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