Monte Carlo modelling of globular star clusters - many primordial binaries, IMBH formation
Mirek Giersz, Nathan Leigh, Michael Marks, Arkadiusz Hypki, Abbas Askar
aa r X i v : . [ a s t r o - ph . GA ] N ov Star Clusters and Black Holes in Galaxies Across Cosmic TimeProceedings IAU Symposium No. 312, 2014A.C. Editor, B.D. Editor & C.E. Editor, eds. c (cid:13) Monte Carlo modelling of globular starclusters – many primordial binaries, IMBHformation
Mirek Giersz , Nathan Leigh , , Michael Marks , Arkadiusz Hypki , and Abbas Askar Nicolaus Copernicus Astronomical Centre, Polish Academy of Sciences,ul. Bartycka 18, 00-716 Warsaw, Polandemails: [email protected]@[email protected] Department of Physics, University of Alberta,CCIS 4-183, Edmonton, AB T6G 2E1, Canadaemail: [email protected] Department of Astrophysics, American Museum of Natural History,Central Park West and 79th Street, New York, NY 10024 Helmholtz-Institut fur Strahlen- und Kernphysik,Nussallee 14-16, D-53115, Bonn, Germanyemail: [email protected] Leiden Observatory, Leiden University,P.O. Box 9513, 2300 RA Leiden, The Netherlands
Abstract.
We will discuss the evolution of star clusters with an large initial binary fraction,up to 95%. The initial binary population is chosen to follow the invariant orbital-parameterdistributions suggested by Kroupa (1995). The Monte Carlo MOCCA simulations of star clusterevolution are compared to the observations of Milone et al. (2012) for photometric binaries. Itis demonstrated that the observed dependence on cluster mass of both the binary fraction andthe ratio of the binary fractions inside and outside of the half mass radius are well recoveredby the MOCCA simulations. This is due to a rapid decrease in the initial binary fraction dueto the strong density-dependent destruction of wide binaries described by Marks, Kroupa &Oh (2011). We also discuss a new scenario for the formation of intermediate mass black holesin dense star clusters. In this scenario, intermediate mass black holes are formed as a result ofdynamical interactions of hard binaries containing a stellar mass black hole, with other starsand binaries. We will discuss the necessary conditions to initiate the process of intermediatemass black hole formation and the dependence of its mass accretion rate on the global clusterproperties.
Keywords. stellar dynamics - globular clusters: general binaries: general - methods: numerical
1. Introduction
Recent high resolution observations of globular clusters (GC) provide a very detailedpicture of their physical status and show complex phenomena connected with multiplestellar populations, binary evolution and the Galactic tidal field. Despite such greatobservational progress there are many theoretical uncertainties connected with the originsof GCs and the properties of their primordial binary populations. To bridge the gapbetween present-day observed binary properties and their properties at the time of clusterformation, we need to discriminate between different theories and models by means of1 Mirek Giersz, Nathan Leigh, Michael Marks, Arkadiusz Hypki & Abbas Askarnumerical dynamical simulations of GCs. Based on then available observations of the late-type stellar binary population in the Galactic field, Kroupa (1995) suggested that, takinginto account dynamical processing, the initial binary population in star clusters is largelyinvariant, in the sense that almost every star forms in a binary system with invariantformal distribution functions (due to energy and angular momentum conservation, thephysics of molecular clouds, all of which are the same everywhere, except perhaps invery intense star bursts). These distribution functions are parent distribution functions,from which a particular case is discretized, or rendered, and their suggested invarianceis tightly connected to the notion of an invariant IMF (Kroupa & Petr-Gotzens 2011).These parent functions can have different properties in different mass ranges (browndwarfs, late and early type stars). The Kroupa (1995) set-up of the primordial binarypopulations has been shown to work well for the late-type stellar population (solar-typestars and below) in young star forming regions (Marks & Kroupa 2012, Marks et al.2014) and the Galactic field (Marks & Kroupa 2011). Such distribution functions areneeded to initialize N-body models in order to study how young and old clusters evolveinto the field and associations. The simulations of GCs described in this talk use theKroupa (1995) initial binary population and were conducted by the Monte Carlo codeMOCCA (Hypki & Giersz 2013, Giersz et al. 2013 and references therein). The resultsof the simulations were compared to observational data using the photometric binariesprovided in Milone et al. (2012), and to the initial dissolution rate of primordial binariesfound using N-body simulations in Marks, Kroupa & Oh (2011).The presence of intermediate mass black holes (IMBH) in the cores of some GCs hasbeen debated for a long time. There are many theoretical arguments in favor of theformation of IMBHs in the centers of GCs (e.g. L¨utzgendorf et al. 2013 and referencestherein), but there is yet no observational confirmation of the presence of any IMBH inany Galactic GCs. All proposed scenarios for the formation of IMBHs in GCs requirespecial initial conditions: 1) the formation of very massive Population III stars (Madau& Rees 2001), 2) runaway merging of main sequence stars in young and very dense starclusters (Portegies Zwart et al. 2004, G¨urkan et al. 2004), 3) accretion of residual gas onstellar mass black holes (BH) formed from the first generation stars (Leigh et al. 2013a)and 4) tidally stripped parent galaxy cores of neighboring dwarf galaxies (e.g. Baumgardtet al. 2003). A new scenario for IMBH formation is proposed in this talk and does notneed very specific initial conditions. An IMBH is built-up only via binary dynamicalinteractions and mass transfer (also induced by dynamical interactions) in binaries.
2. Method
The MOCCA code used for the star cluster simulations presented here is the MonteCarlo code based on H´enon’s implementation of the Monte Carlo method (H´enon 1971),which was further substantially developed by Stod´o lkiewicz in the early eighties (Stodol-kiewicz 1986). This method can be regarded as a statistical way of solving the Fokker-Planck equation. A star cluster is treated as a set of spherical shells, each of whichrepresents an individual object: star, binary or a group of the same objects. Each shellis characterized by mass, energy and angular momentum. Relaxation of a given objectwith all other objects in the system is approximated via the interaction of two neighbor-ing shells. There are two independently developed Monte Carlo codes: by Fred Rasio’sgroup (Morscher et al. 2014 and reference therein) and by my group (Giersz et al. 2013and reference therein). Actually, there are two more Monte Carlo codes, which were re-cently developed by Vasiliev (2014) for non spherical stellar systems and by Sollima &Mastrobuono Battisti (2014) for a realistic treatment of the tidal field. onte Carlo modelling of globular star clusters
3. Results
The results presented in this talk came as a byproduct from two projects carried outwith Nathan Leigh and other collaborators. The aim of the first project (Leigh et al.2013b) was to explain an observed anti-correlation between cluster mass and binaryfraction (Milone et al. 2012) and between the strength of low-mass star depletion inthe present-day mass function (MF) and the cluster concentration (De Marchi et al.2007). The aim of the second project (Leigh et al. 2014) was to constrain the initialproperties of primordial binaries by comparison with observations (Milone et al. 2012)and to check if star cluster simulations with initial conditions drawn from the invariantKroupa (1995) distributions are able to recover the observed spatial distributions ofbinaries. All together, for these projects about 400 models of star clusters (SC) weresimulated by the MOCCA code.The model parameters run for the mentioned projects are as follows. Generally, moremassive models also have larger concentrations (measured as the ratio between the tidaland half-mass radii - R plum = R t /R h ), with some of them being extremely concentrated( R plum as large as 125). Most of the initial models had binary fractions equal to 0.1,but for some of them it varied between 0.3 to 0.95. The binary period distribution wasuniform in the logarithm of the semi-major axis up to 100AU for all standard models,and up to 200AU and 400AU for all other models. For a substantial number of models,instead of the flat semi-major axis distribution, the Kroupa (1995) period distributionwas used, up to log(P)=8.3. Also, different IMFs were used: the Kroupa canonical -a two segmented IMF (Kroupa 2001), the Kroupa standard - a three segmented IMF Mirek Giersz, Nathan Leigh, Michael Marks, Arkadiusz Hypki & Abbas Askar(Kroupa, Tout & Gilmore 1993), and the two segmented modified Kroupa IMF (differentpower-law indexes). Supernovae (SN) natal kick velocities for neutron stars (NS) andBHs were modified for some models according to the mass fallback procedure describedby Belczynski et al. (2002).3.1. Extremely Large Initial Binary Fraction
Time Evolution of Binary Parameters in MOCCA and N-body Computations
The results of the MOCCA computations for GCs with the Kroupa (1995) primordialbinary population and their comparison with observational data (Milone et al. 2012) aredescribed in detail in Leigh et al. (2014). Here we concentrate on the evolution of thebinary parameters in evolving clusters described by tidally filling models (with R plum controlled by the W = 6 King model), and strongly concentrated tidally under-filling W = 6 King models with R plum = 50. Also, we present a comparison between theMOCCA results and the results of the BiPoS code developed by Michael Marks, basedon Marks, Kroupa & Oh (2011) and Marks & Kroupa (2011). The BiPoS code offersan analytic description for the processing of the Kroupa (1995) initial binary populationseen in N-body computations with initial masses up to 10 . M ⊙ . BiPoS thus evolves theinitial binary population efficiently for cluster ages up to 5 Myr, the time for which theircomputations were run. b i na r y _ f r a c t i on ( l og10 ( P )) / D e l t a ( l og10 ( P )) Log10(P/d)M = 500000 Mo, King Wo = 6 underfilled Rt/Rh = 50, Rt = 181 pc0 Myr5.98 Myr12.34 Myr18.82 Myr25.35 Myr252 Myr1 Gyr12 Gyr
Figure 1.
Time evolution of the binary period distribution in one of our tidally under-fillingstar cluster models.
Fig. 1 shows the evolution of the primordial binary period distributions for one of ourtidally under-filling models. As expected, the rate of evolution of the period distributionstrongly depends on the initial cluster concentration. The larger the concentration, thelarger the change in the period distribution. For more strongly concentrated clusters,theperiod distribution after about 10 Myr of cluster evolution is similar to the period dis-tribution after a few Gyr of evolution in an initially tidally filling cluster, known as thedensity degeneracy (Marks & Kroupa 2012, Marks et al. 2014). The maximum of theperiod distribution moves towards smaller periods as the cluster ages and the distribu-tion shape becomes quickly bell-shaped, as observed for Galactic field populations (e.g. onte Carlo modelling of globular star clusters days and 10 days, respectively. b i na r y _ f r a c t i on ( l og10 ( P )) / D e l t a ( l og10 ( P )) Log10(P/d)M = 500000 Mo, King Wo = 6 underfilled Rt/Rh = 50, Rt = 181 pcMOCCA tidally under-filling - 5.98 MyrN-body tidally under-filling - 5MyrMOCCA tidally filling - 4.87 MyrN-body tidally filling - 5Myr
Figure 2.
The binary period distribution for tidally filling and tidally under-filling models forMOCCA and N-body (using the semi-analytical BiPoS code) after 5 Myr computation time.
Fig. 2 shows a comparison between the binary distributions at about 5 Myr for thetidally filling and tidally under-filling MOCCA models and the BiPoS code. The MOCCAand N-body period distributions agree remarkably well, both for the tidally filling andunder-filling models, and so do the distributions for binary binding energy, mass ratioand eccentricity. This is somewhat unexpected, since Marks, Kroupa & Oh (2011) findthat very fast destruction of binaries takes place on a dynamical time scale and stronglydepends on the cluster concentration. The larger the cluster concentration, the larger therate of binary destruction. Processes with characteristic time scales much shorter thanthe local relaxation time, and comparable to the dynamical time scale, are in principle notwell followed by the Monte Carlo method. And yet, the good agreement between BiPoSand MOCCA suggests that the probability of binary dynamical interactions occurringin MOCCA is properly computed (taking into account the local cluster properties), andso the binary destruction rates are well reproduced. In the MOCCA simulations, somecooling of the system is observed (a small decrease in R h ) initially because of binarydisruption (up to a time of 5 Myr), but then heating of the system takes over due tobinary hardening.3.1.2. Comparison to Observed Properties in Globular Clusters
The results of comparing the observational data from Milone et al. (2012) to theresults of our MOCCA simulations are discussed in great detail in Leigh et al. (2014).Here we will only summarize the main conclusions. Only the tidally under-filling modelscan reproduce the observations. For these models, both the binary fractions and the ratioof the binary fractions inside and outside R h reproduce the observations reasonably well. Mirek Giersz, Nathan Leigh, Michael Marks, Arkadiusz Hypki & Abbas AskarThe tidally filling models, however, failed to reproduce the observations. For these models,a correlation is observed between the cluster mass and the binary fraction outside R h ,instead of an anti-correlation. If the initial binary populations are indeed described bythe Kroupa (1995) distribution, then our comparison of the MOCCA computations withMilone et al. (2012) suggests that globular clusters must have formed strongly tidallyunder-filling. This is necessary to create sufficient dynamical processing to reproduce theobserved anti-correlation between the binary fraction outside R h and the total clustermass. It is worth noting that those MOCCA simulations with high initial concentrations,initial binary fractions of about 10% and a flat distribution in the logarithm of the semi-major axis cannot recover the observed anti-correlation for the binary faction outside R h (Leigh et al. 2013b). Of course, this does not rule out other types of distributions ofthe primordial binary parameters, which might also provide a good fit to the observedbinary properties. 3.2. A New IMBH Formation Scenario
As was already mentioned in Section 3, the new scenario for IMBH formation came asa byproduct of projects carried out with Nathan Leigh and collaborators (Leigh et al.2013b, Leigh et al. 2014). While working with the data produced during the simulationsdone for the first project, we noticed rather unexpectedly that for some models a slowbuildup of BH mass is observed. I M B H M a ss ( M o ) Time (Myr)FEXP=1, ACCRETION - 25%
Figure 3.
IMBH mass build up for models with reduced mass accretion onto the IMBH (25%of the standard BSE setup) and reduced standard star expansion after merger events (1 / As is illustrated in Fig. 3, there are two different regimes of BH mass buildup. The firststarts later on in the cluster evolution and has a rather small rate of mass increase (SLOWscenario), while the second starts very early on in the cluster evolution with a very highrate of mass increase (FAST scenario). The BH mass buildup is observed for runs withand without mass fallback (Belczynski et al. 2002) and, what is very unexpected, alsofor simulations done for massive and dense open clusters (project with Christoph Olczak- work in progress). Generally, only a small fraction of all models show a significant onte Carlo modelling of globular star clusters F exp = 3). These are the standard assumptions applied in the BSE code (Hurley etal. 2000, 2002) and in the Fewbody code (Fregeau et al. 2004). As it was pointed outduring the MODEST-14 conference, these assumptions might be too strong. The processof mass accretion onto the BH is very complicated, and recent simulations suggest thatless than 50% of the incoming star mass is directly accreted onto the BH. So, in the nextset of simulations, we weaken the standard assumptions - only 25% of the mass of theincoming star is accreted, and the size of the final merged object is just the sum of theradii of the colliding stars ( F exp = 1). As is clear from Fig. 3, an IMBH still forms. Asexpected, however, the IMBH formation is less efficient. Nevertheless, this strengthensthe evidence in favor of our new scenario for IMBH formation. S e m i M a j o r A x i s ( R o ) Time (Myr)Plummer: N=300000, fb=0.1, rplum=50, Rt=69.0 pcBIN-ANY_FLYBY_EXCHANGEBIN-ANY_MERGERBIN-ANY_TOTAL_MERGER
Figure 4.
Evolution of the semi-major axis for binaries containing an IMBH. Symbols: plus -flyby and exchange, cross - merger, star - total merger.
Fig 4 shows the evolution of the semi-major axes of binaries containing an IMBH forthe SLOW scenario. Clear patterns in the subsequent binary evolution are apparent -e.g. shrinkage of the binary semi-major axis (binary hardening). This is due to dynamicalinteractions with other binaries and single stars, as well as binary evolution connectedeither with stellar evolution or gravitational wave radiation (GR). Binary mergers result-ing purely from binary evolution are rare. More frequent are binary mergers connectedwith dynamical interactions. There are two kinds of dynamical mergers: mergers with onebinary component (which preserve the binary), and total mergers in which all interactingstars merge into one object. The total binary merger events are crucial from the point ofview of IMBH formation. Because of these interactions, an IMBH binary (when its mass Mirek Giersz, Nathan Leigh, Michael Marks, Arkadiusz Hypki & Abbas Askaris still low) cannot harden to the point of being able to escape from the cluster, whichcan occur if it receives a strong recoil during a subsequent dynamical interaction. So, theIMBH remains in the system and, consequently, is able to steadily grow in mass.In the case of the SLOW scenario, the central cluster densities are not very high - only10 M ⊙ /pc . Thus, a special set of initial conditions is not needed to form an IMBH.The situation is different for the case of the FAST scenario. The densities required forsignificant IMBH mass buildup to occur are very high, greater than 10 M ⊙ /pc . Theseextremely high densities are needed when BHs form a bound and very dense subsystemin the cluster center - mergers of binaries with BHs have to be more efficient than theremoval of BHs from the cluster due to strong recoils in dynamical interactions. Suchhigh densities are not very probable in the GCs observed in the Milky Way, but they canoccur in nuclear star clusters (NSC). Perhaps the FAST scenario for IMBH formationdiscussed here occurs commonly in the NSCs of low-mass galaxies.The new scenario for IMBH formation can be summarized as follows: • To initiate the process of BH mass growth, either at least one BH must be left inthe cluster after the early phase of SN explosions, or a single BH must be formed viamergers during dynamical interactions. If several BHs remain in the system, the clusterdensity has to be extremely high for an IMBH to form, greater than 10 M ⊙ /pc ; • Next, the formation of a BH-any star binary forms via three-body interactions. TheBH is the most massive object in the cluster, so there is a high probability that the BHwill be exchanged into, or form a binary. Frequently, BH companions are main sequence(MS), red giant (RG) or asymptotic giant branch (AGB) stars (possibility for X-rayemission); • Dynamical interactions with other binaries and stars: ◦ orbit tightening leading to mass transfer from MS/RG/AGB companions; ◦ exchanges and mergers, leaving the binary in tact; ◦ total mergers in dynamical interactions or the emission of gravitational waves -in this case, the binary is destroyed and only the BH is left. The single BH is thenformed a new binary via another three-body interaction, which is free to undergosubsequent dynamical interactions with other single and binary stars. In this way,the BH mass steadily increases.The buildup of the IMBH mass for a model with N=300000, R plum = 100 and massfallback for SN natal kicks is shown in Fig 5. The mass of the IMBH increases up to7000 M ⊙ . The surface brightness profiles (SBP) and velocity dispersion profiles (VDP)constructed from this simulation were used by Nora L¨utzgendorf to fit the IMBH masswith her code based on Jeans’ model (L¨utzgendorf et al. 2013). As seen in Fig. 5, the fitto the MOCCA data is rather good. MOCCA is able to reproduce more or less correctlythe system structure around an IMBH. This is a rather unexpected result, given thatMOCCA was not designed to model the relevant physics near a massive IMBH. In fairnessthough, the agreement is only good in some of our models. Definitely, more work isneeded.Fig. 6 shows the number of events in which mass is transferred onto an IMBH, eitherfrom its companion during binary evolution, or because of collisions with incoming starsfor the SLOW scenario for standard and reduced accretion. Such mass accretion eventsare potentially observable because of associated electromagnetic or gravitational radia-tion. The number of events for collisions and GR are listed in Fig. 6. The numbers aresubstantial. Interestingly, there are more GR and binary evolution events for the case ofreduced mass accretion onto the IMBH. This is connected to the fact that mergers dur-ing binary dynamical interactions produce far fewer ”total” mergers, due to the smallersize and hence cross-section of the merged object. Instead, there is a large number of onte Carlo modelling of globular star clusters I M B H M a ss ( M o ) Time (Myr)N = 300000 rplum = 100 Rt = 69.0 pc fallback = 1 MOCCAJeans
Figure 5.
IMBH mass from our MOCCA simulations and from fitting Jeans models(L¨utzgendorf et al. 2013) to the SBP and VDP obtained from the MOCCA simulations. I M B H m a ss ( M o ) Time (Myr)N=1800000, Rt=125 pc, Rt/Rh=75, fb=0.1, no FallbackStandard Accretion (SA)Ne = 37743GR all mergers - 87GR BH-WD mergers - 87GR BH-NS mergers - 0GR BH-BH mergers - 0 Reduced Accretion (RA)Ne = 136689GR all mergers - 173GR BH-WD mergers - 159GR BH-NS mergers - 12GR BH-BH mergers - 2Bin_evo (RA) M=277.1Mo, N=6049Mergers with BH (RA), M=236.1Mo, N=1175Collisions (RA), M=8.1Mo, N=23Bin_evo (SA), M=354.1Mo, N=3490Mergers with BH (SA), M=2915.7, N=3110Collisions (SA), M=254.0Mo, N=341
Figure 6.
IMBH mass buildup for models with standard and reduced mass accretion onto theIMBH. Mass transfer events, mergers and collisions with the IMBH are depicted by differentsymbols (see insets). Also listed are the numbers of interactions, and the total mass gained bythe IMBH in each dynamical interaction.
GR events, mainly associated with BH-WD mergers. For the FAST scenario, physicalcollisions are the dominant type of interaction provided the IMBH is sufficiently massive(larger than 5000 - 7000 M ⊙ ).Let’s assume that the probability of IMBH formation depends mainly on the averagebinary interaction probability. Then we can compare models with and without IMBH for-0 Mirek Giersz, Nathan Leigh, Michael Marks, Arkadiusz Hypki & Abbas Askarmation to see if they occupy separate regions in Escape Velocity - Interaction Probabilityspace. To calculate the interaction probability, we assume an interaction involving an av-erage binary at the soft/hard boundary and an average single star, that occurs inside R h . Fig. 7 shows the results of this exercise. Indeed, at time T=0, there is a statisticalboundary above which the probability for IMBH formation is substantial. This boundaryline is drawn by eye. Models with substantially reduced mass accretion are only likelyto form an IMBH for cluster escape velocities larger than about 30-40 km/s. The sameexercise is repeated at time T=12 Gyr (i.e. at the present-day), which shows that indeedsome Galactic GCs occupy a region in Escape Velocity -Interaction Probability space forwhich the MOCCA models do produce an IMBH. These clusters include Omega Cen,47Tuc, M22 and NGC6293. ( M / R _h ) ** . / N / R _h V_esc (km/s)BH mass > 150 Mo T = 0 GyrIMBHnoIMBH0.007*x**(-1.0)FEXP=1 IMBHFEXP=1 noIMBH
Figure 7.
The interaction probability vs escape velocity at time T=0 for all models (see theinset).
Concluding, it is worth mentioning that models with reduced natal kicks (because ofmass fallback) for BHs may still contain a substantial number of stellar mass BHs evenafter a Hubble time of cluster evolution. The number of retained BHs depends on thecluster mass and concentration, via the cluster half-mass relaxation time. The larger thehalf-mass relaxation time, the larger the number of retained BHs. This means that thoseclusters most likely to host stellar mass BHs are massive and have a low concentration,instead of massive and dense. Also, simulations of dense and massive GCs show that NSsand BHs can form in substantial numbers not only due to supernovae explosions, butalso because of physical collisions and binary mergers later on in the cluster evolution.Interestingly, IMBH formation suppresses the production of any binaries with NS or BHcompanions, and even the formation of NSs and BHs themselves. This is because theirprogenitors (white dwarfs, NSs and BHs) are very quickly removed from the system viadynamical interactions with the IMBH. They are the most massive stars in the cluster,and therefore the probability for their involvement in dynamical interactions is high. onte Carlo modelling of globular star clusters
4. Conclusions
Here are our conclusions, which summarize the talk. • The MOCCA code is able to follow the initial destruction of wide binaries. In supportof this, the results are in good agreement with the semi-analytic code BiPoS, which isbased on N-body simulations. • If the initial binary population is described by the Kroupa (1995) distributions, thenour comparison of the MOCCA computations with Milone et al. (2012) suggests thatglobular clusters need to have formed strongly tidally under-filling to produce sufficientdynamical processing, and hence to reproduce the observed anti-correlations between thebinary fractions and the total cluster mass. • NSs and BHs can form (in substantial numbers) in the course of star cluster evolutiondue to dynamical interactions (collisions and binary interactions); • If the cluster density is large enough (about 10 M ⊙ /pc ), an existing BH can expe-rience substantial mass buildup due to collisions/mergers during dynamical interactionsand mass transfer in binaries. The SLOW scenario is more probable; • The process of BH mass buildup, and finally IMBH formation, is highly stochastic.The rate of IMBH mass buildup strongly depends on the cluster density. The larger thedensity, the higher the rate; • There are frequent phases of mass transfer in binaries containing an IMBH and merg-ers of stars with an IMBH. Therefore, X-ray emissions and/or GR could be observableduring these events.Of course one should be aware about possible problems associated with the approxi-mations used in the MOCCA code. • The MOCCA code does not cope well with physical processes that have a charac-teristic time scale comparable to the dynamical time scale; • The MOCCA code is not prepared to follow the dynamical evolution of extremelymassive objects (larger than a few hundred M ⊙ ). Nevertheless, the initial IMBH massbuildup is modeled correctly; • The Fewbody code (Fregeau et al. 2004) seems to work properly for extreme massratios - several checks were carried out; • There are some doubts about the accuracy of the BSE code (Hurley et al. 2000,Hurley et al. 2002), and its ability to follow binary evolution and mass transfer involvingextreme mass ratios and massive compact objects. The mass transferred onto an IMBHbecause of binary/stellar evolution is not the dominant source of mass accretion, so theprocess of IMBH mass buildup can occur even if binary evolution-induced mass transferis completely switched off; • Very large kicks associated with the mergers of BHs having misaligned spin vectors.
ACKNOWLEDGMENTS
AH, MG and AA were partly supported by the Polish Ministry of Science and HigherEducation and by the National Science Centre through the grants DEC-2011/01/N/ST9/06000and DEC-2012/07/B/ST9/04412, respectively. NL is thankful for the generous supportof an NSERC Postdoctoral Fellowship.
References
Baumgardt, H., Makino, J., Hut, P., McMillan, S., & Portegies Zwart, S. 2003
ApJ (Letters),589, L25Belczynski K., Kalogera V., Bulik T. 2002,
ApJ , 572, 407De Marchi, G., Paresce, F. & Pulone, L. 2007,
ApJ (Letters), 656, L65
Fregeau J. M., Cheung P., Portegies Zwart S. F. & Rasio F. A. 2004, textitMNRAS, 352, 1Fukushige T. & Heggie D. C. 2000,
MNRAS , 318, 753Giersz, M., Heggie, D. C., Hurley, J. R. & Hypki, A. 2013,
MNRAS , 431, 2184G¨urkan, M. A., Freitag, M. & Rasio, F. A. 2004,
ApJ , 604, 632Harris, W. E. 1996, AJ . 112, 1487 (2010 update)H´enon, M. H. 1971, Ap&SS , 14, 151Hurley J. R., Pols O. R. & Tout C. A. 2000,
MNRAS , 315, 543Hurley J. R., Tout C. A. & Pols O. R. 2002,
MNRAS , 329, 897Hypki, A. & Giersz, M. 2013,
MNRAS , 429, 1221Kroupa 1995,
MNRAS , 277, 1507Kroupa 2008,
MNRAS , 322, 231Kroupa P. & Petr-Gotzens M. G. 2011,
A&A , 529, A92Kroupa, P., Tout, C. A., Gilmore, G. 1993,
MNRAS , 262, 545Kroupa, P., Weidner, C., Pflamm-Altenburg, J., Thies, I., Dabringhausen, J., Marks, M., &Maschberger, T. 2013, in: Oswalt, T. D. and Gilmore, G. (eds.),
Planets, Stars and StellarSystems. Volume 5: Galactic Structure and Stellar Populations , p. 17Leigh, N. W. C., B¨oker, T., Maccarone, T. J. & Perets, H. B. 2013a,
MNRAS , 429, 2997Leigh, N. W. C., Giersz, Webb, J. J., Hypki, A., De Marchi, G., Kroupa, P., & Sills, A. 2013b,
MNRAS , 436, 3399Leigh, N. W. C., Giersz, M., Marks, M., Webb, J. J., Hypki, A., Heinke, C. O., Kroupa, P., &Sills, A. 2014, arXiv1410.2248
L¨utzgendorf, N., Kissler-Patig, M., Gebhardt, K., Baumgardt, H., Noyola, E., de Zeeuw, P. T.,Neumayer, N., Jalali, B. & Feldmeier, A. 2013,
A&A , 552, 49Madau, P. & Rees, M. J. 2001,
ApJ (Letters), 551, L27Marks, M. & Kroupa, P. 2011,
A&A , 417, 1702Marks, M. & Kroupa, P. 2012,
A&A , 543, A8Marks, M., Kroupa, P., & Oh, S. 2011,
MNRAS , 417, 1684Marks, M., Leigh, N., Giersz, M., Pfalzner, S., Pflamm-Altenburg, J. & Oh, S. 2014,
MNRAS ,431, 3503Milone, A. P., Piotto, G., Bedin, L. R., Aparicio, A., Anderson, J., Sarajedini, A., Marino,A. F., Moretti, A., Davies, M. B., Chaboyer, B., Dotter, A., Hempel, M., Mar´ın-Franch,A., Majewski, S., Paust, N. E. Q., Reid, I. N., Rosenberg, A. & Siegel M., 2012,
A&A , 540,16Morscher, M., Pattabiraman, B., Rodriguez, C. Rasio, F. A. & Umbreit, S. 2014, arXiv1409.0866
Portegies Zwart, S. F., Baumgardt, H., Hut, P., Makino, J. & McMillan, S. L. W. 2004,
NA-TURE , 428, 724Raghavan, D., McAlister, H. A., Henry, T. J., Latham, D. W., Marcy, G. W., Mason, B. D.,Gies, D. R., White, R. J., & ten Brummelaar, T. A. 2-10,
ApJS , 190, 1Sollima, A. & Mastrobuono Battisti, A. 2014,
MNRAS , 443, 3513Stod´o lkiewicz, J. S. 1986,
AcA , 36, 19Vasiliev, E. 2014,, 36, 19Vasiliev, E. 2014,