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.