High energy Astrophysics

Mat Page

Mullard Space Science Lab, UCL

13. Gravitational waves

12. Gravitational Waves

• This lecture:• What are they?

• How are they made?

• Detection: indirect methods

• Detection: direct methods

• Gravitational wave astronomy

Slide 2

• Waves in the gravitational field• We are used to tides on the earth.

– differential gravitational forces due to the difference in distance from the moon to the near and far parts of the Earth.

• Imagine if the sun was a binary star rotating rapidly and you have on the earth a test particle that samples the gravitational field– It would oscillate due to the changing gravity– We can see that an oscillating body will produce a

gravity wave, somewhat analogous to the way an oscillating charge produces an electromagnetic wave

What are gravitational waves?Slide 3

• Mass behaves different to charge.

• Momentum is conserved – Proper treatment of gravitational radiation is

hideous – whole chapter of Misner, Thorne and Wheeler.

– Whenever mass is accelerated one way, other masses experience equal and opposite change in momentum in the other direction

– Radiation does not depend on the dipole moment, so it doesn’t just move things up and down.

But gravitational waves are a little differentSlide 4

• Why are gravitational waves important?

• Predicted by Einstein’s general relativity – Important, testable prediction of the theory.

• Has important astrophysical consequences: – Can be a significant energy loss mechanism– Can cause compact orbits to decay

• Completely different means of astronomical observation– Potentially even more revolutionary than

radio astronomy or X-ray astronomy!

Before we get any further:Slide 5

Displacement of test particles by a gravity wave

Slide 6

• Just like electromagnetic waves, gravitational radiation is able to cause acceleration of external systems and so it carries energy.

• If the separation between orbiting systems is L, power emitted can be written:

Energy of a gravity wave

PGW ~ c5

GGMc2L( ) 5

Slide 7

• Now there is a maximum: L cannot be smaller than half the Schwarzschild radius

• So no pair of orbiting bodies can emit more than 4x1052 W regardless of their mass

• For the Earth around the Sun, about 200W are emitted – so our orbit should last another 1023 years before it decays by gravitational radiation

• When dimensions of orbit approach the Schwarzschild radius, gravitational radiation is pretty serious.

Slide 8

• Very compact binary systems lose energy rapidly by gravitational radiation.

• If short -ray bursts are caused by the coalescence of neutron stars or black holes, there should be a strong gravitational wave signal as the orbit rapidly decays.

So: some obvious predicted sources and consequences of gravitational waves:

Slide 9

Indirect detection

• Gravitational waves remove energy from an orbiting system.

• If we find a system with well defined orbital parameters that imply it should be radiating gravitational radiation– We can predict how fast the orbit should be

slowing due to gravitational radiation– Measure and compare

Slide 10

Binary pulsar• Binary system of two orbiting neutron stars,

one of which a pulsar, discovered by Joseph Taylor and Russel Hulse in 1975. – Orbital period 7.8 hours.– Pulse period 0.059s

• Pulses combined with general relativity allow very accurate determination of the binary parameters.

• Orbital period change prediction in agreement with measurement of rate of period change = -2.1 + - 0.4 x 10-12

• Secured 1993 Nobel prize!

Slide 11

Ultracompact binaries

• The pulsar in the binary pulsar enabled accurate determination of the orbital parameters, but this is not the most extreme binary system in the galaxy.

• There are now (at least) 3 ultracompact binaries known, in which both stars are white dwarfs in which the orbital period is less than 10 minutes!

• All 3 were discovered as X-ray sources within the last 15 years.

• Two of these were discovered by Gavin Ramsay of MSSL and colleagues.

• They will make excellent test cases for gravitational radiation.

Slide 12

Direct detection• The principal observable effect of gravitational

waves is the slight fractional distortion in the distance between two points.

• Called ‘gravitational strain’.• For reference, strain expected from a maximally

emitting source 1kpc distant, the 1kHz strain is only 10-14

• More realistic supernova producing a neutron star a Mpc away may produce a strain more like 10-20

– Absurdly small – atomic nucleus added to a 1 AU baseline

• Two types of detectors: – Resonant bars– Laser interferometers

Slide 13

Resonant bars

• Pioneered by J. Weber.• Gravitational strain will make bars resonate, - like

making a bell ring (but very small amplitude).• 1969 Weber published detection of bursts of

gravitational radiation – about 3 per day(!) using aluminium cylinders about 2m long and resonant frequency 1.6 kHz

• Levine and Garwin (1973) failed to detect any gravity waves with similar apparatus – Weber was not detecting gravity waves.

• Gravity waves have not been detected with resonant bars…

Slide 14

Laser interferometers

• New gravitational wave experiments based on laser interferometers.

• Laser light is transmitted along 2 perpendicular paths, reflected at each end and recombined in the centre to produce interference fringes.

• Movement of the fringes indicates relative movement of the two arms.

Slide 15

Geo 600 (600m German/UK) in HannoverSlide 16

Laser interferometer gravitational-wave observatory (LIGO)

Slide 17

LIGO Hanford interferometer

Slide 18

LIGO

• Two interferometers, Livingstone and Hanford in US. More perhaps to be added.

• The arms are 4km long. The whole light path is in vacuum (all 4km x2 at each station!)

• Two stations so that terrestrial interference such as small scale seismic activity is not confused with gravitational waves

Slide 19

Schematic of LIGO

Slide 20

One arm of the Livingstone interferometer

Slide 21

The interferometer station at Livingstone

Slide 22

So do we expect them to detect gravitational waves?

• Yes!

• But maybe not as soon as the gravitational wave people always claim!

• LIGO will only be sensitive to high-frequency gravitational waves.

• For slower gravitational waves (e.g. from supermassive black holes merging) the only option is space!

Slide 23

Laser interferometer space antenna (LISA)

• Recently selected to be an ESA mission launching 2034.

• By going into space can get much longer interferometer

Slide 24

LISA formation Slide 25

We can really do gravitational wave astronomy with LISA!

Slide 26

Some key points:

• Gravitational radiation is a phenomena predicted from general relativity.

• (sort of) the gravitational equivalent of electromagnetic radiation.

• Causes small oscillations in the fractional displacement between points in space.

• Important energy loss mechanism in very close binaries.

• Detected indirectly in the binary pulsar• Laser interferometers should be capable of

detecting astronomical sources by gravitational radiation

• Could be truly revolutionary new astronomy

Slide 27