Compact Binaries

1. Compact Binaries Cole Miller, University of Maryland

2. Outline • Overview of amplitudes and frequencies • Neutron stars and black holes • Benefits of detection at ~1 Hz The most massive white dwarfs Long lead times for telescopes Nonzero eccentricities? • Intermediate-mass black holes

3. Amplitude of Gravitational Waves Binary of reduced mass , total mass M. At luminosity distance d, frequency fGW, dimensionless strain amplitude is h=2x10-22 (fGW/10Hz)2/3(Mch/10 Msun)5/3(100Mpc/d) where Mch5/3=M2/3 defines the “chirp mass”.

4. Frequency of Waves The frequency at the innermost stable circular orbit (ISCO) for a nonrotating hole is fGW(ISCO)=4.4x103 Hz (Msun/M) For rotating, up to fGW(ISCO)~2x104 Hz (Msun/M) More generally, object of average density  has maximum frequency ~(G)1/2 Neutron star: ~2000 Hz White dwarf: up to ~1 Hz

5. NS-NS Binary Formation • Observation of NS-NS binaries calibrates models Big model uncertainties! • Rate dominated by field binaries, not binaries in globular clusters • Best estimate: 10-6-10-4 yr-1 MWEG-1 • Detection rates: 10s per year for next generation http://www.astro.lu.se/Research/OTA/compactBinaryFormation.jpg

6. Benefits of NS-NS/NS-BH • 10s/yr NS mass determinations, especially accurate for asymmetric systems such as BH-NS • Radius measurements from phase; if dR/R<0.1, goes a long way towards resolving EOS MBH/MNS=3 Nonrotating BH Different NS compactnesses Need h<10-22 at 1-3 kHz Shibata et al. 2009

7. Stellar-mass BH binaries: Born • None observed (how could they be!) Rates unclear • Rely on theory Uncertain common envelope, kicks, etc. • Masses, mass ratios, spins not well constrained • AdLIGO: 10s/yr???

8. Stellar-mass BH Binaries: Made • In dense stellar env, can swap into MS bin • Biases towards high-mass objects • Rates depend on retention in system Easy escape from GC Tougher from nucleus C. Miller

9. Stellar-mass BH Binaries 3: Nuclear Star Clusters • Common in centers of small galaxies Follow M- relation • Escape speeds 150-250 km/s • BH retained after SN • Almost all binaries stay in center after 3-body interactions GW recoil can eject Miller & Lauburg 2009

10. Stellar-mass BH Binaries 3: Nuclear Star Clusters Advanced LIGO noise curve Grav. physics group, Cardiff • AdLIGO estimate: Tens to >100 per year • Strong bias towards massive binaries Heavy things exchange • Low frequencies mean num rel is especially important fISCO=4400Hz/[Mtot(1+z)] =100 Hz if Mtot=30, z=0.5

11. Spin Measurements How can we measure spins? • Fe K line profile fits (Tanaka et al. 1995) • Continuum energy spectral fits • QPO modeling My candidate for most reliable is the line profile fits, but all have large systematic issues (known unknowns and unknown unknowns!) Best estimates of spin vary, from ~0.7 to >0.98 depending on source

12. The Most Massive WD • ~108-9 WD binaries in Milky Way • Even small fraction with M~1.4 Msun gives large number; new category of sources fGW=1 Hz http://cococubed.asu.edu/images/coldwd/mass_radius_web.jpg

13. Advance Warning of Merger • EM counterparts to mergers: lots of info! Precise localization Nature of transients • Time to merger scales as finit-8/3 • At 1 Hz, could be identified days in advance • Key: how soon could GW be localized? Rotation of Earth? 1.4 Msun - 1.4 Msun binary

14. Nonzero Eccentricities? • Usually, think of binary GW as circular ~true for >10 Hz or field binaries • Dynamical interactions can change, e.g., Kozai in dense systems • e~1/f for e<<1 • Low freq important for inferring dynamic origin Miller & Hamilton 2002 L. Wen 2003

15. Intermediate-Mass Black Holes Mass between 102 and 104 Msun Too massive to have formed from solitary star in current universe, but smaller than standard supermassive black holes.

16. Context and Connections • In z~5-30 universe, seeds for SMBH • In local universe, probes of star cluster dynamics • Potentially unique sources of gravitational waves (ground and space) Wechsler et al. 2002

17. Formation of IMBHs >1 IMBH in single cluster? • Problem: ~103 Msun too much for normal star! • Population III stars Low Z; weak winds • Collisions or mergersNeeds dense clusters Young: collisions Old: three-body Gurkan et al. 2006 Portegies Zwart & McMillan

18. IMBH-IMBH Visibility • ~few x 1000 Msun binary visible to z>5. • Reasonable rates: few tens per year at >1 Hz • Unique probe of dense cluster star formation Fregeau et al. 2006

19. Conclusions • Binaries are the only guaranteed gravitational wave sources • Detection of NS-NS or NS-BH will lead to great advances in knowledge of EOS • Nuclear star clusters are promising factories for compact binaries • Many benefits of low frequency, including: Possible detection of white dwarfs Long lead time for EM observations Intermediate-mass black holes

20. What Can Massive WD Do For You? • Precise maximum mass depends on composition, other properties • Massive WD (in binaries with normal stars) thought to be Type Ia SNe progen. • Mergers would be spectacular but short-lived EM events How much lead time do we have?

21. Why Are We Not Sure? • Stellar-mass (5-20 Msun) and supermassive (106-1010 Msun) BH are established with certainty • Why not IMBH (102-104 Msun)? • Lack of dynamical evidence Too rare for easy binary observations Too light for easy radius of influence obs • Attempts being made, but settle for indirect observations in the meantime

22. Low-Mass SMBH? Central massive black holes Masses below ~106 Msun are inferred indirectly, but extrapolation suggests M~104 Msun for numerous small galaxies Greene and Ho 2006

23. Stellar-Mass BH Spin • Is spin changed much by accretion? King & Kolb 1999 • Not a lot, if prograde Little mass accreted • Current spin parameter is ~good representation of spin at birth • Direction not so clear!

24. Observing GW from IMBH • Stellar-mass BH with IMBH? Promising at >1 Hz (Mandel et al. 2008) • IMBH with IMBH Plausible with low freq; occur if binary fraction >10% (Fregeau et al. 2006)