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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? - PowerPoint PPT Presentation
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Compact BinariesCole 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 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”.
Frequency of WavesThe frequency at the innermost stablecircular 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
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
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. 2009
Need h<10-22
at 1-3 kHz
MBH/MNS=3Nonrotating BHDifferent NScompactnesses
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 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
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 curveGrav. physics group, Cardiff
fISCO=4400Hz/[Mtot(1+z)] =100 Hz if Mtot=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 theline profile fits, but all have largesystematic issues (known unknownsand unknown unknowns!)Best estimates of spin vary, from~0.7 to >0.98 depending on source
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
http://cococubed.asu.edu/images/coldwd/mass_radius_web.jpg
fGW=1 Hz
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
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 2002L. Wen 2003
Intermediate-Mass Black Holes
Mass between 102 and 104 Msun
Too massive to have formed from solitary star in current universe, butsmaller than standard supermassiveblack 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: ~103 Msun 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. 2006
Portegies Zwart & McMillan
>1 IMBH in single cluster?
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
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 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
Low-Mass SMBH?
Greene and Ho 2006
Masses below~106 Msun areinferred indirectly,but extrapolationsuggests M~104 Msun
for numerous smallgalaxies
Central massiveblack 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)