Inspiral Binaries as Gravitational Wave Sources The Institute of by nikeborome

VIEWS: 9 PAGES: 32

									Inspiraling Compact Objects:
   Detection Expectations


        Vicky Kalogera
    Physics & Astronomy Dept
    In this talk :

•     Gravitational Waves and Double Neutron Stars


•     Meet PSR J0737-3039:
      a new strongly relativistic binary pulsar


•     Inspiral Event Rates for
      NS-NS, BH-NS, BH-BH

•     Precessing Binaries: astrophysical expectations
       Double Neutron Star Inspiral
 Do they exist ? YES!             What kind of signal ?
   First known NS -NS:
radio pulsar PSR B1913+16            inspiral chirp



                    orbital
                    decay


                              GW emission causes orbital
                              shrinkage leading to higher
     PSR B1913+16             GW frequency and amplitude

       Weisberg &
       Taylor 03
Sensitivity to coalescing binaries
                                       detection rate ~ r3

                                      strength        ~ 1/r

                                     Dmax for each signal
                                     sets limits on the
                                     possible detection rate



What is the expected
detection rate out to
       Dmax ?
   Scaling up from
   the Galactic rate
   Inspiral Rates for the Milky Way
Theoretical Estimates   Empirical Estimates

 Based on models         Based on radio
 of binary evolution     pulsar properties
 until binary compact    and survey
 objects form.           selection effects.

 for NS -NS, BH -NS,     for NS -NS only
 and BH -BH
Properties of known coalescing DNS pulsars


Galactic Disk pulsars

B1913+16

B1534+12

J0737-3039
Burgay et al. 2003



M15 (NGC 7078)

2127+11C
Properties of known coalescing DNS pulsars
                               .
                     Ps (ms)   Ps (ss-1)    L400

Galactic Disk pulsars

B1913+16              59.03    8.6x10-18    270

B1534+12              37.90    2.5x10-18       9

J0737-3039 22.70               2.4x10-18     28
Burgay et al. 2003



M15 (NGC 7078)

2127+11C              30.5     5.0x10 -18   670
Properties of known coalescing DNS pulsars
                               .
                     Ps (ms)   Ps (ss-1)    L400   B9 (G)

Galactic Disk pulsars

B1913+16              59.03    8.6x10-18    270     22.8

B1534+12              37.90    2.4x10-18       9     9.7

J0737-3039 22.70               2.4x10-18    340      7.4
Burgay et al. 2003



M15 (NGC 7078)

2127+11C              30.5     5.0x10 -18   670     12.5
Properties of known coalescing DNS pulsars
                               .
                     Ps (ms)   Ps (ss-1)   L400   B9 (G)   d(kpc)

Galactic Disk pulsars

B1913+16              59.03    8.6x10-18   270     22.8    7.3

B1534+12              37.90    2.4x10-18      9     9.7    0.5

J0737-3039 22.70               2.4x10-18     28     7.4     0.6
Burgay et al. 2003



M15 (NGC 7078)

2127+11C              30.5     5.0x10-18    67      12.5   10.6
Properties of known coalescing DNS pulsars
                              .     -1
                  Ps (ms)     Ps (ss ) Porb (hr)
Galactic Disk pulsars

 B1913+16             59.03   8.6x10-18     7.8

 B1534+12             37.90   2.4x10-18    10.0

 J0737-3039 22.70             2.4x10-18     2.4
 Burgay et al. 2003



M15 (NGC 7078)

 2127+11C             30.5    5.0x10 -18    8.0
Properties of known coalescing DNS pulsars
                              .     -1
                  Ps (ms)     Ps (ss ) Porb (hr)    e
Galactic Disk pulsars

 B1913+16             59.03   8.6x10-18    7.8     0.61

 B1534+12             37.90   2.4x10-18   10.0     0.27

 J0737-3039 22.70             2.4x10-18   2.5      0.09
 Burgay et al. 2003



M15 (NGC 7078)

 2127+11C             30.5    5.0x10-18   8.0      0.68
Properties of known coalescing DNS pulsars
                              .     -1
                  Ps (ms)     Ps (ss ) Porb (hr)     e    Mtot ( Mo)
Galactic Disk pulsars

 B1913+16             59.03   8.6x10-18    7.8     0.61   2.8 (1.39)

 B1534+12             37.90   2.4x10-18   10.0     0.27   2.7 (1.35)

 J0737-3039 22.70             2.4x10-18   2.5      0.09   2.6 (1.24)
 Burgay et al. 2003



M15 (NGC 7078)

 2127+11C             30.5    5.0x10-18   8.0      0.68   2.7 (1.36)
  Properties of known coalescing DNS pulsars
                     c (Myr)   sd (Myr)   mrg (Myr)   · -1
                                                          (yr )
Galactic Disk pulsars

B1913+16              110         65          300         4º.23

B1534+12              250        190         2700         1º.75

J0737-3039             160       100            85        16º.9
Burgay et al. 2003



M15 (NGC 7078)

2127+11C                96         60          220        4º.46
   Radio Pulsars                                 NS-NS
        in                                       Merger
   NS-NS binaries                            Rate Estimates
Use of observed sample and models for PSR survey selection effects:
estimates of total NS- NS number combined with lifetime estimates
                                              (Narayan et al. '91; Phinney '91)


 Dominant sources of rate estimate uncertainties identified:
                                               (VK, Narayan, Spergel, Taylor '01)


                                     X
   small - number observed sample (2 NS - NS in Galactic field)
                                     3
   PSR population dominated by faint objects

       Robust lower limit for the MW (10-6 per yr)
       Upward correction factor
          for faint PSRs:                 ~ 1 - 500
        (VK, Narayan, Spergel, Taylor '01)


            NG
                                 Nest        pulsar luminosity function:
                                                         ~ L-2
                        median                i.e., dominated by faint,
                                               hard-to-detect pulsars
             25%



small-N sample is:
> assumed to be representative of the Galactic population
> dominated by bright pulsars, detectable to large distances

          total pulsar number is underestimated
Radio Pulsars                            NS-NS
     in                                  Merger
NS-NS binaries                       Rate Estimates
                                     (Kim, VK, Lorimer 2002)

It is possible to assign statistical significance
            to NS-NS rate estimates
         with Monte Carlo simulations

      Bayesian analysis developed to derive the
     probability density of NS-NS inspiral rate

 Small number bias and selection effects for faint
 pulsars are implicitly included in our method.
Statistical Method
1.      Identify sub-populations of PSRs with pulse and orbital
        properties similar to each of the observed DNS
       Model each sub-population in the Galaxy
        with Monte-Carlo generations
      Luminosity distribution
       power-law: f(L)  L-p, Lmin < L (Lmin: cut-off luminosity)
      Spatial distribution

2. Pulsar-survey simulation
      consider selection effects of all pulsar surveys
      generate ``observed’’ samples
Statistical Method

 fill a model                        count the number of
 galaxy with Ntot                    pulsars observed (Nobs)
 pulsars



      Earth




3. Derive rate estimate probability distribution P(R)
Statistical Analysis
                           For a given total number of
                           pulsars, Nobs follows a
                           Poisson distribution.

                           We calculate the best-fit
                           value of <Nobs> as a function
                           of Ntot and the probability
                                    P(1; Ntot)

                           We use Bayes’ theorem to
                           calculate P(Ntot) and finally
                           P(R)



P(Nobs) for PSR B1913+16
Results:


           most probable rate Rpeak
P(Rtot)
            statistical confidence levels

             expected GW detection rates
                   Current Rate Predictions
                                           Burgay et al. 2003, Nature, 426, 531
                                           VK et al. 2004, ApJ Letters, in press


3 NS-NS : a factor of 6-7 rate increase

                                                    Initial LIGO      Adv. LIGO
                                                    per 1000 yr            per yr

                                          ref model:
                                          peak           75                400

                                          95%          15 - 275          80 - 1500

                                          opt model:
                                          peak            20               1000

                                          95%          35 - 700        200 - 3700
Results: Rpeak vs model parameters
        Current expectations for LIGO II (LIGO I)
           detection rates of inspiral events


             NS -NS             BH -NS               BH -BH
Dmax          350                700                  1500
(Mpc)         (20)               (40)                 (100)


Rdet         5 - 3700           1.5 -1500          15 -10,000
1/yr)       (10-3 - 0.7)      (3x10-4 -0.3)          (4x10-3 -3)
                                        from population synthesis

   Use empirical NS-NS rates: constrain
                           pop syn models > BH inspiral rates
    What do/will learn from PSR J0737-3039 ?
•     Inspiral detection rates as high as 1 per 1.5 yr (at 95% C.L.)
      are possible for initial LIGO !
      Detection rates in the range 20-1000 per yr are most probable
      for advanced LIGO
                                 VK, Kim, Lorimer, et al. 2004, ApJ Letters, in press
•    NS #2 progenitor is constrained as less massive than ~4.7 Msolar
     NS #2 kick is constrained to be in excess of 60 km/s
     and its most probable value is 150 km/s
                                          Willems & VK 2003, ApJ Letters, submitted

•    Better confirmation of GR
•   First double pulsar with eclipses !   Lyne et al. 2004, Science, in press

        constraints on magnetic field and spin orientation
                       pulsar magnetospheres
                       measurement of new relativistic effects ?
Parkes MultiBeam survey and acceleration searches


Assuming that acceleration searches           VK, Kim et al. 2003
can perfectly correct for any pulse
Doppler smearing due to orbital motion…        < Nobs > = 3.6

How many coalescing DNS pulsars
would we expect the PMB survey to
detect ?




N.B. Not every new coalescing DNS pulsar
will significantly increase the DNS rates …   PMB Nobs
   Challenges in the near future...

Technical: achieve target noise level

Data analysis: optimal methods
                 for signal retrieval
  detection of inspiral signal requires:
   template waveforms and
   matched filtering techniques
    Precession and Inspiral Waveforms

Compact object binaries can precess if spins are
 of significant magnitude and misaligned with
   respect to the orbital angular momentum.

Precession can modify inspiral waveforms and
     decrease the detection efficiency of
      standard non-precession searches.

Precession effects are more important for binaries of
 high mass ratios (BH-NS) and with spin tilt angles
      of the massive object in excess of ~30°.
                  (Apostolatos 95)
   Q: What is the origin of spin tilt angles in
               compact object binaries ?

Mass transfer episodes
                            BH
in binaries tend to align
spin and orbital angular
momentum vectors.

                                 SN + NS kick
Asymmetric supernova
explosions can tilt the
orbital plane relative to
the spin of the             BH
non-exploding star.                             NS
Q: What are the expected spin tilt angles ?
> model BH-NS progenitors and SN kick effects
        VK 2000            Grandclement et al. 2003




             10 Mo BH
             1.4 Mo NS

                                        BH-NS



    BH-NS binaries are expected to
    have significant spin tilt angles
                                                     Grandclement, VK, Vecchio 2002
                                                     Grandclement & VK 2003
  Precessing inspiral binaries                       Grandclement, Ihm, VK, Belczynski 2003
                                                     Buonanno et al. 2003
                                                     Pan et al. 2003
with non-precessing templates:               templates that can mimic
detection rate decreases                     the precession effects
Rdet decrease depends on
                                             can increase the detection rate:
spin magnitude and tilt angle:
                                   For a 10-1.4 Mo BH-NS binary




             Maximum BH spin




            cos(spin tilt angle)                                  cos(spin tilt angle)
                                 Grandclement, Ihm, VK, Belczynski 2003
Rate drop expected
from astrophysical predictions
                                        rate drop
for spin tilts in BH-NS binaries
                                             by 20-30%

Expected rates:

BH-NS
1.5 -1500 per yr             3

3x10-4 -0.3

BH-BH                                      BH-NS
15 -10,000 per yr                                 BH-NS
4x10-3 -3
                                        BH spin magnitude
   In the near and distant future ...
Initial LIGO
      3 NS-NS ---> detection possible
        BH-BH ---> possible detection too

Advanced LIGO
    expected to detect compact object inspiral as well as
     NS or BH birth events, pulsars,
     stochastic background
     past experience from EM: there will be surprises!

Laser Interferometry in space: LISA
   sources at lower frequencies
   supermassive black holes
     and background of
   wide binaries

								
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