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?