Expected Coalescence Rate of NS/NS Binaries for Ground Based Interferometers

Tania RegimbauOCA/ARTEMIS

on the behalf of J.A. de Freitas Pacheco, T. Regimbau, S.

Vincent, A. Spallicci

The Model

a very small fraction of massive binaries remains bounded after 2 supernova explosions

the resulting system consist of:

1. a partially reaccelerated pulsar

2. a young pulsar with

- same period evolution (magnetic dipole spin down) as normal radio pulsars

- same kick velocity as millisecond pulsars (for which the supernova didn’t disrupt the system either)

The Galactic Coalescence Rate

*

40 -1.35

9

( ) : star formation rate (Rocha-Pinto et al., 2000)

: fraction of formed stars in the range 9-40 M ( = Am dm)

: fraction of massive binarie

s formed among all stars

f

:b

NS

R t

f

0

*

raction of massive binaries that remain bounded after the second supernova

( ): probability for a newly formed NS/NS to coalesce in a timescale

: minimum coalescence time

: mean timescale required f

P or the newly formed massive system to evolve into two NSs

* 0

0* *( ) ( ) ( )

t

c b NSt f R t P d

The Galactic Star Formation Rate

previous studies:

the star formation rate is proportional to the available mass of gas as, R*(t) ~ e-t

present work:

the star formation history is reconstructed from observations:

ages of 552 stars derived from chromospheric activity index (Rocha-Tinto et al., 2000)

enhanced periods of star formation at 1 Gyr, 2-5 Gyr and 7-9 Gyr probably associated with accretion and merger episodes from which the disk grows and acquires angular momentum (Peirani, Mohayaee, de Freitas Pacheco, 2004)

The Galactic Coalescence Rate

*

40 -1.35

9

( ) : star formation rate (Rocha-Pinto et al., 2000)

: fraction of formed stars in the range 9-40 M ( = Am dm)

: fraction of massive binarie

s formed among all stars

f

:b

NS

R t

f

0

*

raction of massive binaries that remain bounded after the second supernova

( ): probability for a newly formed NS/NS to coalesce in a timescale

: minimum coalescence time

: mean timescale required f

P or the newly formed massive system to evolve into two NSs

* 0

0* *( ) ( ) ( )

t

c b NSt f R t P d

Numerical Simulations (P(), 0, NS)

initial parameters:

masses: M1, Salpeter IMF, M1/M2: probability derived from observations

separation: P(a)da=da/a between 2RRoche and 200RRoche

eccentricity: P(e)de = 2ede

evolution of orbital parameters due to mass loss (stellar wind, mass transfert, supernova)

statistical properties

NS= 2.4% (systems that remain bounded after the second supernova)

P(0.087/probability for a newly formed system to coalesce in a timescale

2x105 yr (minimum coalescence time)

Vincent, 2002

birth parameters(M1, M2, a, e)0

Mass loss(M1, M2, a, e)1

Supernova 1 disrupted

NS/NS systema, e ->

Mass loss(1.4Mo, M2, a, e)2

Supernova 2 disrupted

E > 0

E > 0

The Galactic Coalescence Rate

*

40 -1.35

9

( ) : star formation rate (Rocha-Pinto et al., 2000)

: fraction of formed stars in the range 9-40 M ( = Am dm)

: fraction of massive binarie

s formed among all stars

f

:b

NS

R t

f

0

*

raction of massive binaries that remain bounded after the second supernova

( ): probability for a newly formed NS/NS to coalesce in a timescale

: minimum coalescence time

: mean timescale required f

P or the newly formed massive system to evolve into two NSs

* 0

0* *( ) ( ) ( )

t

c b NSt f R t P d

Population Synthesis (fb)

birth parametersPo, Bo, vk, do…

magnetic braking

selection effects:sky coverage,

cone, flux

observed hidden

present propertiesP, dP/dt, d, S …

+ -

single radio pulsar properties:

• Np = 250000 (for 1095 observed)

• birth properties

second binary pulsar properties:

• the youngest pulsar has the same: - period evolution (magnetic dipole spin down) as single radio pulsars - kick velocity as millisecond pulsars (remains bounded after the supernova)

• Nb = 730 (for two observed)

3.6 ± 0.211 ± 0.5ln 0 (s)

80± 20240 ± 20P0 (ms)

dispertionmean

1 1 12

0.136

p b NS

b NS b NS

b

N f

N f

f

Regimbau, 2001&2004

The Local Coalescence Rate

( )SEc S S E

S E

Lf f

L

weighted average overspiral (fS=65%) and elliptical (fE=35%) galaxies

same fb and NS as for the Milky Way

spiral galaxy coalescence rate equal to the Milky Way rate:S = MW = (1.7±1)x10-5 yr-1

elliptical galaxy star formation efficiency and IMF estimated from observations - color & metallicity indices (Idiart, Michard & de Freitas Pacheco, 2003)E =8.6x10-5 yr-1

c = 3.4x10-5 yr-1

other estimates: ~10-6 – 10-4 yr-1

(Kalogera et al., 2004: 1.8x10-4 yr-1)

Intermitent star formation history: modulation in the coalescence rate

Bulk of stars formed in the first 1-2 Gyr.

The pairs merging today were formed with

long coalescence times

(P ~1/ )

coalescence rate within the volume V=4/3 D3

counts of galaxies from the LEDA catalog:

- 106 galaxies (completness of 84% up to B = 14.5)

- inclusion of the Great Attractor (intersection of Centaurus Wall and Norma Supercluster) corresponding to 4423 galaxies at Vz = 4844 km/s

The Detection Rate

3V

MW

4(<D) with V= D

3c

L

L

maximum probed distance and mean expected rate

(S/N=7; false alarm rate=1) :

VIRGO LIGO LIGO Ad

13 Mpc

1 event/148 yr

14 Mpc

1 event /125 yr

207 Mpc

6 events/yr

Possible Improvements in the Sensitivity…

gain in the VIRGO thermal mirror noise band (52-148 Hz):reduction of all noises in the band by a factor 10 (Spallicci, 2003; Spallicci et al., submitted)

gain throughout VIRGO full bandwidthreduction of pendulum noise by a factor 28, thermal mirror 7, shot 4 (Punturo, 2004; Spallicci et al., submitted)

• maximum probed distance: 100 Mpc• detection rate: 1.5 events / yr

use networks of detectors:

LIGO-H/LIGO-L/VIRGO(Pai, Dhurandhar & Bose, 2004)

• false alarm rate = 1, detection probability = 95% • maximum probed distance: 22 Mpc• detection rate: 1 events / 26 yrs

Work in progress

compute the GW stochastic background produced by the superposition of all the NS/NS binaries

analytical approach

integration up to to z~6

numerical approach

generating extragalactic populations of NS/NS binaries

Extra slides

.

.

PSR J0737-3039 A+BPSR J0737-3039 A+B

A B

P

dP/dt

Bsurf

22.7 ms

1.7 x 10-18

6 x 109 G

2.77 s

0.88 x 10-15

1.6 x 1012 G

Kalogera, Kim, Lorimer et al., 2004

Numerical simulations• sample of 3 galactic coalescing pulsars, (P, dP/dt)i

• populate a model galaxy (P(L, R, z)) with Ntot pulsars with (P, dP/dt) i

• model radiotelescope survey selection effects and compute Nobsi

Statistics• Nobsi follows a Poisson distribution of mean <Nobs>i

• <Nobs>i = i Ntot

• bayesian statistic to compute Pi(Ntot)

coalescence rate• Ri = Ntoti/life fb

• P(Ri) with mean and confidence level

• combine P(Ri) to obtain P(R)