Expected Coalescence Rate of NSNS Binaries for Ground Based Interferometers

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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
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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 didnt disrupt
  the system either)

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The Galactic Coalescence Rate
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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)

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The Galactic Coalescence Rate
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Numerical Simulations (P(t), t0, bNS)

• initial parameters
• masses M1, Salpeter IMF, M1/M2 probability
  derived from observations
• separation P(a)dada/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 gt 0
E gt 0
Vincent, 2002
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The Galactic Coalescence Rate
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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, 20012004
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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 (fS65) and elliptical (fE35) galaxies
• same fb and bNS as for the Milky Way
• spiral galaxy coalescence rate equal to the
  Milky Way rate
• nS nMW (1.71)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
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The Detection Rate

• coalescence rate within the volume V4/3 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/N7 false alarm rate1)

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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

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Work in progress

• compute the GW stochastic background produced by
  the superposition of all the NS/NS binaries
• analytical approach
• integration up to to z6
• numerical approach
• generating extragalactic populations of NS/NS
  binaries

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Extra slides
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PSR J0737-3039 AB
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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
  ltNobsgti
• ltNobsgti 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)