The spin of the second-born Black hole in coalescing double BH b
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1 The spin of the second-born Black hole in coalescing double BH binaries Ying Qin Tassos Fragos, Georges Meynet Geneva Observatory, University of Geneva FOE, June 5-8, 2017
2 Background: Why the spin of the BH is important? Spin of the stellar-mass BH: a = c ~ J GM 2, 0 6 a Cover Half information of the BH 2 Related to the formation of long Gamma-ray Bursts 3 Distinguish the double BH formation channels
3 Background: Spin measurements from AdLIGO team
4 Progenitor of the GW (Belczynski et al. Nature 534,512B, 2016)
5 The spin of the first BH Metallicity, Mass, Magnetic field (Taylor-Spruit mechanism), init. MESA
6 The spin of the first BH Metallicity, Mass, Magnetic field (Taylor-Spruit mechanism), init. MESA a ) Negligible!
7 Observation from AdLIGO Constraint on the spin of the second-born BH from e
8 Progenitor of the GW (Belczynski et al. Nature 534,512B, 2016)
9 The spin of the second-born BH Angular momentum evolution of the He star Stellar wind () Tides He star: Dynamical tides (Radiative envelope + convective core)
10 The spin of the second-born BH Angular momentum evolution of the He star Stellar wind () Tides He star: Dynamical tides (Radiative envelope + convective core) Timescale of the synchronization (Hut 1981; Zahn 1975,1977) 1 T sync = 1 n d dt =3 (GM R 3 )1/2 q 2 (1 + q) 5/6 MR2 I E 2 ( R a )17/2
11 The spin of the second-born BH Angular momentum evolution of the He star Stellar wind () Tides He star: Dynamical tides (Radiative envelope + convective core) Timescale of the synchronization (Hut 1981; Zahn 1975,1977) 1 T sync = 1 n d dt =3 (GM R 3 )1/2 q 2 (1 + q) 5/6 MR2 I E 2 ( R a )17/2 E 2 = ( M M )2.84 (Hurley et al. 2002) E 2 = ( Rconv R )8 (Yoon et al. 2010)
12 Tidal coe cient E 2 (Zahn 1977) Solution of the E 2 3 8/3 ( (4/3)) 2 3 f R E n = (2n +1)[n(n +1)] 4/3 M [ R ( g s gb x 2 )0 f ] 1/3 2 H n Z 1 xf H n = X (x f )Y (1) 0 [Y 00 n(n +1)Y x 2 ]Xdx Y 00 6(1 X 00 0 ) Y 0 x X 0 n(n +1) x 2 X =0 [n(n +1) 12(1 )] Y x 2 =0
13 Tidal coe cient E 2 (Zahn 1977) Solution of the E 2 3 8/3 ( (4/3)) 2 3 f R E n = (2n +1)[n(n +1)] 4/3 M [ R ( g s gb x 2 )0 f ] 1/3 2 H n Fitting results at di erent metalliciy 1 Hrichstars Z 1 xf H n = X (x f )Y (1) 0 [Y 00 n(n +1)Y x 2 ]Xdx 2 He stars E 2 = ( R conv R )7.46 Y 00 6(1 X 00 0 ) Y 0 x X 0 n(n +1) x 2 X =0 [n(n +1) 12(1 )] Y x 2 =0 E 2 = ( R conv R )8.14
14 Tidal e ciency
15 Tidal e ciency M He [M ]: 4,8,..,50 P orb [days]: ) P orb <2
16 He star (1% Z ) + compact objects: Spin on the second-born BH
17 He star (Z ) + compact objects: Spin on the second-born BH
18 He star (1% Z ) + compact objects: Merger timescale
19 He star (1% Z ) + compact objects: Spin vs Merger timescale Lower spin of the second-born BH () Longer timescale of the merger
20 SUMMARY
21 SUMMARY 1 The spin of the first BH is negligible
22 SUMMARY 1 The spin of the first BH is negligible 2 Tides become important only for close binaries (P orb <2days)
23 SUMMARY 1 The spin of the first BH is negligible 2 Tides become important only for close binaries (P orb <2days) 3 The spin of the second-born BH: 0! 1
24 SUMMARY 1 The spin of the first BH is negligible 2 Tides become important only for close binaries (P orb <2days) 3 The spin of the second-born BH: 0! 1 4 Anti-correlation between the timescale of the merger and the spin of the second-born BH
25 SUMMARY 1 The spin of the first BH is negligible 2 Tides become important only for close binaries (P orb <2days) 3 The spin of the second-born BH: 0! 1 4 Anti-correlation between the timescale of the merger and the spin of the second-born BH Thanks for your attention!!!
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