Nuclear astrophysics with binary neutron stars Luciano Rezzolla Institute for Theoretical Physics, Frankfurt Frankfurt Institute for Advanced Studies, Frankfurt Nuclear Astrophysics in Germany: A Community Meeting Darmstadt, 15-1 November 01
Plan of the talk EOS information from GW signal Nucleosynthesis: quasi-circular and eccentric binaries Electromagnetic counterparts
The two-body problem in GR For BHs we know what to expect: BH + BH BH + GWs For NSs the question is more subtle: the merger leads to an hyper-massive neutron star (HMNS), ie a metastable equilibrium: NS + NS HMNS +...? BH + torus +...? BH HMNS phase can provide clear information on EOS Abbott+ 01 artist impression (NASA) Wex 01 BH+torus system may tell us on the central engine of GRBs
Broadbrush picture proto-magnetar? FRB?
merger HMNS BH + torus Quantitative differences are produced by: total mass (prompt vs delayed collapse) mass asymmetries (HMNS and torus) soft/stiff EOS (inspiral and post-merger) magnetic fields (equil. and EM emission) radiative losses (equil. and nucleosynthesis)
How to constrain the EOS
Anatomy of the GW signal binary black holes
Anatomy of the GW signal 8 h+ 10 [50 Mpc] 0 GNH3, M =1.350M 8 5 0 5 10 15 0 5 t [ms]
Anatomy of the GW signal 8 h+ 10 [50 Mpc] 0 GNH3, M =1.350M 8 5 0 5 10 15 0 5 t [ms] Inspiral: well approximated by PN/EOB; tidal effects important
Anatomy of the GW signal 8 h+ 10 [50 Mpc] 0 GNH3, M =1.350M 8 5 0 5 10 15 0 5 t [ms] Merger: highly nonlinear but analytic description possible
Anatomy of the GW signal 8 h+ 10 [50 Mpc] 0 GNH3, M =1.350M 8 5 0 5 10 15 0 5 t [ms] post-merger: quasi-periodic emission of bar-deformed HMNS
Anatomy of the GW signal 8 h+ 10 [50 Mpc] 0 GNH3, M =1.350M 8 5 0 5 10 15 0 5 t [ms] Collapse-ringdown: signal essentially shuts off.
Anatomy of the GW signal 8 clean peak at high freqs Chirp signal (track from low to high frequencies) h+ 10 [50 Mpc] 0 8 transient (messy but short) GNH3, M =1.350M 5 0 5 10 15 0 5 t [ms] Cut off (very high freqs)
é 1 1ê and Hf h L SSn nhf fl and f»hf HfL» In frequency space Effects of EOS as neutron stars merge -1 10 10 1 effec O G I L l a i Init tivel 10-10 y po int-p artic le NS-NS merger tidans-ns NS NS EOS BH HB EOS HB l effebh cts -3 10 10 3 BH-BH merger AdvancedLIGO 10-10 5 10-5 10 100 Mpc 10 10 post merger Einstein Teles co p e 50 50 100 100 ff HHzL Hz 500 500 1000 1000 5000 5000 8 courtesy of Jocelyn Read
Extracting information from EOS Takami, LR, Baiotti (01, 015), LR+ (01) 1.0 APR 0 M =1.75M M =1.300M M =1.35M M =1.350M M =1.375M 8 0.5 ALF 0 M =1.5M M =1.50M M =1.75M M =1.300M M =1.35M h+ 10 [50 Mpc] 8 0.00 8 0 0.5 8 0 SLy M =1.50M M =1.75M M =1.300M M =1.35M M =1.350M H M =1.50M M =1.75M M =1.300M M =1.35M M =1.350M GNH3 M =1.50M M =1.75M M =1.300M M =1.35M M =1.350M 1.0 8 1.0 5 0 5 10 15 0 5 00.5 5 10 15 0 5 0 5 0.010 15 0 5 0 5 10 15 0.5 0 5 0 5 10 15 0 1.0 t [ms]
Extracting information from EOS Takami, LR, Baiotti (01, 015), LR+ (01) 1.0 1.5.0 APR M =1.75M M =1.300M M =1.35M M =1.350M M =1.375M.5 3.0 3.5 1.5 0.5.0 ALF M =1.5M M =1.50M M =1.75M M =1.300M M =1.35M.5 3.0 log [ h(f) f 1/ ] [ Hz 1/, 50 Mpc ] 3.5 1.5.0.5 0.0 3.0 3.5 1.5.0 SLy H M =1.50M M =1.75M M =1.300M M =1.35M M =1.350M M =1.50M M =1.75M M =1.300M M =1.35M M =1.350M.5 3.0 0.5 3.5 There are lines! Logically not different from 1.5 M =1.50M M =1.75M M =1.300M M =1.35M M =1.350M.0 GNH3 emission lines from stellar atmospheres..5 adligo 3.0 This is GW spectroscopy! 3.5 ET 1.0 01.0 1 3 50 1 0.5 3 50 1 0.0 3 50 1 3 0.5 50 1 3 1.0 5 f [khz]
A new approach to constrain the EOS Oechslin+007, Baiotti+008, Bauswein+ 011, 01, Stergioulas+ 011, Hotokezaka+ 013, Takami 01, 015, Bernuzzi 01, 015, Bauswein+ 015, LR+01 merger frequency
A new approach to constrain the EOS Oechslin+007, Baiotti+008, Bauswein+ 011, 01, Stergioulas+ 011, Hotokezaka+ 013, Takami 01, 015, Bernuzzi 01, 015, Bauswein+ 015, LR+01
Quasi-universal behaviour: inspiral log 10 [ ( M/M )(fmax/hz) ] 3.8 3.7 3. 3.5 APR ALF SLy H GNH3 LS0 Eq. (), Takami et al. (01) Eq. (15) Eq. (), Read et al. (013) Read et al. (013) Bernuzzi et al. (01) 100 00 300 00 apple T surprising result: quasiuniversal behaviour of GW frequency at amplitude peak (Read+013) Many other simulations have confirmed this (Bernuzzi+, 01, Takami+, 015, LR+01). Quasi-universal behaviour in the inspiral implies that once fmax is measured, so is tidal deformability, hence I, Q, M/R = M 5 = 1 3 applet tidal deformability or Love number
Quasi-universal behaviour: post-merger We have found quasi- Eq. (5) in Takami et al. 015 universal behaviour: i.e., f1 [khz].5.0 APR ALF SLy H GNH3 LS0 the properties of the spectra are only weakly dependent on the EOS. This has profound implications for the 1.5 Dietrich et al. 015 Foucart et al. 015 analytical modelling of the GW emission: what we 0.1 0.1 0.1 0.18 M/ R do for one EOS can be extended to all EOSs.
Quasi-universal behaviour: post-merger 3.0 f,i [khz] 3.0.5 Eq. () Correlations with Love number found also for high frequency peak f f [khz].5 APR ALF SLy H GNH3 LS0 Eq. (3) 100 00 300 00 apple T 100 00 300 00 apple T Correlations also with compactness These other correlations are weaker but equally useful.
An example: start from equilibria Assume that the GW signal from a binary NS is detected and with a SNR high enough that the two peaks are clearly measurable. Consider your best choices as candidate EOSs
An example: use the M(R,f1) relation The measure of the f1 peak will fix a M(R,f1) relation and hence a single line in the (M, R) plane. All EOSs will have one constraint (crossing).
An example: use the M(R,f) relations The measure of the f peak will fix a relation M(R,f,EOS) for each EOS and hence a number of lines in the (M, R) plane. The right EOS will have three different constraints (APR, GNH3, SLy excluded)
An example: use measure of the mass If the mass of the binary is measured from the inspiral, an additional constraint can be imposed. The right EOS will have four different constraints. Ideally, a single detection would be sufficient.
This works for all EOSs considered In reality things will be more complicated. The lines will be stripes; Bayesian probability to get precision on M, R. Some numbers: at 50 Mpc, freq. uncertainty from Fisher matrix is 100 Hz at SNR=, the event rate is 0.- yr -1 for different EOSs.
Dynamically captured binaries and nucleosynthesis
animations by J. Papenfort, L. Bovard, LR
Mass ejection Mej [M ] 10 1 10 10 3 10 10 5 LK RP5 LK RP7.5 LK RP10 LK QC 0 10 0 30 0 t [ms] Mass ejected depends on impact parameter and takes place at each encounter. Quasi-circular binaries have smaller ejected masses (1- orders of magnitude) 10 0 10 1 10 HY QC LK QC M0 QC Mass ejected depends on whether neutrino losses are taken into account (less ejected mass if neutrinos are taken into account) Mej [M ] 10 3 10 10 5 10 10 7 HY RPX LK RPX M0 RPX 0.0 5.0 7.5 10.0 15.0 r p /M
r < ( ) [10 3 M 1 ] 0 Waveforms have complex morphology: oscillations triggered after first encounter and typical HMNS signal after merger LK RP10 0 10 0 30 0 t r? [ms] 10 8 Improved neutrino treatment (M0) 0 30 0 30 0 LK QC 10 10 0.5 0.5 0.05 [g cm 3 ] Ye leads to larger values of Ye at high latitudes 0 30 0 30 0 M0 QC 10 8 10 10 0.5 0.5 [g cm 3 ] Ye 0.05 13 1 15 1 17 18 19 0 1 3 5 t [ms]
Distributions in electron fraction, entropy, velocity HY RP10 LK RP10 M0 RP10 HY QC LK QC M0 QC Broad distribution in Ye when neutrino losses are taken into account 0.08 0.1 0. 0.3 0.0 Y e 0.08 0.1 0. 0.3 0.0 Y e HY RP10 LK RP10 M0 RP10 HY QC LK QC M0 QC Mass ejected at all latitudes but predominantly at low elevations 0.5 5 7.5 90 0.5 5 7.5 90 HY RP10 LK RP10 M0 RP10 HY QC LK QC M0 QC Broad distribution in asymptotic velocities independent of initial conditions 0.01 0.17 0.33 0.9 v 1 [c] 0.01 0.17 0.33 0.9 v 1 [c]
Nucleosynthesis 10 1 Relative abundances 10 10 3 10 10 5 Solar HY RP7.5 LK RP7.5 M0 RP7.5 Solar HY RP10 LK RP10 M0 RP10 Solar HY QC LK QC M0 QC 50 100 150 00 A 50 100 150 00 A 50 100 150 00 A Ejected matter undergoes nucleosynthesis as expands and cools. Abundance pattern for A>10 is robust and good agreement with solar (nd and 3rd peak well reproduced) Abundances very robust: essentially the same for eccentric or quasi-circular binaries
Macronova emission Energy via radioactive decay of r-process nuclei powers transients in optical/near-infrared with peak emission after (Grossman+ 1) t peak =.9 Mej 10 M 1/ apple 10 cm g 1 1/ hv1 i 0.1 c 1/ days, The peak bolometric luminosity is estimated to be ( ectonova ) L =.5 10 0 Mej 10 M 1 / apple 10 cm g 1 / hv1 i 0.1 c / erg s 1. with radioactive energy release a power law = 0 (t/t 0 ), ' 1.3 Eccentric binaries: ~ times more luminous than quasi-circular; delayed peak emission: ~ 8 days (cf. 1.5 days)
Conclusions Modelling of binary NSs in full GR is mature: GWs from the inspiral can be computed with precision of binary BHs Spectra of post-merger shows clear peaks, some of which are quasi-universal. If observed, will set tight constraints on EOS Eccentric binaries are rare but with larger ejected matter and macronova emission. high-a nucleosynthesis very robust