( SPH) Simulations of Binary N eutron Star Coalescence

1. Examining the Mass Ratio Dependence of Post-Newtonian Smoothed Particle Hydrodynamics (SPH) Simulations of Binary Neutron Star Coalescence Jonathon Meyers, Yi Mei, Rick Hallett, Margie Michna Purdue University North Central Advisor: Dr. Aaron Warren 2012

2. Introduction • Goals? • What are gravity waves? • Gravity waves are ripples in the curvature of spacetime which propagate as a wave, travelling outward from the source. • 2 Neutron Stars (NS) coalescing • Ripple in space time • Black Holes • What can we learn from them? • Gravity is treated as a phenomenon resulting in the curvature of spacetime. • When gravitational radiation pass a distant observer, that observer will find spacetime distorted by the effects of strain. • Hypothesized that they will be able to provide observers on Earth with information about neutron stars, black holes, and related phenomena such as gamma-ray bursts.

3. Indirect Evidence for Waves • Hulse-Taylor PSR1913+16 • Discovered by Russell Alan Hulse and Joseph Hooton Taylor, Jr. in 1974 • Two radiating NS orbiting around a common center of mass, forming a binary star system. • The two NS lose energy in accordance with GW Hulse Taylor

4. Simulations & Coding • What is “SPH”? • Hydrodynamics is important when tidal effects become significant near end of coalescence. • SPH simulates fluids as a set of particles. Forces are calculated on each particle, and velocity/position updated at each time step. • A smoothing function interpolates particle property values (such as density) to points between the particles. • What is “Post-Newtonian”? • In weak gravity fields, relativistic corrections to Newtonian gravity are small and can be represented as an infinite series. • StarCrash keeps 1PN terms, as well as all 2.5PN terms which represent gravitational radiation reaction.

5. Simulation Setup • Model each neutron star as a polytrope. The pressure • K = polytropic constant, = rest mass density, =adiabatic exponent. • Is a good approximation to many realistic EOS. Higher values of represent stiffer EOS. We chose the realistic value =2.3. • Two polytropic models are built with a chosen mass ratio ≤ 1 where • Models are then placed in synchronized orbit with binary center of mass at the origin.

6. Qualitative Results

7. Leading Lagging

8. Gravity Wave Profiles q = 0.90 q = 1.00 q = 1.00 q = 0.90 • Waveforms for and • Wave strain • (scale by at 100MPc) • Wave luminosity • (scale by for erg/s)

9. Wave Spectrum: Wavelet Analysis • Wavelet transforms enable time-dependent characterization of a signal, unlike traditional Fourier transforms • Build signal from copies of a wavelet, where copies may be translated in time and scaled. Scale ~ frequency. • We used the analytic Morlet wavelet

10. Wave Spectrum: Wavelet Analysis • Primary wave frequencies similar for all q • Find local maxima of CWT coefficients • ~650 Hz for late inspiral & ringdown • ~2000 Hz during chirp • Calculate power spectrum, very weak mass dependence • Would not have detected with LIGO S6 at 100 MPc. LIGO S6 50% Detection threshold h >

11. Mass Ratio Dependences • Least-squares fit with polynomial, residuals tested for normality.

12. Future Work • Extend simulations to cover a greater range of the parameter space; determine how the gravitational wave characteristics depend on these parameters. • Gamma • Mass Ratio • Synchronized vsIrrotational orbits • Estimate which remnants are likely to form black holes or hypermassive neutron stars. Model candidate regions in parameter space using a numerical relativity code, compare with post-Newtonian results.