesvery quickly in the central regions. After six relaxation times theinner regions of the cluster are almost isotropic with β valuesbelow 0 .
2. The relaxation time of NGC 6388 is of order 10 yrs (at the half-mass radius, Harris 1996) which implies that thecluster is about 10 relaxation times old. This shows, that highanisotropies (such as the the ones needed from our best fit mod-els) in NGC 6388 are not stable and would have vanished over ashort time scale. Therefore, we limit our discussion to the resultsfrom our isotropic models. In our analysis we used the assumption of a constant M / L V forthe entire cluster. In reality, this ratio can vary with radius andit may not be well described with a single value if the clusteris mass segregated. The rise in the velocity-dispersion profilecould then be mimicked by a dark remnant cluster at the center.Such a scenario is expected in core collapsed clusters which dis-play surface brightness profiles with logarithmic slopes of -0.8or higher (Baumgardt et al. 2005). We looked at the deprojectedlight-density and mass-density profiles resulting from the sur-face brightness profile and the velocity-dispersion profile. Themass-density profile from the kinematics drops with ∝ r − which . L¨utzgendorf et al.: Kinematic signature of an intermediate-mass black hole in the globular cluster NGC 6388. 11 -0.4 -0.2 0.0 0.2 0.4 β M B H [ M S U N ] Fig. 10.
The result of the Monte Carlo simulations of the surfacebrightness profile. For each fixed β value 1000 realizations of thelight profile have been performed. The black dots mark the av-erage value of the best fit black-hole mass. The shaded contoursrepresent the 68 ,
90 and 95 percent confidence limits. β < 10%20% - 30%40% - 50%60% - 70%80% - 90% Fig. 11.
The anisotropy β as a function of time for di ff erent re-gions in the cluster. The di ff erent colors represent di ff erent per-centages of the cluster total light / mass going from the innerpart of less than 10% to the outskirts of the cluster with 90%light / mass enclosed.would be expected from a core collapsed cluster. But the lightprofile is shallow and does not support that hypotheses: witha concentration of c = . α = − . ± .
08 NGC 6388 does notshow any signs of core collapse in the distribution of the visiblestars. We compared these profiles with simulated core collapsedor mass segregated clusters (described in Baumgardt & Makino2003) and were not able to find a good agreement with eithershape of the light profile or slope of the mass density of the clus-ter. We currently consider the presence of a dark remnant clusterunlikely but we will perform detailed n-body simulations with avariable M / L in the near future.
6. Summary and conclusions
We derived the mass of a potential intermediate-mass black holeat the center of the globular cluster NGC 6388 by analyzingspectroscopic and photometric data. With a set of HST images,the photometric center of the cluster was redetermined and theresult of NG06 confirmed. Furthermore, a color magnitude dia-gram as well as a surface brightness profile, built from a com-bination of star counts and integrated light, were produced. Thespectra from the ground-based integral-field unit ARGUS werereduced and analyzed in order to create a velocity map and avelocity-dispersion profile. In the velocity map, we found sig-natures of rotation or at least complex dynamics in the innerthree arcseconds (0.15 pc) of the cluster. We derived a velocity-dispersion profile by summing all spectra into radial bins andapplying a penalized pixel fitting method.Using the surface brightness profile as an input for spheri-cal Jeans equations, a model velocity-dispersion profile was ob-tained. We ran several isotropic models with di ff erent black-holemasses and scaled them to the observed data in order to measurethe mass-to-light ratio. Using χ statistics, we were able to findthe model which fits the observed data best. We run Monte Carlosimulations on the inner points of the surface brightness profilein order to estimate the errors resulting from the particular choiceof a light profile. From this, we determined the black-hole massand the mass-to-light ratio as well as the scatter of these two re-sults. The final results, with 68% confidence limits are: A black-hole mass of (17 ± × M ⊙ and a global mass-to-light ratio of M / L V = (1 . ± . M ⊙ / L ⊙ . In addition, we run anisotropic mod-els. The confidence of black hole detection is decreasing rapidlywith increasing radial anisotropy. However, using N-body simu-lations, we found that in a relaxed cluster such as NGC 6388 ananisotropy higher than β = . . × M ⊙ by Lanzoni et al. (2007), which they derived from photometryalone, our derived black-hole mass is larger by a factor of threewith our surface brightness profile profile. Using their light pro-file, we obtained a black-hole mass of M • = (11 ± × M ⊙ which includes their value within one sigma error. Cseh et al.(2010) obtained deep radio observations of the inner regionsof NGC 6388 and discussed di ff erent accretion scenarios for apossible black hole. They found an upper limit for the black-hole mass of ∼ M ⊙ since no radio source was detected atthe location of any Chandra X-ray sources. However, insertingour black-hole mass in equation 5 of Cseh et al. (2010) and us-ing their assumptions as well as the Chandra X-ray luminosityof the central region, results in minimal but possible accretionrates and conversion e ffi ciency ( εη ∼ − ). Considering the factthat supermassive black holes have masses not much higher than0 . .
9% seems to be higherthan the predictions for larger systems. Globular clusters in con-trast lose much of their mass during their evolution. This couldnaturally result in higher values of black-hole mass - host systemmass ratios. Due to the complicated dynamics, the 1 σ uncertain-ties are 40 % for our black-hole mass and 10 % for the derived M / L V . Figure 12 shows the position of NGC 6388 in the black-hole mass velocity dispersion relation. With our derived e ff ec-tive velocity dispersion of σ e = (18 . ± .
3) km s − the resultsfor NGC 6388 seem to coincide with the prediction made by the M • − σ relation.The mass-to-light ratio of M / L V = (1 . ± . M ⊙ / L ⊙ derivedin this work is consistent within the error bars with the dynami- cal results of McLaughlin & van der Marel (2005, M / L V ∼ . M / L V = (2 . ± . M ⊙ / L ⊙ for[Fe / H] = − . ±
2) Gyr. Baumgardt & Makino(2003) have shown that dynamical evolution of star clusterscauses a depletion of low-mass stars from the cluster. Sincethese contribute little light, the M / L V value drops as the clus-ter evolves. Dynamical evolution could therefore explain part ofthe discrepancy between theoretical and observed M / L V values.Summarizing, it can be said that the globular cluster NGC6388 shows a variety of interesting features in its photomet-ric properties (e.g. the extended horizontal branch) as well asin its kinematic properties (e.g. the high central velocity dis-persion or the rotation like signature in the velocity map). Inthis work we investigated the possibility of the existence of anintermediate-mass black hole at the center. With simple ana-lytical models we were already able to reproduce the shape ofthe observed velocity-dispersion profile very well if the clus-ter hosts an IMBH. Future work would be to compute detailedN-body simulations of NGC 6388 in order to verify whether adark cluster of remnants at the center would be an alternative.Additionally, it is crucial to obtain kinematic data at larger radiito constrain the mass-to-light ratio and the models further out.Also proper motions for the central regions would further con-strain the black hole hypothesis.The study of black holes in globular clusters is currently lim-ited to a handful of studies. For this reason, it is necessary toprobe a large sample of globular clusters for central massive ob-jects in order to move the field of IMBHs from “whether” to “un-der which circumstances do” globular clusters host them. Thustying this field to the one of nuclear clusters and super-massiveblack holes. From the experience we gathered with NGC 6388,we can say that the dynamics of globular clusters is not as simpleas commonly assumed and by searching for intermediate-massblack holes, we will also be able to get a deeper insight into thedynamics of globular clusters in general. Acknowledgements.
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Fig. 12.