Transcript The Hunt for Einstein’s Ripples and their Sounds

Binary Neutron Star Mergers
Gravitational-Wave Sources
and
Gamma-Ray Bursts
Vicky Kalogera
Dept. of Physics & Astronomy
Northwestern University
Binary Compact Objects
In this talk:
•
Double Neutron Stars: the sample
•
Two new DNS binaries!
•
Empirical DNS rates: updates
•
Theoretical Merger Rates
•
•
•
Constraining population syntheses
Expectations for LIGO - when???
NS mergers and short GRBs?
•
Merger delays and redshift distributions
DNS pulsars: Hulse-Taylor
Indirect evidence for
Gravitational Waves
QuickT ime™ and a GIF decompressor are needed to see this pict ure.
GW
orbital
decay
PSR B1913+16
pulsar
as a
`lighthouse'
Weisberg &
Taylor 03
Direct detection?
Coincidence:
detection confidence
source localization
GW Interferometers: global network
signal polarization
LIGO
GEO
Virgo
TAMA
AIGO
Double Neutron Star (DNS) Systems
 Strong sources of gravitational waves
(waveforms are well understood)
 one of the prime targets of large-scale GW detectors
(e.g. LIGO, VIRGO, GEO, TAMA)
Galactic merger rate
of DNS systems
Event rate estimation
for DNS inspiral
search
Development and designing of GW detectors
Understanding of the astrophysics of compact objects
DNS merger rate calculations
 Empirical method:
based on radio pulsar properties and observational
selection effects of pulsar surveys
(Narayan et al. (1991), Phinney (1991), Curran & Lorimer (1993),
VK, Narayan et al. (2001), Kim, VK et al. (2003), VK, Kim et al. (2004))
 Theoretical method:
based on our understanding of binary formation and
evolution (population synthesis models)
(Portegies Zwart & Yungelson (1998), Nelemans et al. (2001),
Belczynski, VK, & Bulik (2002), O’Shaughnessy, VK et al. (2005)
and many more)
DNS pulsars: the observed sample
PSR name
Ps (ms)
Pb (hr)
e
life (Gyr)
B1913+16
59.03
7.752
0.617
0.365
B1534+12
37.90
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+0748
144.07
3.98
0.085
0.083
Burgay et al. 2003
Faulkner et al. 2004
Lorimer et al. 2005
10.1
Parkes double pulsar
Parkes MB survey, acceleration search
Arecibo ALFA survey
Merger rate R
R =
Number of sources
Lifetime of a system
beaming
x correction factor
Q: How many pulsars “similar” to each of the known
DNS binaries exist in our Galaxy?
Goal : Calculate the probability distribution
of the Galactic DNS merger rates P(R)
Method - Modeling & Simulation (Kim et al. 2003, ApJ, 584, 985 )
1. Model pulsar sub-populations

adapt spin & orbital periods from each observed PSR

assume luminosity & spatial distribution functions
Selection effects for faint pulsars are taken into account.
Method - Modeling & Simulation (Kim et al. 2003, ApJ, 584, 985 )
2. Simulate large-scale pulsar surveys
populate a model
galaxy with Npop PSRs
(same Ps & Porb)
count the number of
pulsars observed (Nobs)
Earth
carefully model
thresholds of PSR surveys
Nobs follows the
Poisson distribution,
P(Nobs; <Nobs>)
Statistical Analysis
 Individual probability density function (PDF)
For an each observed system i,
Pi(R) = Ci2R exp(-CiR)
where Ci =
<Nobs> life
Npop fb
i
 Combine the three individual PDFs and calculate P(Rgal)
Probability density function of Rgal
P(Rgal
Lifetime ~ 80 Myr (shortest)
NJ1906 ~ 300
Lifetime ~ 185 Myr
NJ0737 ~ 1600 (most abundant)
)
The revised DNS merger rate
Increase rate factor
due to PSR J0737-3039:
Rpeak (revised)
~ 6-7
Rpeak (previous)
Increase rate factor
due to PSR J1906+0746:
Rpeak (revised)
Rpeak (previous)
~1.5-1.7
 Reference model:
rate
per Myr
(at 95% CL)
B1913+B1534+J0737+J1906 B1913+B1534+J0737 B1913+B1534
~120
+209
~83-66
+40
~13-11
Detection rate of DNS inspirals for LIGO
 The most probable DNS inspiral detection rates for LIGO
Reference model:
Rdet (ini. LIGO) ~ 1 event per 20 yr
Rdet (adv. LIGO) ~ 350 events per yr
All models:
Rdet (ini. LIGO) ~ 1 event per 5 – 250 yr
Rdet (adv. LIGO) ~ 15 – 850 events per yr
Implications of J1756-2251
J1756-2251: Another merging DNS in the Galactic disk
Similar to the Hulse-Taylor system
(Faulkner et al. 2005)
 Discovered by the Parkes Multibeam Pulsar Survey with
the acceleration search technique.
Standard Fourier techniques failed to detect J1756-2251.
 Contribution of J1756-2251 to the Galactic DNS merger rate.
Rpeak (4 PSRs + J1756)
Rpeak (4 PSRs)
~ 1.04
No significant change in the total rate.
Global P(Rgal): motivation
 Radio pulsar luminosity function
Rpeak (Myr-1)
f(L)  L-p, where Lmin is a cut-off luminosity and p is a power index.
Lmin (mJy kpc2)
p
Global P(Rgal): motivation
 Radio pulsar luminosity function
f(L)  L-p, where Lmin is a cut-off luminosity and p is a power index.
 Rpeak is strongly dependent on Lmin & p.
P(R)  P(R; Lmin,p)
 Global probability density function Pglobal(R)
Pglobal(R)
P(R; Lmin,p) f(Lmin) g(p)
intrinsic functions for Lmin and p
Global P(Rgal) and SNe rate constraints
The empirical SNe rate
SN Ib/c = 600-1600 Myr-1
Probability Density
(Cappellaro, Evans, & Turatto 1999)
SNL5
Suppose, ~5% of Ib/c SNe are
involved in the DNS formation.
SNL5= SN (lower)x0.05 = 30 Myr-1
SNU5= SN (upper)x0.05 = 80 Myr
SNU5
Galactic DNS merger rate (Myr-1)
-1
Compact Binary Inspiral Rates:
What about Black Hole Binaries?

BH-NS binaries could in principle be detected as
binary pulsars, BUT…
the majority of NS in BH-NS
are expected to be
young
short-lived
hard-to-detect
harder to detect than NS-NS by >~10-100 !
So far, inspiral rate predictions
only from population calculations
with uncertainties of ~ 3 orders of mag
We can use NS-NS empirical rates as constraints
on population synthesis models
Binary Compact Objects: Formation
Massive primordial binary
Mass-transfer #1: hydrostatically and
thermally Stable,
but Non-Conservative: mass and A.M. loss
Supernova and NS Formation #1:
Mass Loss and Natal Kick
High-mass X-ray Binary: NS Accretion
from Massive Companion’s Stellar Wind
Mass-transfer #3: Dynamically Unstable
Mass-tranfer #4: Possible and Stable
Supernova and NS Formation #2:
Mass Loss and Natal Kick
Double Neutron-Star Formed!
Population Synthesis Parameter Study
• Large parameter space
• Most important parameters: 7
• 7D parameter study: computationally demanding
• Acceleration of computations:
• Use of Genetic Algorithms
Rate Fits vs. StarTrack calculations: 7D
(Belczynski et al. 2005)
O’Shaughnessy
et al. 2004
BH-BH
Fit accuracy is comparable
or usually smaller than
the Poisson errors of
StarTrack Monte Carlo rates
NS-NS
Black Hole Binary Inspiral: Event Rates
From Population Synthesis Modeling:
1
0.8
BH-NS
PDF
0.6
NS-NS
0.4
BH-BH
0.2
-8
-7
-6
-5
-4
log ( events per yr )
-3
-2
Empirical Constraints imposed
on population synthesis rate predictions
Merging NS-NS
log(rate)
Wide NS-NS
log(rate)
O’Shaughnessy et al. 2006
Four More Rate Constraints:
O’Shaughnessy et al. 2006
SN Ib/c
SN II
merging
PSR-WD
eccentric
PSR-WD
Constrained vs. Unconstrained Rate Predictions
from StarTrack:
O’Shaughnessy et al. 2006
BH-BH
NS-NS
BH-NS
NS-NS
BH-NS
BH-BH
Short GRBs and NS-NS / BH-NS mergers
Short GRB afterglows reveal association with both
elliptical and star-forming galaxies:
Progenitors must exist in both OLD and YOUNG
stellar populations!
NS-NS and BH-NS mergers: prime candidates
What is the event (GRB and mergers) rate vs. redshift ?
What is the spatial distribution w/r to the host galaxies ?
What is the event (GRB and mergers) rate vs. redshift ?
We need to know:
Star-formation rate vs. redshift
Porciani & Madau
Time-Delay between formation and mergers
Formation efficiency (# mergers / unit SF mass)
Relative Contribution of spirals and elliptical galaxies
GRB Luminosity function
unknown …
Time-Delay between formation and mergers
SPIRAL GALAXIES
Belczynski
O’Shaughnessy
ELLIPTICAL GALAXIES
NS-NS
NS-NS
BH-NS
BH-NS
BH-NS
log(Merger Time / Myr)
log(Merger Time / Myr)
Compact Binary Formation efficiencies
Belczynski
O’Shaughnessy
What is the number of binaries formed per unit stellar mass?
SPIRAL GALAXIES
ELLIPTICAL GALAXIES
NS-NS
BH-NS
log(efficiency * Msun)
NS-NS
BH-NS
log(efficiency * Msun)
Merger Rate vs. redshift
If ellipticals contributed 20% of the SF mass in the past
until about redshift of 2
Comparison with observed redshift distribution requires
a luminosity model … ?
Belczynski
O’Shaughnessy
Binary Center-of-mass velocities and Lifetimes:
Where do they merge ?
ELLIPTICAL GALAXIES
SPIRAL GALAXIES
10 kpc
NS-NS
BH-NS
log(merger time / Myr)
log(Vcm / km/s)
log(Vcm / km/s)
1kpc
NS-NS
BH-NS
log(merger time / Myr)