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Compact Objects in Star Clusters

Mirek Giersz

Nicolaus Copernicus Astronomical Center, Polish Academy of SciencesWarsaw, Poland

[email protected]

MODEST 17 WorkshopPrague

22 September 2017

Mirek Giersz Compact Objects in Star Clusters

ObservationsTheory and Simulations

MOCCA Survey Database - ProjectsMOCCA - Work in Progress

Outline of the presentation

OUTLINE

Observations - What do we know about compact objects inGCs? Most recent observations;Theory and Simulations - Recent developments;MOCCA Survey Database - Projects concerning properties ofdifferent populations of compact objects;New Version of the MOCCA Code - Multiple stelar populations,residual gas, GR and tidal dissipative effects.




Observations - X-Ray Sources

Credit: NASA/CXC/M.Weiss

Low mass X-ray binaries (LMXBs) -systems in which a compact object(white dwarf, neutron star or blackhole) accretes matter from alow-mass companion star.

Accretion occurs through Roche-lobeoverflow and disk formation around acompact object, or, because of red giants,wind-fed accretion partially captured bythe compact object.LMXBs classification:

persistent systems with X-rayluminosities & 1036erg/s - accretioncontinues at high rates;transient systems - short intervals ofenhanced accretion as outbursts(days to months), followed by longperiods of quiescence, with little orno accretion and X-ray luminosities. 1030 - 1033erg/s (years to decades).





47 Tuc - Credit: ESA/Hubble & NASA (optical) and Chandra/NASA, Bahramian et al. (X-rays)

X-ray emission is a very good tracer of compact binaries. Goodspatial resolution of Chandra makes it possible to identify hundreds ofsuch sources in GCs, e.g. about 370 in 47 Tuc (Bhattacharya et al.2017).





than X-ray frequencies, implying that the observed high radio/X-ray flux ratio could be explained in this case withoutinvoking an enormous beaming factor. The large radioluminosity may also indicate a higher than average stellar-

Figure 5. Radio/X-ray correlation for stellar-mass BHs in the hard and quiescent states. VLA J2130+12 is represented by the red circle. The black squares representfield BHs from the literature (Miller-Jones et al. 2011b; Gallo et al. 2012, 2014; Ratti et al. 2012; Corbel et al. 2013; Munar-Adrover et al. 2014; Dzib et al. 2015), andthe yellow circles represent the BHCs in M22, M62, and 47 Tuc (Strader et al. 2012b; Chomiuk et al. 2013; Miller-Jones et al. 2015). The blue circles represent NSsystems in the hard state (Rutledge et al. 1998; Moore et al. 2000; Migliari et al. 2003, 2010, 2011; Migliari & Fender 2006; Tudose et al. 2009; Miller-Joneset al. 2010; Tetarenko et al. 2016a). Green triangles and pink stars show the binary transitional millisecond pulsar (Hill et al. 2011; Papitto et al. 2013; Delleret al. 2015) and accreting millisecond pulsar (Gaensler et al. 1999; Rupen et al. 2002; Fender et al. 2004b; Pooley 2004; Rupen et al. 2005; Migliari et al. 2011)systems, respectively. The purple diamonds show the CVs, AE Aqr (Eracleous et al. 1991; Abada-Simon et al. 1993) and SS Cyg (Russell et al. 2016), during brightflare/outburst periods in each source. These points are meant to represent the most radio-bright periods observed in these types of systems. The vast majority of CVslie below these points in the LR/LX plane (Fuerst et al. 1986; Kording et al. 2008, 2011; Byckling et al. 2010). The dotted black line shows the best-fit relation for BHs(Gallo et al. 2006), and the blue dashed and dashed-dotted lines show the two suggested correlations for NS systems (Migliari & Fender 2006).

Figure 6. Color–magnitude diagram of M15 made using data from the ACScluster survey. The data shown has been filtered by the quality flag for I- andV-band magnitudes available in ACS data sets. Only points with quality flagvalues below 0.5 are plotted here. Green points indicate sources within a 4 5radius around the radio coordinates of VLA J2130+12. The identified opticalcounterpart of VLA J2130+12 is plotted in red. All uncertainties are directlyquoted from the ACS database. The position of VLA J2130+12 stronglyindicates that it is not a cluster member and therefore is most likely associatedwith the radio source (see text for details).

Table 5Pysynphot Phoenix Model Fits

Fit IDa Metallicityb Counterpart Mass χ2/dof Pnulle

Assumption Me

star-only solar -+0.150 0.010

0.025 4.12/1 0.04

metal-poor 0.120 ± 0.010 1.36/1 0.24M15 0.330 ± 0.010 7.30/1 0.007

star+disk solarc 0.145 ± 0.010 0.002/0 L0.185 ± 0.010 1.75/0 L

metal-poor 0.115 ± 0.010 0.006/0 LM15d 0.330 ± 0.010 7.30/0 L

Notes. All errors are quoted at the 1σ confidence level. For the solar and metal-poor fits, a distance of 2.2 kpc is assumed. For the M15 metallicity fit, thedistance to M15 (10.4 kpc) is assumed.a Star-only = main-sequence counterpart only model, and star+disk = main-sequence counterpart + power-law accretion disk model.b Metal-poor corresponds to [M/H] = −1, and M15 refers to the metallicity ofthe cluster of [M/H] ≈ −2. See text for details.c Note that we find two minima for this model. This can occur in the low-massregime where one color (V − I) can correspond to multiple magnitudes (mv).Given the data quality (i.e., zero dof), we cannot confidently prefer one fit overthe other. In addition, the known distance to VLA J2130+12 also does notallow us to prefer one fit over the other.d Note that this fit returned a model with zero flux in the accretion disk.e Null hypothesis probability.

7

The Astrophysical Journal, 825:10 (13pp), 2016 July 1 Tetarenko et al.

Credit: Tetarenko et al. (2016)

Challenge - identification of thenature of a compact object.

The ratio of radio/X-ray luminosities -major diagnostics to separateBH-LMXBs from NS-LMXBs(Maccarone, 2005).The best way to identify possible CVs inGCs is by combining differenttechniques: optical variability, blue color,Hα excess, and X-ray emission (Kniggeet al. 2011).




Observations - #s: WDs, NSs, BHs

WD - single: well established cooling sequence on CMDs ofnearby GCs; in binaries: mainly with MS stars and WDs, but whynot the extension of the WD-WD binary cooling sequence?NS - mainly Millisecond Pulsars (MSP), 149 MSP in 28 GCs(http://www.naic.edu/ pfreire/GCpsr.html). Tarzan 5 - 36 MSP, 47Tuc - 25 MSPBH - two BHs candidates in M22 (Strader et al. 2012), onecandidate in M62 (Chomiuk et al. 2013), one candidate in 47 Tuc(Miller-Jones et al. 2015) and one BH candidate in anextra-Galactic GC (Maccarone et al. 2007).Some of the observed GR events could have origin in GC!60 BHs listed in the BHCatalog , some of them could have originin GCs (see Abbas Askar’s talk today)(http://www.astro.puc.cl/BlackCAT/)




Observations - IMBHNO DIRECT OBSERVATIONAL CONFIRMATION of an IMBH PRESENCEin GCs

Need precise velocity dispersion measurements in the close vicinity ofan IMBH. Observational techniques encounter difficulties in crowdedand populated by very bright stars centers of GCs. e.g. NGC6388 -integrated spectroscopy shows signs of IMBH (Lützgendorf et al. 2015),but resolved stellar kinematics does not (Lanzoni et al. 2013).About 107 Ultraluminous X-ray Sources (ULXs) in 122 galaxies - NewULX catalog(https://www.cosmos.esa.int/documents/332006/1402684/TRoberts.pdf)Mostly observed in off-center positions and in star forming regions.Accretion on IMBH is one of the possible scenarios for explaining ULXluminosities.Tidal Disruption Events (TDE). MS or WD disrupted by an IMBH.According to the Open TDE Catalog (https://tde.space/) 67 TDE eventsare listed, some of them (about four) are associated with IMBHs.For a comprehensive review about observational evidences for IMBHsplease see Mezcua 2017




NSs and BHs Retention

SNe natal kicks are believed to arise from asymmetries developedduring the explosion - either asymmetrically ejected mass (Janka 2017)or anisotropic emission of neutrinos (e.g. Fryer & Kusenko 2006).

NS natal kicks are well described by a Maxwellian distribution with thevelocity dispersion of σ = 265km/s - Hobs et al. (2005) (standardiron-core core-collapse supernova (CCSN)). There is mountingevidence that some NSs form with substantially smaller natal kicks(Ivanova et al. 2008). Probably connected with electron-capturesupernova (ECS) or accretion-induced collapse (AIC). For a detaileddiscussion please see Chruslinska et al. 2017.

Usually, for BH natal kicks, it is assumed that the amplitude of kicksdepends on the efficiency of asymmetric matter ejection. For low stellarmasses, kick velocities are as for NSs, for larger masses, kicks arereduced by mass fallback, and finally, for even larger masses, theprompt collapse or complete recapture of all ejected material happens.For a detailed discussion please see Belczynski et al. 2017.




NSs and BHs Retention Neutron star kicks and star cluster survival 3

0 5000 10000 15000 20000 25000 30000

t [Myr]

0.0

0.2

0.4

0.6

0.8

1.0

M M0

Kick

No Kick

BM03

Figure 1. Time evolution of the fraction of bound mass (normalized to theinitial value) of models with initial concentrationW0 = 5, on circularorbits. The models are characterized by different number ofparticles andby the presence (red lines; right to left:128kK, 64kK, 32kK, 16kK and8kK) or the absence (blue lines; right to left:128kN, 64kN, 32kN, 16kNand8kN) of NS kicks. The black dots mark when core collapse occurs. Thecorresponding models studied by BM03, i.e. without NS kicks, are alsoshown (green dashed lines; right to left:128k, 64k, 32k, 16k and8k); thisdata was retrieved by means of the data extraction tool Dexter.

3.2 Detailed comparison with Baumgardt & Makino (2003)

Despite our best efforts in reproducing the initial conditions and thenumerical set-up described by BM03, we note that there are stillnon-negligible discrepancies between our models without NS natalkicks and the corresponding ones in their original investigation (seeTable 1 and Figs. 1 and 2). We have attempted to identify the mainreasons for these discrepancies in the intrinsic differences betweentheN -body codes used to perform the simulations, and in particularslightly different stellar evolution prescriptions.

We performed our simulations by using the GPU version ofNBODY6 (Nitadori & Aarseth 2012), while BM03 used the publicGRAPE-6 version of NBODY4 (Aarseth 1999). The latter treatscomponents of binaries as single stars, without collisionsor ex-change of mass, and the resulting differences might partially ex-plain the increasing discrepancy after core collapse for the modelsdepicted in Fig. 2, because of the increase in the number of binariesat this time. Moreover, BM03 used a prescription for the propertiesof stellar remnants by Hurley et al. (2000), while in NBODY6 theEldridge & Tout (2004) recipe is now used. To test this, we carriedout a simulation of model128kN with the Hurley et al. (2000) pre-scription for stellar remnants, but we obtained a dissolution time ofTdiss = 23.0 Gyr, which reduces the discrepancy by only about30% (see data for model 128kN in Table 1).

To assess stochastic effects (such as run-to-run variations) wealso performed additional simulations of models128kN and64kNby evolving different numerical realizations of the same initial con-ditions, and by evolving the same realization in several indepen-dent simulations (as in BM03). Finally, we performed a simula-tion of model128kN in which the escapers were progressively re-moved (as in BM03), but again without any significant difference(Tdiss = 22.9 Gyr).

0 5000 10000 15000 20000 25000 30000

t [Myr]

0.0

0.2

0.4

0.6

0.8

1.0

M M0

BM03

Kick

No Kick

Figure 2. Time evolution of the fraction of bound mass of models with(i) W0 = 5, on elliptic orbits; (ii) W0 = 7, on circular orbits. As inFig. 1, models with NS kicks are denoted by red lines (right toleft: 128kK7and128kKe), and without NS kicks by blue lines (right to left:128kN7and128kNe). Dashed green lines show the corresponding models (withoutkicks) from BM03.

0 5000 10000 15000 20000 25000 30000

t [Myr]

0.4

0.6

0.8

1.0

1.2

1.4

1.6

<m>

[M⊙]

128kN

128kK

128kNe

128kKe

128kN7

128kK7

Figure 3. Evolution of the mean mass of the stars in the innermost lan-grangian shell, containing 1% of the bound mass, evaluated for all modelswith N=128k. The vertical arrows mark the moment of core collapse (in thefive models which exhibit core collapse).

None of these effects was able, individually, to account forthe observed discrepancy. Therefore, we believe that the small butsystematic discrepancy between our models without NS kicksandthe corresponding ones in BM03 results from a combination ofallthe effects mentioned above, and others which we have not stud-ied, including possible differences in the way in which models arevirialised and scaled in different codes. As we shall show later(Sect. 4.1) the sensitivity of these runs to small effects issuch thatapparently trivial differences could have significant effects.

Credit: Contenta et al. (2015)

The retention (or not) of NSs can have avery strong influence on GC globalevolution. Clear distinction between massloss dominated by the stellar evolution or bythe relaxation

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340

0

10

20

30

40

50

120

160

200

240280320

2E-4 2E-3 8E-3 1.7E-2 5E-4 4E-3 1E-2 2E-2 1E-3 6E-3 1.4E-2

Mre

m (

M�)

MZAMS

(M� )

Credit: Spera & Mapelli. (2017)

Strong dependence of the BH mass onmetallicity. For PISNe and PPISNe andZAMS masses in the range between about60M� and 230M� and low Z the final BHmass is strongly reduced or BH is notformed. For larger ZAMS masses, BH withmasses larger than 200M� can be formed,with small mass loss (see Spera and Mapelli2017).




NSs and BHs Retention

0

200000

400000

600000

800000

1x106

1.2x106

0 5000 10000 15000 20000 25000 30000

Tot

al C

lust

er M

ass

(Mo)

Time (Myr)

N=1200000, Wo=6, tidaly filling, binary-fraction 0.95

Rt=120pc, no fallbackRt=120pc, fallback



Models which retain of larger number ofBHs (mass fallback ON) dissolve faster thanmodels which kick out most of BHs (massfallback OFF). This is opposite behaviorthan for NSs. Models with mass fallbackenter the post-core collapse phase and yetshow the fast dissolution feature.

0

200

400

600

800

1000

1200

1400

1600

0 5000 10000 15000 20000 25000 30000

Tot

al C

lust

er M

ass

(Mo)

Time (Myr)

N=1200000, Wo=6, tidaly filling, binary-fraction 0.95




The reason for such behavior is connectedwith formation BH-subsystems in the clustercenters, which very efficiently generateenergy in dynamical interactions betweenBHs. Such energy generations, for tidallyfilling systems, lead to the unstable massloss.




NS as a Tracers of the GC Potential

Long term observations of radio pulsar timing can be used as a tracer of theglobular cluster potential. The intrinsic changes of the pulsar period aresmaller than changes connected with acceleration or deceleration of a pulsarby the star cluster gravitational potential - cluster mass distribution.

Giersz & Heggie 2011 - Pulsar acceleration for the first time used,together with velocity dispersion profile, surface brightness profile andluminosity functions to constrain model of 47 Tuc - no IMBH verynonstandard IMF.

Kiziltan, Baumgardt & Loeb 2017 - 19 Pulsar timing for 47 Tuc togetherwith N-body simulations were used to infer the IMBH mass, equal toabout of 2300M�

Prager et al. 2017 - 36 pulsar timing for Tarzan 5 were used to infer GCstructural parameters and an IMBH mass, equal to about of 30000M�

Perera et al. 2017 - 25 years of the PSR B1820-3A pulsar timing i GCNGC6624 allow to estimate the IMBH mass to about of 20000M�




Cataclysmic Variables

Already discussedon Tuesday

in Diogo Belloni’s talk




BH MergersBH subsystems 585

as with globular star clusters, the random gravitational encountersbetween stars can substantially affect the structure of these systems,especially for more massive components and in the core. Ignoringthe possible presence of a massive BH, NSC would be expected toevolve dynamically in a similar way to globular star clusters, i.e. to-wards balanced evolution sustained by energy generation involvingbinaries. However, Miller & Davies (2012) argued that the tradi-tional mechanism of energy generation involving binaries wouldnot be able to provide the energy necessary if the central velocitydispersion exceeded ∼40 km s−1 because in that case BH binarieswould coalesce by emission of gravitational radiation before hav-ing time to interact dynamically with the other BH, and would thenescape due to the kick applied at the final merger. They also ar-gued that systems whose central velocity dispersion exceeded thatvalue would undergo a deep core collapse, possibly leading to theformation of a massive central BH.

In the present paper we will re-examine the possibility of BHsubsystems in NSC in the light of the above recent advances instellar dynamics. We will work with the aid of an idealized NSCmodel, consisting of two components (the BH and the other stars),ignoring the dynamical role of the rest of the galaxy, and assumingthat the galaxy does not harbour a central massive BH. We willassume as with globular star clusters that Henon’s principle (Henon1975) applies, i.e. that the energy generating rate of the core isregulated by the bulk of the system. Except for the issue of kicksresulting from merging BH binaries (see above) our discussion isNewtonian. In the next section we will consider the phases throughwhich the evolution of the NSC proceeds. Section 3 considers theevolution of an idealized NSC without dynamically active binaries,where the only mechanism of energy generation is escape of mergedBH. This is followed by a section of conclusions and discussion,where various constraints on the existence of BH subsystems inNSC are discussed.

2 EVO L U TION O F BH S U BS YS T E M S I N N SC

The evolution of the core of a system containing a BH subsystemis illustrated in Fig. 1, which is based on the ideas in Breen &Heggie (2013). The evolution has been divided into four regions:region I, the segregation of the BH and formation of the densecentral BH subsystem; region II, balanced evolution powered byBH binaries; region III, the depletion of the BH, ending in a secondcore collapse, this time in the low-mass component and region IV,the ultimate restoration of balanced evolution, following the secondcore bounce. The region a system will be in at the present time willdepend on its age and its evolutionary time-scale, which in turndepends on the parameters of that system. In the idealistic case ofa system consisting of two populations, the BH and the other stars,these parameters are the half-mass relaxation time, the stellar massratio of the two components and finally the total mass ratio of thetwo components.

For a star cluster with N stars and a Kroupa initial mass function(IMF; Kroupa 2001) one would expect ∼2 × 10−3N BH to form(Banerjee et al. 2010). Assuming that the BH are typically moremassive than other stars by a factor of 20, then the total mass inBH is ∼4 per cent of the total cluster mass (M). To be conservative,in the present paper we will assume that the total mass in BH isalways ∼2 per cent of M initially. We will also make the simplifyingassumption that the initial half-mass relaxation time (trh,i) of a NSCis approximately the same as the present value trh. The effects ofthis assumption are discussed in Section 4.

Figure 1. Schematic diagram of the evolution of the core radius in anidealized star cluster with a BH subsystem. The diagram is divided into fourregions I, II, III and IV. In region I the BH segregate to the core forming theBH subsystem, which rapidly undergoes core collapse. This is followed byregion II, where the system exists in a state of balanced evolution, i.e. thecore of the BH subsystem adjusts so that the energy it produces, throughthree-body interactions, balances the flow of energy by relaxation in thebulk of the system. As the BH population becomes depleted in region II, inregion III the system undergoes another core collapse. Finally in region IVbalanced evolution is restored, although now the core of the low-mass starsneeds to be more compact to allow the formation and interaction of binariescomposed of the less massive stars.

Now we discuss the time-scales of the various phases in Fig. 1. Adirect N-body simulation of an idealized two-component star clusterwith N = 64 000 by Breen & Heggie (2013)1 indicated that it takes≈0.3 trh,i for the bulk of the stellar mass BH to segregate to the centreof the cluster and undergo core collapse. In realistic systems thesegregation time-scale for the BH depends on a number of factors,mainly the initial spatial distribution of BH and the stellar massesof the BH. In an unpublished N-body simulation of the Galacticglobular cluster M4, for example, core collapse of the BH subsystemtook about 0.9 trh,i. Nevertheless, we shall use the foregoing valueas a guide, and assume that it takes approximately 0.3 trh for theBH subsystem to form and reach core bounce. Therefore systemswhich are less than 0.3 trh old are still in the process of forming aBH subsystem, i.e. in region I of Fig. 1.

Shortly after this time balanced evolution is achieved, and the BHpopulation starts to become steadily depleted (region II of Fig. 1).The theoretical estimate from Breen & Heggie (2013) of the time-scale of this phase of evolution is ≈6 trh,i. At some point there areinsufficient BH remaining to maintain balanced evolution. Breen &Heggie (2013) argued that this happens when the number of BHreaches about 40. In the present paper, we shall define the end ofthe subsystem as the time when the number of BH reaches 40 andassume the system then enters region III. Here the system is nolonger in balanced evolution and undergoes core collapse of thelow-mass component. If there are no BH remaining, then the corecollapses until new binaries are formed from the other stars in thesystem, and then balanced evolution is restored (region IV of Fig. 1).If residual BH do remain, then contraction of the core of low-massstars is still needed in order that interactions with the BH and witheach other become efficient enough.

Under our assumptions, there are two constraints for the existenceof a centrally concentrated subsystem of BH: one, that the BHsubsystem has had enough time to form (i.e. the age of the system

1 The parameters of the run were N = 64 000, total mass ratio 0.02 andstellar mass ratio 20.

Downloaded from https://academic.oup.com/mnras/article-abstract/436/1/584/974758/On-black-hole-subsystems-in-idealized-nuclear-starby gueston 05 September 2017

Credit: Breen & Heggie. (2013)

Old theory - BHs are quickly kickedout from the system (Kulkarni,Hut &McMillan 1993, Sigurdsson &Hernquist 1993).New theory - BH subsystem can beformed and preserved during the Hubbletime provided the cluster has long enoughrelaxation time (Breen & Heggie 2013)

Credit: Rodriguez et al. (2016)

Mergers mainly for escaped BH-BHbinaries.The larger the cluster mass, the larger thenumber of BH-BH mergers (Rodriguez et al.2016).




IMBH Observational Suggestions

1e-05

0.0001

0.001

0.01

0.1

1

10

100

0 5000 10000 15000 20000 25000 30000 35000

R (

pc)

Time (Myr)

Wo = 6, T. Underfilling, RG=8kpc, M=500000 Mo, bf=0.95, Rh/Rt=50, Rt=98 pc

Rh

Rc

BIN-SIN_NSBIN-BIN_NS

SIN-EVO_NSBIN-EVO_NS

COLL_NSBIN-BIN_BH

BIN-EVO_BHSIN-EVO_BH

COLL_Bh

NSs and BHs can form later in the clusterevolution because of dynamicalinteractions and stellar evolution inducedby dynamical interactions.

Presence of an IMBH prevents formationof NSs and BHs.

0.0001

0.001

0.01

0.1

1

10

10 100 1000 10000 100000

MIM

BH

/Mto

t at 1

2Gyr

Time of IMBH formation (Myr)

Clusters with high M/L ratio can harbor anIMBH which consists of most of the clustermass.

IMBHs can be formed at the verybeginning of the cluster evolution in verydense and low-mass GCs or massive OCs.




BH-BH MergersTime

0 Myrs

Escape Time 145 Myrs

30.1 M⊙ MS Star

30.0 M⊙ MS Star

25.1 M⊙ BH 25.0 M⊙ BH

Collision

30.1 M⊙ BH

5 M⊙ CHeB Star

3x Binary-Single Flybys

3x Binary-Single Exchange

26x Binary-Single Flybys4x Binary-Single Exchange8x Binary-Binary Interactions1x Binary-Single Merger

3x

7x

8x

3x

M1 = 30.4 M⊙

M2 = 25 M⊙

a = 21.8 R⊙

e = 0.72

see Abbas Askar’s talk todayDynamical interactions leading toBH-BH binary formation and thento its escape and later to itsmerger, because of GR emission,are very numerous and violent.The initial configurations areerased.

Collaborators: Abbas Askar,Arkadiusz Hypki, Jongsuk Hong,Magdalena Szkudlarek, TomaszBulik, Dorota Gondek, ManuelArca Sedda, Jakub Murawski




BH-BH Mergers: Spins and Recoil Kicks

Mergers only inside GCs: primordial -3385, dynamical 1061BH spins according to Belczynski et al.(2017) - BH mass and Z dependencePrimordial - nearly aligned, Dynamical -randomly distributed

where l is the value of a vector−→l parallel to orbital angular momentum, con-

stituting the additional contribution to �nal spin vector besides −→a 1 and −→a 2,given by:

l =s4

(1 + q2)2(a21 + q4a22 + 2q2a1a2 cosα

)+s5η + t0 + 2

1 + q2(a1 cos θ1 + q2a2 cos θ2

)+

+ 2√3 + t2η + t3η

2

(3)

and α is the angle between spin vectors −→a 1 and−→a 2, easy to calculate by cosα =

cos θ1 cos θ2+sin θ1 sin θ2 cos(ϕ2−ϕ1). Constants t0, t2, t3, s4, s5 are values fromnumerical �ts on which the derivation in [2] was based on.Having introduced these two parameters, both of which are some measure ofspin misalignment and magnitude, the natural question arises whether they arecorrelated in any way. Plotting them with respect to each other revealed curiousstructures shown in �gure 2.

Figure 2: Relation between χe� and a�n, on the left for MS0 and on the rightfor MS1. Constraints introduced by Belczynski's mass-spin relation lead to avery interesting "cross" structure.

4.1 Primordial

For the primordial case we can see a clear linear relation between e�ective spinand �nal spin, which is actually not very di�cult to explain. Because in thiscase both masses are usually low (and hence the resulting q is in most cases closeto 1 (η ≈ 0.25)) and spins are approximately aligned with the orbital angularmomentum (3.2), for the simplest approximation we can take m1 = m2 andcos θ1 = cos θ2 = 1. In this case formulas 1 and 2 simplify to:

χe� ≈a1 + a2

2(4)

a�n ≈a1 + a2 + l

4(5)

Additionally from eqation 3 we get:

l ≈s54 + t0 + 2

4(a1 + a2) + 2

√3 +

t24+t364

+s44(a21 + a22 + 2a1a2) (6)

4

The "cross" shape is a consequence of theZ dependence of the BH spins and smallmass ratios for merging BHs.For larger mass ratios the "cross" shapewill still be smeared, but effective spin willbe rather small.




Field BH-LMXBs Originating from GCs

46.4 M⊙ MS StarBinary System:

0.64 and 0.65 M⊙ MS Stars

10.3 M⊙ BH

2x

10x 3x

3x

8x2x

3.4 M⊙ SG Star

Merger with BH during binary-single interaction

BH Mass = 13.7 M⊙ BH3x

11x Binary-Binary Interactions17x Binary-Single Flybys

MBH = 13.7 M⊙

MMS = 0.65 M⊙

a = 13.7 R⊙

e = 0.57

Time0 Myrs

Escape Time 2353

Myrs

Escaped binary is MT after 8 Gyrs of stand-alone binary

evolution.

see Abbas Askar’s talk todayDynamical interactions leading toBH-MS binary formation and thenits escape could be verynumerous and violent. The initialconfigurations are erased.The mass distribution of MSdonors is very similar to theobserved one.

Collaborators: Abbas Askar,Diogo Belloni, Serena Repetto,Jakub Klencki, KrzysztofBelczynski, Hagai Perets




Tidal Disruption Events with IMBH

Collaborators: Jakub Klencki, NathanLeigh, Nicholas Stone

WD-IMBH type - 344755, MS-IMBH type750753, Other-IMBH 42934.

Present day TDE rate density isdominated by WD TDEs.

Present day TDE rate is about 0.2 per GCper Myr, which is close to the observedTDE rate about 2x10−5 per galaxy per yr,if we assume that on average about 100GCs are formed in one galaxy.

Number of "active" GCs in which TDEsare happening is nearly constant in time.

Most TDEs are formed in massive GCswith relatively small Galactocentricdistances. Some of GCs can, in a fewGyrs, migrate to the Galactic center andthen TDEs will have different distribution.




BH Subsystems and IMBHs

0.1

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-10 -8 -6 -4 -2 0 2

Centra

lSurfaceBrightness(L

um/pc2)

TotalAbsoluteVMagnitude

12GyrObservationalPropertiesofModels

All-12Gyrs#BHs>50

IMBHHarrisCatalogue

Collaborators: Abbas Askar,Arkadiusz Hypki, Manuel Arca Sedda,Bülent Kiziltan, Paulo Bianchini,Ruggero de Vita, Sebastian Kamman,Michele Trenti

How to distinguish between GCscontaining an IMBH or aBH-subsystem? - Bright models withIMBHs have larger central surfacebrightness, particularly models withvery massive IMBH. Bright modelswith low central surface brightnessseem to harbor BH-subsystems.

How to decide if a cluster containsdynamically active BH-subsystem? -It seems that the ratio between"running" average mass of BHs andother stars is a good choice. If theratio is greater than 5, whichcorresponds to about 70 BHs, thesystem contains a dynamically activeBH-subsystem.




CV Population, BSE and IBP12 Belloni et al.

7.6 Magnitude during quiescence

Another important observational property of GC CVs is theirmagnitudes. Once a potential candidate is identified via its X-rayluminosity, a confirmation via other techniques (such as identify-ing the optical counterparts) are required in order to improve theconfidence level that the source is in fact a CV candidate2.

In general, for period-bouncers, the optical flux is dominatedby the WD, with little (if any) contribution from the hot spot cor-responding to where the stream of matter from the donor strikesthe accretion disk. This is especially true for the population of faintCVs found in the GC NGC 6397 (Cohn et al. 2010). As claimedby these authors, the WD should be heated by the accretion pro-cess overall, since isolated massive WDs are faint enough to avoiddetection (i.e., they have efficient cooling).

In our simulations, we estimate the CV magnitude as de-scribed in Belloni et al. (2016). No additional heating is added tothe WDs. For the cCAML and eCAML schemes, we do not haveinformation about the WD magnitude or temperature. Thus, wepresent our results only for the MOCCA formulation. Here, wehave information about the WD magnitude and can compute theCV magnitude by adding the flux contributions from the four maincomponents: WD, donor, hot spot and disk.

Present-day CV magnitudes are strongly dependent on thetime since CV formation, as well as on the formation mechanism.Basically, the later the CV is formed (i.e., mass transfer starts), thebrighter it is. Since dynamically formed CVs are more massive,those newly formed CVs are brighter than CVs newly formed fromprimordial binaries. Here, we define newly formed CVs as CVsformed after ∼ 10 Gyr of cluster evolution, i.e. at most 2 Gyr ago.

Among those CVs that form at intermediate times (after ∼ 1Gyr of cluster evolution but before ∼ 10 Gyr), we see a transitionin dynamically formed CVs; those formed a long time ago are cur-rently fainter but those formed more recently are currently brighterthan those CVs formed from primordial binaries. This transition oc-curs at ∼ 6 Gyr. The reason is twofold. On the one hand, this effectis partially due to the above-mentioned cooling efficiency of theWDs. But, on the other hand, the hot spot becomes the brightest CVcomponent at this particular formation-time (and its luminosity isrelated to the donor mass, i.e. the higher the donor mass, the higherthe mass transfer rate, and in turn the higher the hot spot luminos-ity). In other words, CVs formed at maximum ∼ 6 Gyr ago havetheir optical fluxes dominated by their hot spots and those formedbefore this time have their optical fluxes dominated by their WDs.This makes dynamical CVs more luminous (currently) if formedafter ∼ 6 Gyr of cluster evolution and CVs formed from primor-dial binaries more luminous (currently) if formed before ∼ 6 Gyrof cluster evolution.

For CVs that formed a long time ago (before ∼ 1 Gyr of clus-ter evolution), distinguishing between the different formation chan-nels is more difficult. This is because these CVs have more massiveWDs irrespective of their formation channels, such that their WDcooling efficiencies and magnitudes are similar.

The description above is illustrated in Fig. 4, where only CVsformed using the MOCCA scheme are shown. These are separated

2 As in the Galactic field, only spectroscopy can confirm that a CV candi-date is indeed a CV (Knigge 2012). However, since GCs are crowded fields,spectroscopy might be a challenge. The use of a combination of differenttechniques (Hα and FUV imaging, X-ray, colour, late and negative super-humps, etc.) will therefore be needed to confirm the GC CV candidates,especially for DNe.

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BSE group: α=1 and αrec=0.0WDI group: α=1 and αrec=0.0SDI group: α=1 and αrec=0.0

Figure 4. CV absolute V-band magnitude as a function of the CV forma-tion time. We plot all CVs formed in MOCCA, and consider all 12 mod-els. These are separated according to our choices for the CEP parametersand our classifications for the influence of dynamics in CV formation. Notethat, in general, dynamically formed CVs (SDI group) are brighter than CVsformed from primordial binaries (BSE and WDI groups). This is the caseprovided they form close to the present-day (less than ∼ 6 Gyr ago). Atthis point, namely ∼ 6 Gyr ago, a transition occurs in which dynamicallyformed CVs start becoming fainter than CVs formed from primordial bina-ries. This is because, at this point, the CV flux starts to become dominatedby the WD flux. As pointed out in Section 7.1, most CVs formed from pri-mordial binaries have He WDs, which are brighter than C/O WDs (due tothe more efficient cooling in the latter). Finally, for CVs formed at ∼ 1 Gyr(or earlier), it is very difficult to distinguish between CVs formed from dif-ferent formation channels. This is because, at these early times, basically allCVs have C/O WDs irrespective of the formation channel. For more detailssee Section 7.6.

according to our choices for the CEP parameters and our classifica-tions for the influence of dynamics in CV formation. Note that thetrends associated with each formation channel are independent ofthe CEP parameters.

We emphasize here that although we do not consider changesin the WD magnitude arising from the accretion process, we ex-pect the same overall results were this effect to be included. This isbecause the above-described picture concentrates on the effects ofdynamics in shaping present-day GC CV magnitudes and detectionlimits. This feature or transitional path is similar in all models, asoriginally observed in the GC NGC 6397 (Cohn et al. 2010).

7.7 Spatial distributions

Finally, we provide a few words regarding the CV spatial dis-tribution, as a function of the CV brightness. Cohn et al. (2010)found that there is no strong evidence in favour of the radial dis-tribution of main-sequence-turn-off stars being different from thefaint CVs (p-value ∼ 0.04). However, for bright CVs, the evidenceis sufficient (p-value ∼ 0.001) to make the claim that bright CVsare more centrally concentrated.

In our models, we also typically find this trend. However, itstrongly depends on the following properties: (i) the source of en-ergy in the host cluster, (ii) the host cluster evolution, (iii) the av-erage mass in the host cluster core, (iv) the WD-MS binary andCV formation times, (v) the WD-MS binary and CV masses, and(vi) the formation channel (Belloni et al. 2016, see Section 5.7).We emphasize that the inclusion of the six additional models con-

MNRAS 000, 1–18 (2016)

Collaborators: Diogo Belloni, AbbasAskar, Arkadiusz Hypki, Pavel Kroupa,Mónica Zorotovic, Matthias Schreiber,Jangsuk Hong, Enrico Vesperini, HelioRocha-Pinto, Nathan Leigh, JarrodHurley, Krystian Iłkiewicz

Already discussed in DiogoBelloni’s talk on TuesdayBright CVs were formed relativelyrecently in dynamical interactions.Bright CVs are more centrallyconcentrated than dim CVs.Good agreement withobservations for NGC 6397 andNGC 6752 (Cohn et al. (2010),Lugger et al. 2017.




WD-NS Mergers

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Correlation with initial cluster centraldensity and binary fraction. Strongercorrelation for models without anIMBH.Collaborators: Ken Shen, AbbasAskar, Diogo Belloni, Arkadiusz Hypki,Melvyn Davies, Ross Church, AlexeyBobrick

Calcium-Rich-Transients - WD-NSmerger. Their radial distributionextends tens of kpc away from theirhost galaxies - possible connection toGCs.

Ultra-compact X-Ray binaries - NSwith very low mass WD companion.

In 21 MOCCA models 359 NS wereformed through AIC channel inWD-WD binaries. After formation, NSis still in a binary with a very smallmass WD.

Very preliminary results - need moremodels to check correlations betweencluster initial conditions andproperties of WD-NS binaries.




GR effects during BH-BH and BH Interactions

Credit: Samsing et al. (2017)

Collaborators: Abbas Askar,Arkadiusz Hypki, Johan Samsing

MOCCA Survey Database contains:5560858 3-body dynamicalinteractions between only compactobjects and 674079 4-bodyinteractions between compact objects.

Fewbody code with dissipative effects,connected with GR and tidalinteractions will be used to redo all thedynamical interactions from theMOCCA simulations to check how themerger rate between stars, in thoseinteractions, will increase.




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M=1.3x107 Mo, Rh=1 pc, R=300 pc, ρc=1.3x109 Mo/pc3, binary-fraction=0.1

Relative velocity1000 km/s - 150 Mo MS escape velocity

IMBH mass

Collaborators: Abbas Askar, DiogoBelloni, Arkadiusz Hypki, MelvynDavies

First ever done "real size"simulations of Nuclear StarClusters!Extremely fast formation of anIMBH - about 105M� during 100Myr!For most of dynamicalinteractions, relative velocities atinfinity are smaller than theescape velocity from massive MSstars. Interactions are not fullydisruptive!




MOCCA - Work in Progress

New Fewbody code with GR and tidal dissipation effects andbackground gas Mario Spera, Johan Samsing, Taeho Ryu,Nathan Leigh, Aaron Geller, Abbas Askar, Diogo Belloni,Arkadiusz Hypki, Rosalba Perna, Alessandro TraniMultiple Stellar Populations and Residual Gas Removal - MarioSpera, Robert Izzard, Michela Mapelli, Jarrod Hurley, AbbasAskar, Diogo Belloni, Arkadiusz HypkiTwo-Body dissipative interactions - Abbas Askar, ArkadiuszHypki, Diogo BelloniHierarchical Systems - Arkadiusz Hypki


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