Introduction to Gravitational Wave Detection

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

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

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

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

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

7. 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

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

9. Quadrupole Gravitational Waves a ring of free test masses h

10. Let’s do the math

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

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

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

14. 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. hij is a wave, so

15. and or 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<), LIGO Low band of LISA

16. 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 COBE, MAP Planck, etc. snapshots only cosmic structure ULF

17. 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 COBE, MAP Planck, etc. snapshots only cosmic structure ULF

18. now ~1000 years 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. The Pulsar Limit

19. 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.)

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

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