Compact Binaries Cole Miller, University of Maryland

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

Amplitude of Gravitational Waves Binary of reduced mass , total mass M. At luminosity distance d, frequency f GW, dimensionless strain amplitude is h=2x (f GW /10Hz) 2/3( M ch /10 M sun ) 5/3 (100Mpc/d) where M ch 5/3 =  M 2/3 defines the “chirp mass”.

Frequency of Waves The frequency at the innermost stable circular orbit (ISCO) for a nonrotating hole is f GW (ISCO)=4.4x10 3 Hz (M sun /M) For rotating, up to f GW (ISCO)~2x10 4 Hz (M sun /M) More generally, object of average density  has maximum frequency ~(G  ) 1/2 Neutron star: ~2000 Hz White dwarf: up to ~1 Hz

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: yr -1 MWEG -1 Detection rates: 10s per year for next generation

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 Shibata et al Need h< at 1-3 kHz M BH /M NS =3 Nonrotating BH Different NS compactnesses

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???

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

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

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

Spin Measurements Fe K  line profile fits (Tanaka et al. 1995) Continuum energy spectral fits QPO modeling How can we measure spins? 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

The Most Massive WD ~ WD binaries in Milky Way Even small fraction with M~1.4 M sun gives large number; new category of sources f GW =1 Hz

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

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

Intermediate-Mass Black Holes Mass between 10 2 and 10 4 M sun Too massive to have formed from solitary star in current universe, but smaller than standard supermassive black holes.

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

Formation of IMBHs Problem: ~10 3 M sun too much for normal star! Population III stars Low Z; weak winds Collisions or mergers Needs dense clusters Young: collisions Old: three-body Gurkan et al Portegies Zwart & McMillan >1 IMBH in single cluster?

IMBH-IMBH Visibility ~few x 1000 M sun 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

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

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?

Why Are We Not Sure? Stellar-mass (5-20 M sun ) and supermassive ( M sun ) BH are established with certainty Why not IMBH ( M sun )? 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

Low-Mass SMBH? Greene and Ho 2006 Masses below ~10 6 M sun are inferred indirectly, but extrapolation suggests M~10 4 M sun for numerous small galaxies Central massive black holes

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!

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)