Gravitational Wave Detection

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Presentation transcript:

Gravitational Wave Detection Introduction to Gravitational Wave Detection Ronald W. Hellings Montana State University PTA Workshop Penn State 7/20/05

What is a gravitational wave? space A 2-D analogy motion in this dimension is meaningless 2 free masses The masses track each other with lasers

The gravitational wave is a wave of curvature each slice is a section of an arc of constant radius

As a gravitational wave passes through the space... the free masses remain fixed at their coordinate points while the distance between them

increases due to the extra space in the curvature wave. The laser signal has to cover more distance and is delayed

Why are gravitational waves called “a strain in space”? points that are close have little space injected between them points that are further away have more space injected between them

Quadrupole Gravitational Waves a ring of free test masses h+ less space more space

Quadrupole Gravitational Waves a ring of free test masses h

Let’s do the math

Geometry elliptical polarization plane wave polarization angle  polarization angle plane wave propagation vector s pulsar Earth

The Gravitational Wave Metric Tensor e.g. choose the z-axis along and the x-axis so  = 0. Then

The path of the radio signal from the pulsar to the Earth is a null path, so Approximate and integrate where

hij is a wave, so reception occurs at t = t, x = 0 emission occurs at t = t  s, so The change in distance is proportional to the integral of the wave amplitude.

So let’s get an observable that is proportional to the wave Gravitational waves are proportional to the time derivative of pulsar arrival time residuals. But... in the long wavelength limit (s<), and or LIGO Low band of LISA

The Gravitational Wave Spectrum Type Range Run Time Sources Instrument 10 Hz  1000 Hz compact stars bars, LIGOs HF one per day 0.1 Hz  10Hz one per a few days MAGGIE, lunar LIGO MF ? 10 mHz  10 mHz binaries SMBHs LF one per year LISA 1 nHz  10 mHz once in a lifetime cosmic astrophysics VLF PTA 10 nHz  0 Hz snapshots only cosmic structure COBE, MAP Planck, etc. ULF

The Gravitational Wave Spectrum Type Range Run Time Sources Instrument 10 Hz  1000 Hz compact stars bars, LIGOs HF Long wavelength limit one per day 0.1 Hz  10Hz one per a few days MAGGIE, lunar LIGO MF Long and short regimes ? 10 mHz  10 mHz binaries SMBHs LF Long and short regimes one per year LISA 1 nHz  10 mHz once in a lifetime cosmic astrophysics Short wavelength only VLF PTA 10 nHz  0 Hz snapshots only cosmic structure COBE, MAP Planck, etc. ULF

The Pulsar Limit Every pulsar in every direction has correlated timing noise due to this term. This allows a weighted correlation analysis to optimally use data from multiple pulsars. ~1000 years now

The correlated part of the timing noise For the nth pulsar in the direction sn, this may be written (This generalizes the result of Hellings & Downs, 1983, which assumed plane-polarized gravitational waves.)

The cross-correlation of data from 2 pulsars will produce If are isotropic, and uncorrelated, then where But should be uncorrelated? IT DEPENDS ON THE SOURCE!

Needs Calculation of for plane polarization  done Calculation of and for general polarization Thought on sources of stochastic gravitational background