galactic merger rates of pulsar binaries chunglee kim thesis advisor: dr. vicky kalogera thesis...

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Galactic Merger Rates of Pulsar Binaries Chunglee Kim Thesis advisor: Dr. Vicky Kalogera Thesis Defense April 26, 2006

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Galactic Merger Rates of

Pulsar Binaries

Chunglee Kim

Thesis advisor: Dr. Vicky Kalogera

Thesis Defense

April 26, 2006

Outline

Introduction

Method

Results (NS-NS, NS-WD, NS-BH binaries)

Pulsar binaries

~20 ms - 200

ms

~1500 known PSRs

(Credit: M. Kramer)

We consider NS-NS, NS-WD, NS-BH. Pulsars in these systems are

- rare (~8 + 30 in the Galactic disk)- typically old, mildly recycled- strong sources of GW

We are interested in ‘inspiral’ signals

GW signals from pulsar binaries

consider

merging binaries

(mrg < Hubble time)

Credit: K. Thorne

GW astronomy

NS-NSground-based

(fgw~a few x10-103 Hz)

NS-WDspace-based

fgw~0.01-100 mHz

NS-BH

Our work (Kim et al. 2003; Kalogera et al. 2004; Kim et al. 2004)

Problems in pulsar binary event rates until recently:

- rate predictions highly uncertain

(by more than two orders of magnitude)

- lack of quantitative understanding of uncertainties

(statistical & systematic)

We introduce an analysis method to give a

statistical significance of the rate estimates.

Small number bias and selection effects for faint pulsars

are implicitly included in our analysis.

Goal : Calculate P(R) based on the observation

Implications for GW detection

Method

Two key ingredients to model:

(1) PSR population

(2) PSR survey selection effects

Lifetime = current age + remaining time (PSR) (GW emission)

Beaming correction factor = 1/ PSR beaming fraction

Merger rate R

adapted from PSR & binary properties

We calculate the number of sources (Npop) using

SEARCH

Lifetime of a systemNumber of sources

x correction factorR =beaming

Basic strategy

Consider one system at a time (e.g., J0737-3039)

P(Nobs)

PSR population models

(luminosity & spatial distribution)

+PSR survey simulation

obtain Nobs (given Npop)

apply Bayes’ theorem

Input parameters & results are relevant to PSR J0737-3039

PSR population modela PSR population can be defined

Spatial distribution

R=(x2+y2)1/2

Luminosity

distribution

PSR i (R,Z,L)i

fix Ps, pulse width, & Porb

f(R,z) exp

Ro: radial scale length, zo: vertical height

|Z||Z|

ZZoo

RR22

2R2Roo22

-- --

Spatial distribution (Narayan 1991)

Reference model: Ro=4.0 kpc, zo=1.5 kpc

PSR population modelRadio PSR luminosity distribution (Cordes and Chernoff 1997)

power-law:

Lmin: cut-off luminosity (Lmin < L)

Reference model: Lmin=0.3 mJy kpc2, p=2.0

log L

log N

?

Lmin

slope: p

(L; Lmin, p) determines

a fraction of faint PSRs

in a given population

Orbital motion effects are taken into account

PSR B1913+16

credit: M. Kramer

Survey Selection effects

Nobs follows the Poisson distribution, P(Nobs; <Nobs>)

Earth

PSR survey simulation - SEARCH

Calculate Nobs,i varying Npop, i

Same Ps & Pb, but

diff. radio flux densities

S = L/d2L

d

posteria PDF data likelihood x prior PDF

Statistical Analysis

Apply Bayes’ theorem to calculate P(<Nobs>)

P(<Nobs>) P(Nobs; <Nobs>) x P(Nobs)

where P(Nobs; <Nobs>) is obtained from SEARCH.

P(1;

<Nobs>)

P(1; <Nobs>) ; assume P(Nobs)=const.

Nobs = 1

Pi(R)Pi(<Nobs>) chain rule

For an each observed system i,

<Nobs> Npop; and Rlifetime

Npop

For an each observed system i,

Pi(R) = Ci2R exp(-CiR)

where Ci = <Nobs> life

Npop fb i fb: beaming correction factor

Combine individual P(R)’s and calculate P(Rtot)

Individual P(R)

P(Rtot)

NS-NS binaries

LivingstonObservatory

Hanford Observatory

Merging binaries in Galactic disk:PSRs B1913+16, B1534+12, and J0737-3039

Galactic NS-NS merger rate (Myr-1)

P(Rgal )

Detection rate for the initial LIGO (yr-1)

Probability density function of Rgal

NJ0737 ~ 1600 (most abundant)

Lifetime ~ 185 Myr (shortest)

NJ1534 ~ 400

NJ1913 ~ 600

Reference model Detection rate for the initial LIGO (yr-1)

P(Rgal) in a linear scale (reference model)

Detection rate for the initial LIGO (yr-1)

Galactic NS-NS merger rate (Myr-1)

Rpeak

Rpeak (1913+1534+0737) Rpeak (1913+1534)

~ 6-7

Increase rate factor

Detection rate of DNS inspirals for

LIGOdue to the discovery of PSR J0737-3039

Rdet (adv. LIGO) ~ 200 events per yr

Rdet (ini. LIGO) ~ 1 event per 30 yr

The most probable DNS inspiral detection rates for LIGO

Rdet (adv. LIGO) ~ 10 – 500 events per yr

Rdet (ini. LIGO) ~ 1 event per 10 – 400 yr

All models:

Reference model:

Global P(R) and supernovae constraints

for NS-NS binaries

Global P(Rgal): calculation

Rpeak is strongly dependent on the PSR luminosity func.

f(R,z) is relatively poorly constrained, but the rate

estimates are NOT sensitive to the assumed

distribution function.

Global probability density function Pglobal(R)

Pglobal(R) =pdp

Lmin

dLmin P(R; Lmin,p) f(Lmin) g(p)

intrinsic functions for Lmin and p following Cordes & Chernoff (1997) – Based on 22 PSRs with spin period < 20 ms

Global P(Rgal): Result Pro

babili

ty D

ensi

ty

Galactic NS-NS merger rate (Myr-1)

from Tauris & van den Heuvel (2003)

SN rate constraints

Two NS are likely to be formed by SNe type Ib/c. Therefore, SNe (Ib/c) rate can be considered as an upper limit to the NS-NS rate.

SN Ib/c=600-1600 Myr-1 (Cappellaro et al. 1999)

However, the fraction of SN Ib/cactually involved in the formation ofNS-NS systems is uncertain. Based on population syntheses, the fraction could be ~ 5% or less…

Type Ib/c

Type Ib/c

Global P(Rgal) and SN rate constraints Pro

babili

ty D

ensi

ty

Galactic NS-NS merger rate (Myr-1)

SNU5

SNL5

SN Ib/c = 600-1600 Myr-1 (Cappellaro, Evans, & Turatto 1999)

SNL5= SN (lower)x0.05 = 30 Myr-1

SNU5= SN (upper)x0.05 = 80 Myr -1

Suppose, ~5% of Ib/c SNe are

involved in the NS-NS formation.

The empirical SNe rate

Global P(Rgal) and SN rate constraints Pro

babili

ty D

ensi

ty

Galactic NS-NS merger rate (Myr-1)

SNL5 : Conservative upper limit of RNS-NS

SNU5

Implications of new discoveries

(1) PSR J1756-2251 (Faulkner et al. 2005)

(2) PSR J1906+0746 (Lorimer et al. 2006)

Implications of J1756-2251

J1756-2251: The 4-th merging NS-NS known in the Galactic disk (Faulkner et al. 2005)

discovered by the Parkes Multibeam Pulsar Survey with

the acceleration search technique. Detailed simulations for acceleration searches are

needed to calculate P(R) including J1756-2251.

Contribution of J1756-2251 to the Galactic DNS merger rate.

No significant change in the total rate.

Rpeak (3 PSRs + J1756) Rpeak (3 PSRs)

~ 1.04

J1756-2251 ~ another example of 1913-like population

Implications of J1906+0746

J1906+0746: a young pulsar in a relativistic binary in the Galactic disk (Lorimer et al. 2006)

PSR name Ps (ms) Pb (hr) e life (Gyr)

B1913+16 59.03 7.752 0.617 0.365

B1534+12 37.90 10.098 0.274 2.7

J0737-3039A 22.70 2.45 0.088 0.185

J1756-2251 28.46 7.67 0.181 2.0

J1906+0746 144.07 3.98 0.0853 0.82

Characteristic age ~ 112 kyr !

Death time ~ 82 Myr (< tmrg) ~lifetime

J1141-6545 393.90 4.744 0.172 0.105

Implications of J1906+0746

Follow-up (optical/timing) observations are crucial

Rpeak (3 PSRs + J1906) Rpeak (3 PSRs)

~ 2

Assume J1906+0746 is a NS-NS binary:

N1906 ~ 300

t1906 ~ 82 Myr

N0737 ~1600

t0737 ~ 185Myr~ 0.5 x

companion is an NS or WD

total mass ~ 2.61 ± 0.02

M

NS-WD binaries

(1) Merging binaries:

PSRs J0751+1807, J1757-5322, and J1141-6545

(2) Eccentric binaries:

PSRs J1141-6545 and B2303+46

NS-WD binaries as GW sources for LISA

The GW background

due to the large number of sources

limits the detectability of weak sources in fgw < 3 mHz

Calculate the contribution from NS-WD binaries to the GW background for LISA.

In-spiraling NS-WD binaries emit gravitational waves in a frequency range fgw ~ 0.01 – 100 mHz

Consider 3 merging systems

(PSR J0751+1807, J1757-5322, and J1141-6545)

GW signals from NS-WD binaries

The contribution from NS-WD

binaries to the GW background

would be negligible

confusion noise level

due to WD-WD binaries

fmax,0751

fmax,1757

fmax,1141

GW

am

plitu

de (

h rm

s)

1 yr obs

J0751+J1757+J1141J1757+J1141

J1141

chirpmass GW freq. source

number

density

integration time

standard binary scenario predicts - circular orbit

- NS formation first - recycled PSR

“non-zero eccentricity” implies

- WD formed first

- non-recycled PSR

J1141-6545 : e=0.172 (Kaspi et al. 2000, Bailes et al. 2003)

B2303+46 : e=0.658 (Stokes et al. 1985, van Kerkwijk & Kulkarni 1999)

Galactic birthrate of eccentric NS-WD binaries

Empirical estimates

- Kalogera, CK, Ihm, Belczynski 2005 (StarTrack)

Nelemans, Portegies Zwart, & Yungelson 2001 (upper limit)

Tauris & Sennels 2001

Brown et al. 2002

Portegies Zwart & Yungelson 1999

- Davies, Ritter, King 2003

Theoretical predictions on birthrates

Theoretical estimates

Compare theoretical & empirical estimates Empirical estimates -Kalogera, CK, Ihm, Belczynski 2005 (error bar @95% CL) “Lower Limits”

- Kalogera, CK, Ihm, Belczynski 2005 (StarTrack)

Nelemans, Portegies Zwart, & Yungelson 2001 (upper limit)

Tauris & Sennels 2001

Brown et al. 2002

Portegies Zwart & Yungelson 1999

- Davies, Ritter, King 2003

REF :4 Myr-1

Theoretical estimates

No beaming correction

J1141-6545 and B2303+46

~h 2

d

Mchirp fh: GW amplitude

f: GW frequency = 2/Porb

d: distance to the source

Detection distance for advanced LIGO:

NS-NS ~ up to 350 Mpc

NS-BH (10 ) ~ up to 740 Mpc

(almost an order of magnitude increase in Vdet)

M

BH binaries (BH-BH, BH-NS) are

even stronger GW sources than NS binaries.

However, they have not been observed, yet.

NS-BH binaries

Empirical estimates using SEARCH Fix Ps = 50ms,

pulse width = 0.15

Adapt flux degradation factors

from known NS-NS binaries

RNS-BH < 1000 Myr-1

(upper limit @ 95% prob.)

with beaming correction

Pro

babi

lity

dens

ity

0 200 600 1000

Galactic merger rate (Myr-1)

Calculate P(R) given

Nobs=0

Constrain theoretical models

Theoretical predictions on RNS-BH ~ 10-8 – 10-5 yr -1

O’shaughnessy, CK, et al. 2005, ApJ, 633, 1076

accepted range of parameters

parameterspace used in theoretical model (StarTrack)

Calculate Rgal of BH binaries using only those models.

Give strong constraints on

Rdet of BH binaries and

population synthesis models

Establish a set of models (or parameters), which are

consistent with the estimated RNS-NS based on our

empirical method

NS-NS binariesNS-NS binaries

Empirical rate constraints

Galactic merger rate (Myr-1)10-2 0.1 1 10 102 103

10-2 0.1 1 10 102 103

log (Probability Density)

log (Probability Density)

StarTrack results

wide NS-NS

merging NS-NS

Only a few % of modelssatisfy both constraintssimultaneously

MergingB1913+16, B1534+12, J0737-3039

Wide (mrg > Hubble time)J1181-1736, J1518+4904, J1829+2456

Consistent with empirical rates

more than 95% of models

are ruled out;

Still, wide range of

parameters are possible.

Constrained predictions w/ StarTrack lo

g (P

roba

bilit

y D

ensi

ty)

Galactic merger rate in (Myr-1)

10-2 0.1 1 10 102

BH-BH

NS-BH

NS-NS

Dashed lines: unconstrained

Solid lines: constrained (NS-NS)

no recycled PSR-BH

NS-BH binaries: discussions

Pfahl et al. (2005) suggested that the Galactic birthrate of recycled PSR-BH binaries ~ less than 10-7 yr-1

consistent with our work (RMSP-BH < 10-8 yr-1)

If any, presumably, slow/normal PSR-BH binaries

dominate the NS-BH population

Recycled PSR-BH

NS-NS << 10-4 and R NS-NS < 10-4 yr-1

StarTrack results:

NS-BH binaries: discussions

Observational challenges

pulsars in NS-BH binaries are expected to have relatively short observable lifetimes, large accelerations in orbital motions than those of NS-NS binaries.

Large-scale interferometers

Square Kilometer Array (SKA) … radio (EM)

GEO/LIGO/TAMA/VIRGO … GW

death-time (Myr) spin-down age (Gyr)observable lifetime ~ 10% of MSP lifetime

Summary

We study

empirical Rgal of pulsar binaries (NS-NS & NS-WD)

detectability of such systems for GW detectors

constraints on theoretical models and BH rate estimates

Pulsar binaries are one of the most promising targets for GW

detectors, and they are likely to provide some of the first GW

detections.