Prospects for detection of intermediate-mass black holes in globular clusters using integrated-light spectroscopy
Ruggero de Vita, Michele Trenti, Paolo Bianchini, Abbas Askar, Mirek Giersz, Glenn van de Ven
MMNRAS , 1–10 (2016) Preprint 20 September 2018 Compiled using MNRAS L A TEX style file v3.0
Prospects for detection of intermediate-mass black holes inglobular clusters using integrated-light spectroscopy
R. de Vita, (cid:63) M. Trenti, P. Bianchini, A. Askar, M. Giersz, G. van de Ven The University of Melbourne, School of Physics, VIC 3010, Australia Max-Planck Institute for Astronomy, Koenigstuhl 17, 69117 Heidelberg, Germany Nicolaus Copernicus Astronomical Centre, Polish Academy of Sciences, ul. Bartycka 18, 00-716 Warsaw, Poland
Accepted 2017 February 3. Received 2017 January 30; in original form 2016 October 14
ABSTRACT
The detection of intermediate mass black holes (IMBHs) in Galactic globular clus-ters (GCs) has so far been controversial. In order to characterize the effectiveness ofintegrated-light spectroscopy through integral field units, we analyze realistic mockdata generated from state-of-the-art Monte Carlo simulations of GCs with a centralIMBH, considering different setups and conditions varying IMBH mass, cluster dis-tance, and accuracy in determination of the center. The mock observations are modeledwith isotropic Jeans models to assess the success rate in identifying the IMBH pres-ence, which we find to be primarily dependent on IMBH mass. However, even for aIMBH of considerable mass (3% of the total GC mass), the analysis does not yieldconclusive results in 1 out of 5 cases, because of shot noise due to bright stars closeto the IMBH line-of-sight. This stochastic variability in the modeling outcome growswith decreasing BH mass, with approximately 3 failures out of 4 for IMBHs with 0.1%of total GC mass. Finally, we find that our analysis is generally unable to excludeat 68% confidence an IMBH with mass of 10 M (cid:12) in snapshots without a centralBH. Interestingly, our results are not sensitive to GC distance within 5-20 kpc, nor tomis-identification of the GC center by less than 2 (cid:48)(cid:48) ( <
20% of the core radius). Thesefindings highlight the value of ground-based integral field spectroscopy for large GCsurveys, where systematic failures can be accounted for, but stress the importanceof discrete kinematic measurements that are less affected by stochasticity induced bybright stars.
Key words: globular clusters: general - stars: kinematics and dynamics - black holephysics - instrumentation: spectrographs
The existence of intermediate mass black holes (IMBHs)with masses between few M (cid:12) (stellar black holes of ≈ M (cid:12) ) and billions of M (cid:12) (supermassive black holes of ≈ M (cid:12) ) is of particular interest, especially in the con-text of the formation and evolution of galaxies and densestellar systems such as globular clusters (GCs). The natu-ral extension of the well-known M − σ relation for galaxiessuggests that the typical central velocity dispersions in GCsmight be associated to the presence of IMBHs with massesof 10 − M (cid:12) (see, e.g., Ferrarese & Merritt 2000, Gebhardtet al. 2000). To support this extrapolation, several scenariosfor the formation of such objects have been proposed, includ-ing run-away collapse of massive stars (Portegies Zwart et al.2004), early-time accretion of ejecta from asymptotic giant (cid:63) E-mail: [email protected] branch stars in the context of multiple stellar populationformation (Vesperini et al. 2010), dynamical interactions ofhard binaries (Giersz et al. 2015), or possibly seeding frommassive Population III stars if the oldest globular clustersform during the epoch of reionization at redshift z ∼ − c (cid:13) a r X i v : . [ a s t r o - ph . GA ] F e b R. de Vita et al. but measurements are very challenging because the sphereof influence of the BH is limited to a few arcsec, even forthe closest and most massive GCs such as ω Cen (see Noy-ola et al. 2010; van der Marel & Anderson 2010). Finally,the fact that these events are expected to be also sources ofgravitational radiation promotes the interferometers such asadvanced-LIGO as further instruments to search for IMBHs(see, e.g., Mandel et al. 2008, Konstantinidis et al. 2013,MacLeod et al. 2016).A complementary tool to approach the problem is thatof identifying novel dynamical signatures for the presence ofIMBH in globular clusters based on numerical modeling ofglobular cluster dynamics in presence of an IMBH. Startingfrom initial direct N-body simulations more than a decadeago (Baumgardt et al. 2004a,b; Trenti et al. 2007), simula-tions have progressed significantly, and are now approachingrealistic particle numbers with direct integration algorithmsthat include post-newtonian corrections (e.g. MacLeod et al.2016; Wang et al. 2016), and routinely include more thanone million particles through Monte Carlo methods (Gierszet al. 2015; see also Rodriguez et al. 2015). These inves-tigations have shown that a central massive black hole isexpected to induce the formation of a shallow cusp in theprojected surface brightness and to prevent the core collapseby enhancing three-body interactions within its sphere of in-fluence (see, e.g, Baumgardt et al. 2005). In addition, it hasbeen shown that the IMBH is able to quench the process ofmass segregation (see e.g., Gill et al. 2008, Pasquato et al.2009, Pasquato et al. 2016). However, one important caveatis that these signatures may be only necessary but not suf-ficient conditions to infer the presence of an IMBH, becauseother dynamical processes could mimic them (see, e.g., Hur-ley 2007; Trenti et al. 2010; Vesperini & Trenti 2010).Recently, the majority of the observational claims aboutthe presence of IMBHs comes from kinematic measurementsin the inner core of Galactic GCs. Kinematic observationssuggesting the presence of IMBHs are traditionally based onthe search for a rise of the central velocity dispersion. Thismethod requires both high spatial resolution, to resolve thevery crowded central region of GCs (few central arcseconds),and very precise velocity measurements with accuracy ≈ − .So far, the available observations of the central regionsof Galactic GCs have led to contradictory results when ap-plied to the same object in a few instances (e.g., Noyolaet al. 2010, van der Marel & Anderson 2010, L¨utzgendorfet al. 2013, Lanzoni et al. 2013, L¨utzgendorf et al. 2015).In general, two different strategies are used in order to inferthe presence of IMBHs: resolving individual star velocities(line-of-sight velocities or proper motions) or using unre-solved kinematic measurements, for example with integralfield unit (IFU) spectroscopy. Both these methods suffertechnical difficulties in obtaining the critically needed kine-matic measurements in the very center of the system (e.g.,the problem of shot-noise for integrated-light measurementsand the effects of crowding for line-of-sight velocities andproper motions). In particular, integrated-light spectroscopytends to detect rising central velocity dispersions, suggest-ing the presence of IMBHs (see for example, Noyola et al.2010 for ω Cen, or L¨utzgendorf et al. 2011 for NGC 6388),while resolved stellar kinematics are consistent with a flatvelocity dispersion profile, that is no massive black hole (see van der Marel & Anderson 2010 for proper motion measure-ments of ω Cen, and Lanzoni et al. 2013 for discrete line-of-sight measurements in NGC 6388). However, in a few othercases where both discrete and integrated-light profiles areavailable for the inner 10 (cid:48)(cid:48) , the observational methods agree(e.g., see NGC 2808, NGC 6266, NGC 1851 in L¨utzgendorfet al. 2013).For both unresolved and resolved kinematics, the con-straints on the IMBH mass are generally determined by fit-ting the observed velocity dispersion profiles with differentfamilies of Jeans models (e.g, van der Marel & Anderson2010). These models are typically constructed by making as-sumptions on the mass-to-light ratio profile
M/L ( r ) in orderto calculate the intrinsic mass distribution of the luminouscomponent from the surface brightness profile. The veloc-ity dispersion profile is then calculated by solving the Jeansequation for hydrostatic equilibrium in a spherical stellarsystem (see e.g., Bertin 2014). Besides the Jeans modeling,other analysis techniques used include the Schwarzschild’sorbit superposition method used in van de Ven et al. 2006or a method in which the fit of the observed velocity disper-sion profiles is performed using a grid of N-body simulations(see e.g., Jalali et al. 2012; Baumgardt 2017).The main goal of this work is to characterize underwhich conditions (IMBH mass, GC distance, accuracy in thedetermination of the center) the integrated-light IFU dataare able to measure accurately the mass of the IMBH, asinferred from realistic mock observations of simulated starclusters with a central IMBH. By means of the softwareSISCO developed by Bianchini et al. 2015, we are able tocreate mock IFU observations of the central regions of GCs.The set of observations is produced starting from a set ofMonte Carlo cluster simulations (MOCCA simulations byGiersz et al. 2015; Askar et al. 2017a; see also Askar et al.2017b, for a similar application of SISCO to MOCCA simu-lations) that include a range of different IMBH masses (from0 to 10 M (cid:12) ). In order to quantify the significance of a cen-tral rise in the simulated velocity dispersion profiles, we fitthese profiles with a one-parameter family of isotropic Jeansmodels. In this way, we are able to estimate quantitativelyand objectively the IMBH mass and, thus, to directly testthe ability of the observations to successfully recover themass of the central black hole.The paper is organised as follows. In Sect.2 we presentthe set of simulations used and we briefly describe the SISCOcode used to produce the mock IFU observations. Moreover,we describe the dynamical models used to fit the observedprofiles. In Sect.3 we present the results of our analysis andin Sect.4 we give our conclusions. In this work we resort to Monte Carlo simulations of GCsthat include the presence of a central IMBH. These simula-tions are part of about 2000 GC models run in the frameworkof the MOCCA SURVEY I project (see Askar et al. 2017afor a description of the Survey). The IMBH in the simulatedclusters is formed dynamically from stellar-mass BH seedsas a result of dynamical interactions and mergers in binaries.
MNRAS000
MNRAS000 , 1–10 (2016) etection of IMBHs in GCs using integrated-light spectroscopy All models have a stellar initial mass function (IMF)given by Kroupa (2001) with minimum and maximum stel-lar masses taken to be 0 . M (cid:12) and 100 M (cid:12) , respectively.Supernovae (SN) natal kick velocities for neutron stars andBHs were drawn from a Maxwellian distribution with a dis-persion of 265 km/s (Hobbs et al. 2005). For most models,natal kicks for BHs were modified according to the massfallback procedure described by Belczynski et al. (2002). Tomodel the Galactic potential, a point mass approximationwith the Galaxy mass equal to the mass enclosed inside thecluster Galactocentric distance is assumed. Additionally, it isalso assumed that all clusters have the same rotation veloc-ity, equal to 220 km/s. So, depending on the cluster mass andtidal radius the Galactocentric distances span from about 1kpc to about 50 kpc.Here, we selected a subsample of MOCCA runs for anal-ysis, and report in Table 1 the key properties at time t = 12Gyr. In addition to this snapshot, we also consider threeadditional snapshots at 11.7, 11.8, 11.9 Gyr to assess the ro-bustness of our conclusions against variance introduced bya different dynamical state of a system of otherwise similarglobal properties. The software SISCO (Simulating Stellar Cluster Observa-tion) produces a mock IFU data cube starting from a sim-ulated star cluster (for a detailed description see Bianchiniet al. 2015). The software derives a medium-high resolutionspectrum ( R ≈ ×
20 arcsec and the spaxel scaleto 0 .
25 arcsec; we adopt a Moffat shape for the point spreadfunction with seeing condition of 1 arcsec and shape param-eter β = 2 .
5. Finally, we mimic an observation with an aver-age signal-to-noise ratio of
S/N (cid:39)
10 per ˚A (for a discussionon the fixed values of the parameters used in our mock ob-servations, see Bianchini et al. 2015). In order to simulatedifferent observing conditions, we change three parameters:the distance to the cluster, the direction of its projectionin the sky, and optionally introduce an off-set between thecentre of the simulated IFU field and the centre of the clus-ter, to reflect the uncertainty in determining the centre ofan observed GC. The final output of the code is a three-dimensional data cube in which each spatial pixel has anassigned spectrum.
In order to mimic real observation as closely as possible,we construct the observed velocity dispersion profile by in-tegrating our mock IFU data available for the region insidethe FOV, and combine it with a line-of-sight velocity disper-sion obtained for the outer parts of the system. The outerprofile is obtained directly from the simulation by using only the velocities of the red giant stars, which are those gener-ally used for resolved kinematics from the ground. For thisanalysis, we treat the binary stars as single objects with thevelocity of their center of mass. For the inner profile, oncethe IFU data cube is simulated through SISCO, we dividethe FOV in radial bins, summing the spectra in each bin,with the aim of interpreting the data cube through a spheri-cal dynamical model. The binned spectra are analysed withthe pPXF code (Cappellari & Emsellem 2004) to derive thevelocity dispersion (and the corresponding error) from linebroadening.As highlighted in Bianchini et al. (2015), whenintegrated-light measurements are used, the presence of afew bright stars can introduce systematic effects in the re-construction of the observed velocity dispersion profile. Forthis reason, we introduced masking of the brightest sources.Specifically, we exclude from the analysis the spaxels inwhich the contribution of a single stars exceeds the 60%of the total luminosity (we adopt the same percentage usedin L¨utzgendorf et al. 2013). This information is provided di-rectly by the simulation, thus, from an observational pointof view, we are considering an ideal case scenario. In Fig. 1we show the luminosity map (left panel) and the radial ve-locity dispersion profile (right panel) for the central region ofsimulation S0 at a distance of 10 kpc. The velocity disper-sion profile constructed from the simulation (blue circles)is obtained by considering objects with mass in the range0 . − M (cid:12) to mimic the average (luminosity weighted) massin the FOV and by using the barycentre line of sight veloci-ties for the binary stars to avoid great scatter in the profile(the binning must be fine in order to sample the central re-gion). The velocity dispersion profile obtained by maskingthe IFU data over the regions shown as green diamonds isconsistent with that constructed directly from the simula-tion. Without the masking, there is an evident discrepancyin the range 4 − > (cid:48)(cid:48) . This effect is possibly due to thepresence of hard binaries which may influence the velocitydispersion determination. Indeed, the observed velocity as-sociated to a binary system could largely exceed the meanfield velocity because of the high-speed orbital motions. Thiseffect is merely an observational feature associated to line-of-sight velocity dispersion measurements, and in principleit could be accounted for if proper-motion kinematic is avail-able (see e.g., Bianchini et al. 2016b), or through theoreticalmodeling of the binary population, both in energy and posi-tion space. However, this investigation is beyond the scopeof the present paper and we limit our analysis to include theeffects of the population of binaries into the construction ofour mock observations.Finally, we produced different realisations of the samesimulation to test the intrinsic scatter of the velocity dis-persion profile. In particular, we changed the direction ofthe line-of-sight for the mock observation of the cluster S0under canonical conditions (that is, at 10 kpc and with theFOV pointing to the centre). For three different projectionsof the simulated cluster we obtained a velocity dispersion MNRAS , 1–10 (2016)
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Table 1.
Set of MOCCA simulations, labeled S0-S5, used in this paper and taken from MOCCA-SURVEY Database I Askar et al.(2017a). For each simulation we report the quantities relative to the snapshot at 12 Gyr: number of stars N ; total mass M and IMBHmass m • (solar units); binary fraction f b ; projected truncation radius R t , projected core radius R c (from the surface brightness profile),projected half-light radius R h and intrinsic radius for the IMBH sphere of influence r • (pc); concentration parameter C = log( R t /R c ).S0 S1 S2 S3 S4 S5 N . × . × . × . × . × . × M . × . × . × . × . × . × m • . × . × . × . × . × - f b
7% 8% 4% 5% 5% 3.6% R t R c R h r • C − − − − − X[arcsec] − − − − − Y [ a r cs e c ] l u m [ L (cid:12) ] σ p [ k m / s ] simulationno maskingmasking 60% Figure 1.
Left panel: luminosity map of the simulated cluster S0 observed at a distance of 10 kpc with a FOV around the centre ofthe cluster. The masked spaxels are indicated with the ‘x’ symbols.
Right panel:
Central velocity dispersion profiles for the same cluster.The blue circles show the profile measured directly from the MOCCA simulation considering objects with masses between 0 . M (cid:12) and1 M (cid:12) and using the barycentre velocity for binary systems. The profile inferred from analysis of the mock IFU data cube is plotted inred squares without masking, and in green diamonds with the bright-object masking procedure discussed in the text. profile for which the scatter is uniform along the entire pro-file and it does not exceed the 30% of the central value (seeFig. 2). Especially for the outer points, where the signal isstronger, the intrinsic scatter is much larger than the errorscalculated by the pPXF software from line broadening. Forthis reason, for the rest of our analysis, we will consider anerror δσ for all the points in the observed profile calculatedby considering the error δσ obtained by pPXF for the in-nermost point. In particular, the error for any outer pointis given by δσ = δσ ( σ/σ ), where σ and σ are the veloc-ity dispersions of the innermost point and the outer point,respectively. As usually done in the literature, we fit the velocity disper-sion profile derived from the mock observations with a familyof dynamical models in which the IMBH mass is treated as afree parameter. We place ourself under the ideal conditions of assuming a perfect knowledge of the spherically symmetricdistribution of the stellar particles. Thus, we adopt a spheri-cal and isotropic Jeans model in which the total gravitationalpotential of the system, Φ( r ), is given by the sum of the stel-lar/remnant contribution Φ ∗ ( r ) and the IMBH contributionΦ • ( r ) = − m • /r (we fixed the gravitational constant G=1).The mass distribution of stars and remnants is directly in-ferred from the simulation. The density ρ at each radius r is estimated using spherical cells, by dividing the total mass(including the IMBH in the innermost cell) of the particlesby the shell volume. The radial profile ( d Φ ∗ /dr )( r ) followsfrom the Gauss theorem as d Φ ∗ dr ( r ) = M ( < r ) r , (1) Note that this approach is different from what usually done inreal observations, for which the inferred mass distribution can beaffected by observational biases or specific assumptions on themass-to-light ratio profile. MNRAS000
Central velocity dispersion profiles for the same cluster.The blue circles show the profile measured directly from the MOCCA simulation considering objects with masses between 0 . M (cid:12) and1 M (cid:12) and using the barycentre velocity for binary systems. The profile inferred from analysis of the mock IFU data cube is plotted inred squares without masking, and in green diamonds with the bright-object masking procedure discussed in the text. profile for which the scatter is uniform along the entire pro-file and it does not exceed the 30% of the central value (seeFig. 2). Especially for the outer points, where the signal isstronger, the intrinsic scatter is much larger than the errorscalculated by the pPXF software from line broadening. Forthis reason, for the rest of our analysis, we will consider anerror δσ for all the points in the observed profile calculatedby considering the error δσ obtained by pPXF for the in-nermost point. In particular, the error for any outer pointis given by δσ = δσ ( σ/σ ), where σ and σ are the veloc-ity dispersions of the innermost point and the outer point,respectively. As usually done in the literature, we fit the velocity disper-sion profile derived from the mock observations with a familyof dynamical models in which the IMBH mass is treated as afree parameter. We place ourself under the ideal conditions of assuming a perfect knowledge of the spherically symmetricdistribution of the stellar particles. Thus, we adopt a spheri-cal and isotropic Jeans model in which the total gravitationalpotential of the system, Φ( r ), is given by the sum of the stel-lar/remnant contribution Φ ∗ ( r ) and the IMBH contributionΦ • ( r ) = − m • /r (we fixed the gravitational constant G=1).The mass distribution of stars and remnants is directly in-ferred from the simulation. The density ρ at each radius r is estimated using spherical cells, by dividing the total mass(including the IMBH in the innermost cell) of the particlesby the shell volume. The radial profile ( d Φ ∗ /dr )( r ) followsfrom the Gauss theorem as d Φ ∗ dr ( r ) = M ( < r ) r , (1) Note that this approach is different from what usually done inreal observations, for which the inferred mass distribution can beaffected by observational biases or specific assumptions on themass-to-light ratio profile. MNRAS000 , 1–10 (2016) etection of IMBHs in GCs using integrated-light spectroscopy σ p [ k m / s ] x losy losz los s c a tt e r Figure 2.
Observed velocity dispersion profiles of the cluster S0at a distance of 10kpc for three different directions of the line-of-sight. The bottom panel shows the scatter in the velocity disper-sion, that is, the difference of the greater and the lower value foreach radial position divided by an average central value for thevelocity dispersion. where M ( < r ) is the stellar and remnants mass (excludingthe central IMBH) contained in the sphere of radius r .We then calculate the intrinsic velocity dispersion pro-file σ ( r ) from the spherical isotropic Jeans equation1 ρ ddr (cid:0) ρσ (cid:1) = − d Φ dr , (2)which has the solution σ ( r ) = 1 ρ ( r ) (cid:90) ∞ r ρ ( r (cid:48) ) d Φ dr ( r (cid:48) ) dr (cid:48) . (3)By defining the first derivative of the gravitational potentialas d Φ dr ( r ) = m • r + η d Φ ∗ dr ( r ) , (4)where η is a constant, the total velocity dispersion in Eq. (3)can be explicitly written as the sum of the IMBH contribu-tion and the stellar/remnant contribution. In this way, fora given mass density profile, the velocity dispersion profiledepends only on the mass m • of the central IMBH and on η , which are free parameters of the model. Note that thesecond parameter η ∼ R [arcsec]10152025 σ p [ k m / s ] log( m • )[ M fl ] -1 r [pc] Figure 3.
Projected velocity dispersion profiles in the centre ofthe cluster of the cluster in simulation S0 considered at a distanceof 10 kpc. The solid lines represent six velocity dispersion profilesderived from different Jeans model obtained by varying the IMBHmass from 10 to 10 . M (cid:12) with a logarithmic separation of 0.25.By increasing the mass, the central peak becomes steeper. Thecircles represent the velocity dispersion profile derived directlyfrom the simulation considering objects with masses between 0 . M (cid:12) . η to the plausible range [0 . , . σ p ( R )obtained by integrating the density-weighted intrinsic profilealong the line-of-sight direction: σ p ( R ) = (cid:34) (cid:82) ∞ R r ( r − R ) − / ρ ( r ) σ ( r ) dr (cid:82) ∞ R r ( r − R ) − / ρ ( r ) dr (cid:35) / . (5)In Fig. 3 we show the dynamical modeling predictionsfor the velocity dispersion profiles obtained by changing themass of the central IMBH for the simulation S0 (we fixed η = 1). As reference, we plot also the velocity dispersionprofile constructed directly from the simulation for object inthe mass range [0 . − . M (cid:12) ], that is the range that includesthe average mass observed in our FOV. It is noteworthy thatthere is good agreement between the inner profile and theJeans model profile with an IMBH of 10 M (cid:12) , which is theactual value for this simulation.To quantify the recovery of the IMBH mass we carry outa maximum likelihood fit by minimizing the two-dimensionalchi-square function χ ( m • , η ) = N (cid:88) i =1 (cid:20) σ obs ( R i ) − σ p ( R i ; m • , η ) δσ ( R i ) (cid:21) , (6)where σ obs ( R i ) are the observed velocity dispersion values(with the error δσ ( R i )) for the N radial bins in which theFOV has been divided (see the previous subsection for aproper description of the error δσ ( R i )). MNRAS , 1–10 (2016)
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In this section we consider the cluster S0 at 12Gyr. This clus-ter is characterized by a central IMBH of 1 . × M (cid:12) whichrepresents ∼
3% of the total mass (and it thus serves as aclear case to test detection in our study under the favourableconditions of a massive central IMBH).At a distance of 10 kpc, a total of 38400 stars fall inthe field of view (see the luminosity map in Fig. 1). The ob-served velocity dispersion profile is constructed by maskingthe IFU data following the procedure described in Sec. 2.3.Then, the chi-square function in Eq. (6) is minimised in thetwo dimensional parameter space, giving a best fit value forthe IMBH mass of 6 . +0 . − . × M (cid:12) and a value for η of1 . +0 . − . (the errors are estimated with 68.3% confidence).In the left panel of Fig. 4 we plot the best fit Jeans model incomparison with the observed velocity dispersion profile. Wealso identify the regions corresponding to confidence levelsof 68.3%, 95.4% and 99% (see Fig. 4, right panel) findingthat the true IMBH mass is higher by a factor ≈ .
25 with3 σ confidence. As described in Sec. 2.1, our set of simulations includessystems with a range of IMBH masses but otherwise sim-ilar properties. By applying the same analysis presented inSec. 3.1 to the different models listed in Table 1, we aim tostudy the fidelity of the IMBH mass measurement as a func-tion of mass itself. Qualitatively, we expect that, at fixed ob-servational setup, the chances of recovering the IMBH masscorrectly increase with mass (since the sphere of influenceand the IMBH contribution to the central velocity dispersionprofile are both larger).In Fig. 5 we show the IMBH mass recovered from thebest fitting Jeans models as a function of the intrinsic IMBHmass. We present the results for each of the 4 snapshots (at11.7, 11.8, 11.9 and 12 Gyr) of the simulations S1-S5 con-sidered at a distance of 10 and 20 kpc (for the simulation S0we considered only the snapshot at 12 Gyr). The results arecolor-coded according to the ability of the models to inferthe presence of an IMBH with 1-sigma confidence. The redopen circles represent the cases in which a solution withoutan IMBH is allowed at 1-sigma (or, for the simulation S5,in which a solution with m • > η . Thus,our analysis may tend to overestimate the contribution of stars (and, subsequently, underestimate the contribution ofthe IMBH) to the central velocity dispersion. By taking intoconsideration this effect in a more refined modeling we wouldexpect the green circles below the reference line to uniformlyshift upwards and, eventually, intercept the true mass. How-ever a more sophisticated treatment of the impact of binarieswould rely on knowledge that is generally not available, norused, in Jean-model analysis of actual observations, ratherthan mock data. Therefore, it would not be appropriate toimplement such modeling to our mock IFU dataset.The expected trend with the IMBH mass is partially re-covered (see Fig. 5). Indeed, from an IMBH of few hundred M (cid:12) to a high mass IMBH of 10 M (cid:12) the successful probabil-ity increases from the 0% to the 80% of the cases consideredat 10kpc. Also, we notice that, even for the high range ofIMBH mass, some observations fail. This confirms how thestochasticity, which affects integrated-light measurements,arises even for a single cluster observed at different dynami-cal times. Finally, for the simulation S5 without the IMBH,all the cases at both distances are consistent with a clusterwith no IMBH, even though the model is in general unableto exclude at 68% confidence a IMBH with mass of 10 M (cid:12) .Besides the dependence on the IMBH mass, we are in-terested in studying how two other parameters can affectthe probability of recovering the IMBH mass. In particular,we want to quantify the importance of identifying the rightcentre for the observation and to explore the dependence onthe distance to the cluster. The identification of the centre in which to carry out theanalysis is fundamental within the typical observational as-sumption of modeling in spherical geometry. In practicalcases, there are two main sources of uncertainty associatedwith the centre. First, it is often challenging to determinethe position of the cluster centre to high accuracy, as illus-trated, for example, by the extensive debate on where thecentre of ω Cen is (see, e.g, Noyola et al. 2010; van derMarel & Anderson 2010). In addition, even when the centreof light (or the kinematic centre) of the system is identifiedwith high-accuracy, there is no guarantee that the BH loca-tion coincides with it, especially in the case of a light IMBH(see e.g., Giersz et al. 2015, Haster et al. 2016).For two snapshots (at 11.7 and 12 Gyr) of the simula-tions S1 (high mass IMBH) and S3 (low mass IMBH), weanalyse FOVs placed at different radial offsets of the centre(the distance to the clusters is fixed at 10 kpc). We considera total of 9 different centres, three for each radial positions0 . (cid:48)(cid:48) , 0 . (cid:48)(cid:48) and 1 . (cid:48)(cid:48) corresponding for both clustersto radial offsets of 5%, 10% and 20% of the core radius (seeFig. 6). In terms of the sphere of influence of the centralIMBH (whose radius r • is defined as the radius at whichthe cumulative mass equals the IMBH mass), the offsets arein the range 0 . − . r • for the simulation S1 and in therange 0 . − . r • for the simulation S3.With the same notation used in the previous subsectionwe show the results of the analysis in Fig. 7. For both theclusters we analyse two different snapshots at 11.7 and 12Gyr. In both cases the probability of detecting an IMBHslightly decreases by increasing the off-set. However, thistrend is deeply influenced by the stochasticity as for a fixed MNRAS000
25 with3 σ confidence. As described in Sec. 2.1, our set of simulations includessystems with a range of IMBH masses but otherwise sim-ilar properties. By applying the same analysis presented inSec. 3.1 to the different models listed in Table 1, we aim tostudy the fidelity of the IMBH mass measurement as a func-tion of mass itself. Qualitatively, we expect that, at fixed ob-servational setup, the chances of recovering the IMBH masscorrectly increase with mass (since the sphere of influenceand the IMBH contribution to the central velocity dispersionprofile are both larger).In Fig. 5 we show the IMBH mass recovered from thebest fitting Jeans models as a function of the intrinsic IMBHmass. We present the results for each of the 4 snapshots (at11.7, 11.8, 11.9 and 12 Gyr) of the simulations S1-S5 con-sidered at a distance of 10 and 20 kpc (for the simulation S0we considered only the snapshot at 12 Gyr). The results arecolor-coded according to the ability of the models to inferthe presence of an IMBH with 1-sigma confidence. The redopen circles represent the cases in which a solution withoutan IMBH is allowed at 1-sigma (or, for the simulation S5,in which a solution with m • > η . Thus,our analysis may tend to overestimate the contribution of stars (and, subsequently, underestimate the contribution ofthe IMBH) to the central velocity dispersion. By taking intoconsideration this effect in a more refined modeling we wouldexpect the green circles below the reference line to uniformlyshift upwards and, eventually, intercept the true mass. How-ever a more sophisticated treatment of the impact of binarieswould rely on knowledge that is generally not available, norused, in Jean-model analysis of actual observations, ratherthan mock data. Therefore, it would not be appropriate toimplement such modeling to our mock IFU dataset.The expected trend with the IMBH mass is partially re-covered (see Fig. 5). Indeed, from an IMBH of few hundred M (cid:12) to a high mass IMBH of 10 M (cid:12) the successful probabil-ity increases from the 0% to the 80% of the cases consideredat 10kpc. Also, we notice that, even for the high range ofIMBH mass, some observations fail. This confirms how thestochasticity, which affects integrated-light measurements,arises even for a single cluster observed at different dynami-cal times. Finally, for the simulation S5 without the IMBH,all the cases at both distances are consistent with a clusterwith no IMBH, even though the model is in general unableto exclude at 68% confidence a IMBH with mass of 10 M (cid:12) .Besides the dependence on the IMBH mass, we are in-terested in studying how two other parameters can affectthe probability of recovering the IMBH mass. In particular,we want to quantify the importance of identifying the rightcentre for the observation and to explore the dependence onthe distance to the cluster. The identification of the centre in which to carry out theanalysis is fundamental within the typical observational as-sumption of modeling in spherical geometry. In practicalcases, there are two main sources of uncertainty associatedwith the centre. First, it is often challenging to determinethe position of the cluster centre to high accuracy, as illus-trated, for example, by the extensive debate on where thecentre of ω Cen is (see, e.g, Noyola et al. 2010; van derMarel & Anderson 2010). In addition, even when the centreof light (or the kinematic centre) of the system is identifiedwith high-accuracy, there is no guarantee that the BH loca-tion coincides with it, especially in the case of a light IMBH(see e.g., Giersz et al. 2015, Haster et al. 2016).For two snapshots (at 11.7 and 12 Gyr) of the simula-tions S1 (high mass IMBH) and S3 (low mass IMBH), weanalyse FOVs placed at different radial offsets of the centre(the distance to the clusters is fixed at 10 kpc). We considera total of 9 different centres, three for each radial positions0 . (cid:48)(cid:48) , 0 . (cid:48)(cid:48) and 1 . (cid:48)(cid:48) corresponding for both clustersto radial offsets of 5%, 10% and 20% of the core radius (seeFig. 6). In terms of the sphere of influence of the centralIMBH (whose radius r • is defined as the radius at whichthe cumulative mass equals the IMBH mass), the offsets arein the range 0 . − . r • for the simulation S1 and in therange 0 . − . r • for the simulation S3.With the same notation used in the previous subsectionwe show the results of the analysis in Fig. 7. For both theclusters we analyse two different snapshots at 11.7 and 12Gyr. In both cases the probability of detecting an IMBHslightly decreases by increasing the off-set. However, thistrend is deeply influenced by the stochasticity as for a fixed MNRAS000 , 1–10 (2016) etection of IMBHs in GCs using integrated-light spectroscopy R [arcsec]05101520253035 d i s p [ k m / s ] JMSimObs -2 -1 r [pc] Figure 4.
Left panel:
Best fit Jeans model for the cluster in simulation S0 at 12 Gyr. The observed inner profile (solid circles) is obtainedat a distance of 10 kpc pointing the FOV to the right centre of the cluster. The outer profile (open squares) is obtained directly fromthe simulation by considering only the velocities of the red giants.
Right panel:
2D map of the chi-square function in the two parameters η and m • . The three regions correspond to confidence levels of 68.3%, 95.4% and 99%. The dotted line indicates the true mass of theIMBH. The Jeans model is not able to recover the mass of the IMBH (10 M (cid:12) ) in the 3-sigma confidence. Figure 5.
Comparison between the true mass of the IMBH from the simulations and the mass recovered for the best fit of the mockobservation. All the clusters are considered at a fixed distance of 10 kpc ( left panel ) and 20 kpc ( right panel ) by identifying the rightcentre for the FOV. The black line represents the relation m ( true ) • = m ( recov ) • . Every circle is the best fit mass m • of the IMBH, whilethe error bars correspond to the confidence interval of 68 . radial off-set the success of the observation changes accord-ing to the angular position of the centre (e.g., see the highIMBH mass case with a fixed off-set of 1 . (cid:48)(cid:48) ).We wish to emphasise the fact that for our observationswe are using all the information available from the simula-tion to produce the Jeans models used in the fitting proce-dure. The same modeling procedure is unavailable for real observations and, thus, we expect a wrong identification ofthe centre to reduce the successful probability found in ourwork (for a comparison with real observations, see the dis-crepancy of (cid:39) R c for the centre of Omega Cen in Noyolaet al. 2008 and van der Marel & Anderson 2010). MNRAS , 1–10 (2016)
R. de Vita et al. X [arcsec] Y [ a r cs e c ] l u m [ L ] X [arcmin] Y [ a r c m i n ] l u m [ L ] Figure 6.
Left panel : Luminosity map of the cluster S1 at a distance of 10 kpc.
Right panel : detail of the 20 (cid:48)(cid:48) × (cid:48)(cid:48) FOV. The bluecrosses represent the 9 different centres of the analysis we investigate, distributed at three different radial positions with a 5%, 10% and20% off-sets with respect to the projected core radius from the intrinsic density centre of the simulation.
Figure 7.
Recovered IMBH mass for the 11.7 and 12 Gyr snapshots of the cluster S1 ( left panel , high BH mass) and the cluster S3( right panel , low BH mass) considered at a distance of 10 kpc (for a detailed descriptions of the symbols used see Fig. 5). For every(positive) radial off-set there are 6 estimates of the mass, two (from different snapshots) for each of the three points equidistant from thecentre (see Fig. 6), which are shown with a slight shift along the x-axis in the figure for improving clarity. The probability of detectingan IMBH slightly decreases by increasing the off-sets.
Among the parameter that we change in our mock observa-tions there is the distance to the cluster. The central IMBHis characterized by a sphere of influence that, in first ap- proximation, depends only on its mass. Therefore, for oneparticular simulation and for a fixed resolution of the instru-ment, increasing the distance to the cluster has the sameeffect of reducing the sphere of influence of the black hole.As consequence, the central peak in the velocity dispersion
MNRAS000
MNRAS000 , 1–10 (2016) etection of IMBHs in GCs using integrated-light spectroscopy is expected to reduce with increasing distance. As oppositeeffect, a more crowded FOV obtained by considering higherdistances should limit discreteness effects such as the shotnoise introduced by bright stars.We consider 3 different selected distances: 5, 10 and 20kpc. In Fig. 8, we plot the recovered mass as a function of thedistance to the cluster for each of the 4 snapshots availablefor the simulations S1 and S3. The probability of recoveringan IMBH is marginally influenced by the distance to thecluster with the higher number of successes found at 20 kpc,where the influence of shot noise on the velocity dispersionprofile is reduced. We simulated different integrated-light IFU observations fora sample of MOCCA simulations characterized by a series ofrealistic ingredients (high number of stars, stellar evolution,primordial binaries) and by different IMBH mass. Our goalwas to test under which conditions the IMBH is recoveredfrom the fit of a family of Jeans models to the mock ob-served velocity dispersion profile. We started by consideringthe different simulated clusters in canonical observationalconditions, that is at a typical distance of 10 kpc and byidentifying the right centre of the field of view. Even thoughwe adopted an optimal masking procedure to limit the ef-fect of the most bright stars, we find that our results aresignificantly influenced by the intrinsic stochasticity of theIFU measurements. Indeed, for every class of IMBH con-sidered we found at least one snapshot in four for whichthe observed IMBH mass is consistent with the case with-out black hole. Decreasing the IMBH mass leads to a largerprobability of failing to infer the BH presence from Jeansmodeling, with probability of obtaining a null result goingup to ∼
75% for IMBH mass 0.1% of the total cluster mass.In addition, even when the IMBH presence is successfullyrecovered from the modeling, the inferred mass is system-atically under-estimated, possibly because of the hard-to-quantify impact of binary stars (see Fig. 5). Finally, in thelarge majority of snapshots without an IMBH, the Jeansmodeling was not able to set reasonably low constraints tothe inferred IMBH mass, that is even if the best fit mass wasconsistent with 0, it was impossible to exclude the presenceof a massive IMBH at 68% confidence.In the second part of the paper we focused on changingcrucial parameters of the observational setup. In particular,we explored the effects that the distance to the cluster andthe centre of the field of view have to the inferred IMBHmass. The dependences on these two observational featureshave been analysed for two different regimes: high IMBHmass and low IMBH mass. In both cases we found similartrends.For a misidentification of the cluster centre not greaterthan the 5-20% of the core radius we find that the presenceof a central IMBH is successfully recovered in most observa-tions. For both simulations, the highest number of failed ob-servations corresponds to an off-set of 20% R c (correspond-ing to ∼ . (cid:48)(cid:48) at 10 kpc), suggesting a slight dependence ofthe successful probability with the centre off-set. We expectthat this trend dramatically increases in real observations, for which the Jeans modeling is based on some assumptionson the light distribution.Finally, the recovered IMBH mass is not particularlyinfluenced by changing the distance between 5 and 20 kpc,even if the number of successes is higher at 20 kpc. Accordingto the Harris catalogue (Harris 1996, 2010 edition) the 71%of all the Galactic GCs are found in this range of distances.Overall, our findings demonstrate that ground-basedIFU observations of the cores of GCs can be very helpfultools to investigate whether IMBHs are present in galacticGCs, especially because it does not appear that increaseddistance induces a higher failure rate in the recovery of in-put IMBHs. However, a large sample of objects would berequired in order to draw meaningful conclusions on the av-erage IMBH occupation fraction in GCs. In fact, the failurerate of any single observation is high (25-100% dependingon BH mass) due to stochastic superposition of bright starsalong the line of sight to the IMBH, and this bias needs to becorrected for. In conclusion, this work shows how any futureIFU observation needs to be supported by other techniqueswith the purpose of providing complementary approaches.Even with their own observational limitations, either proper-motion based kinematics, such as that available from Hub-ble Space Telescope imaging at multiple epochs (Anderson& van der Marel 2010; Bellini et al. 2014), or discrete kine-matics from resolved-star spectroscopy (Lanzoni et al. 2013;Kamann et al. 2016) may be used to constrain (especially inthe outer regions) any tentative detection from integrated-light IFU observations . ACKNOWLEDGEMENTS
This work was partially supported by the A.A.H. Pierce Be-quest at the University of Melbourne and by the “Angelodella Riccia” grant to fund a visit of RdV to MPIA. PBacknowledges partial support from a CITA National Fellow-ship. AA and MG were partially supported by the PolishNational Science Centre (PNSC) through the grant DEC-2012/07/B/ST9/04412. AA would also like to acknowledgepartial support by the PNSC through the grant UMO-2015/17/N/ST9/02573 and partial support from NCACgrant for young researchers. GvdV acknowledges partial sup-port from Sonderforschungsbereich SFB 881 ”The MilkyWay System” (subproject A7 and A8) funded by the GermanResearch Foundation.
REFERENCES
Anderson J., van der Marel R. P., 2010, ApJ, 710, 1032Askar A., Szkudlarek M., Gondek-Rosi´nska D., Giersz M., BulikT., 2017a, MNRAS, 464, L36Askar A., Bianchini P., de Vita R., Giersz M., Hypki A., KamannS., 2017b, MNRAS, 464, 3090Baumgardt H., 2017, MNRAS, 464, 2174Baumgardt H., Makino J., 2003, MNRAS, 340, 227Baumgardt H., Makino J., Ebisuzaki T., 2004a, ApJ, 613, 1133Baumgardt H., Makino J., Ebisuzaki T., 2004b, ApJ, 613, 1143Baumgardt H., Makino J., Hut P., 2005, ApJ, 620, 238Belczynski K., Kalogera V., Bulik T., 2002, ApJ, 572, 407Bellini A., et al., 2014, ApJ, 797, 115Bertin G., 2014, Dynamics of GalaxiesMNRAS , 1–10 (2016) R. de Vita et al.
Figure 8.
Recovered IMBH mass as function of the distance to the sun for the cluster S1 ( left panel , high BH mass) and S3 ( right panel ,low BH mass) at 11.7, 11.8, 11.9 and 12Gyr. The symbol used are the same of Fig. 5.Bianchini P., Norris M. A., van de Ven G., Schinnerer E., 2015,MNRAS, 453, 365Bianchini P., van de Ven G., Norris M. A., Schinnerer E., VarriA. L., 2016a, MNRAS, 458, 3644Bianchini P., Norris M. A., van de Ven G., Schinnerer E., BelliniA., van der Marel R. P., Watkins L. L., Anderson J., 2016b,ApJ, 820, L22Cappellari M., Emsellem E., 2004, PASP, 116, 138Farrell S. A., et al., 2012, ApJ, 747, L13Ferrarese L., Merritt D., 2000, ApJ, 539, L9Gebhardt K., et al., 2000, ApJ, 539, L13Giersz M., Leigh N., Hypki A., L¨utzgendorf N., Askar A., 2015,MNRAS, 454, 3150Gill M., Trenti M., Miller M. C., van der Marel R., Hamilton D.,Stiavelli M., 2008, ApJ, 686, 303Haggard D., Cool A. M., Heinke C. O., van der Marel R., CohnH. N., Lugger P. M., Anderson J., 2013, ApJ, 773, L31Harris W. E., 1996, AJ, 112, 1487Haster C.-J., Antonini F., Kalogera V., Mandel I., 2016, ApJ,832, 192Hobbs G., Lorimer D. R., Lyne A. G., Kramer M., 2005, MNRAS,360, 974Hurley J. R., 2007, MNRAS, 379, 93Jalali B., Baumgardt H., Kissler-Patig M., Gebhardt K., NoyolaE., L¨utzgendorf N., de Zeeuw P. T., 2012, A&A, 538, A19Kamann S., et al., 2016, A&A, 588, A149Konstantinidis S., Amaro-Seoane P., Kokkotas K. D., 2013, A&A,557, A135Kroupa P., 2001, MNRAS, 322, 231Lanzoni B., et al., 2013, ApJ, 769, 107L¨utzgendorf N., Kissler-Patig M., Noyola E., Jalali B., de ZeeuwP. T., Gebhardt K., Baumgardt H., 2011, A&A, 533, A36L¨utzgendorf N., et al., 2013, A&A, 552, A49L¨utzgendorf N., Gebhardt K., Baumgardt H., Noyola E., Neu-mayer N., Kissler-Patig M., de Zeeuw T., 2015, A&A, 581,A1MacLeod M., Trenti M., Ramirez-Ruiz E., 2016, ApJ, 819, 70Mandel I., Brown D. A., Gair J. R., Miller M. C., 2008, ApJ, 681,1431Mezcua M., Roberts T. P., Sutton A. D., Lobanov A. P., 2013,MNRAS, 436, 3128Noyola E., Gebhardt K., Bergmann M., 2008, ApJ, 676, 1008 Noyola E., Gebhardt K., Kissler-Patig M., L¨utzgendorf N., JalaliB., de Zeeuw P. T., Baumgardt H., 2010, ApJ, 719, L60Pasquato M., Trenti M., De Marchi G., Gill M., Hamilton D. P.,Miller M. C., Stiavelli M., van der Marel R. P., 2009, ApJ,699, 1511Pasquato M., Miocchi P., Won S. B., Lee Y.-W., 2016, ApJ, 823,135Pasquini L., et al., 2012, A&A, 545, A139Portegies Zwart S. F., Baumgardt H., Hut P., Makino J., McMil-lan S. L. W., 2004, Nature, 428, 724Ricotti M., Parry O. H., Gnedin N. Y., 2016, ApJ, 831, 204Rodriguez C. L., Pattabiraman B., Chatterjee S., ChoudharyA., Liao W.-k., Morscher M., Rasio F. A., 2015, preprint,( arXiv:1511.00695 )Trenti M., van der Marel R., 2013, MNRAS, 435, 3272Trenti M., Ardi E., Mineshige S., Hut P., 2007, MNRAS, 374, 857Trenti M., Vesperini E., Pasquato M., 2010, ApJ, 708, 1598Trenti M., Padoan P., Jimenez R., 2015, ApJ, 808, L35Vesperini E., Trenti M., 2010, ApJ, 720, L179Vesperini E., McMillan S. L. W., D’Ercole A., D’Antona F., 2010,ApJ, 713, L41Wang L., et al., 2016, MNRAS, 458, 1450van de Ven G., van den Bosch R. C. E., Verolme E. K., de ZeeuwP. T., 2006, A&A, 445, 513van der Marel R. P., Anderson J., 2010, ApJ, 710, 1063This paper has been typeset from a TEX/L A TEX file prepared bythe author. MNRAS000