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Expected Coalescence Rate of NS/NS Binaries for Ground Based Interferometers

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

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Expected Coalescence Rate of NS/NS Binaries for Ground Based Interferometers

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  1. 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

  2. The Model • a very smallfraction 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)

  3. The Galactic Coalescence Rate

  4. 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 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)

  5. The Galactic Coalescence Rate

  6. birth parameters (M1, M2, a, e)0 Mass loss (M1, M2, a, e)1 Supernova 1 disrupted Mass loss (1.4Mo, M2, a, e)2 Supernova 2 disrupted NS/NS system a, e -> t Numerical Simulations (P(t), t0, bNS) • initial parameters: • 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 • evolution of orbital parameters due to mass loss (stellar wind, mass transfert, supernova) • statistical properties • bNS= 2.4% (systems that remain bounded after the second supernova) • P(t) = 0.087/t (probability for a newly formed system to coalesce in a timescale t) • t0 =2x105 yr (minimum coalescence time) E > 0 E > 0 Vincent, 2002

  7. The Galactic Coalescence Rate

  8. birth parameters Po, Bo, vk, do… mean dispertion P0 (ms) 240 ± 20 80± 20 magnetic braking ln t0 (s) 11 ± 0.5 3.6 ± 0.2 present properties P, dP/dt, d, S … selection effects: sky coverage, cone, flux + - observed hidden Population Synthesis (fb) • single radio pulsar properties: • Np = 250000 (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) Regimbau, 2001&2004

  9. The Local Coalescence Rate Bulk of stars formed in the first 1-2 Gyr. The pairs merging today were formed with long coalescence times (P (t) ~1/t ) • weighted average over spiral (fS=65%) and elliptical (fE=35%) galaxies • same fb and bNS as for the Milky Way • spiral galaxy coalescencerate equal to the Milky Way rate: nS = nMW = (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) • nE =8.6x10-5 yr-1 • nc = 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

  10. The Detection Rate • coalescence rate within the volume V=4/3 p D3 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):

  11. 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

  12. 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

  13. Extra slides

  14. PSR J0737-3039 A+B . .

  15. 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 = ai Ntot • bayesian statistic to compute Pi(Ntot) • coalescence rate • Ri = Ntoti/tlife fb • P(Ri) with mean and confidence level • combine P(Ri) to obtain P(R)

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