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2013-11-08-Gravasco-Ziosi_NO_appendix

Brunetto Ziosi
Brunetto Ziosi

This document summarizes a study on the influence of dynamics and metallicity on the formation and evolution of black hole binaries in star clusters. The study used direct N-body simulations of star clusters with different metallicities to model the dynamics and stellar evolution. The results show that lower metallicity leads to heavier black holes forming and black hole binaries assembling earlier. Dynamics enhances the formation of black hole binaries through exchanges and hardening. While the average number of black hole binaries is independent of metallicity, their lifetimes are longer at lower metallicity due to the heavier black holes formed. The orbital properties and chirp masses of the black hole binaries also depend on the metallicity through its effect on the black hole masses.

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In鍖uence of dynamics and metallicity on the formation and evolution of black-hole binaries in star clusters Brunetto M. Ziosi (University of Padova, INAF-Padova) Collaborators: Michela Mapelli (INAF-Padova), Marica Branchesi (University of Urbino), Giuseppe Tormen (Univ. Padova) Gravasco, W2 workshop Paris, 2013-11-08 B. Ziosi (Univ. of Padova) W2, 2013-11-08
Dynamics, Z and DCOBs Outline 1 Overview DCOBs and GWs Stellar evolution and BH mass Star cluster dynamics 2 Tools Direct N-body simulations 3 Results DCOB population Life-times & Exchanges Orbital properties distribution Mass distribution Coalescence times 4 Conclusions B. Ziosi (Univ. of Padova) W2, 2013-11-08
Dynamics, Z and DCOBs Overview Why DCOBs? DCO binaries during inspiral and merger events produce GWs we could observe in the near future Simulations provide theoretical models to interpret Advanced Virgo/LIGO upcoming data Key quantities: Number of DCOBs BH mass spectrum Binary orbital properties B. Ziosi (Univ. of Padova) W2, 2013-11-08 1 / 12
Dynamics, Z and DCOBs Overview Why stellar evolution and metallicity (Z)? Massive stars lose mass by stellar winds Winds e鍖ciency depends on metallicity Stars with M鍖n 40M are expected to collapse to a BH without SN explosion (Fryer 1999, Fryer&Kalogera 2001) BHs formed from direct collapse are more massive than BHs formed from SN Metal-poor stars lose less mass by stellar winds more likely to collapse to BH directly B. Ziosi (Univ. of Padova) W2, 2013-11-08 2 / 12
Dynamics, Z and DCOBs Overview Why dynamics? Why YSCs? YSCs are birthplace for > 80% of stars in the local universe (Lada&Lada, 2003) (Collisional) YSCs are young (< 100 Myr) relatively massive (103 107 M ), dense (103 106 /pc3 ) groups of stars YSCs are sites of intense dynamical activity: central trelax < 10 Myr B. Ziosi (Univ. of Padova) W2, 2013-11-08 3 / 12
Dynamics, Z and DCOBs Overview Why dynamics? Why YSCs? Focus on 3-body encounters: close encounters between a single object and a binary If kinetic energy is tranferred from the binary to the single object SMA decrease (hardening) Hard binary: Gm1m2 a 1 2 m 2 Hard binaries tend to become harder, soft binaries tend to become softer as e鍖ect of three-body encounters (Heggie 1975) If msingle m2 the single star can take the place of one of the stars in the binary exchange B. Ziosi (Univ. of Padova) W2, 2013-11-08 3 / 12
Dynamics, Z and DCOBs Overview Why dynamics? Why YSCs? Dynamics enhances the formation of hard compact-object binaries (exhanges also produces very high eccentricity binaries) Key processes: mass segregation 3-body exchanges hardening B. Ziosi (Univ. of Padova) W2, 2013-11-08 3 / 12
Dynamics, Z and DCOBs Tools Tools 200 N-body realizations of the same cluster for each Z = 0.01, 0.1, 1Z StarLab: Kira (GPU) + SeBa (CPU) (Portegies Zwart et al. 2001) Our simulations combines dynamics + up-to-date recipes for Z-dependent stellar evolution Custom recipes: accurate metallicity-dependent stellar evolution (Hurley et al. 2000) and stellar winds (Vink et al. 2001; Vink & de Koter 2005; Belczynski et al. 2010) the possibility of massive BHs formation by direct collapse (Fryer et al. 2012; Mapelli et al. 2013) 600 simulations Parameter Value W0 5 N 5500 Mtot 3500M rc [pc] 0.4 c = rt/rc 1.03 IMF Kroupa (2001) mmin [M ] 0.1 mmax [M ] 150 fPB 0.1 Z [Z ] 0.01, 0.1, 1 Sim. time 100 Myr MW typical, e.g. Orion Nebula Cluster B. Ziosi (Univ. of Padova) W2, 2013-11-08 4 / 12
Dynamics, Z and DCOBs Results DCOB population DBH distribution Mean number of DBHs: 3 Max number of DBHs: 18 # NS 4 # BH but # DBH 10 # DNS due to dynamics Negligible dependence on Z, but... (see after) Ziosi et al., in prep B. Ziosi (Univ. of Padova) W2, 2013-11-08 5 / 12
Dynamics, Z and DCOBs Results DBH population in time Low-Z case vs higher metallicities: Build up the DBH population before high-Z case Higher DBH mass allowed earlier DBHBs formation But mean # and mean # in time of DBHs do not agree Higher DBH mass allowed more stable binaries & longer lifetime Ziosi et al., in prep B. Ziosi (Univ. of Padova) W2, 2013-11-08 6 / 12
Dynamics, Z and DCOBs Results DBH population in time Low-Z case vs higher metallicities: Build up the DBH population before high-Z case Higher DBH mass allowed earlier DBHBs formation But mean # and mean # in time of DBHs do not agree Higher DBH mass allowed more stable binaries & longer lifetime Ziosi et al., in prep B. Ziosi (Univ. of Padova) W2, 2013-11-08 6 / 12
Dynamics, Z and DCOBs Results Exchanges & mean DCOB life time Z=0.01 Z DBHBs live longer than at higher Z but the avg number of exchanges is similar Z=0.1, 1 Z DBHBs tend to break-up DNS are 10 times less numerous but are much more stable Avg exchanges per CO and Z Type 0.01Z 0.1 Z Z DBH 9.92 9.91 10.14 DNS 0.00 0.5 0.26 97% of all the DBHBs come from exchanges Distribution of DBHBs lifetimes Ziosi et al., in prep B. Ziosi (Univ. of Padova) W2, 2013-11-08 7 / 12
Dynamics, Z and DCOBs Results Orbital properties Distribution of orbital parameters at minimum semi-major axis Critical for coalescence times and mergers detection SMA and period span a wide range Eccentricity follows the thermal distribution f (e) 2e but excess in e 0: GW and tidal circularization DNS (grey) are 10 times less numerous but have small SMA and short periods Ziosi et al., in prep Z=0.01 Z犢 Total#ofbinaries 100 101 102 sma [AU] 103 100 103 106 Z=0.01 Z犢 Total#ofbinaries 100 period [yr] 106 103 100 103 106 Z=0.01 Z犢 Total#ofbinaries 100 ecc 0 0.2 0.4 0.6 0.8 1 Z=0.1Z犢 Total#ofbinaries 100 101 102 sma [AU] 103 100 103 106 Z=0.1Z犢 Total#ofbinaries 100 period [yr] 106 103 100 103 106 Z=0.1Z犢 Total#ofbinaries 100 ecc 0 0.2 0.4 0.6 0.8 1 Z=1Z犢 Total#ofbinaries 100 101 102 sma [AU] 103 100 103 106 Z=1Z犢 Total#ofbinaries 100 period [yr] 106 103 100 103 106 Z=1Z犢 Total#ofbinaries 100 ecc 0 0.2 0.4 0.6 0.8 1 B. Ziosi (Univ. of Padova) W2, 2013-11-08 8 / 12
Dynamics, Z and DCOBs Results Masses High BH masses because of direct collapse at low metallicity Chirp mass mchirp = (m1m2)3/5 (m1+m2)1/5 Why chirp mass: 僚GW m 5/8 chirp, hGW m 5/3 chirp So from observations we can reconstruct mchirp In our model mchirp strongly depends on Z Z-dependent BH mass model test But: in black chirp mass distribution of the best merger-candidates Ziosi et al., in prep B. Ziosi (Univ. of Padova) W2, 2013-11-08 9 / 12
Dynamics, Z and DCOBs Results Coalescence times Time to reach SMA=0 considering only GW emission tGW a4 (1e2 )7/2 m1m2mtot (Peters, 1964) GW emission: SMA shrink and orbit circularization Dynamical outlier: signal detectability depends on e 7 DBHs with tGW < 13 Gyr (0 for Z=Z ) 17 DNSs with tGW < 13 Gyr, 11 DNS mergers during the simulations Ziosi et al., in prep B. Ziosi (Univ. of Padova) W2, 2013-11-08 10 / 12
Dynamics, Z and DCOBs Conclusions Conclusions DCOBs during mergers emits GWs likely to be detected in the near future Metallicity is important: Heavier BHs form at low Z They tend to form DBHBs at early times and these binaries are more stable BHBs lifetimes are longer at low Z Dynamics is important Dynamics enhances the formation of DCOBs: 97% of DBHBs come from exchanges Dynamics hardens binaries and can modify the eccentricity increase detection probability DNSBs are 10 times less numerous but are harder Fewer exchanges and shorter coalescence times than DBHBs Selection e鍖ect B. Ziosi (Univ. of Padova) W2, 2013-11-08 11 / 12
Dynamics, Z and DCOBs Conclusions Thank you B. Ziosi (Univ. of Padova) W2, 2013-11-08 12 / 12

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2013-11-08-Gravasco-Ziosi_NO_appendix

  • 1. In鍖uence of dynamics and metallicity on the formation and evolution of black-hole binaries in star clusters Brunetto M. Ziosi (University of Padova, INAF-Padova) Collaborators: Michela Mapelli (INAF-Padova), Marica Branchesi (University of Urbino), Giuseppe Tormen (Univ. Padova) Gravasco, W2 workshop Paris, 2013-11-08 B. Ziosi (Univ. of Padova) W2, 2013-11-08
  • 2. Dynamics, Z and DCOBs Outline 1 Overview DCOBs and GWs Stellar evolution and BH mass Star cluster dynamics 2 Tools Direct N-body simulations 3 Results DCOB population Life-times & Exchanges Orbital properties distribution Mass distribution Coalescence times 4 Conclusions B. Ziosi (Univ. of Padova) W2, 2013-11-08
  • 3. Dynamics, Z and DCOBs Overview Why DCOBs? DCO binaries during inspiral and merger events produce GWs we could observe in the near future Simulations provide theoretical models to interpret Advanced Virgo/LIGO upcoming data Key quantities: Number of DCOBs BH mass spectrum Binary orbital properties B. Ziosi (Univ. of Padova) W2, 2013-11-08 1 / 12
  • 4. Dynamics, Z and DCOBs Overview Why stellar evolution and metallicity (Z)? Massive stars lose mass by stellar winds Winds e鍖ciency depends on metallicity Stars with M鍖n 40M are expected to collapse to a BH without SN explosion (Fryer 1999, Fryer&Kalogera 2001) BHs formed from direct collapse are more massive than BHs formed from SN Metal-poor stars lose less mass by stellar winds more likely to collapse to BH directly B. Ziosi (Univ. of Padova) W2, 2013-11-08 2 / 12
  • 5. Dynamics, Z and DCOBs Overview Why dynamics? Why YSCs? YSCs are birthplace for > 80% of stars in the local universe (Lada&Lada, 2003) (Collisional) YSCs are young (< 100 Myr) relatively massive (103 107 M ), dense (103 106 /pc3 ) groups of stars YSCs are sites of intense dynamical activity: central trelax < 10 Myr B. Ziosi (Univ. of Padova) W2, 2013-11-08 3 / 12
  • 6. Dynamics, Z and DCOBs Overview Why dynamics? Why YSCs? Focus on 3-body encounters: close encounters between a single object and a binary If kinetic energy is tranferred from the binary to the single object SMA decrease (hardening) Hard binary: Gm1m2 a 1 2 m 2 Hard binaries tend to become harder, soft binaries tend to become softer as e鍖ect of three-body encounters (Heggie 1975) If msingle m2 the single star can take the place of one of the stars in the binary exchange B. Ziosi (Univ. of Padova) W2, 2013-11-08 3 / 12
  • 7. Dynamics, Z and DCOBs Overview Why dynamics? Why YSCs? Dynamics enhances the formation of hard compact-object binaries (exhanges also produces very high eccentricity binaries) Key processes: mass segregation 3-body exchanges hardening B. Ziosi (Univ. of Padova) W2, 2013-11-08 3 / 12
  • 8. Dynamics, Z and DCOBs Tools Tools 200 N-body realizations of the same cluster for each Z = 0.01, 0.1, 1Z StarLab: Kira (GPU) + SeBa (CPU) (Portegies Zwart et al. 2001) Our simulations combines dynamics + up-to-date recipes for Z-dependent stellar evolution Custom recipes: accurate metallicity-dependent stellar evolution (Hurley et al. 2000) and stellar winds (Vink et al. 2001; Vink & de Koter 2005; Belczynski et al. 2010) the possibility of massive BHs formation by direct collapse (Fryer et al. 2012; Mapelli et al. 2013) 600 simulations Parameter Value W0 5 N 5500 Mtot 3500M rc [pc] 0.4 c = rt/rc 1.03 IMF Kroupa (2001) mmin [M ] 0.1 mmax [M ] 150 fPB 0.1 Z [Z ] 0.01, 0.1, 1 Sim. time 100 Myr MW typical, e.g. Orion Nebula Cluster B. Ziosi (Univ. of Padova) W2, 2013-11-08 4 / 12
  • 9. Dynamics, Z and DCOBs Results DCOB population DBH distribution Mean number of DBHs: 3 Max number of DBHs: 18 # NS 4 # BH but # DBH 10 # DNS due to dynamics Negligible dependence on Z, but... (see after) Ziosi et al., in prep B. Ziosi (Univ. of Padova) W2, 2013-11-08 5 / 12
  • 10. Dynamics, Z and DCOBs Results DBH population in time Low-Z case vs higher metallicities: Build up the DBH population before high-Z case Higher DBH mass allowed earlier DBHBs formation But mean # and mean # in time of DBHs do not agree Higher DBH mass allowed more stable binaries & longer lifetime Ziosi et al., in prep B. Ziosi (Univ. of Padova) W2, 2013-11-08 6 / 12
  • 11. Dynamics, Z and DCOBs Results DBH population in time Low-Z case vs higher metallicities: Build up the DBH population before high-Z case Higher DBH mass allowed earlier DBHBs formation But mean # and mean # in time of DBHs do not agree Higher DBH mass allowed more stable binaries & longer lifetime Ziosi et al., in prep B. Ziosi (Univ. of Padova) W2, 2013-11-08 6 / 12
  • 12. Dynamics, Z and DCOBs Results Exchanges & mean DCOB life time Z=0.01 Z DBHBs live longer than at higher Z but the avg number of exchanges is similar Z=0.1, 1 Z DBHBs tend to break-up DNS are 10 times less numerous but are much more stable Avg exchanges per CO and Z Type 0.01Z 0.1 Z Z DBH 9.92 9.91 10.14 DNS 0.00 0.5 0.26 97% of all the DBHBs come from exchanges Distribution of DBHBs lifetimes Ziosi et al., in prep B. Ziosi (Univ. of Padova) W2, 2013-11-08 7 / 12
  • 13. Dynamics, Z and DCOBs Results Orbital properties Distribution of orbital parameters at minimum semi-major axis Critical for coalescence times and mergers detection SMA and period span a wide range Eccentricity follows the thermal distribution f (e) 2e but excess in e 0: GW and tidal circularization DNS (grey) are 10 times less numerous but have small SMA and short periods Ziosi et al., in prep Z=0.01 Z犢 Total#ofbinaries 100 101 102 sma [AU] 103 100 103 106 Z=0.01 Z犢 Total#ofbinaries 100 period [yr] 106 103 100 103 106 Z=0.01 Z犢 Total#ofbinaries 100 ecc 0 0.2 0.4 0.6 0.8 1 Z=0.1Z犢 Total#ofbinaries 100 101 102 sma [AU] 103 100 103 106 Z=0.1Z犢 Total#ofbinaries 100 period [yr] 106 103 100 103 106 Z=0.1Z犢 Total#ofbinaries 100 ecc 0 0.2 0.4 0.6 0.8 1 Z=1Z犢 Total#ofbinaries 100 101 102 sma [AU] 103 100 103 106 Z=1Z犢 Total#ofbinaries 100 period [yr] 106 103 100 103 106 Z=1Z犢 Total#ofbinaries 100 ecc 0 0.2 0.4 0.6 0.8 1 B. Ziosi (Univ. of Padova) W2, 2013-11-08 8 / 12
  • 14. Dynamics, Z and DCOBs Results Masses High BH masses because of direct collapse at low metallicity Chirp mass mchirp = (m1m2)3/5 (m1+m2)1/5 Why chirp mass: 僚GW m 5/8 chirp, hGW m 5/3 chirp So from observations we can reconstruct mchirp In our model mchirp strongly depends on Z Z-dependent BH mass model test But: in black chirp mass distribution of the best merger-candidates Ziosi et al., in prep B. Ziosi (Univ. of Padova) W2, 2013-11-08 9 / 12
  • 15. Dynamics, Z and DCOBs Results Coalescence times Time to reach SMA=0 considering only GW emission tGW a4 (1e2 )7/2 m1m2mtot (Peters, 1964) GW emission: SMA shrink and orbit circularization Dynamical outlier: signal detectability depends on e 7 DBHs with tGW < 13 Gyr (0 for Z=Z ) 17 DNSs with tGW < 13 Gyr, 11 DNS mergers during the simulations Ziosi et al., in prep B. Ziosi (Univ. of Padova) W2, 2013-11-08 10 / 12
  • 16. Dynamics, Z and DCOBs Conclusions Conclusions DCOBs during mergers emits GWs likely to be detected in the near future Metallicity is important: Heavier BHs form at low Z They tend to form DBHBs at early times and these binaries are more stable BHBs lifetimes are longer at low Z Dynamics is important Dynamics enhances the formation of DCOBs: 97% of DBHBs come from exchanges Dynamics hardens binaries and can modify the eccentricity increase detection probability DNSBs are 10 times less numerous but are harder Fewer exchanges and shorter coalescence times than DBHBs Selection e鍖ect B. Ziosi (Univ. of Padova) W2, 2013-11-08 11 / 12
  • 17. Dynamics, Z and DCOBs Conclusions Thank you B. Ziosi (Univ. of Padova) W2, 2013-11-08 12 / 12