Binary Black Hole Population Properties Inferred from the First and Second Observing Runs of Advanced LIGO and Advanced Virgo Tomofumi Shimoda Ando lab seminar on Dec. 7
Paper • arXiv:1811.12940
Paper2 • arXiv:1811.12907
Abstract 10 BBHs (+1 BNS) during O1 and O2 BBHs, better or new constrains on the population properties of BBHs have been inferred formation process and surrounding environments • LIGO & Virgo have reported the detection of • 6 already reported BBHs + 4 new BBHs • Based on the parameters of the detected • BBH population will provide information on the
Observation runs 9/12 LLO update technical O2 BBH : ? BNS : 26 Mpc Virgo 8/25 11/30 2016 1/19 2016 2017 2015 LHO BNS : 69 Mpc O1 LLO BNS : 84 Mpc BBH : 1029 Mpc BBH : 845 Mpc BNS : 68 Mpc BBH : 831 Mpc LHO BNS : 76 Mpc BBH : 931 Mpc G G G G G G LVT151012 W W W W W W 1 1 1 1 1 1 7 7 7 7 5 5 0 0 0 0 0 1 1 6 8 8 9 2 0 0 1 1 1 2 4 8 4 7 4 6
Newly reported binaries 2016 LLO update technical O2 BBH : ? BNS : 26 Mpc Virgo 8/25 2017 11/30 2016 1/19 10 BBHs & 1 BNS 9/12 LHO 2015 BBH : 845 Mpc LLO BNS : 84 Mpc BBH : 1029 Mpc BNS : 69 Mpc BNS : 68 Mpc O1 LHO BNS : 76 Mpc BBH : 931 Mpc BBH : 831 Mpc !? G G G G G G G G G GW151012 G W W W W W W W W W W 1 1 1 1 1 1 1 1 1 1 7 7 7 7 7 7 7 5 5 7 0 0 0 0 0 0 0 0 1 0 1 6 8 7 8 8 8 9 2 8 0 0 2 2 1 1 1 1 0 2 4 8 3 9 4 7 8 4 9 6
Parameters of BBHs >0 LHV arXiv:1811.12907
Component mass • m 1 > m 2 , q = m 2 /m 1 • many m ~ 30 M sun BHs were observed arXiv:1811.12907
Mass ratio • q = m 2 /m 1 ~1 is favored arXiv:1811.12907
Spin moment L χ 2 χ 1z • χ eff = 1 : spin is aligned to orbital angular moment • χ eff = 0 : spin is small or misaligned to orbital angular arXiv:1811.12907 most observed BBHs have χ eff ~ 0 (except for GW151226 & GW170729) Low spin suggests “first generation mergers”
Sky localization • Virgo contributed to three events arXiv:1811.12907
Binary population properties evolutionary environments of binaries from the distribution of mass, spin, etc... • is determined by the physical process and • isolated massive binaries through common envelope • dynamical processes in stellar clusters • ... • common processes to most pathways • mass loss • supernova (affected by metalicity) • ... • Information on these process can be inferred
Models of mass distribution GW170104, with fixed mass range : ⇒ α = 2.3 + 1.3 - 1.4 • flat-in-log distribution : • power law : • Previous works used these models • The power law index α was estimated after m 1 > 5 M sun , m 1 +m 2 < 100 M sun
New (more general) model • three models (A, B, C) parametrized by low-mass cutoff power law component Gaussian component (only included in model C) to capture high-mass BHs probability created from PPISN ∝ m -α m min m max mass arXiv:1811.12940 free parameters
Gaussian component : PPISN prior to the core collapse ⇒ mass distribution of born BHs have cutoff • Pulsational Pair Instability SuperNova • one of the types of supernova • remove significant amount of mass from star chirp mass arXiv:1810.13412
Inferred distribution 7.3 -1.7 +1.6 -1.9 +1.3 -1.9 +1.3 -4.6 +4.2 -1.7 +1.5 41.8 7.0 model C 43.8 model A 5(fixed) 0.4 model B 1.6 7.9 42.8 maximum α m min [M sun ] mass (99%) previous assumotion arXiv:1811.12940 cutoff at ~ 45 M sun m min < 9 M sun
Inferred distribution arXiv:1811.12907 arXiv:1811.12940 cutoff at ~ 45 M sun m min < 9 M sun
BF 12 How likely? : Bayesian factor model1 Bayesian factor model2 ( ln BF ic >0 : model i is more preferred than model C ) not significant difference (model A) < (model B) < (model C) contribution from Gaussian component is likely to exist
Mass gap at 2 - 5 M sun no BBHs at this mass was observed • suggested by X-ray binary (origin is uncertain) • BBH distribution cannot confirm this because • detectability was not enough gap
Mass gap above 50 M sun predicted to be 50 M sun • The maximum mass of BHs born after PPISN is • BBH mass distribution is consistent with this • high-mass cutoff at ~ 45 M sun arXiv:1811.12940 (gap) (BH mass) (initial mass)
Mass ratio • Model B and C give consistent β > 0 ( 95% conf. ) • large mass ratio (q ~ 0) is disfavored ∝ q β arXiv:1811.12940
9 - 240 Gpc -3 yr -1 Merger rate 25.9 - 108.5 Gpc -3 yr -1 Phys. Rev. X 6, 041015 • after O1 (3 BBHs) : • flat-in-log + power-law • after O2 (10 BBHs) : • model C (power law + Gaussian)
Redshift dependence related? • λ= 0 : uniform merger rate • λ~ 3 : (approximately) follows star formation rate • other factors : • metallicity evolution • globular cluster formation • Redshift dependence implies which factors are
Evolution of merger rate with z +9.1 • λ= 6.5 (using model A with zero spin for simplicity) - 9.3 • cannot distinguish different formation rate histories • λ > 0 at 88% credibility arXiv:1811.12940
Spin magnitude distribution • large spins are disfavored • 50% of BH spins : < 0.27 • 90% of BH spins : < 0.55 arXiv:1811.12940
ζ = 0.5 Spin tilt distribution +0.4 - 0.5 • modeled with parameter ζ as follows isotropic ζ = 0 : isotropic ζ = 1 : Gaussian (aligned) Gaussian arXiv:1811.12940 almost no constrain on the spin orientation distribution is achieved
Interpretation of spins distribution processes theoretical models • observation provided only spin magnitude • spin magnitude is affected by many uncertain • mass transfer • tidal interaction • internal mixing • ... Ø magnitude distribution is difficult to predict
Summary • Mass distribution : • high-mass cutoff at ~ 45 M sun is consistent with PPISN prediction • low-mass cutoff at < 9 M sun , but cannot set constrain on the suggested mass gap between 2 M sun (NS) and 5 M sun (BH) • large mass ratio is disfavored • Merger rate : • updated : 9 - 240 Gpc -3 yr -1 (O1) ⇒ 25.9 - 108.5 Gpc -3 yr -1 • increasing with redshift (88% credibility), but the origin cannot be clarified due to large uncertainty • Spin distribution : • large spin magnitude is disfavored (90% of BHs have spins less than 0.55) • observation can not provide any preference for orientation distribution • due to many uncertain effects, spin magnitude distribution cannot predict theoretical model
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