Progenitors of binary black hole mergers detected by LIGO
Konstantin Postnov Alexandre Kuranov






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        #1eq. (<ref>)#1Eq. (<ref>)#1 (<ref>)#1#2(#1/#2)#1⟨#1⟩#1LIGO binary BH mergers progenitors] 
        Progenitors of binary black hole mergers detected by LIGOKonstantin Postnov & Alexander Kuranov]   
        Konstantin Postnov 
        
          Alexander KuranovSternberg Astronomical Institute, Moscow M.V.Lomonosov State University 
        
        13, Universitetskij pr., 119234 Moscow, Russia
        
         email:  pk@sai.msu.ru
        
        2017329
        The lives and death-throes of massive starsJ.J. Eldridge, ed.[
            [
            
        =====
        
        
        Possible formation mechanisms of massive close binary black holes that can merge in the Hubble time to produce powerful gravitational wave bursts 
        detected during advanced LIGO O1 science run are briefly discussed. The pathways include the evolution from field low-metallicity massive binaries, 
        the dynamical formation in globular clusters and primordial black holes. Low effective black hole spins inferred for LIGO GW150914 and LTV151012 
        events are discussed. Population synthesis calculations of the expected spin and chirp mass distributions from the standard field massive binary formation channel are presented for different metallicities (from zero-metal Population III stars up to solar metal abundance). We conclude that that merging binary black holes can contain systems from different formation channels, discrimination between which can be made with increasing
        statistics of mass and spin measurements from ongoing and future gravitational wave observations. 
        
        
        
        
                      
        
        
        § INTRODUCTION AND HISTORICAL REMARKS
        
        The epochal discovery of the first gravitational wave source GW150914 from coalescing binary black hole (BH) system 
        <cit.> not only heralded the beginning of gravitational wave astronomy era, but also stimulated a wealth of works on 
        fundamental physical and astrophysical aspects of the formation and evolution of binary BHs. The LIGO detection of  GW150914 
        and of the second robust binary BH merging event GW151226 <cit.> enables BH masses and spins before the merging, 
        the luminosity distance to the sources and the binary BH merging rate in the Universe to be estimated <cit.>. 
        Astrophysical implications of these measurements were discussed, e.g., in <cit.>. 
        
        This discovery of gravitational waves from coalescing binary BHs was long awaited. 
        Evolution of massive binary systems was elaborated in the 1970s to explain a rich variety of newly discovered galactic 
        X-ray binaries <cit.>. Formation of two relativistic compact remnants (neutron stars (NSs) or black holes) naturally
        followed from the binary evolution scenario <cit.>. 
        At the dawn of the LIGO Project, Tutukov and Yungelson 
        <cit.> calculated, using the standard assumptions of massive binary evolution, the 
        expected galactic merging rate of binary NSs and BHs. They pointed out that although the galactic merging rate of 
        binary NSs is much larger than that of binary BHs, their detection rates by gravitational-wave interferometers 
        can be comparable due to the strong 
        dependence of the characteristic GW amplitude h_c on the total mass M=M_1+M_2 of the coalescing binaries, h_c∼ M^5/2. 
        A few years later, independent population synthesis calculations by the Scenario Machine code were reported in a series of papers 
        <cit.>. They showed that in a wide range of possible BH formation parameters 
        (masses,kick velocities) and under standard assumptions of the massive star evolution, the detection rate of binary BH mergings
        should be much higher than that of binary NSs, and the first LIGO event should most likely to be a binary BH merging. Interestingly, 
        the mean BH masses known at that time from dynamical measurements in galactic BH X-ray binaries were about 
        10 M_⊙, which forced (cautiously) the authors of 
        <cit.> to fix the parameter k_BH=M_BH/M_c, where M_c is the mass of the star before the collapse,
        around ∼ 0.3 (see Fig. 4 in that paper) in order to produce the chirp mass of coalescing binary BHs around 15 M_⊙. Taking k_BH=1, one immediately obtains the BH masses around 30-40 M_⊙, which seemed outrageously high at that time. 
        
        Starting from the end of the 1990s, various groups have used different population synthesis codes to calculate the merging rates of double compact objects 
        (see especially many papers by the Polish group based on the StarTrack code <cit.>), yielding a wide range of possible 
        BH-BH merging rates (see e.g. Table 6  in <cit.>). Clearly, the degeneracy of binary evolution and BH formation parameters
        has been so high <cit.> that only real observations could narrow the wide parameter range. 
        
        
        
        
        
        
        
        § STANDARD SCENARIO OF BINARY BH FORMATION
        
        
        
        The standard scenario of double BH formation from field stars is based on well-recognized evolution of single massive stars <cit.>. 
        To produce a massive BH with M≃ 10M_⊙ in the end of evolution, the progenitor star should have a large mass and low mass-loss rate. 
        The mass-loss rate is strongly dependent on the metallicity, which plays the key role in determining the final mass of 
        stellar remnant (see <cit.> and N. Yusof's contribution in this conference). The metallicity effects were included in the population synthesis calculations <cit.>, and the most massive BHs were found to be produced by the low-metallicity progenitors.
        Here early metal-free Population III stars provide an extreme example, see calculations by <cit.>. After the discovery of GW150914, 
        several independent population synthesis calculations were performed to explain the observed masses of binary BH in GW150914 and the inferred binary BH 
        merging rate ∼ 9-240 Gpc^-3yr^-1<cit.><cit.>. 
        
        In addition to the metallicity that affects the intrinsic evolution of the binary components, 
        the most important uncertainty in the binary evolution is the efficiency of the common envelope (CE) stage which 
        is required to form a compact double BH binary merging in the Hubble time. The common envelope stage remains a highly debatable issue. 
        For example, in recent hydro simulations <cit.> a low CE efficiency was found, while successful CE calculations 
        were reported by other groups (see, e.g., N. Ivanova contribution at this conference).  
        Another recent study <cit.> argues that 
        it is possible to reconcile the BH formation rate through the CE channel taking into account the stability of mass transfer in massive binaries 
        in the Hertzsprung gap stage, which 
        drastically reduces the otherwise predicted overproduction of binary BH merging rate in some population synthesis calculations.
        Also, the so-called stable 'isotropic re-emission' mass transfer mode can be realized in high-mass X-ray binaries with massive BHs, thus helping to avoid 
        the merging of the binary system components in the common envelope <cit.>. This stable mass transfer mode 
        can explain the surprising stability of kinematic characteristics observed in the galactic microquasar SS433 <cit.>.
        
        Of course, much more
        empirical constraints on and hydro simulations of the common evolution formation and properties are required, but the formation 
        channel with common envelope of binary BHs with properties similar to GW150914  remains quite plausible.
        
        
        
        
        § OTHER SCENARIOS
        
        
        To avoid the ill-understood common envelope stage, several alternative scenarios of binary BH formation from massive stars were proposed. 
        For example, in short-period  massive binary systems chemically homogeneous evolution due to rotational mixing can be realized. The stars remain
        compact until the core collapse, and close binary BH system is formed without common envelope stage <cit.>.
        In this scenario, a pair of nearly equal massive BHs can be formed with the merging rate comparable to the empirically inferred from the first LIGO observations. 
        
        Another possible way to form massive binary BH system is through dynamical interactions in a dense stellar systems (globular clusters). This 
        scenario was earlier considered by <cit.>. In the core of a dense globular clusters, stellar-mass BH form multiple systems, and 
        BH binaries are dynamically ejected from the cluster. 
        This mechanism was shown to be quite efficient in producing 30+30 M_⊙ merging binary BHs <cit.>, and 
        binary BH formed in this way can provide a substantial fraction of all binary BH mergings in the local Universe <cit.>. 
        
        Finally, there can be more exotic channels of binary BH formation. For example, primordial black holes (PBHs) 
        formed in the early Universe can form pairs which could be 
        efficient sources of gravitational waves <cit.>. After the discovery of GW150914, the interest to binary PBHs
        has renewed <cit.>. Stellar-mass PBHs can form a substantial part of dark matter in the Universe <cit.>. The PBHs formed
        at the radiation-dominated stage can form pairs like GW150914 with the merging rate compatible with empirical LIGO results, being only a small fraction of all 
        dark matter <cit.>. Different class of PBHs with a universal log-normal mass spectrum produced in the frame of a modified Affleck-Dine supersymmetric baryogenesis <cit.> were shown to be able to match the observed properties of GW150914 <cit.>. 
         
        
        
        
        
        § LOW SPINS OF BH IN GW150914 AND LTV151012 EVENTS
        
        
        In the framework of general relativity, a BH is fully characterized by its mass M and dimensionless 
        angular momentum a=J/M (in geometrical units G=c=1) (the possible BH electric charge is negligible in real astrophysical conditions). 
        The LIGO observations enable measurements of both masses of the coalescing BH components, M_1 and M_2, and the chirp mass that determines the strength of gravitational wave signal M=(M_1M_2)^3/5/M^1/5. From the analysis of waveforms at the inspiral stage, individual BH spins before the merging are poorly constrained, but their
        mass-weighted total angular momentum parallel to the orbital angular momentum, χ_eff, can be estimated with good accuracy 
        <cit.>[The parameter χ_eff=(M_1χ_1+M_2χ_2)/M, where χ_i=a_icosθ_i with θ_i being the angle between the angular momentum of the i-th BH and orbital angular momentum of the binary system.]. The O1 LIGO detections suggest that the most massive GW150914 and (less certain) LTV151012 have very low χ_eff≃ 0.
        
        
        
        This observational fact has important evolutionary implications (see <cit.>). It suggests a very slow rotation of BH progenitors, which by itself strongly constraints, for example, chemically homogeneous pathways mentioned above in which tidally induced rotation of the close binary  
        components plays the key role. Massive stars are observed to be rapid rotators. No significant angular momentum loss is expected during
        their evolution with low mass loss rate by stellar wind and at the pre-collapse stage as required to produce massive BHs <cit.>. 
        Note that low effective spin values can imply either small intrinsic BH spins a∼ 0, or unusual orientations of BH spins with respect to the 
        orbital angular momentum at the inspiral stage. The last case can well be reconciled with the dynamical formation scenario <cit.>, where the BH spins are not expected to be correlated with the orbital angular momentum. In the PBH scenario, BH spins must be zero as there are no vorticity 
        in primordial cosmological perturbations. 
        
        
        Therefore, the mass-spin distribution of BHs can serve as a sensitive tool to discriminate between different 
        astrophysical formation channels of coalescing massive binary BHs. To estimate the spin distribution of BH remnants in binaries, 
        it is necessary to know how to treat the spin evolution of the stellar core, which is ill-understood and strongly model-dependent. 
        One possible approach is to match theoretical predictions of the core rotation with observed period distribution of the young neutron stars observed as radio pulsars <cit.>. Initially, a star is assumed to rotate rigidly, but after the main sequence the star can be separated in
        two parts – the core and the envelope, with some effective coupling between these two parts. The coupling between the core and envelope rotation can be mediated by magnetic forces, internal gravity waves (see <cit.> and J.Fuller's talk at this conference), etc.
        The validity of such an approach was checked by direct MESA calculations of the rotational evolution of a 15 M_⊙ star <cit.>.
        It was found that the observed period distribution of young pulsars can be reproduced if the effective coupling time between the core and envelope is τ_c=5× 10^5 years (see Fig. 1 in <cit.>). Below we shall assume that this time is also applicable to the evolution of very massive stars leaving behind BH remnants.
        
        Each angular momentum of the main-sequence components of the initial binary is assumed to be arbitrarily distributed in space, its absolute 
        value being connected to the initial stellar mass using the empirical relation between the equatorial rotation velocity of a star with its mass
        v_rot=330M_0^3.3/(15+M_0^3.45) km s^-1 (here M_0 is in solar units). It was assumed that the rotation of the stellar envelope gets synchronized with the orbital motion with the characteristic synchronization time t_sync, and the process of tidal synchronization was treated as in the BSE code <cit.>. Due to intrinsic misalignment of the spin vectors of the stars with the binary orbital angular momentum L̂, we separately treated the core-envelope coupling for the spin components parallel and perpendicular to L̂. On evolutionary stages prior to the compact remnant formation, for each binary component we assumed that due to tidal interactions the parallel component of the stellar envelope spin J_|| gets synchronized with the orbital motion on  the characteristic time t_sync, while the normal spin component J_⊥ of the stellar envelope decreases due to the tidal interaction in the binary system the on 
        the same characteristic time scale, which leads to the secular evolution of the spin-orbit misalignment. The parallel component of the 
        envelope spin also evolves due to the core-envelope interaction with the characteristic time τ_c. These processes were added to 
        the updated BSE population synthesis code. 
        
        With these additions, the population synthesis of typically 100000 binaries per run has been carried out for different parameters of binary evolution (the common envelope stage efficiency α_CE, stellar metallicities etc.). 
        No generic BH kick was assumed. The results of calculations of BH spin distributions for different stellar metallicites and for the standard CE efficiency parameter α_CE=1 are shown in Fig.  <ref>. Evolution of zero-metallicity (primordial Population III) stars was parametrized as in <cit.>. 
        Fig. <ref> shows the plot of coalescing binary BHs on the M-χ_eff plane for different metallicities.
        BH spin misalignments with orbital angular momentum in coalescing binary BHs for different stellar metallicities are presented in Fig. <ref>.
        
        
        
        
        A detailed analysis of these simulations will be published elsewhere (Postnov & Kuranov, in preparation), but the main conclusions 
        can be drawn from Figs. 1-3. It is seen (expectedly) from Fig. 1 that the effective spin χ_eff of binary BH from field massive stars (the standard formation scenario) is distributed in a wide range, but the M-χ_eff plot (Fig. 2) suggests that large chirp masses 
        can hardly have χ_eff≃ 0. This (model) result can signal potential difficulty in explaining the most massive merging BH binaries by this formation channel only. Fig. 3 suggests that even in the absence of BH kicks, which were assumed in the present calculations, the BH spin
        misalignments can be quite high even for field binaries. 
        
        
        
        
        § CONCLUSIONS
        
        
        Presently, there are different astrophysical pathways of producing massive binary BHs that merge in the Hubble time.
        They can be formed from low-metallicity massive field stars, primordial Pop III remnants, can be results of dynamical evolution in dense 
        stellar clusters or even primordial black holes. It is not excluded that all channels contribute to the observed 
        binary BH population. For example, the discovery of very massive Schwarzschild BHs would be difficult to reconcile with the
        standard massive binary evolution, but can be naturally explained in the PBH scenario <cit.>. 
        
        As of the time of writing, 
        another two event candidates were reported by the LIGO collaboration from the analysis of 12 days of joint operation of two LIGO interferometers during O2 run (see 
        ). With the current LIGO sensitivity, the detection horizon of binary BH with masses around 30 M_⊙ 
        reaches 700 Mpc. So far the statistics of binary BH merging rate as a function of BH mass as inferred from three
        reported LIGO O1 events is consistent with a power-law dependence, dR/dM∼ M^-2.5<cit.>, which does not contradict the general power-law behavior of the stellar mass function. Clearly, more statistics of BH masses and spins inferred from 
        binary BH mergings is required to distinguish between the possible binary BH populations which can exist in the Universe. 
        
        Acknowledgements. KP acknowledges the support from RSF grant 16-12-10519.
        
        
        
        50[Abadie et al.(2010)]2010CQGra..27q3001AAbadie, J. et al. 2010, Classical and Quantum Gravity, 27, 173001
        
        [Abbott et al.(2016a)]2016ApJ...818L..22AAbbott, B.P. et al. 2016a, , 818, L22
        
        [Abbott et al.(2016b)]2016PhRvX...6d1015AAbbott, B.P. et al. 2016b, Physical Review X, 6, 041015
        
        [Abbott et al.(2016c)]2016PhRvL.116x1103AAbbott, B.P. et al. 2016c, Physical Review Letters, 116,
          241103
        
        [Abbott et al.(2016d)]LIGO-PRLAbbott, B.P. et al. 2016d, Physical Review Letters, 116,
          061102
        
        [Abbott et al.(2016e)]2016ApJ...833L...1AAbbott, B.P. et al. 2016e, , 833, L1
        
        [Belczynski et al.(2016)Belczynski, Holz, Bulik, &O'Shaughnessy]2016Natur.534..512BBelczynski, K., Holz, D.E., Bulik, T., &O'Shaughnessy, R. 2016,
          , 534, 512
        
        [Belczynski et al.(2002)Belczynski, Kalogera, &Bulik]2002ApJ...572..407BBelczynski, K., Kalogera, V., &Bulik, T. 2002, , 572, 407
        
        [Bird et al.(2016)]2016PhRvL.116t1301BBird, S. et al. 2016, Physical Review Letters, 116, 201301
        
        [Blinnikov et al.(2016)Blinnikov, Dolgov, Porayko, &Postnov]2016JCAP...11..036BBlinnikov, S., Dolgov, A., Porayko, N.K., &Postnov, K. 2016,
          , 11, 036
        
        [Carr et al.(2016)Carr, Kühnel, &Sandstad]2016PhRvD..94h3504CCarr, B., Kühnel, F., &Sandstad, M. 2016, , 94, 083504
        
        [Davydov et al.(2008)Davydov, Esipov, &Cherepashchuk]2008ARep...52..487DDavydov, V.V., Esipov, V.F., &Cherepashchuk, A.M. 2008, Astronomy
          Reports, 52, 487
        
        [de Mink&Mandel(2016)]2016MNRAS.460.3545Dde Mink, S.E. &Mandel, I. 2016, , 460, 3545
        
        [Dolgov&Silk(1993)]ad-jsDolgov, A. &Silk, J. 1993, , 47, 4244
        
        [Dolgov et al.(2009)Dolgov, Kawasaki, &Kevlishvili]ad-mk-nkDolgov, A.D., Kawasaki, M., &Kevlishvili, N. 2009, Nuclear
          Physics B, 807, 229
        
        [Dominik et al.(2012)]2012ApJ...759...52DDominik, M. et al. 2012, , 759, 52
        
        [Dominik et al.(2013)]2013ApJ...779...72DDominik, M. et al. 2013, , 779, 72
        
        [Eldridge&Stanway(2016)]2016MNRAS.462.3302EEldridge, J.J. &Stanway, E.R. 2016, , 462, 3302
        
        [Eroshenko(2016)]2016arXiv160404932EEroshenko, Y.N. 2016, ArXiv e-prints[Flannery&van den Heuvel(1975)]1975A   A....39...61FFlannery, B.P. &van den Heuvel, E.P.J. 1975, , 39, 61
        
        [Fuller et al.(2015)Fuller, Cantiello, Lecoanet, &Quataert]2015ApJ...810..101FFuller, J., Cantiello, M., Lecoanet, D., &Quataert, E. 2015,
          , 810, 101
        
        [Hartwig et al.(2016)]2016MNRAS.460L..74HHartwig, T. et al. 2016, , 460, L74
        
        [Hotokezaka&Piran(2017)]2017arXiv170203952HHotokezaka, K. &Piran, T. 2017, ArXiv e-prints[Hurley et al.(2002)Hurley, Tout, &Pols]2002MNRAS.329..897HHurley, J.R., Tout, C.A., &Pols, O.R. 2002, , 329, 897
        
        [Kinugawa et al.(2014)Kinugawa, Inayoshi, Hotokezaka,
          Nakauchi, &Nakamura]Kinugawa2014Kinugawa, T., Inayoshi, K., Hotokezaka, K., Nakauchi, D., &Nakamura, T. 2014, , 442, 2963
        
        [Kushnir et al.(2016)Kushnir, Zaldarriaga, Kollmeier, &Waldman]2016MNRAS.462..844KKushnir, D., Zaldarriaga, M., Kollmeier, J.A., &Waldman, R. 2016,
          , 462, 844
        
        [Lipunov et al.(1997a)Lipunov, Postnov, &Prokhorov]1997AstL...23..492LLipunov, V.M., Postnov, K.A., &Prokhorov, M.E. 1997a,
          Astronomy Letters, 23, 492
        
        [Lipunov et al.(1997b)Lipunov, Postnov, &Prokhorov]1997NewA....2...43LLipunov, V.M., Postnov, K.A., &Prokhorov, M.E. 1997b,
          , 2, 43
        
        [Lipunov et al.(1997c)Lipunov, Postnov, &Prokhorov]1997MNRAS.288..245LLipunov, V.M., Postnov, K.A., &Prokhorov, M.E. 1997c,
          , 288, 245
        
        [Lipunov et al.(2017)]2017NewA...51..122LLipunov, V.M. et al. 2017, , 51, 122
        
        [Mandel&de Mink(2016)]2016MNRAS.458.2634MMandel, I. &de Mink, S.E. 2016, , 458, 2634
        
        [Marchant et al.(2016)Marchant, Langer, Podsiadlowski,
          Tauris, &Moriya]2016A   A...588A..50MMarchant, P., Langer, N., Podsiadlowski, P., Tauris, T.M., &Moriya,
          T.J. 2016, , 588, A50
        
        [Nakamura et al.(1997)Nakamura, Sasaki, Tanaka, &Thorne]1997ApJ...487L.139NNakamura, T., Sasaki, M., Tanaka, T., &Thorne, K.S. 1997,
          , 487, L139
        
        [Ohlmann et al.(2016)Ohlmann, Röpke, Pakmor, &Springel]2016ApJ...816L...9OOhlmann, S.T., Röpke, F.K., Pakmor, R., &Springel, V. 2016,
          , 816, L9
        
        [Pavlovskii et al.(2017)Pavlovskii, Ivanova, Belczynski, &Van]2017MNRAS.465.2092PPavlovskii, K., Ivanova, N., Belczynski, K., &Van, K.X. 2017,
          , 465, 2092
        
        [Postnov et al.(2016)Postnov, Kuranov, Kolesnikov, Popov, &Porayko]2016MNRAS.463.1642PPostnov, K.A., Kuranov, A.G., Kolesnikov, D.A., Popov, S.B., &Porayko, N.K. 2016, , 463, 1642
        
        [Postnov&Yungelson(2014)]2014LRR....17....3PPostnov, K.A. &Yungelson, L.R. 2014, Living Reviews in Relativity,
          17, 3
        
        [Rodriguez et al.(2016a)Rodriguez, Chatterjee, &Rasio]2016PhRvD..93h4029RRodriguez, C.L., Chatterjee, S., &Rasio, F.A. 2016a,
          , 93, 084029
        
        [Rodriguez et al.(2016b)Rodriguez, Haster,
          Chatterjee, Kalogera, &Rasio]2016ApJ...824L...8RRodriguez, C.L., Haster, C.J., Chatterjee, S., Kalogera, V., &Rasio, F.A. 2016b, , 824, L8
        
        [Sasaki et al.(2016)Sasaki, Suyama, Tanaka, &Yokoyama]2016PhRvL.117f1101SSasaki, M., Suyama, T., Tanaka, T., &Yokoyama, S. 2016,
          Physical Review Letters, 117, 061101
        
        [Sigurdsson&Hernquist(1993)]1993Natur.364..423SSigurdsson, S. &Hernquist, L. 1993, , 364, 423
        
        [Spera et al.(2015)Spera, Mapelli, &Bressan]2015MNRAS.451.4086SSpera, M., Mapelli, M., &Bressan, A. 2015, , 451, 4086
        
        [The LIGO Scientific Collaboration
          et al.(2016)]2016arXiv160203842TThe LIGO Scientific Collaboration et al. 2016, ArXiv e-prints[Tutukov&Yungelson(1973)]1973NInfo..27...70TTutukov, A. &Yungelson, L. 1973, Nauchnye Informatsii, 27, 70
        
        [Tutukov et al.(1973)Tutukov, Yungelson, &Klayman]1973NInfo..27....3TTutukov, A., Yungelson, L., &Klayman, A. 1973, Nauchnye
          Informatsii, 27, 3
        
        [Tutukov&Yungelson(1993)]1993MNRAS.260..675TTutukov, A.V. &Yungelson, L.R. 1993, , 260, 675
        
        [van den Heuvel&Heise(1972)]1972NPhS..239...67Vvan den Heuvel, E.P.J. &Heise, J. 1972, Nature Physical Science,
          239, 67
        
        [van den Heuvel et al.(2017)van den Heuvel, Portegies Zwart, &de Mink]2017arXiv170102355Vvan den Heuvel, E.P.J., Portegies Zwart, S.F., &de Mink, S.E. 2017,
          ArXiv e-prints[Woosley et al.(2002)Woosley, Heger, &Weaver]2002RvMP...74.1015WWoosley, S.E., Heger, A., &Weaver, T.A. 2002, Reviews of Modern
          Physics, 74, 1015
