Equation of State Dependence of Gravitational Waves from Core-Collapse Supernovae

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1 Equation of State Dependence of Gravitational Waves from Core-Collapse Supernovae Sherwood Richers California Institute of Technology NSF Blue Waters Graduate Fellow Christian Ott, Ernazar Abdikamalov Evan O Connor, Chris Sullivan Sherwood Richers 1/14

2 Rotating Core-Collapse Core-Collapse Supernovae SN-GRB Association Hypernovae Coincident GRB + SN Ic/bl Young star-forming regions Interior rotation is still poorly understood. (Ott 2009) Sherwood Richers 2/14

3 Gravitational Waves from Core Collapse h 2G c 4 dï (Finn & Evans 1990) High-β dynamical instability Low-β secular instability Post-bounce convection / SASI r-mode instability Asymmetric energy distribution Rotating collapse and bounce... Andresen et al Sherwood Richers 3/14

4 Gravitational Waves from Rapidly Rotating Core Collapse Sherwood Richers 4/14

5 Many Available Equations of State J M [M ] BHBΛΦ R [km] Sherwood Richers 5/14

6 Parameter Study Methods 1824 Simulations 18 equations of state, 98 rotation profiles 2D Simulations (CoCoNuT) Conformally flat GRHD Neutrino Leakage (Dimmelmeier+02,05) Deleptonization (GR1D) Spherically symmetric GRHD M1 neutrino transport (O Connor 2015) Ye BHBLP ρ [g/cm 3 ] Sherwood Richers 6/14

7 GW Observables h h+ tb tbe tbe + 6ms A = 634km Ω 0 = 5.0s 1 BHBΛΦ t t b [ms] h+ f [Hz 1/2 ] Virgo aligo Bounce signal h + in time domain Peak frequency f peak in frequency domain. bkagra f [Hz] Sherwood Richers 7/14

8 Bounce Amplitude 30 8 (GM)2 Rc 4 D T W A1 (Dimmelmeier et al. 2008) h+ 20 A2 10 A5 A4 A3 BHBΛΦ T/ W EOS and rotation influence M IC,b. Rotation increases deformation. Sherwood Richers 8/14

9 Peak Frequency 1100 Slow Rapid Extreme fpeak [Hz] weak signal 700 (Dimmelmeier+08) 150 Hz variation due to EOS Explained by the dynamical frequency. 2π fpeak/ G ρc f dyn = 2π G ρ c BHBΛΦ T / W Sherwood Richers 9/14

10 fpeak 2π/ G ρc Peak Frequency Now, let s measure rotation differently. BHBΛΦ Ω max / G ρ c Inertial effects increase frequency and confine modes to poles h + vr, e [10 3 cm/s] vr, p [10 3 cm/s] tb t t b [ms] Ω 0 [s 1 ] A = 634 km R = 5 km Sherwood Richers 10/14

11 Inertial Mode Character t tb =4.5 ms Ω0 = 4.0 rad s 1 Ω0 = 8.0 rad s 1 r = 15 km Entropy [kb baryon 1] 5 High rotation rates suppress equatorial fluctuations. Sherwood Richers 11/14

12 Can We Constrain the EOS? f peak [Hz] Weak Signal BHBΛΦ h + Probably not. Need detailed treatment of neutrino transport and electron capture rates. Sherwood Richers 12/14

13 Take Away A universal relations is obeyed by all EOS and rotation profiles. We quantify uncertainties in GW observables due to nuclear physics. GWs are sensitive to EOS properties at both subnuclear and supernuclear densities. Detailed neutrino transport and electron capture rates during collapse are required for reliable GW predictions. arxiv: srichers@tapir.caltech.edu Sherwood Richers 13/14

14 Fourier Analysis h+ f [10 22 Hz 1/2 ] t be + 50 ms 0 t be + 6 ms 0 t be t be t be + 6 ms A = 634 km Ω 0 = 5.0 rad s f [Hz] Sherwood Richers 13/14

15 18 Equations of State E(x, β) = E 0 + K 18 x2 + K x S 2 (x)β 2 + S 4 (x)β Constrained Parameter Value max M min Mmax > M 220 MeV < K < 260 MeV 28 MeV < S(0) < 34 MeV 20 MeV < L(0) < 120 MeV Parameters between the lines satisfy constraints. LS180 LS375 BHBL BHBLP HSIUF HSFSG GSFSU1.7 GSFSU2.1 GSNL3 HShen HShenH HSNL3 HSTMA HSTM1 S 2 (x) = J + L 3 x +... x = n ns n s β = 2(0.5 Y e ) Sherwood Richers 13/14

16 fpeak 2π/ G ρc Peak Frequency Now, let s measure rotation differently. BHBΛΦ Ω max / G ρ c Inertial effects increase frequency and 1 confine modes to poles π fpeak [10 3 s 1 ] Ωmax [10 3 s 1 ] Ωmax = G ρc ρnuc BHBLΛΦ G ρc [10 3 s 1 ] 2π fpeak = G ρc Sherwood Richers 13/14

17 Correlations C AB = ( A Ā B B )( ) s A s B N 1 M IC,b j IC,b T/ W Ωmax Ωmax h+ f peak f peak Ω0 A Y e,c,b L K R1.4 Mmax J M IC,b j IC,b T/ W Ω max Ω max Ωmax < G ρc h + f peak f peak Ω 0 A Y e,c,b Ωmax G ρc L J R 1.4 K M max Sherwood Richers 14/14

18 Can We Constrain the EOS? Ye Fiducial ecap0.1 ecap1.0 ecap ρ [g cm 3 ] The GW signal is sensitive to systematic biases in electron capture rates. f peak [Hz] h Fiducial ecap0.1 ecap1.0 ecap10.0 Slow Rapid Extreme weak signal T/ W Sherwood Richers 14/14

19 Can We Constrain the EOS? Optimal SNR BHBΛΦ Slow Rapid Extreme T/ W Mismatch with Weak Signal Slow Rapid Extreme BHBΛΦ T/ W High SNR at 10 kpc. Must be in the Milky Way or Magellanic Clouds. Large mismatch between EOS due to pre- and post-collapse physics. Looks great, right? Sherwood Richers 14/14

Comparison of Neutrino Transport Approximations in Core-Collapse Supernova Simulations

Comparison of Neutrino Transport Approximations in Core-Collapse Supernova Simulations Sherwood Richers 1 Evan O Connor 2 Christian Ott 1 1 TAPIR, California Institute of Technology 2 CITA, University