expected coalescence rate of ns/ns binaries for ground based interferometers tania regimbau...
TRANSCRIPT
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)