Jeffrey Silverman Ay 250: Transient Universe April 24, 2007

1. Gravitational Wave Astronomy: Past, Present, and Future~or~How To Get Lots of Science Out of Null Results Jeffrey Silverman Ay 250: Transient Universe April 24, 2007

2. Introduction to Gravity Waves (GW) • E-M radiation observations biased towards “hot” objects. • GW observations biased toward compact, massive, rapidly moving objects. • GW astronomy will open “a whole new window” on the sky (much like the advent of radio and X-ray astronomy). • GWs probe places with extreme gravity: • Usually opaque to E-M radiation. • Great places to test GR and other gravitational theories.

3. The Physics of GWs • Like Maxwell’s Equations (E-M waves), Einstein’s field equations have radiative solutions. • In Einstein’s formulation, GWs propagate at c (i.e. the graviton has zero mass). • GWs are produced by accelerated mass-energy (like E-M waves produced by accelerated charges). • Also like E-M waves, flux falls as r-2. • GW exist in all theories of gravity. c. 1947, Princeton University

4. More Physics of GWs • The first non-vanishing radiative multipole is the quadrupole. • There are two independent polarizations separated by 45˚: h (“h-cross”) and h+ (“h-plus”). • In general, GWs consist of a linear combination of the two states. • Einstein never took GWs seriously, he thought their effect was just too small to ever be detected. • Arthur Eddington commented, “Gravitational waves propagate at the speed of thought.” h h+ LIGO website Wikipedia Wikipedia

5. What Will We See? • Strength of GWs best expressed as a dimensionless quantity, the strain: h ≡ DL / L (i.e. the fractional length change). • Assuming GWs couple only to the quadrupole moment: • If the energy ~ Mc2 then: h ~ 510-14 / (r / pc)

6. What Will We See? • 1M of GWs  h ~ 510-14 / (r / pc) • Galactic center (8kpc)  h ~ 10-17 • Virgo cluster (17Mpc)  h ~ 10-21 • Hubble distance (c/H0~4Gpc)  h ~ 10-23 • This OoM estimate is optimistic; most sources will radiate much less than 1M in GWs. • Notice strain goes as r-1 (flux goes as r-2). • Note that the strain is tiny NOT because the radiated energy is small (it’s huge), but because space-time is a “stiff medium”.

7. What Else Will We See? • GW sources cannot be much smaller than a Schwarzschild radius: 2GM / c2 • They also cannot emit strongly at periods shorter than the light travel time around the circumference: P  2pRSch / c  4pGM / c3 • This implies frequencies (f = P-1): f  c3 / 4pGM ~ 1.6104 Hz (M / M)

8. (Indirect) Evidence of GWs • PSR B1913+16 was the first binary pulsar to be discovered (Hulse & Taylor 1975). • Observed for over 30 years. • Weak radio source (1 mJy at 1400 MHz). • Joseph H. Taylor Jr. and Russell A. Hulse shared the Nobel Prize in Physics in 1993: "for the discovery of a new type of pulsar, a discovery that has opened up new possibilities for the study of gravitation." c. 1993, Nobel Foundation c. 1993, Nobel Foundation

9. GWs Are Out There! • Orbital parameters for PSR B1913+16 are known to extremely high accuracy (both relativistic and non-relativistic measurables). • Binary should emit energy as GWs  system loses energy  orbit should shrink  the period should decrease • GR says the rate of period decrease is: (Weisberg & Taylor 2004) • Using the measured values and correcting for the relative acceleration between the solar system and the binary:

10. Building Up Our Confidence • The dominant dissipation in the binary is energy loss by GWs (not mass loss or tidal drag). • No GWs directly detected yet. • However, the Hulse-Taylor PSR has convinced us they exist (and that we understand them relatively well). Weisberg & Taylor 2004

11. Orbital Shrinkage • The two NSs will merge in about 300 Myr. Weisberg et. al, 1981

12. Sources of GWs I • Coalescing Compact Binaries • Binary companions will eventually merge (since orbit is shrinking). • Can consist of NS/NS (e.g. Hulse-Taylor), BH/BH, or BH/NS. • Small sizes, large masses, and huge orbital velocities  efficient GW emission. • Signal will look like a chirp (a technical term).

13. Coalescing Compact Binaries • To first order, a chirp signal is described by its amplitude and change in frequency over time: where Mc is the “chirp mass”: • Measure f, f-dot, and A, solve for Mc and get r (distance to source).

14. Coalescing Compact Binaries • Can learn much from the exact waveform: • Harmonic content  eccentricity of orbit • Overall modulation  mass ratio of the two objects and spin-orbit coupling (i.e. frame-dragging) • Higher-order corrections  mass and spin of constituents • h versus h+  orbital inclination • Timing of end point (merger)  equation of state of nuclear matter Sigg 1998

15. Coalescing BHs • The BH/BH chirp waveform has three phases: • Inspiral (BHs approach each other) • Merger (actual coalescence of BHs) • Ringdown (new BH relaxes from excited state) MPI for Gravitational Physics/W.Benger-ZIB

16. Sources of GWs I Sources of GWs II • Normal Binary Stars • Orbital periods  1 hour  fGW 10-3 Hz • Can only be detected in space (discussed later) LISA website

17. Sources of GWs III • Core Collapse Supernovae (CC SNe), if they explode asymmetrically: • Some explosions are asymmetric. • How asymmetric, we don’t know very well. • Initial neutrino emission drains much of the energy that could go into GWs. • Possibly ~10-3 Mc2 could go into GWs. • If we observe a CC SN in E-M radiation and GWs, we can compare the propagation speed of GWs to c. LISA website

18. Sources of GWs IV • (Super) Massive BHs • M  105 M BH swallowing a nearby object (especially another Massive BH). • Can only be detected in space (discussed later). LISA website

19. Sources of GWs V • Isolated PSRs: • Asymmetric about their rotation axis  nonzero quadrupole moment. • Stochastic Background • Could be caused by density fluctuations in the early universe (like a GW CMB). • If measured, it links us to the Planck Era and can discriminate between different cosmological models! • Most models predict that the strain would be quite small.

20. Joseph Weber (1919 – 2000) • Father of GW astronomy • Started on GW detection in 1958 (Weber 1960) • Built first detector in 1966 at Univ. of MD • “Resonant Mass” detector (or “Weber Bar”) • Two 1.5-ton Al cylinders (i.e. bars) with piezoelectric crystals glued on. • When squeezed (by a passing GW) the crystals develop electric voltages. • Strung many crystals together to amplify the signal. • Bars were placed at separate locations sift out random noise. • A GW could excite the fundamental longitudinal mode of the bar, ~1657 Hz, which would induce a voltage across the bar.

21. Direct “Detection” of GWs • Weber claimed extremely strong GW detections, ~1 per month, from the late 60’s through the 70’s. • No one could explain the large amplitudes theoretically. • Other groups built bigger and more sensitive Weber Bars, but could not reproduce his results. • By 1975, nearly everyone in the field agreed that Weber’s detections were simply noise. • Through the early 80’s, better Weber bars were built using better digital electronics and cryogenic cooling techniques (to decrease noise), but none successfully detected GWs. AIP Emilio Segrè Visual Archives

22. Using Lasers to See GWs • As early as 1956, laser interferometry was proposed to search for GWs. • Even Weber suggested this in the late 60’s. • If a laser is bounced between two mirrors, the distance between them can be accurately measured. • If the separation is large compared to the GW, then it will appear as a plane wave. • The GW will stretch and compress the space-time distance between the mirrors. • This tiny change in distance can be detected using interferometry.

23. Michelson Interferometers • Most designs are based on the Michelson interferometer with response function A(W)  sinc(WL/c) • To effectively increase L, can bounce the light many times (off-axis) before detection, but this degrades the signal. • Instead, use a Fabry-Perot cavity: • Partially transmitting input mirror • Highly reflective rear mirror • Adjust length to multiple of laser wavelength and cavity becomes resonant • This increases power without degrading signal! • Response becomes A(W)  sinc(WL/c)FPI(WL/pc) where FPI(x) = |t1 / 1-r1r2eix|2 L L Sigg 1998

24. More Michelson Interferometers • Recycle lost input power with a Power-Recycling mirror: • Place another partially transmitting mirror at the input. • Form another resonant cavity. • Recycle light that would be lost back out the input. • Make signal resonant with a Signal-Recycling mirror: • Place another partially transmitting mirror to the anti-symmetric port. • Can shape interferometer response around a narrow frequency band. • If both are used, it’s called Dual-Recycled. • Response becomes A(W)  sinc(WL/c)FPI(WL/pc)GR where GR is the total gain from the recycling cavity(ies). • All combinations of recycling and Fabry-Perot arms can be used. Sigg 1998

25. The LIGO Project • Laser Interferometer Gravitational wave Observatory • Collaboration between Cal Tech and MIT. • Two widely separated sites under common management (to make coincidence measurements) Hanford, WA (LIGO website) Livingston, LA (LIGO website)

26. The LIGO Project • Interferometers with 4km arms. • Can operate several interferometers simultaneously. • Hanford site has 4km and 2km arm detectors. • Well collimated lasers. • Vacuum of 10-9 torr H and 10-10 torr other gases. • Lifetime of at least 20 years. Beam splitter (LIGO website) One 4km arm (LIGO website)

27. The LIGO Interferometer • Power-recycled Fabry-Perot interferometer. • Sensing and control system • Seismic isolation system (not shown) • Suspensions Interferometer (Abbott et al. 2007) Interferometer (LIGO website)

28. The LIGO Mirrors • ~10 kg cylinders 25cm in diameter and 10cm thick. • Made of high-purity fused silica. • Permanent magnets glued to the back to control longitudinal and angular orientation. • Permanent magnets glued to the side to control sideways motion. • Coil drivers mounted on suspension cage to adjust force on magnets/mirrors (by changing current in the coils). Mirror and Cage (LIGO website)

29. The LIGO Laser • Solid state diode-pumped Nd:YAG laser. • Operates at 10W and 1064nm. • Diffraction limited beam of width ~30 to 40mm. Part of the laser setup (LIGO website)

30. The LIGO Scientific Collaboration!!!

31. Sources of Noise From the Laser • Shot noise: fluctuations in the number of photons in the beam • Light amplitude and laser frequency noise: the laser’s beam isn’t perfect Sigg 1998

32. Sources of Noise From the Laser • Scattered light: light can scatter into and out of the beam path (back scatter is why fiber optics aren’t used) • Beam jitter: the laser’s output angle and position isn’t perfect Sigg 1998

33. Sources of Noise From the Laser • Residual gas column density fluctuations: if the vacuum isn’t perfect, changes in gas density will change the index of refraction Sigg 1998

34. Seismic Noise • Affects mirror motion directly • The Earth is in constant motion from volcanoes, ocean waves, wind, and lunar tidal forces • Strongest from 0.1Hz to 10Hz • Huge source of noise on Earth at low frequencies • Absent in space Sigg 1998

35. Thermal Noise in Suspensions • Also affects mirror motion directly • Heat excites motion in suspension elements • Damped by suspending mirrors as pendulums hung with thin wire. Sigg 1998

36. Thermal Noise in Mirrors • Again affects mirror motion directly • Heat excites normal modes in the mirrors themselves • Frequencies are more toward kHz range (sorta) • Can be modeled well if the mirrors are fabricated accurately Sigg 1998

37. Radiation Pressure Imbalance • Number of photons hitting a mirror will fluctuate based on photon counting statistics • The recoil of these photons will introduce a small force on the mirrors Sigg 1998

38. Gravity Gradient Noise • Any mass place near a mirror will exert a gravitational force on the mirror • The Earth’s internal seismic waves and density fluctuations in the atmosphere are the main concern • Sets the ultimate limit in sensitivity for Earth-based detectors Sigg 1998

39. Other (Extreme) Sources of Noise • Radiometer noise • Electric field fluctuations • Magnetic field fluctuations • Cosmic ray muons

40. Noise Summary • Red curve is LIGO goal (current LIGO). • Blue curve is theoretical limit on Earth. Sigg 1998

41. Noise Summary LIGO website

42. Noise Summary (on Earth) • Red curve is Initial (current) LIGO. • Blue curve is theoretical limit on Earth. • Can possibly (one day) model or eliminate noise from all sources and get down to blue curve on Earth. (A LIGO) • Or, you can go into space!!! (LISA) Sigg 1998

43. LIGO Results: Fourth Science Run (S4) • Most recently released data set. • 22 Feb 2005 to 23 Mar 2005. • Used all three LIGO interferometers (2km and 4km at Hanford, 4km at Livingston) and GEO 600 in Germany (more on GEO later). • ~570 hours of observation time on each LIGO interferometer. • ~402 hours when all three were collecting data simultaneously.

44. LIGO Results: Stochastic Background • A stochastic background of GWs has been predicted from many possible sources: • Amplification of quantum vacuum fluctuations (Grishchuk 1975, Grishchuk 1997, Starobinsky 1979) • Pre-Big-Bang models (Gasperini & Veneziano 1993, Buonanno et al. 1997) • Phase transitions (Kosowky et al. 1992, Apreda et al. 2002) • Cosmic strings (Caldwell & Allen 1992, Damour & Vilenkin 2005) • Rotating NSs (Regimbau 2001) • Supernovae (Coward et al. 2002) • Low-mass X-ray binaries (Cooray 2004) • Despite much searching, none have been discovered thus far.

45. LIGO Results: Stochastic Background • 192 second long intervals of data with 1/32 Hz frequency resolution. • S4 results are beginning to differentiate between different cosmological models. • S5 (and A LIGO) will probe even more parameter space. • Results are a 90% upper limit on the GW background. Abbott et al. 2006

46. LIGO Results: Stochastic Background • 10 trials were performed with artificially injected amplitudes. • Left (gray) error bars denote the theoretical errors. • Right (black) error bars denote the standard errors over the 10 trials. • Seem to recover injected signal quite accurately! Abbott et al. 2006

47. LIGO Results: GWs From Single PSRs • Appeared on astro-ph on 4 Apr 2007. • 95% upper limits on GW amplitudes for 78 PSRs. • Tightest strain upper limit is 3.210-25 • Strain is directly related to e, a PSR’s equatorial ellipticity. • Smallest ellipticity is 8.5  10-7 • Strange quark stars or hybrid stars have e ~ 10-5 • More conventional NS EOSs have e ~ 10-7 Abbott et al. 2007

48. LIGO Results: Transient GW Bursts • Appeared on astro-ph on 6 Apr 2007. • 90% upper limit on mean rate of GW bursts: 0.15 per day • Assuming isotropic emission of GWs (for OoM): • hmin = best sensitivity and assume 50% efficiency • r ~ 10kpc  810-8 M in GWs • r ~ 16Mpc  0.2 M in GWs Abbott et al. 2007

49. LIGO Results: Transient GW Bursts • Monte Carlo was run to test efficiency. • Statistical errors comparable to size of symbols. Abbott et al. 2007

50. LIGO Results: Transient GW Bursts • CC SN model with non-spinning 11M progenitor (and 50% detection efficiency) visible to ~0.2kpc. • CC SN model with spinning 15M progenitor (and 50% detection efficiency) visible to ~8kpc. • A pair of merging 10M BHs visible to ~1.5Mpc. • A pair of merging 50M BHs visible to ~60Mpc.