Download Chapter 10: The Sun-

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 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 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
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
MBH/MNS=3
Nonrotating BH
Different NS
compactnesses
Need h<10-22
at 1-3 kHz
Shibata et al. 2009
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 highmass 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 150250 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
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
f
ISCO=4400Hz/[Mtot(1+z)]
=100 Hz if Mtot=30, z=0.5
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
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
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 2002
L. Wen 2003
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.
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 >1 IMBH in single cluster?
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
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 shortlived 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?
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
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)