1. Gravitational Waves
ASTR 3010
Lecture 24

2. Propagation Speed of Information
EM waves : this should be propagated at c
Object with mass : gravity  curvature in the space-time fabric
change at A  how fast the change would be felt by B A B
Vprop= ∞ Newtonian
Vprop= c General Relativity

3. Gravitational Waves Another confirmation of General Relativity
Hulse-Taylor Binary
PSR J
Binary pulsars
1.4 Msun
7.75 hours of orbit ( Rsun)
59 milli-sec of rotation
1993 Nobel Physics Prize
Gravitational radiation takes away energy from the system
Orbital period decreases 76.5μsec / year (-3.5 m/year)

4. Gravitational Waves versus EM Waves
Gravity is a weak force, but has only one sign of charge. Electromagnetism is much stronger, but comes in two opposing signs of charge.
Significant gravitational fields are generated by accumulating bulk concentrations of matter. Electromagnetic fields are generated by slight imbalances caused by small (often microscopic) separations of charge.
Gravitational waves, similarly, are generated by the bulk motion of large masses, and will have wavelengths much longer than the objects themselves. Electromagnetic waves, meanwhile, are typically generated by small movements of charge pairs within objects, and have wavelengths much smaller than the objects themselves.
Gravitational waves are weakly interacting, making them extraordinarily difficult to detect; at the same time, they can travel unhindered through intervening matter of any density or composition. Electromagnetic waves are strongly interacting with normal matter, making them easy to detect; but they are readily absorbed or scattered by intervening matter.

5. Importance of Gravitational Waves
It can probe more distant (E~1/r) and bizarre places
Near to the black hole
Before the epoch of recombination of Universe : Universe was opaque to EM
t~300,000 years after Big Bang
z~1,100
WMAP cosmic microwave background map

6. Gravitational Waves
Monopole : An object's gravitational monopole is just the total amount of its mass  conservation of mass (can’t radiate!)
Dipole : An object's gravitational dipole is a measure of how much that mass is distributed away from some center in some direction  conservation of momentum (can’t radiate!)
Quadrupole : The quadrupole represents how stretched-out along some axis the mass is. A sphere has zero quadrupole.
Power radiated by two orbiting bodies

7. Gravitational Waves
Two objects orbiting each other in a Keplerian planar orbit (basically, as a planet would orbit the Sun) will radiate.
A spinning non-axisymmetric planetoid — say with a large bump or dimple on the equator — will radiate.
A supernova will radiate except in the unlikely event that the explosion is perfectly symmetric.
An isolated non-spinning solid object moving at a constant speed will not radiate. This can be regarded as a consequence of the principle of conservation of linear momentum.
A spinning disk will not radiate. This can be regarded as a consequence of the principle of conservation of angular momentum.
A spherically pulsating spherical star (non-zero monopole moment or mass, but zero quadrupole moment) will not radiate

8. Propagation of GW Fluctuations in the X-Y plane, prop direction in +z
Amplitude of waves : h (“strain”)
For Earth-Sun, R~1Ly
 h~10-26

9. Detecting Methods : resonant bar
Resonant Bars (“Weber Bar”)
Aluminum cylinder 2m x 1m
Resonant frequency of 1660Hz
Piezoelectric sensors to detect changes in length as small as 10-7 nano meter
Claimed to detect GW from SN1987A, but…

10. Resonant Bar
AURIGA gravity wave detector consists of a 3 m long one-metric-ton aluminum bar that is in thermal contact with a liquid helium reservoir.

11. Detecting Methods : interferometers
Two 4km arms with Fabry-Perot cavities
Can detect GW as small as
LIGO (Laser Interferometer Gravitational Wave Observatory)

12. Range of sensitivity on earth 10-1000 Hz In space 10^-4-1 Hz
Interferometers
Mirror
LIGO (USA, Louisiana & Washington)
VIRGO (ITALY, Pisa)
TAMA (JAPAN)
GEO 600 (GERMANy, Postdam)
LISA (NASA-ESA, In space, 2016)
4 km
Vacuum Pipes
Mirror
Laser 10 Watts
Semi-transparent Mirror
Range of sensitivity on earth Hz
In space 10^-4-1 Hz
Photodetector

13. Detecting Methods : Pulsar timing array
If changes are coherent across a large sky ares  GW!
Due to the passing GW, timings of pulsars change.

14. The network of gravitational wave detectors
LIGO/VIRGO/GEO/TAMA
LISA
ground based laser interferometers
space-based laser interferometer (hopefully with get funded for a 20?? Launch)
LIGO Hanford
LIGO Livingston
ALLEGRO/NAUTILUS/AURIGA/…
Pulsar timing network, CMB anisotropy
resonant bar detectors
Segment of the CMB from WMAP
AURIGA
The Crab nebula … a supernovae remnant harboring a pulsar
ALLEGRO

15. Detection Sensitivity of LIGO

16. Various noise sources

17. Astronomical Sources of GW
Relic background: A stochastic signal from the Big Bang itself, this consists of quantum fluctuations in the initial explosion that have been amplified by the early expansion of the Universe. While the spectral shape of this source can be predicted, its overall strength is highly uncertain, but is constrained by the fact that gravitational wave perturbations are one of several components contributing to the observed temperature fluctuations in the cosmic microwave background. This limits the maximum strength of gravitational waves at cosmological length scales. Two curves are shown: one at the upper limit of the observational constraints, and another an order of magnitude weaker.
Binary background: Another stochastic signal, this one arising from thousands of binary systems emitting gravitational waves continuously in overlapping frequency bands. The individual signals are unresolvable. At long wavelengths (larger than 1014m), the binaries in question are pairs of supermassive black holes (millions of times the mass of the Sun) orbiting in the centers of galaxies. The hump at shorter wavelengths (1013 to 1011m) is contributed by binary white dwarf stars within our own Galaxy.
SMBHB (Super-Massive Black Hole Binaries): Occasionally, one of the supermassive black hole systems mentioned above will merge, producing a huge burst of gravitational waves at millihertz frequencies. Such bursts would be detectable throughout most of the known Universe, though the rate is highly uncertain: one per year is an optimistic estimate.
WDB (White Dwarf Binaries): Above the white dwarf stochastic background are a few thousand individually-resolvable white dwarf binary systems in our Galaxy. Some of these systems have already been charted with conventional astronomy, and thus would be known callibrators for future gravitational-wave detectors.
EMRI (Extreme-Mass-Ratio Inspirals): These are compact stellar remnants (white dwarfs, neutron stars, or stellar-mass black holes only a few times more massive than our Sun) in the process of being captured and swallowed by a supermassive black hole (millions of times more massive than the Sun).
BHB (Black Hole Binaries): These are binary systems consisting of two stellar-mass black holes (a few times the mass of the Sun).
NSB (Neutron Star Binaries): These are binary systems consisting of two neutron stars.
NS (Neutron Stars): This refers to the gravitational waves generated by individual neutron stars as they spin. In order to generate gravitational waves, the neutron star must deviate from pure axisymmetry. Several mechanisms have been proposed for generating or sustaining such asymmetries, but their magnitudes are highly uncertain; the plot indicates some optimistic upper limits.