Astrophysics of Gravitational-Wave Sources Vicky Kalogera Dept. of Physics & Astronomy Northwestern University

Einstein’s theory of Gravity and Gravitational Waves Mass curves spacetime and affects distances between reference points communication of spacetime deformations occurs through ripples: gravitational wave propagation at the speed of light

Propagation and Generation of Gravitational Waves Wave Solution to Sourceless linearized Metric Equation: Wave Solution to linearized Metric Equation with Source: transverse wave at speed light

Source of Gravitational Waves Dipole moment: double time derivative is zero due to linear momentum conservation “magnetic” moment: time derivative is zero due to angular momentum conservation Gravitational Radiation is of Quadrupole Order

Gravitational Radiation Amplitude: Source: Time-dependent mass quadrupole moment tensor I jk :

The Effect of Gravitational Waves 10 M o BH at the Galactic center: h ~ M o BH at the Virgo cluster: h ~ polarizations

Evidence 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: pulsar as a `lighthouse'

Do Gravitational Waves really exist ? orbital decay PSR B Weisberg & Taylor 03 Measurement of orbital decay is consistent with the gravitational radiation prediction within 0.3% !

PSR J : The first DOUBLE PSR and the most relativistic DNS so far! P A = 22ms P B = 2.7s P orb = 2.4hr e = 0.09 Beyond the Hulse-Taylor Binary… more relativistic DNS have been discovered: PSR B and the most recent one: PSR J Burgay et al. 2003

How about direct detection? LIGOGEOVirgoTAMA AIGO Coincidence:detection confidence source localization signal polarization

GW Sources: High Frequency

GW Sources: Chirps inspiral chirp GW emission causes orbital shrinkage leading to higher GW frequency and amplitude f GW = 2xf orb

Binary Compact Objects How do Double Compact Objects Form ? How do Double Compact Objects Form ? What are the Predicted What 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 ?

Binary Compact Objects: Formation from Tauris & van den Heuvel 2003 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!

NS-NS Formation Channel animation credit: John Rowe

Understanding Core-Collapse and NS formation Use known DNS: PSRs B B J and 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? with Bart Willems & Mike Henninger ApJ Letters & ApJ 2004, PRL 2005

Understanding 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? with Bart Willems & Mike Henninger ApJ Letters & ApJ 2004, PRL 2005

Understanding 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? with Bart Willems & Mike Henninger ApJ Letters & ApJ 2004, PRL 2005

What do we learn about Core-Collapse and NS formation ? with Bart Willems & Mike Henninger Tight and Robust Constraints on NS Kick magnitude: Most probable value: ~150 km/s Double Pulsar:

What do we learn about Core-Collapse and NS formation ? with Bart Willems & Mike Henninger Double Pulsar: polar angle between pre- SN orbital velocity V 0 and kick velocity V k Kick is directed opposite to the orbital motion

What do we learn about Core-Collapse and NS formation ? with Bart Willems & Mike Henninger Tight Physical anti-Correlation between: NS progenitor mass and NS kick magnitude Large Mass Loss is balanced by Small Kick and vice versa

What do we learn about Core-Collapse and NS formation ? with Bart Willems & Mike Henninger NS Progenitor Mass NS Kick Magnitude 2-D probability Density distribution

What do we learn about 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 report a spin-tilt measurement 25 (+- 4) deg consistent with our predictions ! of 25 (+- 4) deg consistent with our predictions ! Prediction: spin-tilt smaller than 30-40deg

What Is the Physical Origin 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 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 statistical analysis reveals: zero-kick model likelihood is zero! Typical NS kicks models Zero-kick models

What Is the Physical Origin 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: GR 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 that Merge very soon after formation: Implications for merger rates and GR detection … Models at birth Models at present

Compact Binary Inspiral: Event 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 Rates Problems until recently: Rate Predictions highly uncertain (by ) Lack of quantitative understanding of uncertainties (statistical & systematic)

Compact Binary Inspiral: Event Rates Radio Pulsars in NS-NS binaries NS-NS Merger Rate Estimates (Phinney ‘91; Narayan et al. ‘91; Lorimer & vdHeuvel ‘97; Arzoumanian et al. ‘99) It is possible to assign statistical significance to DNS rate estimates Bayesian analysis developed to derive the probability density of NS-NS inspiral rate Small number bias and selection effects for faint pulsars are implicitly included in our method. with Chunglee Kim et al. ApJ 2002; Nature 2003; ApJ Letters 2004

PSR Survey Simulations count the number of pulsars observed (N obs ) populate a model galaxy with N tot PSRs (same P s & P orb ) N obs follows the Poisson distribution, P(N obs ; ) ---> … … … … … ---> P(N tot )  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 Rates 3 NS-NS : a factor of 6-7 rate increase Initial LIGO Adv. LIGO per 1000 yr per yr ref model: peak % Current Rate Predictions with Chunglee Kim et al. Event Rates:

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 >~ ! So farrate predictions So far, inspiral rate predictions from population calculations only from population calculations with uncertainties of ~ 3 orders of mag We can use NS-NS empirical rates as constraints on population synthesis models

Black Hole Binary Inspiral: Event Rates From Population Synthesis Modeling: log ( events per yr ) PDF BH-BH BH-NS NS-NS with Richard O’Shaughnessy, C. Kim, T. Fragos ApJ 2004, 2005

Black Hole Binary Inspiral: Event Rates Constraints from both tight and wide DNS: with Richard O’Shaughnessy, C. Kim, T. Fragkos NS-NS BH-NS BH-BH 1 advanced LIGO IFO

Plans for the Future … Focus on Astrophysical Interpretation of GW Observations: - Development of optimal data analysis methods for “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: LISA

LISA Astrophysics: 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 between stars and orbit: NOT a pure GR inspiral signal - Black-hole captures in galactic centers around super-massive black holes: event rate predictions and waveform calculations needed …

Thanks to: Postdocs M. Freitag N. Ivanova R. O’Shaughnessy B. Willems P. Grandclement Grad Students T. Fragos C. Kim J. Sepinksky Undergrad Students L. Blecha M. Ihm R. Jones J. Kaplan T. Levin M. Henninger P. Nutzman Funding Sources NASA, NSF Packard Foundation, Research Corporation, NU