Gravitational waves (...and GRB central engines...) from neutron star mergers Roland Oechslin MPA Garching, SFB/TR 7 Ringberg Workshop, 27.3.2007
Gravitational waves (...and GRBcentral engines...) from neutron
star mergers
Roland OechslinMPA Garching, SFB/TR 7
Ringberg Workshop, 27.3.2007
In this talk:
-Intro:-Overview & Motivation-Neutron star mergers as gamma-ray burst engines and as GW emitters
-Results from hydrodynamic simulations of NSM:-A parameter study-How do GW pattern and postmerger configuration depend on the EoS and on the NS mass & spin ?
Merging neutron stars: Why are they interesting ?
strong gravitational wavesource
Potential central enginefor short gamma-raybursts
r-process nucleosynthesis
large, time-dependentquadrupole
hot, n-emitting accretiontorus around compact mergerremnant
neutron rich ejecta
Merging neutron stars: Schematic timetable
Hulse-Taylor:PSR1913+16forb~3£10-5Hztmerger~240Mio. yr
adiabatic inspiral due to GW backreaction merger postmerger
Tightest DNS:J0373-3039forb~1£10-4Hztmerger~85Mio. yr
NSs are ripped apartby tidal forces:forb~500Hzdmerger» 3RNS
O(Myrs-Gyrs) O(ms) O(ms to s)
(M. Kramer, Jodrell Bank Obs.)
time
Formation of a dense mergerremnant/BH surrounded bya hot accretion torus:Mtorus» 0.01..0.3M¯Mremnant» 3M¯
Short Gamma-Ray bursts: The Merger model
Merger of a NS/NS or NS/BH binary andformation of a BH - torus systemMBH'3M¯, Mdisc'0.05M¯
Internal shocks between the jet shells lead to emission ofg-photons
Baryonic jet along the rotation axis, collimated by the torus(Other possibility: MHD pinching)
Energy deposition through nnbar-annilihation in thebaryon-poor funnel around the rotation axis
Viscous heating in the torus, emission of neutrions
(S. Rosswog, 2003)
(Aloy et al., 2004)
The merger model: Energetics
• generic torus mass: 0.05M¯ ' 1053erg• gravitational energy ! n´s ~10%• nnbar ! e+e- ! 2g ! Ekin,ouflow ~ 0.1%-1%• Ekin,outflow ! GRB-g´s · 10%• EGRB ! EGRB
iso £10-100• EGRB
iso' 1049-1051erg: compatible with observations!
! The torus- and BH-masses are of crucial importance to power a GRB!
Generic GW waveform and spectrum
Chirp-like inspiral partSpectrum: Broadband contribution . 1 kHz
Quasi-periodic postmerger partSpectrum: Large peak(s) around 2-4kHz
(& 5 kHz in case of prompt BH formation)
How do the unknown parameter influence the torus und GWsignal ?
„Clean“ system, but several free parameters:
- NS spins: irrotating, corotating, counterrotating, tilted spins- gravitational NS masses: from 1.07M¯ – 1.6 M¯- Mass ratio: from q=0.55 – 1- EoS: Shen, Lattimer-Swesty, ideal gas
EoS
Mass ratio, total mass
NS spins
Reference model:1.4+1.4M¯, no NS spin,Shen EoS
Hydrodynamical simulations of merging NS
General relativity
Microphysics
Polytropic EoSNewtonian
1PN
Conformallyflat
Physical EoS
Oohara & Nakamura (1989),Rasio et al, Centrella et al.Zhuge et al.
Ayal et al., Faber et al.Oohara & Nakamura
(Wilson et al.)RO et al, Faber et al.
Shibata et al.(Miller at al.)
Neutrino physics
Ruffert et al.Rosswog et al.
Magnetic fields
RO & Janka
(Shibata & Taniguchi)
Price & Rosswog
Physical and numerical ingredients
- Fully relativistic hydrodynamics using SPH, ~400‘000 particles
- Einstein eqns. are solved approximately:- assume for the spatial metric gij=y4dij (conformally flat condition)
! EE reduce to 5 nonlinear, coupled, elliptic PDEs! Metric is not evolved independently, but is coupled to the matter.
-Physical, non-zero temperature EoS (Shen et al.,1999; Lattimer & Swesty, 1991) / ideal gas EoS / zero temperature EoS (Akmal, Pandharipande & Ravenhall, 1998) with „thermal extension“
-No neutrinos, no MHD, dynamically unimportant on this timescales.
- Initial data: Binary in equilibrium near ISCO, T=0, n-less b-equilibirum
Finite temperature dense matter EoSs:
L&S: Lattimer & Swesty, 1991, with K=188MeVShen: Shen et al., 1998
Available as 3D tables, EoS as function of (r , T, Ye)
Ye=0.05
Merger dynamics & torus formation:green/blue: star 1/2red: particles ending up in the diskyellow: particles that currently fulfill thetorus criterion
Torus:=matter with j>jLSOwhere LSO=last stable orbit arounda BH with MBH=Mremnant & aBH=aremnant
Varying the binary parameters:
corotating
Asymmetric,Mass ratio q=0.75
Lattimer-Swesty-EoS
Torus masses: Dependence on binary parameters
! Strong dependence on the mass ratio q. Saturation at about Mtorus=0.2M¯
! Weak dependence on the total mass!
! NS spin influence via total angular momentum. Detailed merger dynamics seems to be of minor importance.
counterrot. irrot.
corot.
Torus masses: Dependence on the EoSTwo possibilities to transfer ang.mom. out to torus:
• At premerger/merger if the NSs are large enough: ! Shen EoS
• At postmerger by gravitational torques. Effective for very compact and non-axisymmetric remnants: ! APR, (LS)
How does the GW signal depend on the free parameters?
fmax: Frequency at the amplitudemaximum of the inpiral chirp
fpeak: Frequency of the dominatingoscillation in the postmergerwavetrain
Try to identify characteristic quantities:
fmax=f@hmax
fpeakD Ein
D Ein, D Epm: Radiated energies during 3ms just before and during 5ms just after merging
D Epm
Dependence of the GW signal/spectrum ±: Shen-EoS (stiff)*: LS-EoS (soft)D,r: APR-EoS (soft, very stiff @large r )
+: Counterrotatingx: CorotatingNS spin
nuclear EoS
total mass
mass ratio
Conclusions
Neutron star mergers are a strong gravitational wave source and thus a primecandidate for detection by one of the ground based interferometers.Currently, they are also the preferred model for the central engine of short GRBs.
Using hydrodynamic simulations, we have investigated the merger dynamics and thefollowing torus formation depending on the initial NS mass ratio, spin and the EoS.
We found torus masses between ~0.03M¯ (q=1, no spin, LSEoS) and ~0.30M¯(q=0.55, no spin, Shen EoS). These results are compatible with estimates inferredfrom observations of the first 4 short GRBs.
The merger and postmerger GW signal and spectrum depend very sensitivelyon the nuclear EoS. A measurement of a merger signal may help to further restrict theEoS parameter space.