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!
First known NS -NS:
radio pulsar PSR B1913+16
What kind of signal ?
inspiral chirp
orbital
decay
PSR B1913+16
Weisberg &
Taylor 03
GW emission causes orbital
shrinkage leading to higher
GW frequency and amplitude
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
of binary evolution
until binary compact
objects form.
Based on radio
pulsar properties
and survey
selection effects.
for NS -NS, BH -NS,
and BH -BH
for NS -NS only
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
5.0x10 -18
670
12.5
Burgay et al. 2003
M15 (NGC 7078)
2127+11C
30.5
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
5.0x10-18
67
12.5
10.6
Burgay et al. 2003
M15 (NGC 7078)
2127+11C
30.5
Properties of known coalescing DNS pulsars
Ps (ms)
.
-1
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
5.0x10 -18
8.0
Burgay et al. 2003
M15 (NGC 7078)
2127+11C
30.5
Properties of known coalescing DNS pulsars
Ps (ms)
.
-1
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
5.0x10-18
8.0
0.68
Burgay et al. 2003
M15 (NGC 7078)
2127+11C
30.5
Properties of known coalescing DNS pulsars
Ps (ms)
.
-1
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)
5.0x10-18
8.0
0.68
2.7 (1.36)
Burgay et al. 2003
M15 (NGC 7078)
2127+11C
30.5
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
60
220
4º.46
Burgay et al. 2003
M15 (NGC 7078)
2127+11C
96
Radio Pulsars
in
NS-NS binaries
NS-NS
Merger
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)
X3
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:
~ 1 - 500
(VK, Narayan, Spergel, Taylor '01)
NG
Nest
median
pulsar luminosity function:
~ L-2
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
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.
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
galaxy with Ntot
pulsars
count the number of
pulsars observed (Nobs)
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:
P(Rtot)
most probable rate Rpeak
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
per 1000 yr
ref model:
peak
95%
opt model:
peak
95%
Adv. LIGO
per yr
75
400
15 - 275
80 - 1500
20
1000
35 - 700
200 - 3700
Results: Rpeak vs model parameters
Current expectations for LIGO II (LIGO I)
detection rates of inspiral events
Dmax
(Mpc)
Rdet
1/yr)
NS -NS
350
(20)
BH -NS
700
(40)
BH -BH
1500
(100)
5 - 3700
1.5 -1500
15 -10,000
(3x10-4 -0.3)
(4x10-3 -3)
(10-3 - 0.7)
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
can perfectly correct for any pulse
Doppler smearing due to orbital motion…
VK, Kim et al. 2003
< 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
in binaries tend to align
spin and orbital angular
momentum vectors.
Asymmetric supernova
explosions can tilt the
orbital plane relative to
the spin of the
non-exploding star.
BH
SN + NS kick
BH
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
Precessing inspiral binaries
with non-precessing templates:
detection rate decreases
Rdet decrease depends on
spin magnitude and tilt angle:
Grandclement, VK, Vecchio 2002
Grandclement & VK 2003
Grandclement, Ihm, VK, Belczynski 2003
Buonanno et al. 2003
Pan et al. 2003
templates that can mimic
the precession effects
can increase the detection rate:
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%
BH-NS
1.5 -1500 per yr
3
Expected rates:
3x10-4 -0.3
BH-BH
15 -10,000 per yr
BH-NS
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