The physics and astrophysics of merging neutron-star binaries Luciano Rezzolla Institute for Theoretical Physics, Frankfurt Frankfurt Institute for Advanced Studies, Frankfurt GSI-FAIR Colloquium Darmstadt 18 May 2016
Plan of the talk ✴ Numerical relativity as a theoretical laboratory ✴ Anatomy of the GW signal ✴ Role of B-fields and EM counterparts ✴ Ejected matter and nucleosynthesis
The goals of numerical relativity Einstein’s theory is as beautiful as intractable analytically Numerical relativity solves Einstein/HD/MHD eqs. in regimes in which no approximation is expected to hold. To do this we build codes: our ”theoretical laboratories”.
Theoretical laboratory G µ ν =8 π GT µ ν , r µ T µ ν =0 Think of them as a ” factory ” of “gedanken experiments”
The equations of numerical relativity R µ ν − 1 (field equations) 2 g µ ν R = 8 π T µ ν , r µ T µ ν = 0 , (cons . energy / momentum) r µ ( ρ u µ ) = 0 , (cons . rest mass) p = p ( ⇢ , ✏ , Y e , . . . ) , (equation of state) r ν F µ ν = I µ , ν F µ ν = 0 , (Maxwell equations) r ∗ EM T µ ν = T fluid (energy − momentum tensor) + T µ ν + . . . µ ν In vacuum space times the theory is complete and the truncation error is the only error made : “CALCULATION”
The equations of numerical relativity R µ ν − 1 (field equations) 2 g µ ν R = 8 π T µ ν , r µ T µ ν = 0 , (cons . energy / momentum) r µ ( ρ u µ ) = 0 , (cons . rest mass) p = p ( ⇢ , ✏ , Y e , . . . ) , (equation of state) r ν F µ ν = I µ , ν F µ ν = 0 , (Maxwell equations) r ∗ EM T µ ν = T fluid (energy − momentum tensor) + T µ ν + . . . µ ν In non-vacuum space times the truncation error is the only error that is measurable : “SIMULATION” It’s our approximation to “reality”: improvable via microphysics, magnetic fields, viscosity, radiation transport, ...
The two-body problem: Newton vs Einstein Take two objects of mass and m 1 m 2 interacting only gravitationally In Newtonian gravity solution is analytic: there exist closed orbits (circular/elliptic) with r = − GM ¨ r d 3 12 where M ≡ m 1 + m 2 , r ≡ r 1 − r 2 , d 12 ≡ | r 1 − r 2 | . In Einstein’s gravity no analytic solution! No closed orbits: the system loses energy/angular momentum via gravitational waves.
Catastrophic events… Back-of-the-envelope calculation (Newtonian quadrupole approx.) shows the energy emitted in GWs per unit time is ✓ G ◆ 2 ◆ 2 ✓ h v i ◆ 6 ◆ ✓ M h v 2 i ✓ c 5 ◆ ✓ R Schw . L GW ' ' c 5 G R c τ Near merger the binary is very compact (R Schw. =2GM/c 2 ) and moving at fraction of speed of light: GR is indispensable R ' 10 R Schw . h v i ' 0 . 1 c As a result, the GW luminosity is: ✓ c 5 ◆ ' 10 50 erg s � 1 ' 10 17 L � L GW ' 10 � 8 G This is roughly the combined luminosity of 1million galaxies!
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 Abbott+ 2016 • HMNS phase can provide strong and clear information on EOS • BH+torus system may tell us on the central engine of GRBs
Animations: Breu, Radice, LR M = 2 × 1 . 35 M � LS220 EOS
“merger HMNS BH + torus” Quantitative differences are produced by: - differences induced by the gravitational MASS: a binary with smaller mass will produce a HMNS further away from the stability threshold and will collapse at a later time
Broadbrush picture proto-magnetar? FRB?
“merger HMNS BH + torus” Quantitative differences are produced by: - differences induced by the gravitational MASS: a binary with smaller mass will produce a HMNS further away from the stability threshold and will collapse at a later time - differences induced by MASS ASYMMETRIES: tidal disruption before merger; may lead to prompt BH
Animations: Giacomazzo, Koppitz, LR Total mass : 3 . 37 M � ; mass ratio :0 . 80; ✴ the torii are generically more massive ✴ the torii are generically more extended ✴ the torii tend to stable quasi-Keplerian configurations ✴ overall unequal-mass systems have all the ingredients needed to create a GRB
“merger HMNS BH + torus” Quantitative differences are produced by: - differences induced by the gravitational MASS: a binary with smaller mass will produce a HMNS further away from the stability threshold and will collapse at a later time - differences induced by MASS ASYMMETRIES: tidal disruption before merger; may lead to prompt BH - differences induced by the EOS: stiff/soft EOSs will have different compressibility and deformability, imprinting on the GW signal - differences induced by MAGNETIC FIELDS: the angular momentum redistribution via magnetic braking or MRI can increase/decrease time to collapse; EM counterparts! - differences induced by RADIATIVE PROCESSES: radiative losses will alter the equilibrium of the HMNS
How to use gravitational waves to constrain the EOS
Anatomy of the GW signal 8 6 4 h + ⇥ 10 22 [50 Mpc] 2 0 � 2 � 4 GNH3, ¯ M =1.350 M � � 6 � 8 � 5 0 5 10 15 20 25 t [ms]
Anatomy of the GW signal 8 6 4 h + ⇥ 10 22 [50 Mpc] 2 0 � 2 � 4 GNH3, ¯ M =1.350 M � � 6 � 8 � 5 0 5 10 15 20 25 t [ms] Inspiral : well approximated by PN/EOB; tidal effects important
Anatomy of the GW signal 8 6 4 h + ⇥ 10 22 [50 Mpc] 2 0 � 2 � 4 GNH3, ¯ M =1.350 M � � 6 � 8 � 5 0 5 10 15 20 25 t [ms] Merger : highly nonlinear but analytic description possible
Anatomy of the GW signal 8 6 4 h + ⇥ 10 22 [50 Mpc] 2 0 � 2 � 4 GNH3, ¯ M =1.350 M � � 6 � 8 � 5 0 5 10 15 20 25 t [ms] post-merger : quasi-periodic emission of bar-deformed HMNS
Anatomy of the GW signal 8 6 4 h + ⇥ 10 22 [50 Mpc] 2 0 � 2 � 4 GNH3, ¯ M =1.350 M � � 6 � 8 � 5 0 5 10 15 20 25 t [ms] Collapse-ringdown : signal essentially shuts off.
Anatomy of the GW signal 8 clean peak 6 at high freqs 4 h + ⇥ 10 22 [50 Mpc] 2 0 Chirp signal � 2 (track from � 4 low to high Cut off (very GNH3, ¯ M =1.350 M � � 6 frequencies) transient high freqs) � 8 � 5 0 5 10 15 20 25 t [ms]
Anatomy of the GW signal Inspiral f max frequency frequency waveform t max
Hints of quasi-universality Read+, 2013 , found rather “surprising” result: quasi- 3 . 8 universal behaviour of GW frequency at amplitude peak M/M � )( f max / Hz) ] Eq. (24), Takami et al. (2014) Eq. (15) Bernuzzi+, 2014, Takami+, 2015, Eq. (22), Read et al. (2013) 3 . 7 Read et al. (2013) LR+2016 confirmed with new Bernuzzi et al. (2014) simulations. log 10 [ (2 ¯ Quasi-universal behaviour APR4 3 . 6 ALF2 in the inspiral implies that SLy H4 once f max is measured, so is GNH3 tidal deformability, hence LS220 3 . 5 I, Q, M/R 100 200 300 400 κ T 2 λ M 5 = 16 tidal deformability or Love number 3 κ T Λ = ¯ 2
Anatomy of the GW signal merger/post-merger 8 6 4 h + ⇥ 10 22 [50 Mpc] 2 0 � 2 � 4 GNH3, ¯ M =1.350 M � � 6 � 8 � 5 0 5 10 15 20 25 t [ms]
Extracting information from the EOS Takami, LR, Baiotti (2014, 2015), LR+ (2016) 1 . 0 6 APR4 4 2 0 � 2 � 4 ¯ ¯ ¯ ¯ ¯ M =1.275 M � M =1.300 M � M =1.325 M � M =1.350 M � M =1.375 M � � 6 � 8 6 ALF2 4 0 . 5 2 0 � 2 � 4 ¯ ¯ ¯ ¯ ¯ M =1.225 M � M =1.250 M � M =1.275 M � M =1.300 M � M =1.325 M � � 6 � 8 h + ⇥ 10 22 [50 Mpc] 6 SLy 4 2 0 . 0 0 � 2 � 4 ¯ ¯ ¯ ¯ ¯ M =1.250 M � M =1.275 M � M =1.300 M � M =1.325 M � M =1.350 M � � 6 � 8 6 H4 4 2 0 � 2 � 4 � 0 . 5 ¯ ¯ ¯ ¯ ¯ M =1.250 M � M =1.275 M � M =1.300 M � M =1.325 M � M =1.350 M � � 6 � 8 6 GNH3 4 2 0 � 2 � 4 ¯ ¯ ¯ ¯ ¯ M =1.250 M � M =1.275 M � M =1.300 M � M =1.325 M � M =1.350 M � � 6 � 8 � 1 . 0 � 1 . 0 � 5 0 5 10 15 20 � 5 � 0 . 5 0 5 10 15 20 � 5 0 5 0 . 0 10 15 20 � 5 0 5 10 15 0 . 5 20 � 5 0 5 10 15 20 1 . 0 t [ms]
Extracting information from the EOS Takami, LR, Baiotti (2014, 2015), LR+ (2016) 1 . 0 � 21 . 5 ¯ ¯ ¯ ¯ ¯ M =1.275 M � M =1.300 M � M =1.325 M � M =1.350 M � M =1.375 M � APR4 � 22 . 0 � 22 . 5 � 23 . 0 � 23 . 5 � 21 . 5 ¯ ¯ ¯ ¯ ¯ M =1.225 M � M =1.250 M � M =1.275 M � M =1.300 M � M =1.325 M � ALF2 0 . 5 � 22 . 0 � 22 . 5 � 23 . 0 h ( f ) f 1 / 2 ] [ Hz � 1 / 2 , 50 Mpc ] � 23 . 5 � 21 . 5 ¯ ¯ ¯ ¯ ¯ M =1.250 M � M =1.275 M � M =1.300 M � M =1.325 M � M =1.350 M � SLy � 22 . 0 � 22 . 5 0 . 0 � 23 . 0 � 23 . 5 log [ ˜ � 21 . 5 ¯ ¯ ¯ ¯ ¯ M =1.250 M � M =1.275 M � M =1.300 M � M =1.325 M � M =1.350 M � H4 � 22 . 0 � 22 . 5 � 23 . 0 � 0 . 5 � 23 . 5 � 21 . 5 ¯ ¯ ¯ ¯ ¯ M =1.250 M � M =1.275 M � M =1.300 M � M =1.325 M � M =1.350 M � GNH3 � 22 . 0 There are lines! Logically not different from � 22 . 5 adLIGO � 23 . 0 emission lines from stellar atmospheres ET � 23 . 5 � 1 . 0 � 1 . 0 0 1 2 3 4 5 0 1 � 0 . 5 2 3 4 0 5 1 2 0 . 0 3 4 5 0 1 2 3 0 . 5 4 5 0 1 2 3 4 1 . 0 5 f [kHz]
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