1. Inspiraling Compact Objects: Detection Expectations
Vicky Kalogera
Physics & Astronomy Dept

2. In this talk : Gravitational Waves and Double Neutron Stars
Meet PSR J :
a new strongly relativistic binary pulsar
Inspiral Event Rates for
NS-NS, BH-NS, BH-BH
Precessing Binaries: astrophysical expectations

3. Double Neutron Star Inspiral
Do they exist ? YES!
What kind of signal ?
First known NS -NS:
radio pulsar PSR B
inspiral chirp
orbital
decay
GW emission causes orbital
shrinkage leading to higher
GW frequency and amplitude
PSR B
Weisberg &
Taylor 03

4. detection rate ~ r3 strength ~ 1/r Dmax for each signal
Sensitivity to coalescing binaries
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

5. Inspiral Rates for the Milky Way
Theoretical Estimates
Based on models
Empirical Estimates
Based on radio
of binary evolution
until binary compact
objects form.
for NS -NS, BH -NS,
and BH -BH
pulsar properties
and survey
selection effects.
for NS -NS only

6. Properties of known coalescing DNS pulsars
Galactic Disk pulsars B B J
Burgay et al. 2003 C
M15 (NGC 7078)

7. Properties of known coalescing DNS pulsars
Ps (ms) (ss-1) L400 Ps .
Galactic Disk pulsars
B x
B x
J x
Burgay et al. 2003
C x
M15 (NGC 7078)

8. Properties of known coalescing DNS pulsars
Ps (ms) (ss-1) L B9 (G) Ps .
Galactic Disk pulsars
B x
B x
J x
Burgay et al. 2003
C x
M15 (NGC 7078)

9. Properties of known coalescing DNS pulsars
Ps (ms) (ss-1) L B9 (G) d(kpc) Ps .
Galactic Disk pulsars
B x
B x
J x
Burgay et al. 2003
C x
M15 (NGC 7078)

10. Properties of known coalescing DNS pulsars
Ps (ms) (ss-1) Porb (hr) Ps .
Galactic Disk pulsars
B x
B x
J x
Burgay et al. 2003
M15 (NGC 7078)
C x

11. Properties of known coalescing DNS pulsars
Ps (ms) (ss-1) Porb (hr) e Ps .
Galactic Disk pulsars
B x
B x
J x
Burgay et al. 2003
M15 (NGC 7078)
C x

12. Properties of known coalescing DNS pulsars
Ps (ms) (ss-1) Porb (hr) e Mtot ( ) Ps . Mo
Galactic Disk pulsars
B x (1.39)
B x (1.35)
J x (1.24)
Burgay et al. 2003
M15 (NGC 7078)
C x (1.36)

13. Properties of known coalescing DNS pulsars
c (Myr) sd (Myr) mrg (Myr) (yr-1) 
Galactic Disk pulsars
B º.23
B º.75
J º.9
Burgay et al. 2003
C º.46
M15 (NGC 7078)

14. X Radio Pulsars in NS-NS binaries NS-NS Merger Rate Estimates 3
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)
small - number observed sample (2 NS - NS in Galactic field)
PSR population dominated by faint objects
Robust lower limit for the MW (10-6 per yr)
Upward correction factor
for faint PSRs: ~ X 3

15. pulsar luminosity function: hard-to-detect pulsars
(VK, Narayan, Spergel, Taylor '01) NG
Nest
pulsar luminosity function:
~ L-2
i.e., dominated by faint,
hard-to-detect pulsars
median
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

16. It is possible to assign statistical significance
Radio Pulsars in
NS-NS binaries
NS-NS
Merger
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.

17. Statistical Method
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
 Spatial distribution
power-law: f(L)  L-p, Lmin < L (Lmin: cut-off luminosity)
2. Pulsar-survey simulation
 consider selection effects of all pulsar surveys
 generate ``observed’’ samples

18. Statistical Method
fill a model galaxy with Ntot pulsars
count the number of
pulsars observed (Nobs)
Earth
3. Derive rate estimate probability distribution P(R)

19. Statistical Analysis pulsars, Nobs follows a Poisson distribution.
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 B

20. Results: most probable rate Rpeak P(Rtot)
statistical confidence levels
expected GW detection rates

21. 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
95%
opt model:
peak
95%

22. Results: Rpeak vs model parameters

23. Current expectations for LIGO II (LIGO I)
detection rates of inspiral events
NS -NS BH -NS BH -BH
Dmax
(Mpc) (20) (40) (100)
Rdet ,000
(1/yr) ( ) (3x ) (4x )
from population synthesis
Use empirical NS-NS rates: constrain
pop syn models > BH inspiral rates

24. 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 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 ?

25. Parkes MultiBeam survey and acceleration searches
Assuming that acceleration searches
can perfectly correct for any pulse
Doppler smearing due to orbital motion…
How many coalescing DNS pulsars
would we expect the PMB survey to
detect ?
VK, Kim et al. 2003
< Nobs > = 3.6
N.B. Not every new coalescing DNS pulsar
will significantly increase the DNS rates …
PMB Nobs

26. 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

27. 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)

28. Q: What is the origin of spin tilt angles in compact object binaries ?BH
Mass transfer episodes
in binaries tend to align
spin and orbital angular
momentum vectors.
SN + NS kick BH NS
Asymmetric supernova
explosions can tilt the
orbital plane relative to
the spin of the
non-exploding star.

29. BH-NS binaries are expected to have significant spin tilt angles
Q: What are the expected spin tilt angles ?
> model BH-NS progenitors and SN kick effects
VK 2000
BH-NS
Grandclement et al. 2003
10 Mo BH
1.4 Mo NS
BH-NS binaries are expected to
have significant spin tilt angles

30. Precessing inspiral binaries
Grandclement, VK, Vecchio 2002
Grandclement & VK 2003
Grandclement, Ihm, VK, Belczynski 2003
Buonanno et al. 2003
Pan et al. 2003
Precessing inspiral binaries
with non-precessing templates:
detection rate decreases
Rdet decrease depends on
spin magnitude and tilt angle:
templates that can mimic
the precession effects
can increase the detection rate:
For a Mo BH-NS binary
Maximum BH spin
cos(spin tilt angle)
cos(spin tilt angle)

31. Expected rates: BH-NS 1.5 -1500 per yr BH-BH 15 -10,000 per yr
Rate drop expected
from astrophysical predictions
for spin tilts in BH-NS binaries
Grandclement, Ihm, VK, Belczynski 2003
rate drop
by 20-30%
Expected rates:
BH-NS
per yr 3x
BH-BH
15 -10,000 per yr 4x 3
BH-NS
BH-NS
BH spin magnitude

32. 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