Askar, A.

Giersz, M.

Hypki, A.P.

Leigh, N.

Lützgendorf, N.

arXiv

Leiden University Scholary Publications

Mem. S.A.It. Vol. 87, 555c© SAIt 2016 Memorie dellaFormation mechanisms of IMBH in globularclustersM. Giersz1, N. Leigh2, A. Hypki3, A. Askar1, and N. Lützgendorf41 Nicolaus Copernicus Astronomical Centre, Polish Academy of Sciences, ul. Bartycka 18,00-716 Warsaw, Poland, e-mail: mig@camk.edu.pl2 Department of Astrophysics, American Museum of Natural History, Central Park West and79th Street, New York, NY 100243 Leiden Observatory, Leiden University, PO Box 9513, NL-2300 RA Leiden, the Netherlands4 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USAAbstract. We very briefly discuss proposed in the literature possible scenarios for intermediatemass black holes formation in globular clusters. We also discuss the results of the MOCCAsimulations of about 2000 models (BigSurvey) regarding the distribution of events connectedwith electromagnetic and gravitational radiations, namely: mass transfer on IMBH, collisionsand mergers with IMBH and mergers with IMBH due to gravitational radiation. The rates ofthese events are very small, so their observation is very improbable.Key words. Stars: black holes – star clusters: general – Methods: numerical1. IntroductionIntermediate mass black holes (IMBH) arethought to be a missing link between stellar-mass black holes (BH) and supermassive BHs(SMBH). There are many theoretical argu-ments in favor of the formation of IMBHsin the centers of globular clusters (GCs) (e.g.Lützgendorf et al. 2013, and reference therein).Observational confirmation of the existence ofIMBHs would have an important impact on anumber of open astrophysical problems relatede.g. formation of SMBHs and their host galax-ies, origins of ultraluminous X-ray sources innearby galaxies, and detection of gravitationalwaves (GR). GCs are thought to be a natu-ral site for IMBH formation. The proximity ofGCs makes possible to directly observe kine-matic and structural imprints of IMBHs. Thereare a lot of observations indirectly suggestingthe presence of IMBHs in GCs in nearby galax-ies or Milky Way. They are based on the de-tection of strong X-ray or radio emissions atof-centre positions in distant galaxies, not con-firmed X-ray or/and radio emissions in someGalactic GCs or on kinematic and spatial struc-ture of central parts of GCs. Up to now, thereis no firm observational confirmation of IMBHpresence in GCs.2. IMBH formation mechanismsIn the literature, so far, there were proposedfive possible scenarios for IMBH formation inGCs:1. Direct collapse of very massive PopulationIII stars (Madau & Rees 2001). The veryfirst generation of stars must have formedout of unmagnetized, metal-free gas. Stars556 Giersz et al.: IMBH in globular clusterswere formed at so called mini halos ofmass about 105M at redshift about 20. ThePopulation III stars are formed with initialmass function (IMF) extremely top heavy,so stars with masses larger than 200 −300M can be formed. After a few Myrof evolution the most massive PopulationIII stars ended up as BHs, IMBH seeds,of masses larger than 150 − 200M, loos-ing only small fraction of mass (Fryer,Woosley & Heger 2001). However, one canask a question relevant for the presenceof IMBHs in GCs. How could such ex-tremely massive BHs become members ofGCs consisting of Population II stars?2. Runaway merging of very massive mainsequence stars (MS) stars in denseyoung star clusters was first discussedby Portegies Zwart et al. (2004). In thisscenario there are needed very tailoredinitial conditions to initiate a runawaymerging process. Time scale of the masssegregation of the most massive stars(about 100M) has to be shorter thanthe evolution time-scale for those stars,otherwise massive stars will evolve beforethey will start to collide. The velocitydispersion in the collapsed star clustercannot be larger than a few hundred km/s,otherwise collisions would disrupt stars.Frequent collisions between stars lead tothe formation of very massive stellar typeobjects like MS. Such star will quicklyevolve and become a massive BH and anIMBH seed.3. Accretion of the residual gas on stellarmass BHs formed from the first genera-tion stars was proposed by Leigh et al.(2013). Actually, the main purpose of thismodel was to explain multiple stellar popu-lations in GCs. Interactions between inter-stellar medium remaining after formationof the first generation stars and BHs formedfrom the most massive first generation starsis associated with substantial mass accre-tion onto stellar mass BHs. This leads tosubstantial increase of the BH masses andspeedup of their mass segregation and fi-nally, to formation of a very massive BHs,IMBH seeds. But we should be aware thatthe residual gas removal takes a few Myrand it is comparable with BH formationtime-scale, so probably there is not enoughtime and not enough residual gas to buildvery massive BHs, unless the residual gasis very dense and can stay in the clusterlonger.4. A more observational than theoretical sce-nario, which is based on the observedrelation between the BH mass and thevelocity dispersion of its host galaxy(e.g. Gültekin et al. 2009, and refer-ences therein). Extrapolating this relationto the velocity dispersions characteristic ofGalactic GCs, one expects to find centralBHs with masses similar to those charac-teristic of IMBHs.5. And finally, the new, just recently pre-sented, scenario based on results ofMOCCA simulations of evolution of densestellar systems (Giersz et al. 2015). Inthis scenario IMBH is formed because ofbuildup of BH mass solely due to mergersin dynamical interactions and mass trans-fers in binaries. In this scenario, in contrastto the scenarios presented above, there isno need for any special conditions to ini-tiate the process of IMBH mass buildup.However, the process of IMBH formationis highly stochastic. The larger the ini-tial cluster concentration, the earlier, fasterand with higher probability an IMBH willform. It is worth to stress that IMBH for-mation does not strongly depend on detailsof mass accretion onto BH and the detailedstructure of a star after physical collisionwith another star.3. Method and modelsThe MOCCA (MOnte Carlo Cluster simulA-tor) code used for the star cluster simula-tions presented here is a numerical simulationcode based on Hénon’s implementation of theMonte Carlo method (Hénon 1971) to followthe long term evolution of stellar clusters. Thismethod was substantially developed and im-proved by Stodółkiewicz in the early eighties(Stodółkiewicz 1986) and later by Giersz andhis collaborators (Giersz et al. 2013, and refer-Giersz et al.: IMBH in globular clusters 557Table 1. Initial conditions for the BigSurvey of the MOCCA simulations.N Rt (pc) Rt/Rh W0 Z fb amax (AU) IMF Kicks (km/s)4.0x104 30, 60 25, 50 3.0, 6.0 0.001, 0.005 0.05, 0.1 100 IMF2 265120 filling 9.0 0.02 0.3, 0.95 Period Fallback1.0x105 30, 60 25, 50 3.0, 6.0 0.001, 0.005 0.05, 0.1 100 IMF2 265120 filling 9.0 0.02 0,3, 0.95 Period Fallback4.0x105 30, 60 25, 50 3.0, 6.0 0.001 0.05, 0.1 100 IMF2 265120 filling 9.0 0.95 Period Fallback7.0x105 30, 60 25, 50 3.0, 6.0 0.0002, 0.001, 0.005 0.05, 0.1 100 IMF2 265120 filling 9.0 0.006, 0.02 0,3, 0.95 Period Fallback1.2x106 30, 60 25, 50 3.0, 6.0 0.001 0.05, 0.1 100 IMF2 265120 filling 9.0 0.95 Period FallbackNotes: BH and NS kicks are the same (Hobbs et al. 2005), except the case of mass fallback (Belczynski,Kalogera & Bulik 2002). IMF2 - two segmented initial mass function (Kroupa 2001), Period - binary perioddistribution (Kroupa 1995). fb - binary fraction, N - number of stars, Rt - tidal radius, Rh - half-mass radius,W0 - King model parameter, Z - cluster metalicity, fb - binary fraction, amax - maximum value for semi-majoraxis (distribution uniform in log(a), filling - tidally filling model).ence therein). The method can be regarded asa statistical way of solving the Fokker-Planckequation. The MOCCA code has been exten-sively tested against the results of N-body sim-ulations of star clusters containing from thirtythousands up to one million stars (Giersz etal. 2013; Heggie 2014; Giersz et al. 2015;Long et al. 2016; Mapelli 2016, and referencestherein). The agreement between these two dif-ferent types of simulations is excellent. Thisincludes the global cluster evolution, mass seg-regation time scales, the properties of primor-dial binaries (energy, mass and spatial distri-butions), and the numbers of retained neutronstars (NS) and BHs.For the new scenario of IMBH formationwe analyse results from 1950 star cluster mod-els that were simulated using the MOCCAcode (so called BigSurvey). The simulationsare characterized by very diverse parametersdescribing not only the initial global clusterproperties, but also star and binary properties.The parameters of these models are listed inTable 1.We would like to strongly stress thatmodels for the BigSurvey were not selectedto match the observed Milky Way GCs.Nevertheless, as it is shown in Askar, Bulik,Giersz, Rosińska & Szkudlarek (2016) theagreement with the observational propertiesof observed Galaxy GCs (Harris 1996, up-dated 2010) and modeled ones is quite goodfor the cluster absolute magnitude and the av-erage surface brightness. Despite this agree-ment, its is important to state that any com-bination of global observational properties ofGCs cannot be used to distinguish between dif-ferent cluster models because there is a strongdegeneracy with respect to the initial condi-tions. Taking into account the relatively goodagreement between the observed Milky WayGCs and the modeled ones we can assume thatthe BigSurvey cluster models are representa-tive for the GC population.4. Observational properties of IMBHbinariesAs it is well known, BHs cannot be directlyobserved because no light can leave them.Nevertheless, we can observe them indirectlyby characteristic electromagnetic or gravita-tional emissions or because of their influenceon spatial and kinematic characteristics of starclusters. Here, we will concentrate only on cu-mulative distributions of events connected withelectromagnetic emissions during mass trans-fer on IMBH from a companion star, elec-tromagnetic emissions during tidal disruptionevents (TDE) or direct collisions with IMBHs.We also provide cumulative distributions formerger events between IMBHs and compact558 Giersz et al.: IMBH in globular clusters 0 0.2 0.4 0.6 0.8 1 0  5000  10000  15000  20000  25000  30000N/NtotTime (Myr)Mass Transfers - 7269GR mergers - 10609Collisions and Mergers - 25311120.73/Myr,   MW_GC - 0.057/Myr0.41/Myr,   MW_GC - 0.032/Myr0.095/Myr,   MW_GC - 0.008/Myr0.35/Myr,   MW_GC - 0.027/Myr96.18.Myr,   MW_GC - 7.5/MyrFig. 1. The cumulative distributions of GR merg-ers, mass transfer and merger/collision events withIMBHs. Line descriptions and total number ofevents are given in the figure inserts.stars (white dwarfs (WD, NS or BHs) that areinduced by gravitational radiation (GR).On the Fig. 1 you can see the cumula-tive distributions of all GR merger, mass trans-fer and merger/collision events with IMBH.The total numbers of GR events, mass transferevents and mergers/collisions events are verylarge and are 10609, 7269 and 2531112, re-spectively. Those numbers are for models inwhich IMBH is formed (about 25% of all mod-els in the BigSurvey). Roughly, the cumulativedistributions can be approximated by straightlines. Assuming that simulated models are rep-resentative for population of real GCs we canestimate the rate of occurrence of a particulartype of events. These numbers are very small.The largest rate is for mergers/collisions withIMBH. It is about 100 per Myr. Others are lessthan 1 per Myr. If we scale those rates to thenumber of Milky Way GCs we will get evensmaller values. For mergers/collisions it is ofthe order of a few per Myr. Moreover, suchevents have a very short duration, so there isa low probability of observing them. So, weshould not be surprised that there is a rathersmall chance to observe events connected withelectromagnetic or gravitationalevents and why they were not observed yet.5. ConclusionsThe MOCCA code shows clearly its ability tomodel in a very efficient way a large number(thousands) of GC models. The observation ofany events connected with accretion of matteron IMBHs or connected with mergers due togravitational radiation is very improbable. Wewill have to have a lot of luck to see one ofthem. All the simulations data discussed here isa part of the BigSurvey database. This databasecan be freely accessed. If you are interested inusing the data from the BigSurvey in your ownresearch please send an email to Mirek Giersz.Acknowledgements. MG, AH and AA were par-tially supported by Polish National Science Centerthrough grant DEC-2012/07/B/ST9/04412.ReferencesAskar, A. et al. 2016, MNRAS submittedBelczynski, K., Kalogera, V., & Bulik, T. 2002,ApJ, 572, 407Fryer, C. L., Woosley, S. E., & Heger, A. 2001,ApJ, 550, 332Harris, W. E. 1996, AJ, 112, 1487Hobbs, G., et al. 2005, MNRAS, 360, 974Giersz, M., et al. 2013, MNRAS, 411, 2184Giersz, M., et al. 2015, MNRAS, 454, 3150Gültekin, K., et al. 2009, ApJ, 706, 404Heggie, D. C. 2014, MNRAS, 445, 3435Hénon, M. H. 1971, Ap&SS, 14, 151Kroupa, P. 1995, MNRAS, 277, 1507Kroupa, P. 2001, MNRAS, 322, 231Leigh, N. W. C., et al. 2013, MNRAS, 433,1958Lützgendorf, N., et al. 2013, A&A, 552, 49Madau, P. & Rees, M. J. 2001, ApJ, 551, L27Mapelli, M. 2016, arXiv1604.03559Portegies Zwart, S. F, et al. 2004, Nature, 428,724Stodółkiewicz, J. S. 1986, Acta Astron., 36, 19Wang, L., et al. 2016 MNRAS, 458, 1450

Formation mechanisms of IMBH in globular clusters

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