gravitational waves & intermediate mass black...
TRANSCRIPT
Gravitational Waves & Intermediate Mass
Black Holes Lee Samuel Finn
Center for Gravitational Wave Physics
Outline
• What are gravitational waves?
• How are they produced?
• How are they detected?
• Gravitational Wave Detectors
• Gravitational Waves and IMBHs
Gravitational radiation: What is it?
• Key Facts:
• Transverse, area-preserving shear
• Deformation proportional to separation
• No inertial acceleration!
Traveling wave,normal incidence
/2
Corner cubesarrayed in a disk
lj = hij ljhij = “grav. field”
• Two satellites in Earth orbit
• Satellites in free-fall: neither feels any force
Gravity and acceleration
Periodic change in separation ... but no acceleration!Accelerating coordinate system: fictional force
• Slow-motion (multipole) expansion
• Monopole contribution?• Charge monopole is mass• Mass conservation ⇒ No monopole radiation
• Dipole contribution?• d(charge dipole)/dt is total momentum• Momentum conservation ⇒ no dipole radiaton
• Radiation quadrupole at leading order
Gravitational radiation: How is it generated?
hij = 2
rGc4
[Q̈ij
]TT
, []TT
≡
(Make transverse
& area preserving
)
Qij =∫
d3x(xixj −
r2
3δij
)ρ
• Spinning dumbbelll
l~ 10 39 1 Km
r
M
1000 Kg
v
300ms
2
Gravitational radiation: How strong is it?
l
l~ 10 23100 Mpc
r
M
3Msun
2150 Km
R
• Binary neutron star system
forb~125 Hz
Detecting Gravitational Waves: Interferometry
t–
LIGO: The Laser Interferometer Gravitational-wave Observatory
• United States effort funded by the National Science Foundation
• Two sites
• Hanford, Washington & Livingston, Louisiana
• Construction from 1994 – 2000
• Commissioning from 2000 – 2004
• Interleaved with science runs from Sep’02
• First science results gr-qc/0308050, 0308069, 0312056, 0312088
Astronomical Sources:NS/NS Binaries
• Now: NG,NS~1 MWEG over 1 week
• Target: NG,NS ~ 600 MWEG over 1 year
• Adv. LIGO: NG,NS ~
6x106 MWEG over 1 year
Astronomical Sources:Rapidly Rotating NSs
Initial, advanced LIGO Limits on for 1 yr observation of pulsar @ 10 Kpc
range Pulsar
10-2-10-1 B1951+32, J1913+1011, B0531+21
10-3-10-2
10-4-10-3 B1821-24, B0021-72D, J1910-5959D, B1516+02A, J1748-2446C, J1910-5959B
10-5-10-4
J1939+2134, B0021-72C, B0021-72F, B0021-72L, B0021-72G, B0021-72M, B0021-72N, B1820-30A, J0711-6830, J1730-2304, J1721-2457, J1629-6902,
J1910-5959E, J1910-5959C, J2322+2057
10-6-10-5 J1024-0719, J2124-3358, J0030+0451, J1744-1134
Preliminary S2 upper limits on ellipticity of 28 known pulsars
Astronomical Sources: Stochastic Background
• Primordial or “confusion-limit”
• Now: GW < 2x10-2 (preliminary S2 result)
• Target: GW < 10-6 in (40,150) Hz over 1 yr
• Advanced LIGO: GW < 10-9 in (10, 200) Hz over 1 yr
Laser Interferometer Space Antenna
• Joint NASA, ESA project
• Launch 2013
• Advantages:
• Longer arms: 5x106 Km
• No Seismic Noise
• Tricky bits:
• Interferometry in space
• Controlling buffeting by solar wind, other forces
Courtesy Rutherford Appleton Laboratory, UK
Characterizing Detector Noise
< h2n >= limT→
1T
Z T/2
−T/2hn(t)2dt
hn,T≡{hn(t)|t| < T/20 |t| > T/2
< h2n >= limT→
1T
Z−hn,T(t)2dt
= limT→
1T
Z−h̃n,T( f )2d f
=Z−limT→
1Th̃n,T( f )2d f
=Z0Sn( f )d f
Power Spectral Density: Contribution per unit frequency
to mean-square noise
Sensitivity, cont’d
• What is sensitivity to a particular source?• PSD is source
independent
• Sensitivity characterized by “signal to noise” ratio• Depends on source,
detection technique
• Best attainable sensitivity:
106
104
102
100
1018
1016
1014
1012
Frequency [Hz]
Sn(f
)1/2 [
Hz
1/2 ]
LISA Noise PSD2 = 2
Z0
|h̃( f )|2Sn( f )
d f
Gravitational Waves and IMBHs
• Formation
• IMBH binary system coalescence
• IMBH Extreme Mass-Ratio Inspiral (EMRI)
Formation By Stellar Collapse
• Collapse of supermassive population III stars (M>260 M )
• Asymmetric collapse
• Bar mode or other instabilities; core bounce
• Asymmetric neutrino emission
• Core convection
IMBH Binary Coalescence
• Inspiral Perturbation theory: adiabatic orbit decay driven by rad. reaction
• RingdownPerturbation theory: discrete quasi-normal mode spectrum
• MergerNumerical relativity: highly dynamical & nonlinear
Orbit Evolution During Inspiral
• Power radiated at twice orbital frequency
• Inspiral rate determined by “chirp mass”
• Radiation amplitude increases with orbital frequency
• But dE/df decreases with frequency
forb =1
2πM
(5
256
M
Tc − t
)
M := µ3/5M2/5
Extreme Mass Ratio Inspiral on IMBH
• Neutron star or solar mass black hole orbiting an IMBH
• Scatters into loss cone may lead to moderate to high e “zoom-whirl” orbits: depends on IMBH mass
• Radiation pulses at periastron
• Also IMBH on SMBH
Questions
• Formation:• Supermassive stellar collapse: Rate? Angular
momentum? Asymmetry? Bar mode? Redshift? • Hierarchical build-up: Merger rate? Redshift?
• Coalescence:• Redshift? Rate? Eccentricity? IMBH spin?
• EMRI: • How is loss-cone filled (i.e., P(E,L|M))? Rate?
Redshift? IMBH, SMBH Spin?