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GRAVITATIONAL WAVE SOURCES AND RATES FOR LISA
W. Z. Korth, PHZ6607, Fall 2008
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Outline
Introduction What is LISA? Gravitational waves
Characteristics Detection (LISA design)
Sources Stochastic Monochromatic Chirping
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What is LISA?
Laser Interferometer Space Antenna (LISA) Planned space-based gravitational wave detector
Why in space? Dramatically reduced environmental noise compared to
terrestrial detectors (i.e. LIGO, VIRGO, GEO600, TAMA3000 Longer leg length (5,000,000 km vs. 4 km)
Better strain sensitivity Sensitive at lower frequencies (0.05 mHz – 0.1 Hz)
New sources!
Complications Solar winds Radiation pressure
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Gravitational Waves
Plane wave solution in weak field limit GR is extremely nonlinear near source Far from source, we use a perturbation
Solution to wave equation
with
gµ! = !µ! + hµ!
hµ! = Cµ!eik!x!
Cµ! =
!
""#
0 0 0 00 h+ h! 00 h! !h+ 00 0 0 0
$
%%& k! = {!, 0, 0, !}
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GW Characteristics
Tends to “stretch” a distribution of matter in orthogonal directions, in an oscillating fashion
hµ!!
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Polarizations
+ Polarized Elliptically polarized
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Three separate spacecraft with 2 incoming beams and 2 outgoing beams each. Define two independent Michelson interferometers (for redundancy)
LISA
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Three separate spacecraft with 2 incoming beams and 2 outgoing beams each. Define two independent Michelson interferometers (for redundancy)
LISA
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Sources
Four classifications: Stochastic
Backgrounds
Monochromatic Galactic binaries
Chirping Massive black hole binaries EMRIs
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Stochastic Sources
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Inflationary Waves
Arose from quantum fluctuations in early universe Amplified by cosmic inflation
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Inflationary Waves
Random, essentially “white” over wide range
Very interesting Wave amplitudes determined by potential driving inflation
Direct probe of inflationary physics!
TOUGH to detect Drowned out by foreground sources Current estimates suggest amplitudes ~4-5 orders of magnitude
lower than LISA sensitivity. Side note:
GWs have a distinct effect on CMB photons, may be detected indirectly using this method
10!16 Hz < f < 1010 Hz
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Phase Changes
Additional backgrounds known to have been produced during universal phase changes
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Phase Changes
Example: At electroweak force
separates into electromagnetic and weak nuclear forces Not spatially homogenous
Background!
Estimated that waves borne at this time will have frequencies , right in LISA band Good chance of detection
Tuniverse = 1015 K
f ! 10!2 Hz
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Monochromatic Sources
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Monochromatic Sources
Compact galactic binaries Trillions of binary systems in our galaxy Tens of millions compact (enough)
Radiate GWs in LISA band
GUARANTEED source
Not truly monochromatic, but sllloooww
f =485!
µM2/3(2!f)11/3
MA = MB = MJ !" f = 9.2# 10!18 Hz/sec
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Monochromatic sources
Over-guaranteed?
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Chirping Sources
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Chirping Sources
Massive black hole binaries
For appreciable frequency increase (‘chirp’), need high mass
For a system with
GWs produced start in LISA band and sweep out in a period of between a few months and a few years
f =485!
µM2/3(2!f)11/3
Msystem = 104MJ ! 107MJMA
MB=
120
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Chirping Sources
Monte Carlo simulation showing mass and spin measurement errors for a set of 10,000 binaries randomly distributed on the sky. Solid line: Dashed line:
m1 = 106MJ
m2 = 3! 105MJ
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Chirping Sources
Massive black hole binaries believed to be a side effect of galaxy merger. Depending on conditions, expectations are between a few and a few hundred events over LISA’s lifetime.
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“Even a pessimist who assumes a rather long quasi-stellar object lifetime and only one binary coalescence per newly-formed halo should expect a couple of supermassive black hole binary coalescences during the lifetime of LISA while an optimist might expect to see up to several hundred of these exciting events.”
Martin G. Haehnelt
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Chirping Sources
Extreme Mass Ratio Inspirals (EMRI) Formation:
Compact object (~stellar mass) scattered onto highly eccentric orbit about supermassive galactic black hole
Waveform: Strong-field effects
Complicated chirps
Event Rates Estimates predict 1,000+ events over LISA’s lifetime
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Chirping Sources
EMRI Infalling object executes 10,000 – 100,000 orbits before
coalescence Three periods (converge in Newtonian limit)
Unique GW signature Provides unprecedented description of spacetime near SMBH IF orbit can be tracked throughout infall (difficult)
T! (axial)T" (poloidal)Tr (radial)
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LISA will embody an unprecedented tool for the study of important and exotic processes of the universe. Together with the family of terrestrial detectors, such as LIGO, it represents an entirely new probe of the sky.
Summary
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Acknowledgements
References S. Carroll, Spacetime and Geometry S. A. Hughes, LISA Sources and Science, arXiv: 0711.0188v1 [gr-qc] B. Allen, The stochastic gravity-wave background: source sand detection, arXiv: 9604033v3
[gr-qc] G. Nelemans, http://www.astro.ru.nl/~Nelemans/Research/GWR.html C. Hopman, Astrophysics of extreme mass ratio inspiral sources, arXiv: 0608460 [gr-qc]
Image credits LISA (NASA/ESA) G. Nelemans Albert Einstein Institute Many others! (Google Image Search)
Professor Dr. Bernard Whiting