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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 c (t ) f b NS t * 0 0 R* (t * ) P( )d R* (t ) : star formation rate (Rocha-Pinto et al., 2000) 40 : fraction of formed stars in the range 9-40 M ( = Am-1.35dm) 9 f b : fraction of massive binaries formed among all stars NS : fraction of massive binaries that remain bounded after the second supernova P( ): probability for a newly formed NS/NS to coalesce in a timescale 0 : minimum coalescence time * : mean timescale required for the newly formed massive system to evolve into two NSs The Galactic Star Formation Rate previous studies: the star formation rate is proportional to the available mass of gas as, R*(t) ~ e-at 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 79 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 c (t ) f b NS t * 0 0 R* (t * ) P( )d R* (t ) : star formation rate (Rocha-Pinto et al., 2000) 40 : fraction of formed stars in the range 9-40 M ( = Am-1.35dm) 9 f b : fraction of massive binaries formed among all stars NS : fraction of massive binaries that remain bounded after the second supernova P( ): probability for a newly formed NS/NS to coalesce in a timescale 0 : minimum coalescence time * : mean timescale required for the newly formed massive system to evolve into two NSs Numerical Simulations (P(), 0, NS) initial parameters: birth parameters (M1, M2, a, e)0 masses: M1, Salpeter IMF, M1/M2: probability derived from observations separation: P(a)da=da/a between 2RRoche and 200RRoche eccentricity: P(e)de = 2ede Mass loss (M1, M2, a, e)1 E>0 evolution of orbital parameters due to mass loss (stellar wind, mass transfert, supernova) statistical properties Mass loss (1.4Mo, M2, a, e)2 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 ) disrupted Supernova 1 E>0 Supernova 2 disrupted 0 2x105 yr (minimum coalescence time) NS/NS system a, e -> Vincent, 2002 The Galactic Coalescence Rate c (t ) f b NS t * 0 0 R* (t * ) P( )d R* (t ) : star formation rate (Rocha-Pinto et al., 2000) 40 : fraction of formed stars in the range 9-40 M ( = Am-1.35dm) 9 f b : fraction of massive binaries formed among all stars NS : fraction of massive binaries that remain bounded after the second supernova P( ): probability for a newly formed NS/NS to coalesce in a timescale 0 : minimum coalescence time * : mean timescale required for the newly formed massive system to evolve into two NSs Population Synthesis (fb) single radio pulsar properties: birth parameters Po, Bo, vk, do… • Np = 250000 (for 1095 observed) • birth properties mean dispertion P0 (ms) 240 ± 20 80± 20 ln 0 (s) 11 ± 0.5 3.6 ± 0.2 magnetic braking present properties P, dP/dt, d, S … 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) selection effects: sky coverage, cone, flux + - • Nb = 730 (for two observed) 1 1 fb 1 NS 2 N b NS f b NS Np f b 0.136 observed hidden Regimbau, 2001&2004 The Local Coalescence Rate E LS c S ( fS fE ) S LE weighted average over spiral (fS=65%) and elliptical (fE=35%) galaxies same fb 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 – 10-4 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/ ) The Detection Rate coalescence rate within the volume V=4/3 p D3 (<D) c LV 4 with V= p D3 LMW 3 counts of galaxies from the LEDA catalog: - 106 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 maximum probed distance and mean expected rate (S/N=7; false alarm rate=1) : VIRGO LIGO LIGO 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 (52-148 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 J0737-3039 A+B . . P dP/dt Bsurf A B 22.7 ms 1.7 x 10-18 6 x 109 G 2.77 s 0.88 x 10-15 1.6 x 1012 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 Nobsi Statistics Nobsi follows a Poisson distribution of mean <Nobs>i <Nobs>i = a Ntot bayesian statistic to compute Pi(Ntot) i coalescence rate Ri = Ntoti/life fb P(Ri) with mean and confidence level combine P(Ri) to obtain P(R)