Revised Inspiral Inspiral Rates for Double Rates for Double - - PowerPoint PPT Presentation

Revised Revised Inspiral Inspiral Rates for Double Rates for Double Neutron Star Systems Neutron Star Systems

Chunglee Chunglee Kim (Northwestern) Kim (Northwestern)

with with Vicky Kalogera (Northwestern) & Duncan R. Lorimer (Manchester) Vicky Kalogera (Northwestern) & Duncan R. Lorimer (Manchester) 8th Gravitational Wave Data Analysis Workshop

Milwaukee, WI (Dec. 17, 2003)

Why are they interesting? Why are they interesting?

• Coalescing Double Neutron Star (DNS) systems are

Coalescing Double Neutron Star (DNS) systems are strong strong candidates of GW detectors. candidates of GW detectors.

• Before 2003

Before 2003 5 systems are known in our Galaxy. 5 systems are known in our Galaxy. 2 2 coalescing systems in the Galactic disk. coalescing systems in the Galactic disk. ( (PSR B1913+16 PSR B1913+16 and and B1534+12 B1534+12) )

• PSR J0737-3039 (Burgay et al. 2003)

the 3rd coalescing DNS: strongly relativistic !! NEW NEW Galactic coalescence Galactic coalescence rate of rate of DNSs DNSs Event rate estimation Event rate estimation for for inspiral inspiral search search

Properties of pulsars in Properties of pulsars in DNSs DNSs

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) Galactic disk pulsars Ps (ms) (ss-1) Porb (hr) e Mtot ( ) Ps

.

• M

J0737-3039 22.70 2.4x10 -18 2.4 0.087 2.6 (1.24)

Properties of pulsars in Properties of pulsars in DNSs DNSs (cont.) (cont.)

B1913+16 110 65 300 4º.23 B1534+12 250 190 2700 1º.75 Galactic disk pulsars

τc (Myr) τsd (Myr) τmrg (Myr)

(yr-1)

ω

·

J0737-3039 160 100 85 16º.9 Lifetime=185 Myr ~4 times

larger than B1913+16

Coalescence rate Coalescence rate R R (Narayan et al.; Phinney 1991)

• Lifetime of a system = current age + merging time

Lifetime of a system = current age + merging time

• f a pulsar
• f a pulsar of a system
• f a system
• Correction factor : beaming correction for pulsars

Correction factor : beaming correction for pulsars

• Number of sources : number of pulsars in coalescing

Number of sources : number of pulsars in coalescing binaries in the galaxy binaries in the galaxy Lifetime of a system Lifetime of a system Number of sources Number of sources x correction factor x correction factor R = R = Q: How many pulsars “similar” to the Hulse-Taylor pulsar exist in our galaxy?

Method Method -

• Modeling & Simulation

Modeling & Simulation (Kim et al. 2003, ApJ, 584, 985 )

• 1. Model pulsar sub
• 1. Model pulsar sub-
• populations

populations

• 2. Simulate pulsar
• 2. Simulate pulsar-
• survey selection effects

survey selection effects count the number of pulsars observed (Nobs)

Earth Earth

• luminosity & spatial distribution functions

luminosity & spatial distribution functions

• spin & orbital periods from each observed PSR binary

spin & orbital periods from each observed PSR binary populate a model galaxy with Ntot PSRs (same Ps & Porb) Nobs follows the Poisson distribution, P(Nobs; <Nobs>)

Method (cont.) Method (cont.) -

• Statistical Analysis

Statistical Analysis

• 3. Calculate a probability density function of coalescence rate R

P(R)

We consider each observed pulsar separately. Calculate the likelihood of observing just one example

• f each observed pulsar, P(1; <Nobs>) (e.g. Hulse-Taylor pulsar)

For an each observed system For an each observed system i i, ,

P Pi

i(R) =

(R) = C Ci

i2 2R exp(

R exp(-

• C

Ci

iR

R) )

where where C Ci

i =

= calculate calculate P( P(R Rtot

tot)

) < <N Nobs

• bs>

> τ τlife

life

N Ntot

tot f

fb

b i i

combine combine all all P(R) P(R)’ ’s s

P(1; < P(1; <N Nobs

• bs>)

>)

Bayes’ theorem P(< P(<N Nobs

• bs>)

>)

P(R P(Rtot

tot)

) most probable rate most probable rate R Rpeak

peak

statistical confidence levels statistical confidence levels detection rates for GW detectors detection rates for GW detectors

• Double neutron star (DNS) systems

Double neutron star (DNS) systems

3 3 coalescing s

coalescing sy ystems in the Galactic disk stems in the Galactic disk ( (PSR PSR B1913+16 B1913+16, , B1534+12 B1534+12, and , and J0737 J0737-

• 3039

3039) ) ground based fgw~10-1000 Hz

Results Results (Kalogera, Kim, Lorimer et al. 2003, ApJL submitted)

Results Results

• Detection rates of DNS

Detection rates of DNS inspirals inspirals for LIGO for LIGO

Detection rate = R x number of galaxies within Vmax 180 180

+477 +477

• 144

144

27 27

+80 +80

• 23

23

(Ref.) (Ref.) R Rpeak

peak (revised)

(revised) (Myr (Myr-

• 1

1)

) R Rpeak

peak (previous) (Myr

(previous) (Myr-

• 1

1)

)

Coalescence Coalescence rate rate R

R R Rdet

det (

(ini

• ini. LIGO) (yr

. LIGO) (yr-

• 1

1)

) R Rdet

det (adv. LIGO) (yr

(adv. LIGO) (yr-

• 1

1)

) 0.075 0.075

+0.2 +0.2

• 0.06

0.06

405 405

+1073 +1073

• 325

325

(Ref.) (Ref.)

Detection Detection rate rate

where Vmax= maximum detection volume of LIGO (DNS inspiral)

Summary Summary

R Rpeak

peak (revised)

(revised)

R Rpeak

peak (previous)

(previous)

~ ~ 6 6-

• 7

7

• The Galactic coalescence of

The Galactic coalescence of DNSs DNSs is more frequent is more frequent than previously thought! than previously thought! R Rdet

det (adv. LIGO)

(adv. LIGO) = 20

= 20 – – 1000 events per yr (all models) 1000 events per yr (all models) R Rdet

det (

(ini

• ini. LIGO)

. LIGO) = 1 event per 5

= 1 event per 5 – – 250 yrs (all models) 250 yrs (all models)

• The most probable

The most probable inspiral inspiral detection rates for LIGO detection rates for LIGO ~1 event per 1.5 yr ~1 event per 1.5 yr (95% CL, most optimistic)

(95% CL, most optimistic)

~ 4000 events per yr ~ 4000 events per yr (95% CL, most optimistic)

(95% CL, most optimistic)

Inspiral detection rates as high as 1 per 1.5 yr (at 95% C.L.) are possible for initial LIGO !

Future work Future work

• Apply the method to other classes of pulsar binaries

Apply the method to other classes of pulsar binaries

(e.g. (e.g. NS NS-

• NS in globular clusters

NS in globular clusters) )

• Give statistical constraints on binary evolution theory

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)

Summary Summary

• Galactic coalescence rate of

Galactic coalescence rate of DNSs DNSs

R Rpeak

peak (revised)

(revised) (Myr (Myr-

• 1

1)

) R Rpeak

peak (previous) (Myr

(previous) (Myr-

• 1

1)

) (all models) (all models) R Rpeak

peak = 10

= 10 – – 500 per 500 per Myr Myr R Rpeak

peak (revised)

(revised)

R Rpeak

peak (previous)

(previous)

~ ~ 6 6-

• 7

7 The Galactic coalescence of The Galactic coalescence of DNSs DNSs is more frequent than is more frequent than previously thought! previously thought! 180 180

+477 +477

• 144

144

27 27

+32 +32

• 16

16

(Ref.) (Ref.)

Results: Results: correlation between

correlation between R Rpeak

peak and model parameters

and model parameters

• Luminosity distribution

Luminosity distribution power power-

• law:

law: f(L)

f(L) ∝ ∝ L L-

• p

p,

, L Lmin

min < L

< L (

(L Lmin

min: cut

: cut-

• off luminosity)
• ff luminosity)

give constraint give constraint to modeling of a to modeling of a PSR population PSR population Correlations between Correlations between the merger rate with the merger rate with parameters of PSR parameters of PSR population models population models