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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 - PowerPoint PPT Presentation
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Binary Neutron Star MergersBinary Neutron Star MergersGravitational-Wave SourcesGravitational-Wave Sources
andand
Gamma-Ray BurstsGamma-Ray Bursts
Vicky KalogeraDept. of Physics & Astronomy
Northwestern University
Binary Compact ObjectsBinary Compact Objects
• Double Neutron Stars: the sampleDouble Neutron Stars: the sample• Two new DNS binaries! Two new DNS binaries!
• Empirical DNS rates: updatesEmpirical DNS rates: updates
• Theoretical Merger RatesTheoretical Merger Rates• Constraining population synthesesConstraining population syntheses
• Expectations for LIGO - when???Expectations for LIGO - when???
• NS mergers and short GRBs?NS mergers and short GRBs?• Merger delays and redshift distributionsMerger delays and redshift distributions
In this talk:
DNS pulsars: Hulse-Taylor DNS pulsars: Hulse-Taylor
QuickTime™ and aGIF decompressorare needed to see this picture.
pulsar as a`lighthouse'
GWorbitaldecay
PSR B1913+16
Weisberg &Taylor 03
Indirect evidence forIndirect evidence forGravitational WavesGravitational Waves
DirectDirect detection? detection?
LIGO GEO VirgoTAMA
AIGO
Coincidence: detection confidence source localization
signal polarizationGW Interferometers: global network
Double Neutron Star (DNS) SystemsDouble Neutron Star (DNS) Systems
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
Strong sources of gravitational waves (waveforms are well understood)
Development and designing of GW detectors
Understanding of the astrophysics of compact objects
DNS merger rate calculationsDNS 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 sampleDNS 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 10.1 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 Parkes double pulsarFaulkner et al. 2004 Parkes MB survey, acceleration searchLorimer et al. 2005 Arecibo ALFA survey
Merger rate Merger rate RR
Q: How many pulsars “similar” to each of the known DNS binaries exist in our Galaxy?
Lifetime of a systemNumber of sources
x correction factorR =beaming
Goal : Calculate the probability
distribution of the Galactic DNS
merger rates P(R)
Method - Modeling & Simulation (Kim et al. 2003, ApJ,
584, 985 )
assume luminosity & spatial distribution functions
adapt spin & orbital periods from each observed PSR
1. Model pulsar sub-populations
Selection effects for faint pulsars are taken into account.
Method - Modeling & Simulation (Kim et al. 2003, ApJ,
584, 985 )
count the number of pulsars observed (Nobs)
populate a model galaxy with Npop PSRs (same Ps & Porb)
Nobs follows the Poisson distribution,P(Nobs; <Nobs>)
carefully model thresholds of PSR surveys
Earth
2. Simulate large-scale pulsar surveys
For an each observed system i,
Pi(R) = Ci2R exp(-CiR)
where Ci =
Combine the three individual PDFs and calculate P(Rgal)
Statistical Analysis
Individual probability density function (PDF)
<Nobs> life Npop fb i
Probability density function of Rgal
P(Rgal )
Lifetime ~ 185 Myr
NJ0737 ~ 1600 (most abundant)
Lifetime ~ 80 Myr (shortest)
NJ1906 ~ 300
The revised DNS merger rate
~83 +209
-66 ~13+40
-11
raterateper Myrper Myr
Reference model:
Rpeak (revised) Rpeak (previous)
~ 6-7
Increase rate factor due to PSR J0737-3039:
B1913+B1534+J0737 B1913+B1534
(at 95% CL)
Rpeak (revised) Rpeak (previous)
~1.5-1.7
Increase rate factor due to PSR J1906+0746:
B1913+B1534+J0737+J1906
~120
Detection rate of DNS inspirals for LIGO
Rdet (adv. LIGO) ~ 350 events per
yr
Rdet (ini. LIGO) ~ 1 event per 20 yr
The most probable DNS inspiral detection rates for LIGO
Rdet (adv. LIGO) ~ 15 – 850 events
per yr
Rdet (ini. LIGO) ~ 1 event per 5 – 250 yr
All models:
Reference model:
Implications of J1756-2251
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.
No significant change in the total rate.
Rpeak (4 PSRs + J1756) Rpeak (4 PSRs)
~ 1.04
J1756-2251: Another merging DNS in the Galactic disk
Similar to the Hulse-Taylor system
(Faulkner et al. 2005)
Global P(Rgal): motivation
f(L) L-p, where Lmin is a cut-off luminosity and p is a power index.
Lmin (mJy kpc2)
p
Rpeak (Myr-1)
Radio pulsar luminosity function
Global P(Rgal): motivation
, where Lmin is a cut-off luminosity and p is a power index.
Radio pulsar luminosity function
Global probability density function Pglobal(R)
Pglobal(R) P(R; Lmin,p) f(Lmin)
g(p)intrinsic functions for Lmin and p
P(R) P(R; Lmin,p)
Rpeak is strongly dependent on Lmin & p.
f(L) L-p
Global P(Rgal) and SNe rate constraints
Probability Density
Galactic DNS
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 DNS formation.
The empirical SNe rate
Compact Binary Inspiral Rates: Compact Binary Inspiral Rates: What about Black Hole Binaries?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 farSo far, inspiral rate predictionsrate predictions only from population calculations from population calculations with uncertainties of ~ 3 orders of mag
We can use NS-NS empirical rates as constraintson population synthesis models
Binary Compact Objects: FormationBinary Compact Objects: FormationMassive 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 StudyPopulation 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: 7DRate Fits vs. StarTrack calculations: 7D
BH-BH
NS-NS
O’Shaughnessy et al. 2004
Fit accuracy is comparableor usually smaller thanthe Poisson errors of StarTrack Monte Carlo rates
(Belczynski et al. 2005)
Black Hole Binary Inspiral: Event RatesBlack Hole Binary Inspiral: Event Rates
From Population Synthesis Modeling:
- 8 -7 -6 -5 -4 -3 -2
0.2
0.4
0.6
0.8
1
log ( events per yr )
BH-BH
BH-NS
NS-NS
Empirical Constraints imposed on population synthesis rate predictions
Merging NS-NS Wide NS-NS
O’Shaughnessy et al. 2006
log(rate) log(rate)
Four More Rate Constraints: O’Shaughnessy et al. 2006
SN Ib/c
SN II
mergingPSR-WD
eccentricPSR-WD
BH-BH BH-NS
NS-NS
Constrained vs. Unconstrained Rate Predictions from StarTrack:
O’Shaughnessy et al. 2006
BH-BHBH-NS
NS-NS
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 ?
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 …
We need to know:
Time-Delay between formation and mergers
NS-NS
SPIRAL GALAXIES
BH-NS
log(Merger Time / Myr)
BH-NS
ELLIPTICAL GALAXIES
log(Merger Time / Myr)
NS-NS
BH-NS
BelczynskiO’Shaughnessy
Compact Binary Formation efficiencies
What is the number of binaries formed per unit stellar mass?SPIRAL GALAXIES ELLIPTICAL GALAXIES
NS-NS NS-NS
BH-NS BH-NS
log(efficiency * Msun) log(efficiency * Msun)
BelczynskiO’Shaughnessy
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 … ?
Binary Center-of-mass velocities and Lifetimes: Where do they merge ?
SPIRAL GALAXIES ELLIPTICAL GALAXIES
NS-NS NS-NS
BH-NS BH-NS
1kpc 10 kpc
log(merger time / Myr)log(merger time / Myr)
log(Vcm / km/s)
log(Vcm / km/s)
BelczynskiO’Shaughnessy