Binary Neutron Star Mergers Gravitational-Wave Sources and Gamma-Ray Bursts Vicky Kalogera Dept. of Physics & Astronomy Northwestern University

Binary Compact Objects Double Neutron Stars: the sample Double Neutron Stars: the sample Two new DNS binaries! Two new DNS binaries! Empirical DNS rates: updates Empirical DNS rates: updates Theoretical Merger Rates Theoretical Merger Rates Constraining population syntheses Constraining population syntheses Expectations for LIGO - when??? Expectations for LIGO - when??? NS mergers and short GRBs? NS mergers and short GRBs? Merger delays and redshift distributions Merger delays and redshift distributions In this talk:

DNS pulsars: Hulse-Taylor pulsar as a `lighthouse' GW orbital decay PSR B Weisberg & Taylor 03 Indirect evidence for Gravitational Waves

Direct detection? LIGOGEOVirgoTAMA AIGO Coincidence:detection confidence source localization signal polarization GW Interferometers: global network

Double Neutron Star (DNS) Systems  one of the prime targets of large-scale GW detectors (e.g. LIGO, VIRGO, GEO, TAMA) Galactic merger rate of DNS systems Event rate estimation for DNS inspiral search  Strong sources of gravitational waves (waveforms are well understood) Development and designing of GW detectors Understanding of the astrophysics of compact objects

DNS merger rate calculations  Empirical method: based on radio pulsar properties and observational selection effects of pulsar surveys (Narayan et al. (1991), Phinney (1991), Curran & Lorimer (1993), VK, Narayan et al. (2001), Kim, VK et al. (2003), VK, Kim et al. (2004))  T heoretical method: based on our understanding of binary formation and evolution (population synthesis models) (Portegies Zwart & Yungelson (1998), Nelemans et al. (2001), Belczynski, VK, & Bulik (2002), O’Shaughnessy, VK et al. (2005) and many more)

DNS pulsars: the observed sample PSR name P s (ms) P b (hr) e  life (Gyr) B B J A J J Burgay et al. 2003Parkes double pulsar Faulkner et al. 2004Parkes MB survey, acceleration search Lorimer et al. 2005Arecibo ALFA survey

Merger rate R Q: How many pulsars “similar” to each of the known DNS binaries exist in our Galaxy? Lifetime of a system Number of sources x correction factor R = beaming Goal : Calculate the probability distribution of the Galactic DNS merger rates P(R)

Method - Modeling & Simulation (Kim et al. 2003, ApJ, 584, 985 )   assume luminosity & spatial distribution functions   adapt spin & orbital periods from each observed PSR 1. Model pulsar sub-populations Selection effects for faint pulsars are taken into account.

Method - Modeling & Simulation (Kim et al. 2003, ApJ, 584, 985 ) count the number of pulsars observed (N obs ) populate a model galaxy with N pop PSRs (same P s & P orb ) N obs follows the Poisson distribution, P(N obs ; ) carefully model thresholds of PSR surveys Earth 2. Simulate large-scale pulsar surveys

For an each observed system i, P i (R) = C i 2 R exp(-C i R) where C i =  Combine the three individual PDFs and calculate P(R gal ) Statistical Analysis  Individual probability density function (PDF)  life N pop f b i

Probability density function of R gal P(R gal ) Lifetime ~ 185 Myr N J0737 ~ 1600 (most abundant) Lifetime ~ 80 Myr (shortest) N J1906 ~ 300

The revised DNS merger rate ~ ~ rate per Myr  Reference model: R peak (revised) R peak (previous) ~ 6-7 Increase rate factor due to PSR J : B1913+B1534+J0737B1913+B1534 (at 95% CL) R peak (revised) R peak (previous) ~ Increase rate factor due to PSR J : B1913+B1534+J0737+J1906 ~120

Detection rate of DNS inspirals for LIGO R det (adv. LIGO) ~ 350 events per yr R det (ini. LIGO) ~ 1 event per 20 yr  The most probable DNS inspiral detection rates for LIGO R det (adv. LIGO) ~ 15 – 850 events per yr R det (ini. LIGO) ~ 1 event per 5 – 250 yr All models: Reference model:

Implications of J  Discovered by the Parkes Multibeam Pulsar Survey with the acceleration search technique. Standard Fourier techniques failed to detect J  Contribution of J to the Galactic DNS merger rate. No significant change in the total rate. R peak (4 PSRs + J1756) R peak (4 PSRs) ~ 1.04  J : Another merging DNS in the Galactic disk Similar to the Hulse-Taylor system (Faulkner et al. 2005)

Global P(R gal ): motivation f(L)  L -p, where L min is a cut-off luminosity and p is a power index. L min (mJy kpc 2 ) p R peak (Myr -1 )  Radio pulsar luminosity function

Global P(R gal ): motivation, where L min is a cut-off luminosity and p is a power index.  Radio pulsar luminosity function  Global probability density function P global (R) P global (R) P(R; L min,p) f(L min ) g(p) intrinsic functions for L min and p P(R)  P(R; L min,p)  R peak is strongly dependent on L min & p. f(L)  L -p

Global P(R gal ) and SNe rate constraints Probability Density Galactic DNS merger rate (Myr -1 ) SN U5 SN L5 SN Ib/c = Myr -1 (Cappellaro, Evans, & Turatto 1999) SN L5 = SN (lower)x0.05 = 30 Myr -1 SN U5 = SN (upper)x0.05 = 80 Myr -1 Suppose, ~5% of Ib/c SNe are involved in the DNS formation. The empirical SNe rate

Compact Binary Inspiral Rates: What about Black Hole Binaries?  BH-NS binaries could in principle be detected as binary pulsars, BUT… the majority of NS in BH-NS are expected to be young short-lived hard-to-detect harder to detect than NS-NS by >~ ! So farrate predictions So far, inspiral rate predictions from population calculations only from population calculations with uncertainties of ~ 3 orders of mag We can use NS-NS empirical rates as constraints on population synthesis models

Binary Compact Objects: Formation from Tauris & van den Heuvel 2003 Massive primordial binary Mass-transfer #1: hydrostatically and thermally Stable, but Non-Conservative: mass and A.M. loss Supernova and NS Formation #1: Mass Loss and Natal Kick High-mass X-ray Binary: NS Accretion from Massive Companion’s Stellar Wind Mass-transfer #3: Dynamically Unstable Mass-tranfer #4: Possible and Stable Supernova and NS Formation #2: Mass Loss and Natal Kick Double Neutron-Star Formed!

Population Synthesis Parameter Study Large parameter space Most important parameters: 7 7D parameter study: computationally demanding Acceleration of computations: Use of Genetic Algorithms

Rate Fits vs. StarTrack calculations: 7D BH-BH NS-NS O’Shaughnessy et al Fit accuracy is comparable or usually smaller than the Poisson errors of StarTrack Monte Carlo rates (Belczynski et al. 2005)

Black Hole Binary Inspiral: Event Rates From Population Synthesis Modeling: log ( events per yr ) PDF BH-BH BH-NS NS-NS

Empirical Constraints imposed on population synthesis rate predictions Merging NS-NSWide NS-NS O’Shaughnessy et al log(rate)

Four More Rate Constraints: O’Shaughnessy et al SN Ib/c SN II merging PSR-WD eccentric PSR-WD

BH-BHBH-NS NS-NS Constrained vs. Unconstrained Rate Predictions from StarTrack: O’Shaughnessy et al BH-BH BH-NS NS-NS

Short GRBs and NS-NS / BH-NS mergers Short GRB afterglows reveal association with both elliptical and star-forming galaxies: Progenitors must exist in both OLD and YOUNG stellar populations! NS-NS and BH-NS mergers: prime candidates What is the event (GRB and mergers) rate vs. redshift ? What is the spatial distribution w/r to the host galaxies ?

What is the event (GRB and mergers) rate vs. redshift ? Star-formation rate vs. redshift Porciani & Madau Time-Delay between formation and mergers Formation efficiency (# mergers / unit SF mass) Relative Contribution of spirals and elliptical galaxies GRB Luminosity function unknown … We need to know:

Time-Delay between formation and mergers NS-NS SPIRAL GALAXIES BH-NS log(Merger Time / Myr) BH-NS ELLIPTICAL GALAXIES log(Merger Time / Myr) NS-NS BH-NS Belczynski O’Shaughnessy

Compact Binary Formation efficiencies What is the number of binaries formed per unit stellar mass? SPIRAL GALAXIESELLIPTICAL GALAXIES NS-NS BH-NS log(efficiency * Msun) Belczynski O’Shaughnessy

Merger Rate vs. redshift If ellipticals contributed 20% of the SF mass in the past until about redshift of 2 Comparison with observed redshift distribution requires a luminosity model … ?

Binary Center-of-mass velocities and Lifetimes: Where do they merge ? SPIRAL GALAXIES ELLIPTICAL GALAXIES NS-NS BH-NS 1kpc 10 kpc log(merger time / Myr) log(Vcm / km/s) Belczynski O’Shaughnessy