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

Chunglee Kim (Northwestern)Chunglee Kim (Northwestern)

with with Vicky Kalogera (Northwestern) & Duncan R. Lorimer Vicky Kalogera (Northwestern) & Duncan R. Lorimer

(Manchester)(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 areCoalescing Double Neutron Star (DNS) systems are

strong candidates of GW detectors.strong candidates of GW detectors.

Before 2003Before 2003

5 systems are known in our Galaxy.5 systems are known in our Galaxy. 22 coalescing systems in the Galactic disk.coalescing systems in the Galactic disk. ((PSR B1913+16PSR B1913+16 and and B1534+12B1534+12))

PSR J0737-3039 (Burgay et al. 2003) the 3rd coalescing DNS: strongly relativistic !!

NEWNEW

Galactic coalescence Galactic coalescence rate of DNSsrate of DNSs

Event rate estimation Event rate estimation for inspiral searchfor inspiral search

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

B1913+16 110 65 300 4º.23

B1534+12 250 190 2700 1º.75

Galactic disk pulsars

c (Myr) sd (Myr) mrg (Myr) (yr-1) ·

J0737-3039 160 100 85 16º.9

Lifetime=185 Myr

~4 times larger than B1913+16

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

Lifetime of a system = current age + merging time Lifetime of a system = current age + merging time of a pulsar of a systemof a pulsar of a system

Correction factor : beaming correction for pulsarsCorrection factor : beaming correction for pulsars

Number of sources : number of pulsars in coalescing Number of sources : number of pulsars in coalescing binaries in the galaxybinaries in the galaxy

Lifetime of a systemLifetime of a systemNumber of sourcesNumber of sources

x correction factorx correction factorR =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-populations1. Model pulsar sub-populations

2. Simulate pulsar-survey selection effects2. Simulate pulsar-survey selection effects

count the number of pulsars observed (Nobs)

EarthEarth

luminosity & spatial distribution functionsluminosity & spatial distribution functions spin & orbital periods from each observed PSR binaryspin & 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 AnalysisStatistical 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 exampleof each observed pulsar, P(1; <Nobs>) (e.g. Hulse-Taylor pulsar)

For an each observed system For an each observed system ii,,

PPii(R) = (R) = CCii22R exp(-CR exp(-CiiR)R)

where Cwhere Cii = =

calculate calculate P(RP(Rtottot))

<N<Nobsobs> > ττ lifelife

NNtot tot ffbb ii

combine combine all all P(R)P(R)’s’s

P(1; <NP(1; <Nobsobs>)>) Bayes’ theorem

P(<NP(<Nobsobs>)>)

P(RP(Rtottot))most probable rate Rmost probable rate Rpeakpeak

statistical confidence levelsstatistical confidence levels

detection rates for GW detectorsdetection rates for GW detectors

Double neutron star (DNS) systemsDouble neutron star (DNS) systems

33 coalescing systems in the Galactic diskcoalescing systems in the Galactic disk

((PSRPSR B1913+16B1913+16, , B1534+12B1534+12, and , and J0737-3039J0737-3039))

ground based

fgw~10-1000 Hz

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

ResultsResults

Detection rates of DNS inspirals for LIGODetection rates of DNS inspirals for LIGO

Detection rate = R x number of galaxies within Vmax

180180 +477+477-144-144 2727 +80+80

-23-23(Ref.)(Ref.)

RRpeakpeak (revised) (revised) (Myr(Myr-1-1) R) Rpeakpeak (previous) (Myr (previous) (Myr-1-1)) Coalescence Coalescence rate rate RR

RRdetdet (ini. LIGO) (yr (ini. LIGO) (yr-1-1) R) Rdetdet (adv. LIGO) (yr (adv. LIGO) (yr-1-1))

0.0750.075+0.2+0.2

-0.06-0.06 405405 +1073+1073

-325-325(Ref.)(Ref.)

Detection Detection raterate

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

SummarySummary

RRpeak peak (revised)(revised) RRpeak peak (previous)(previous)

~~ 6-7 6-7

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

RRdetdet (adv. LIGO) (adv. LIGO) = 20 – 1000 events per yr (all models)= 20 – 1000 events per yr (all models)

RRdetdet (ini. LIGO) (ini. LIGO) = 1 event per 5 – 250 yrs (all models)= 1 event per 5 – 250 yrs (all models)

The most probable inspiral detection rates for LIGOThe most probable inspiral 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 workFuture work

Apply the method to other classes of pulsar binariesApply the method to other classes of pulsar binaries (e.g. (e.g. NS-NS in globular clustersNS-NS in globular clusters))

Give statistical constraints on binary evolution theoryGive 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)

SummarySummary

Galactic coalescence rate of DNSsGalactic coalescence rate of DNSs

RRpeakpeak (revised) (revised) (Myr(Myr-1-1) R) Rpeakpeak (previous) (Myr (previous) (Myr-1-1) )

(all models) (all models) RRpeak peak = 10 – 500 per Myr= 10 – 500 per Myr

RRpeak peak (revised)(revised) RRpeak peak (previous)(previous)

~~ 6-7 6-7The Galactic coalescence of The Galactic coalescence of DNSs is more frequent thanDNSs is more frequent thanpreviously thought!previously thought!

180180 +477+477-144-144 2727 +32+32

-16-16(Ref.)(Ref.)

Results: Results: correlation between Rcorrelation between Rpeakpeak and model parameters and model parameters

Luminosity distributionLuminosity distribution

power-law: power-law: f(L) f(L) L L-p-p, L, Lminmin < L < L (L (Lminmin: cut-off luminosity): cut-off luminosity)

give constraint give constraint to modeling of a to modeling of a PSR populationPSR population

Correlations between Correlations between the merger rate with the merger rate with parameters of PSR parameters of PSR population modelspopulation models