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Astrophysics of Gravitational-Wave Sources. Vicky Kalogera Dept. of Physics & Astronomy Northwestern University. Einstein’s theory of Gravity and Gravitational Waves. communication of spacetime deformations occurs through ripples: gravitational wave propagation at the speed of light. - PowerPoint PPT Presentation
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Astrophysics of Astrophysics of Gravitational-Wave SourcesGravitational-Wave Sources
Vicky KalogeraDept. of Physics & Astronomy
Northwestern University
Einstein’s theory of GravityEinstein’s theory of Gravityand Gravitational Wavesand Gravitational Waves
Mass curves spacetime and affects distances between reference points
communication of spacetime
deformations occurs through
ripples: gravitational wave
propagationat the speed of
light
Propagation and Generation of Propagation and Generation of Gravitational WavesGravitational Waves
Wave Solution to Sourceless linearized Metric Equation:Wave Solution to Sourceless linearized Metric Equation:
Wave Solution to linearized Metric Equation with Source:Wave Solution to linearized Metric Equation with Source:
transverse wavetransverse wave
at speed at speed lightlight
Source of Gravitational WavesSource of Gravitational Waves
Dipole moment:
double time derivative is zero due to linear momentum conservation
“magnetic” moment:
time derivative is zero due toangular momentum conservation
Gravitational Radiation is of Quadrupole Order
Gravitational RadiationGravitational Radiation
Amplitude:
Source: Time-dependent mass quadrupole moment tensor Ijk:
The Effect of Gravitational WavesThe Effect of Gravitational Waves
10 M10 Moo BH at the Galactic center: BH at the Galactic center: h h
~ 10 ~ 10 -17-17
10 M10 Moo BH at the Virgo cluster: BH at the Virgo cluster: h ~ h ~
10 10 -20-20
2 polarizations
Evidence for Gravitational WavesEvidence for Gravitational Waves
Hulse-Taylor Binary Pulsar: The first relativistic binary pulsar
A binary system with with two neutron stars, one or two of which emit radio pulses:
QuickTime™ and aGIF decompressorare needed to see this picture.
pulsar as a`lighthouse'
Do Gravitational Waves Do Gravitational Waves reallyreally exist ? exist ?
orbitaldecay
PSR B1913+16
Weisberg &Taylor 03
Measurement of orbital decayis consistent with the gravitational radiation prediction within 0.3% !
PSR J0737-3039: The first DOUBLE PSRand the most relativistic DNS so far!
PA = 22msPB = 2.7s
Porb = 2.4hre = 0.09
Beyond the Hulse-Taylor Binary…Beyond the Hulse-Taylor Binary…more relativistic DNS have been discovered:
PSR B1534+12
and the most recent one:PSR J1756-2251
Burgay et al. 2003
How about How about directdirect detection? detection?
LIGO GEO VirgoTAMA
AIGO
Coincidence: detection confidence source localization
signal polarization
GW Sources: High FrequencyGW Sources: High Frequency
GW Sources: ChirpsGW Sources: Chirps
inspiral chirp
GW emission causes orbital shrinkage leading to higher GW frequency and amplitude
fGW = 2xforb
Binary Compact ObjectsBinary Compact Objects
• How do Double Compact Objects Form ? How do Double Compact Objects Form ?
• What are the PredictedWhat are the Predicted Binary Inspiral Event Rates ? Binary Inspiral Event Rates ? (NS-NS, BH-NS, BH-BH) (NS-NS, BH-NS, BH-BH)
• What are the Best Methods for What are the Best Methods for Gravitational-Wave Data Analysis ? Gravitational-Wave Data Analysis ?
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!
NS-NS Formation ChannelNS-NS Formation Channel
animation credit:
John Rowe
QuickTime™ and aYUV420 codec decompressor
are needed to see this picture.
Understanding Understanding Core-Collapse and NS formation Core-Collapse and NS formation
Use known DNS: PSRs B1913+16 B1534+12 J0737-3037and their measured properties:
- NS masses- orbital semi-major axis and eccentricity- transverse velocity on the sky- PSR spin tilt w/r to orbital a.m. axis (for some)
WHAT?WHAT?
with Bart Willems & Mike HenningerApJ Letters & ApJ 2004, PRL 2005
Understanding Understanding Core-Collapse and NS formation Core-Collapse and NS formation
Investigate their evolutionary history backwards in time to the last Supernova event and NS formation
Simulate: - systemic motion in the Galactic gravitational potential- binary orbital dynamics through asymmetric SN event
Account for all unknown properties: - e.g., systemic velocity along line-of-sight
HOW?HOW?
with Bart Willems & Mike HenningerApJ Letters & ApJ 2004, PRL 2005
Understanding Understanding Core-Collapse and NS formation Core-Collapse and NS formation
To uncover the conditions at NS formation: - NS progenitor mass- NS natal kick magnitude and direction
and make predictions testable by near-future observations: - e.g., PSR spin tilts and DNS age
WHY?WHY?
with Bart Willems & Mike HenningerApJ Letters & ApJ 2004, PRL 2005
What do we learn about What do we learn about Core-Collapse and NS formation ? Core-Collapse and NS formation ?
with Bart Willems & Mike Henninger
Tight and Robust Constraints on NS Kick magnitude:
Most probable value: Most probable value: ~150 km/s~150 km/s
Double Pulsar:
What do we learn about What do we learn about Core-Collapse and NS formation ? Core-Collapse and NS formation ?
with Bart Willems & Mike Henninger
Double Pulsar:
polar angle between polar angle between pre-SN orbital velocity pre-SN orbital velocity VV00 and kick velocity V and kick velocity V
kk
Kick is directed opposite to the orbital motion
What do we learn about What do we learn about Core-Collapse and NS formation ? Core-Collapse and NS formation ?
with Bart Willems & Mike Henninger
Tight Physical anti-Correlationbetween: NS progenitor mass and NS kick magnitude
Large Mass Loss is balanced by Small Kickand vice versa
What do we learn about What do we learn about Core-Collapse and NS formation ? Core-Collapse and NS formation ?
with Bart Willems & Mike Henninger
NS
Pro
gen
itor
Mas
s
NS Kick Magnitude
2-D probabilityDensity distribution
What do we learn about What do we learn about Core-Collapse and NS formation ? Core-Collapse and NS formation ?
with Bart Willems & Mike Henninger
Predictions for NS spin tilt: important for understanding long-term behavior of pulsar emission
Thorsett et al. 2005 report a spin-tilt measurement of 25 (+- 4) deg 25 (+- 4) deg consistent with our predictions !consistent with our predictions !
Prediction: spin-tilt smaller than 30-40deg
What Is the Physical Origin What Is the Physical Origin of Small DNS eccentricities ? of Small DNS eccentricities ?
with Mia Ihm & Chris Belczynski(Physics Senior Thesis; ApJ 2005)
Observed DNS eccentricities: 0.09, 0.18, 0.27, 0.62
Is this due to small (or zero) natal kicks imparted to SOME NS ? (van den Heuvel 2004)
At first glance: possibly …
Models with typical NS kicks
Models with zero NS kicks
What Is the Physical Origin What Is the Physical Origin of Small DNS eccentricities ? of Small DNS eccentricities ?
with Mia Ihm & Chris Belczynski
Observed DNS eccentricities: 0.09, 0.18, 0.27, 0.62
Is this due to zero natal kicks imparted to second NS ?
At first glance: possibly … However, Bayesian statisticalanalysis reveals: zero-kick model likelihood is zero!
Typical NS kicks models
Zero-kick models
What Is the Physical Origin What Is the Physical Origin of Small DNS eccentricities ? of Small DNS eccentricities ?
with Mia Ihm & Chris Belczynski
Observed DNS eccentricities: 0.09, 0.18, 0.27, 0.62
High-eccentricity DNS are depleted due to GR evolution: Circularization and Mergers
P(e) at birth
P(e) at present, affected by GR
Models with typical NS kicks:
Physical Origin of Small DNS eccs: Physical Origin of Small DNS eccs: GR circularization & MergersGR circularization & Mergers
with Mia Ihm & Chris Belczynski
Observed DNS eccentricities: 0.09, 0.18, 0.27, 0.62
Results indicate the existence of a significant fraction of DNS thatMerge very soon after formation: Implications for merger rates and GR detection …
Models at birth
Models at present
Compact Binary Inspiral: Compact Binary Inspiral: Event RatesEvent Rates
Theoretical Estimates
Based on models of binary evolution until binary compact objects form.
for NS -NS, BH -NS, and BH -BH
Empirical Estimates
Based on radio pulsar properties and survey selection effects.
for NS -NS only
Compact Binary Inspiral: Event RatesCompact Binary Inspiral: Event Rates
Problems until recently:
• Rate Predictions highly uncertain (by 103-104)
• Lack of quantitative understanding of uncertainties (statistical & systematic)
Compact Binary Inspiral: Event RatesCompact Binary Inspiral: Event Rates
Radio Pulsars inNS-NS binaries
NS-NS MergerRate Estimates
(Phinney ‘91; Narayan et al. ‘91; Lorimer & vdHeuvel ‘97; Arzoumanian et al. ‘99)
It is possible to assign statistical significance
to DNS rate estimatesBayesian analysis developed to derive theBayesian analysis developed to derive the probability densityprobability density of NS-NS inspiral rateof NS-NS inspiral rate
Small number biasSmall number bias and and selection effects for selection effects for faint pulsarsfaint pulsars are implicitly are implicitly includedincluded in our in our method.method.
with Chunglee Kim et al. ApJ 2002; Nature 2003; ApJ Letters 2004
PSR Survey SimulationsPSR Survey Simulations
count the number of pulsars observed (Nobs)
populate a model galaxy with Ntot PSRs (same Ps & Porb)
Nobs follows the Poisson distribution,P(Nobs; <Nobs>) ---> …… … … … ---> P(Ntot)
assume PSR distribution functions in luminosity & space
consider each observed pulsar separately
(adopt spin & orbital periods of the observed DNS system)
carefully model thresholds of PSR surveys
Earth
Compact Binary Inspiral: Event RatesCompact Binary Inspiral: Event Rates
3 NS-NS : a factor of 6-7 rate increase
Initial LIGO Adv. LIGO per 1000 yr per yr
ref model: peak 35 175
95% 10 - 120 35 - 630
Current Rate Predictionswith Chunglee Kim et al.
Event Rates:
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
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 )
PD
F
BH-BH
BH-NS
NS-NS
with Richard O’Shaughnessy, C. Kim, T. FragosApJ 2004, 2005
Black Hole Binary Inspiral: Event RatesBlack Hole Binary Inspiral: Event Rates
Constraints from both tight and wide DNS:
with Richard O’Shaughnessy, C. Kim, T. Fragkos
NS-NSBH-NSBH-BH
1 advanced LIGO IFO
Plans for the Future … Plans for the Future …
Focus on Astrophysical Interpretation of GW Observations:
- Development of optimal data analysis methodsfor “non-simple” signals with astrophysical guidance
- Extraction of physical properties from one (or a few)GW detections: NS interiors and EOS, compact object formation
on all scales - Analysis of population characteristics:
masses, spins, spatial distribution, galactic structure
- Interpretation of multi-messenger observations: interplay of GW and EM astrophysics
Beyond Earth-Bound: LISABeyond Earth-Bound: LISA
LISA Astrophysics: LISA Astrophysics: even richer … even richer …
Focus on White Dwarfs and Massive Black Holes:
- Move away from point-mass treatment for WD-WDs:Tidal effects and dissipative processes (viscosity, convection, radiative cooling) lead to energy and angular momentum exchanges betweenstars and orbit: NOT a pure GR inspiral signal
- Black-hole captures in galactic centers around super-massive black holes: event rate predictions and waveform calculationsneeded …
Thanks to: Thanks to:
PostdocsM. FreitagN. Ivanova
R. O’ShaughnessyB. Willems
P. Grandclement
Grad StudentsT. Fragos
C. KimJ. Sepinksky
Undergrad StudentsL. BlechaM. IhmR. JonesJ. KaplanT. Levin
M. HenningerP. Nutzman
Funding SourcesNASA, NSF
Packard Foundation,Research Corporation,
NU