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? /2 Traveling wave, normal incidence Corner cubes arrayed in a disk l j = h ij l j h ij = grav. field Key Facts: Transverse, area-preserving shear Deformation proportional to separation No inertial acceleration!
Gravity and acceleration Two satellites in Earth orbit Satellites in free-fall: neither feels any force Periodic change in separation... but no acceleration! Accelerating coordinate system: fictional force
Gravitational radiation: How is it generated? 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 G [ ] TT h ij = 2 r c Qij, [] TT 4 Q ij = ( ) d 3 x x i x j r2 3 δ ij ρ ( Make transverse & area preserving )
Gravitational radiation: How strong is it? Spinning dumbbell l l l l ~10 39 1 Km r ~10 23 100 Mpc r M 1000 Kg M 3M sun v 300 m s Binary neutron star system 2 2 150 Km R f orb ~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: N G,NS ~1 MWEG over 1 week Target: N G,NS ~ 600 MWEG over 1 year Adv. LIGO: N G,NS ~ 6x10 6 MWEG over 1 year
Astronomical Sources: Rapidly Rotating NSs 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 J1939+2134, B0021-72C, B0021-72F, 10-5 -10-4 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 Initial, advanced LIGO Limits on for 1 yr observation of pulsar @ 10 Kpc
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: 5x10 6 Km No Seismic Noise Tricky bits: Interferometry in space Controlling buffeting by solar wind, other forces Courtesy Rutherford Appleton Laboratory, UK
Characterizing Detector Noise Z T /2 < h 2 1 n >= lim h n (t) 2 dt T T T /2 { hn (t) t < T /2 h n,t 0 t > T /2 Z < h 2 1 n >= lim h n,t (t) 2 dt T T Z = lim h n,t ( f ) 2 df = = 1 T Z T Z 0 lim T S n ( f )df 1 T h n,t ( f ) 2 df 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: 2 = 2 Z 0 h( f ) 2 S n ( f ) df S n (f) 1/2 [Hz 1/2 ] 10 12 10 14 10 16 10 18 10 6 10 4 10 2 10 0 Frequency [Hz] LISA Noise PSD
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 Merger Numerical relativity: highly dynamical & nonlinear Ringdown Perturbation theory: discrete quasi-normal mode spectrum
Orbit Evolution During Inspiral Power radiated at twice orbital frequency Inspiral rate determined by chirp mass Radiation amplitude increases with orbital frequency f orb = 1 2πM ( 5 256 M := µ 3/5 M 2/5 ) M T c t But de/df decreases with frequency
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?