Astrophysics of Gravitational-Wave Sources

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

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

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

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

5. Source: Time-dependent mass quadrupole moment tensor Ijk: Amplitude: Gravitational Radiation

6. The Effect of Gravitational Waves 2 polarizations 10 Mo BH at the Galactic center:h ~ 10 -17 10 Mo BH at the Virgo cluster:h ~ 10 -20

7. 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'

8. Do Gravitational Waves really exist ? orbital decay Measurement of orbital decay is consistent with the gravitational radiation prediction within 0.3% ! PSR B1913+16 Weisberg & Taylor 03

9. PA = 22ms PB = 2.7s Porb = 2.4hr e = 0.09 PSR J0737-3039: The first DOUBLE PSR and the most relativistic DNS so far! Burgay et al. 2003 Beyond the Hulse-Taylor Binary… more relativistic DNS have been discovered: PSR B1534+12 and the most recent one: PSR J1756-2251

10. LIGO Virgo GEO TAMA How about direct detection? Coincidence: detection confidence source localization signal polarization AIGO

11. GW Sources: High Frequency

12. GW Sources: Chirps inspiral chirp fGW = 2xforb GW emission causes orbital shrinkage leading to higher GW frequency and amplitude

13. Binary Compact Objects • How do Double Compact Objects Form ? • What are the Predicted Binary Inspiral Event Rates ? (NS-NS, BH-NS, BH-BH) • What are the Best Methods for Gravitational-Wave Data Analysis ?

14. 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! from Tauris & van den Heuvel 2003

15. NS-NS Formation Channel animation credit: John Rowe

16. Understanding Core-Collapse and NS formation WHAT? Use known DNS: PSRsB1913+16 B1534+12 J0737-3037 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) with Bart Willems & Mike Henninger ApJ Letters & ApJ 2004, PRL 2005

17. Understanding Core-Collapse and NS formation HOW? 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 with Bart Willems & Mike Henninger ApJ Letters & ApJ 2004, PRL 2005

18. Understanding Core-Collapse and NS formation WHY? 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 with Bart Willems & Mike Henninger ApJ Letters & ApJ 2004, PRL 2005

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

20. What do we learn about Core-Collapse and NS formation ? with Bart Willems & Mike Henninger Double Pulsar: polar angle between pre-SN orbital velocity V0 and kick velocity Vk Kick is directed opposite to the orbital motion

21. 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

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

23. 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 Prediction: spin-tilt smaller than 30-40deg Thorsett et al. 2005 report a spin-tilt measurement of 25 (+- 4) deg consistent with our predictions !

24. Models with typical NS kicks Models with zero NS kicks 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 …

25. 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 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!

26. 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 Models with typical NS kicks: P(e) at birth P(e) at present, affected by GR

27. 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 present Models at birth

28. Compact Binary Inspiral: Event Rates Empirical Estimates Based on radio Theoretical Estimates Based on models of binary evolution until binary compact objects form. for NS -NS, BH -NS, and BH -BH pulsar properties and survey selection effects. for NS -NS only

29. Compact Binary Inspiral: Event Rates Problems until recently: • Rate Predictions highly uncertain (by 103-104) • Lack of quantitative understanding of uncertainties (statistical & systematic)

30. It is possible to assign statistical significance to DNS rate estimates Bayesian analysis developed to derive the probability densityof 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 Compact Binary Inspiral: Event Rates NS-NS Merger Rate Estimates Radio Pulsars in NS-NS binaries (Phinney ‘91; Narayan et al. ‘91; Lorimer & vdHeuvel ‘97; Arzoumanian et al. ‘99)

31. Earth PSR Survey Simulations assume PSR distribution functions in luminosity & space consider each observed pulsar separately (adopt spin & orbital periods of the observed DNS system) populate a model galaxy with Ntot PSRs (same Ps & Porb) count the number of pulsars observed (Nobs) Nobs follows the Poisson distribution, P(Nobs; <Nobs>) ---> … … … … … ---> P(Ntot) carefully model thresholds of PSR surveys

32. Compact Binary Inspiral: Event Rates with Chunglee Kim et al. Current Rate Predictions 3 NS-NS : a factor of 6-7 rate increase Event Rates: Initial LIGO Adv. LIGO per 1000 yr per yr ref model: peak 35 175 95% 10 - 120 35 - 630

33. 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 ! Compact Binary Inspiral Rates: What about Black Hole Binaries? • BH-NS binaries could in principle be detected as binary pulsars, BUT… 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

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

35. 1 advanced LIGO IFO Black Hole Binary Inspiral: Event Rates with Richard O’Shaughnessy, C. Kim, T. Fragkos Constraints from both tight and wide DNS: NS-NS BH-NS BH-BH

36. 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

37. Beyond Earth-Bound: LISA

38. 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 …

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