1. 8th Gravitational Wave Data Analysis Workshop
Revised Inspiral Rates for Double Neutron Star Systems Chunglee Kim (Northwestern)
Advanced School and Conference on Sources of Gravitational Waves, ICTP, Trieste, Italy (Sep , 2003)
with
Vicky Kalogera (Northwestern) & Duncan R. Lorimer (Manchester)
8th Gravitational Wave Data Analysis Workshop
Milwaukee, WI (Dec. 17, 2003)

2. Why are they interesting?
 Coalescing Double Neutron Star (DNS) systems are
strong candidates of GW detectors.
 Before 2003
5 systems are known in our Galaxy.
2 coalescing systems in the Galactic disk.
(PSR B and B )
Event rate estimation
for inspiral search
Galactic coalescence
rate of DNSs
Conference at ICTP, Trieste, Italy (Sep , 2003)
 PSR J (Burgay et al. 2003)
the 3rd coalescing DNS: strongly relativistic !!
NEW

3. Properties of pulsars in DNSs
Ps (ms) (ss-1) Porb (hr) e Mtot ( ) Ps .  M
Galactic disk pulsars
B x (1.39)
B x (1.35)
J x (1.24)
Conference at ICTP, Trieste, Italy (Sep , 2003)

4. Properties of pulsars in DNSs (cont.)
c (Myr) sd (Myr) mrg (Myr) (yr-1) 
Galactic disk pulsars
B º.23
B º.75
Lifetime=185 Myr
J º.9
Conference at ICTP, Trieste, Italy (Sep , 2003)
~4 times larger than B

5. Coalescence rate R (Narayan et al.; Phinney 1991)
Lifetime of a system
Number of sources
x correction factor
R =
Correction factor : beaming correction for pulsars
Lifetime of a system = current age merging time
of a pulsar of a system
Conference at ICTP, Trieste, Italy (Sep , 2003)
Number of sources : number of pulsars in coalescing
binaries in the galaxy
Q: How many pulsars “similar” to the Hulse-Taylor
pulsar exist in our galaxy?

6. Method - Modeling & Simulation (Kim et al. 2003, ApJ, 584, 985 )
1. Model pulsar sub-populations
2. Simulate pulsar-survey selection effects
luminosity & spatial distribution functions
spin & orbital periods from each observed PSR binary
populate a model galaxy with Ntot PSRs (same Ps & Porb)
count the number of
pulsars observed (Nobs)
Conference at ICTP, Trieste, Italy (Sep , 2003)
Earth
Nobs follows the Poisson distribution,
P(Nobs; <Nobs>)

7. Method (cont.) - Statistical Analysis
3. Calculate a probability density function of coalescence rate R
We consider each observed pulsar separately.
Calculate the likelihood of observing just one example
of each observed pulsar, P(1; <Nobs>) (e.g. Hulse-Taylor pulsar)
Bayes’ theorem
P(<Nobs>)
P(R)
P(1; <Nobs>)
For an each observed system i,
Pi(R) = Ci2R exp(-CiR)
where Ci =
calculate P(Rtot)
<Nobs> τlife
Ntot fb i
combine
all P(R)’s
Conference at ICTP, Trieste, Italy (Sep , 2003)

8. most probable rate Rpeak P(Rtot)
statistical confidence levels
detection rates for GW detectors
 Double neutron star (DNS) systems
3 coalescing systems in the Galactic disk
(PSR B , B , and J )
ground based
fgw~ Hz
Conference at ICTP, Trieste, Italy (Sep , 2003)

9. Results (Kalogera, Kim, Lorimer et al. 2003, ApJL submitted)
Conference at ICTP, Trieste, Italy (Sep , 2003)

10. Results  Detection rates of DNS inspirals for LIGO
Detection rate = R x number of galaxies within Vmax
where Vmax= maximum detection volume of LIGO (DNS inspiral)
180
+477
-144 27
+80
-23
(Ref.)
Rpeak (revised) (Myr-1) Rpeak (previous) (Myr-1)
Coalescence rate R
Rdet (ini. LIGO) (yr-1) Rdet (adv. LIGO) (yr-1)
0.075
+0.2
-0.06
405
+1073
-325
(Ref.)
Detection
rate
Conference at ICTP, Trieste, Italy (Sep , 2003)

11. Summary  The Galactic coalescence of DNSs is more frequent
than previously thought!
Rpeak (revised)
Rpeak (previous)
~ 6-7
Rdet (adv. LIGO) = 20 – 1000 events per yr (all models)
Rdet (ini. LIGO) = 1 event per 5 – 250 yrs (all models)
 The most probable inspiral detection rates for LIGO
~1 event per 1.5 yr (95% CL, most optimistic)
Conference at ICTP, Trieste, Italy (Sep , 2003)
~ 4000 events per yr (95% CL, most optimistic)
Inspiral detection rates as high as 1 per 1.5 yr (at 95% C.L.) are possible for initial LIGO !

12. Future work  Apply the method to other classes of pulsar binaries
(e.g. NS-NS in globular clusters)
 Give statistical constraints on binary evolution theory
(talk by Richard O’Shaughnessy)
determine a favored parameter space
based on the rate calculation
can be used for the calculation of coalescence rates of BH binaries (e.g.NS-BH)
Conference at ICTP, Trieste, Italy (Sep , 2003)

13. Summary  Galactic coalescence rate of DNSs (Ref.) 180 27
Rpeak (revised) (Myr-1) Rpeak (previous) (Myr-1)
(Ref.)
180
+477
-144 27
+32
-16
(all models) Rpeak = 10 – 500 per Myr
Rpeak (revised)
Rpeak (previous)
~ 6-7
The Galactic coalescence of
DNSs is more frequent than
previously thought!
Conference at ICTP, Trieste, Italy (Sep , 2003)

14. the merger rate with parameters of PSR population models
Results: correlation between Rpeak and model parameters
 Luminosity distribution
power-law: f(L)  L-p, Lmin < L (Lmin: cut-off luminosity)
Correlations between
the merger rate with parameters of PSR population models
Conference at ICTP, Trieste, Italy (Sep , 2003)
give constraint
to modeling of a
PSR population