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

                             Tania Regimbau
                                  on the behalf of
               J.A. de Freitas Pacheco, T. Regimbau, S. Vincent, A. Spallicci
The Model

Ø   a very small fraction of massive binaries remains
    bounded after 2 supernova explosions
Ø   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
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-at

present work:
the star formation history is reconstructed from observations:
Ø ages of 552 stars derived from chromospheric activity
index (Rocha-Tinto et al., 2000)
Ø 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(t), t0, bNS)

                                                                                        birth parameters
                                                                                        (M1, M2, a, e)0
Ø initial parameters:
§ masses: M1, Salpeter IMF, M1/M2: probability derived from observations
§ separation: P(a)da=da/a between 2RRoche and 200RRoche                                   Mass loss
                                                                                        (M1, M2, a, e)1
§ eccentricity: P(e)de = 2ede

Ø evolution of orbital parameters due to mass loss (stellar wind,                        Supernova 1               disrupted
mass transfert, supernova)
                                                                                            Mass loss
Ø statistical properties                                                                (1.4Mo, M2, a, e)2

§ bNS= 2.4% (systems that remain bounded after the second supernova)                                         E>0
§ P(t) = 0.087/t (probability for a newly formed system to coalesce in a timescale t)    Supernova 2                disrupted
§ t0 =2x105 yr (minimum coalescence time)

                                                                                        NS/NS system
                                                                                          a, e -> t

                                                                                                              Vincent, 2002
The Galactic Coalescence Rate
 Population Synthesis (fb)

Ø single radio pulsar properties:
                                                                                                  birth parameters
• Np = 250000 (for 1095 observed)                                                                  Po, Bo, vk, do…
• birth properties

                        mean          dispertion                                                      magnetic
     P0 (ms)           240 ± 20         80± 20

     ln t0 (s)         11 ± 0.5        3.6 ± 0.2
                                                                                                  present properties
                                                                                                   P, dP/dt, d, S …

Ø second binary pulsar properties:
• the youngest pulsar has the same:                                                               selection effects:
    - period evolution (magnetic dipole spin down) as single radio pulsars                         sky coverage,
    - kick velocity as millisecond pulsars (remains bounded after the supernova)
                                                                                   +                  cone, flux
• Nb = 730 (for two observed)

                                                                                       observed                        hidden

                                                                                                               Regimbau, 2001&2004
                                                                                          Bulk of stars formed
                                                                                           in the first 1-2 Gyr.

 The Local Coalescence Rate
                                                                                       The pairs merging today
                                                                                            were formed with
                                                                                        long coalescence times
                                                                                             (P (t) ~1/t )

Ø weighted average over
spiral (fS=65%) and elliptical (fE=35%) galaxies

Ø same fb and bNS as for the Milky Way

Ø spiral galaxy coalescence rate equal to the Milky Way rate:
  nS = nMW = (1.7±1)x10-5 yr-1

Ø 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                                               Intermitent star
                                                                  formation history:
Ø nc = 3.4x10-5 yr-1                                              modulation in the
                                                                   coalescence rate
other estimates: ~10-6 – 10-4 yr-1
(Kalogera et al., 2004: 1.8x10-4 yr-1)
 The Detection Rate

 Ø 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

Ø maximum probed distance and mean expected rate
(S/N=7; false alarm rate=1) :

      VIRGO              LIGO            LIGO Ad

     13 Mpc              14 Mpc          207 Mpc
  1 event/148 yr     1 event /125 yr    6 events/yr
Possible Improvements in the Sensitivity…

 Ø 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

 Ø 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

Ø   compute the GW stochastic background produced by the superposition of all
    the NS/NS binaries

Ø   analytical approach
integration up to to z~6

Ø  numerical approach
generating extragalactic populations of NS/NS binaries
Extra slides
    PSR J0737-3039 A+B

                     A              B

        P         22.7 ms         2.77 s
        dP/dt    1.7 x 10-18   0.88 x 10-15
.       Bsurf    6 x 109 G     1.6 x 1012 G
Kalogera, Kim, Lorimer et al., 2004

Ø   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

Ø   Statistics
•   Nobsi follows a Poisson distribution of mean <Nobs>i
•   <Nobs>i = a Ntot

•   bayesian statistic to compute Pi(Ntot)

Ø   coalescence rate
•   Ri = Ntoti/tlife fb
•   P(Ri) with mean and confidence level
•   combine P(Ri) to obtain P(R)

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