Expected Coalescence Rate of NS/NS Binaries for Ground Based Interferometers Tania Regimbau OCA/ARTEMIS on the behalf of J.A. de Freitas Pacheco, T. Regimbau, S. Vincent, A. Spallicci

The Model  a very small fraction of massive binaries remains bounded after 2 supernova explosions  the resulting system consist of: 1. a partially reaccelerated pulsar 2. a young pulsar with - same period evolution (magnetic dipole spin down) as normal radio pulsars - same kick velocity as millisecond pulsars (for which the supernova didn’t disrupt the system either)

The Galactic Coalescence Rate

The Galactic Star Formation Rate previous studies: the star formation rate is proportional to the available mass of gas as, R * (t) ~ e -  t present work: the star formation history is reconstructed from observations:  ages of 552 stars derived from chromospheric activity index (Rocha-Tinto et al., 2000)  enhanced periods of star formation at 1 Gyr, 2-5 Gyr and 7- 9 Gyr probably associated with accretion and merger episodes from which the disk grows and acquires angular momentum (Peirani, Mohayaee, de Freitas Pacheco, 2004)

The Galactic Coalescence Rate

Numerical Simulations (P(  ),  0,  NS )  initial parameters:  masses: M 1, Salpeter IMF, M 1 /M 2 : probability derived from observations  separation: P(a)da=da/a between 2R Roche and 200R Roche  eccentricity: P(e)de = 2ede  evolution of orbital parameters due to mass loss (stellar wind, mass transfert, supernova)  statistical properties   NS = 2.4% (systems that remain bounded after the second supernova)  P(  0.087/  probability for a newly formed system to coalesce in a timescale      2x10 5 yr (minimum coalescence time) Vincent, 2002 birth parameters (M1, M2, a, e) 0 Mass loss (M1, M2, a, e) 1 Supernova 1 disrupted NS/NS system a, e ->  Mass loss (1.4Mo, M2, a, e) 2 Supernova 2 disrupted E > 0

The Galactic Coalescence Rate

Population Synthesis (f b ) birth parameters P o, B o, v k, d o … magnetic braking selection effects: sky coverage, cone, flux observedhidden present properties P, dP/dt, d, S … +-  single radio pulsar properties: N p = (for 1095 observed) birth properties  second binary pulsar properties: the youngest pulsar has the same: - period evolution (magnetic dipole spin down) as single radio pulsars - kick velocity as millisecond pulsars (remains bounded after the supernova) Nb = 730 (for two observed)  3.6 ± ± 0.5 ln  0 (s) 80± ± 20P 0 (ms) dispertionmean Regimbau, 2001&2004

The Local Coalescence Rate  weighted average over spiral (f S =65%) and elliptical (f E =35%) galaxies  same f b and  NS as for the Milky Way  spiral galaxy coalescence rate equal to the Milky Way rate:  S = MW = (1.7±1)x10 -5 yr -1  elliptical galaxy star formation efficiency and IMF estimated from observations - color & metallicity indices (Idiart, Michard & de Freitas Pacheco, 2003)  E =  8.6x10 -5 yr -1  c = 3.4x10 -5 yr -1 other estimates: ~10 -6 – yr -1 (Kalogera et al., 2004: 1.8x10 -4 yr -1 ) Intermitent star formation history: modulation in the coalescence rate Bulk of stars formed in the first 1-2 Gyr. The pairs merging today were formed with long coalescence times (P  ~1/  )

 coalescence rate within the volume V=4/3  D 3 counts of galaxies from the LEDA catalog: galaxies (completness of 84% up to B = 14.5) - inclusion of the Great Attractor (intersection of Centaurus Wall and Norma Supercluster) corresponding to 4423 galaxies at Vz = 4844 km/s The Detection Rate  maximum probed distance and mean expected rate (S/N=7; false alarm rate=1) : VIRGOLIGOLIGO Ad 13 Mpc 1 event/148 yr 14 Mpc 1 event /125 yr 207 Mpc 6 events/yr

Possible Improvements in the Sensitivity…  gain in the VIRGO thermal mirror noise band ( Hz): reduction of all noises in the band by a factor 10 (Spallicci, 2003; Spallicci et al., submitted) gain throughout VIRGO full bandwidth reduction of pendulum noise by a factor 28, thermal mirror 7, shot 4 (Punturo, 2004; Spallicci et al., submitted) maximum probed distance: 100 Mpc detection rate: 1.5 events / yr  use networks of detectors: LIGO-H/LIGO-L/VIRGO(Pai, Dhurandhar & Bose, 2004) false alarm rate = 1, detection probability = 95% maximum probed distance: 22 Mpc detection rate: 1 events / 26 yrs

Work in progress  compute the GW stochastic background produced by the superposition of all the NS/NS binaries  analytical approach integration up to to z~6  numerical approach generating extragalactic populations of NS/NS binaries

Extra slides

.. PSR J A+B AB P dP/dt Bsurf 22.7 ms 1.7 x x 10 9 G 2.77 s 0.88 x x G

Kalogera, Kim, Lorimer et al., 2004  Numerical simulations sample of 3 galactic coalescing pulsars, (P, dP/dt) i populate a model galaxy (P(L, R, z)) with Ntot pulsars with (P, dP/dt) i model radiotelescope survey selection effects and compute Nobs i  Statistics Nobs i follows a Poisson distribution of mean i i =  i Ntot bayesian statistic to compute P i (Ntot)  coalescence rate R i = Ntot i /  life f b P(R i ) with mean and confidence level combine P(R i ) to obtain P(R)