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Gravitational wave standard sirens as cosmological probes

Gravitational wave standard sirens as cosmological probes. Neal Dalal (CITA) with D. Holz, S. Hughes, B. Jain. figure courtesy of AEI. Outline. overview of gravitational waves & detection GW’s from inspiraling binaries constraining cosmology. What are gravitational waves?.

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Gravitational wave standard sirens as cosmological probes

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  1. Gravitational wave standard sirens as cosmological probes Neal Dalal (CITA) with D. Holz, S. Hughes, B. Jain figure courtesy of AEI

  2. Outline • overview of gravitational waves & detection • GW’s from inspiraling binaries • constraining cosmology

  3. What are gravitational waves? • Consider metricperturbation gmn=a2(t) [hmn+hmn]. • h is a symmetric 4£4 tensor, so 10 components: • 4 scalar (spin 0) • 4 vortical (spin 1) • 2 shear (spin 2) • For ||h|| << 1, linearized vacuum Einstein equations ! so h satisfies a wave equation. The two spin-2 modes are transverse shear waves propagating at v=c.

  4. What are gravitational waves? think of GW’s as waves of tidal gravity. change distance between free-falling observers DL¼L h(t) generated by moving masses, with amplitude So need large m, v to be interesting! e.g. NS pair withv/c~0.3, observed atr = 1000 km, hash~3¢10-4. So for a person of height 2m, DL~1mm!

  5. What are gravitational waves? • essentially non-interacting with matter, once produced. • act transverse to propagation direction. • seem wimpy, but are dominant mechanism of energy loss for highly relativistic binaries! Hulse-Taylor binary pulsar PSR 1913+16

  6. GWology GW generated by bulk motion of matter, unlike EM waves which are generated by many incoherent patches. GW are coherent, with a characteristic frequency of order the dynamical frequency, f / (G)1/2. Therefore GW wavelength exceeds the size of the emitting region, ' R c/v. GW cannot resolve their sources and so cannot be used for imaging. Also – important to remember that strain h is the observable, not the power. So the observable falls off like 1/r, not 1/r2 !

  7. GWology Schutz (1999)

  8. ground vs. space-based

  9. How to detect? Laser interferometry! Split laser beam, send light down long paths, with mirrors at each end. Bounce back, recombine. Absence of a GW: Armlengths are arranged so that the light destructively interferes – no signal is measured.

  10. How to detect? Laser interferometry! Split laser beam, send light down long paths, with mirrors at each end. Bounce back, recombine. Presence of a GW: Positioning of mirrors changes, so armlengths change! Interference is no longer perfect, and we measure an output signal.

  11. 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 201? Lauch) 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

  12. How do we observe sources? • the gravitational wave strain is too small by the time the wave reaches earth to directly “see” the signal Simulated waveform from a binary black hole merger (M1=M2 ~ 10 M๏, at ~ 15 Mpc) LIGO GW channel (as of ~ year ago) + injected waveform Detection of the inspiral with a SNR~16 after application of the matched filtering algorithm Images from Patrick Brady

  13. How do we observe sources? • For the majority of sources, some knowledge of the nature of the source is required for detection of a signal • Matched filteringwill be the primary tool for extracting small, quasi-periodic signals from the data stream • But because many templates must be run, the SNR threshold for detection must be set high, typically SNR>8.5 • Techniques such as theexcess power methodcan be used for other sources, or if less is known about the exact nature of the source

  14. How well do we know the expected waveforms? For some sources, well enough!

  15. Survey of some sources Waves from the early universe: Initial state fluctuations Phase transitions Cosmic strings Rotating and vibrating compact objects: Rotating neutron stars Modes of neutron star fluid Modes of black holes (defer to binaries) Binaries: Combinations of white dwarfs, neutron stars, and black holes.

  16. Three phases of coalescence figure from K. Thorne

  17. 1. Inspiral Members are widely separated, distinct bodies. “Post-Newtonian” expansion works well. “Chirping” gravitational waveform

  18. Post-Newtonian expansion • iterative approximation to fully dynamical spacetime • expansion in (v/c)2. • For 2-body problem, an accuracy of 3PN has been achieved by several independent methods; all approaches agree. • [Blanchet, Damour, Esposito-Farèse, Iyer; Damour, Jarownowski, Schaefer; Itoh] • reliable up to v/c ' 0.3-0.5 • expect orbits to be circularized quickly if GW emission is dominant energy loss

  19. slide from Samaya Nissanke

  20. 2.Merger Spacetime transition: From two distinct bodies to a single body. NO expansion works well! Modeling requires tackling full nastiness of nonlinear field equations, properties of stars. Image credit: Teviet Creighton, Caltech Waveform unknown!

  21. Recent progress in numerical GR! within past 1-2 yrs, several groups have successfully calculated mergers of comparable-mass BH’s! lapse function a in orbital plane courtesy F. Pretorius

  22. Recent progress in numerical GR! within past 1-2 yrs, several groups have successfully calculated mergers of comparable-mass BH’s! Newman-Penrose scalar y4 (like h+) courtesy F. Pretorius

  23. 3.Ringdown If final state is a black hole, last waves come a system a distorted Kerr black hole. Black hole perturbation theory describes the system. Waveform: Damped harmonic oscillator.

  24. Three phases of coalescence only rely upon well-understood inspiral phase! figure from K. Thorne

  25. GW from inspirals • can get useful insight from quadrupole approximation • if we observe how fast the frequency chirps, we know how much energy is being radiated in GW. By comparing to the measured strain amplitude, this tells us how distant the source is! (Schutz 1986)

  26. GW from inspirals • the phase evolution is just determined by time until coalescence, tc-t, and by a combination of masses called the (redshifted) chirp mass • the strain amplitude also depends on same combination! • but – emission is not isotropic: depends on inclination • can measure inclination if polarization is measured! • measured amplitude depends on source direction • can measure this from timing of received signals

  27. LIGO Hanford LIGO Livingston GW standard sirens so the gravitational radiation from inspiraling binaries provides a self-calibrating distance indicator. Just need detectors with different locations and different orientations, to measure polarization and timing. can achieve this with a network of detectors on Earth … … while LISA can do both in space!

  28. Cosmology with standard sirens GW observatories can measure precise distances to sources at cosmological distances.  can be useful for cosmology! H2(z)=8G/3 [m(z)+(z)+K(z)+…] and dL(z)=(1+z)s(c/H) dz One problem: distances but no redshifts! So we need merger events that have some sort of EM counterpart to use them as standard sirens.

  29. Binary neutron stars • known to exist and radiate in GW. • Galactic merger rate about 10-4 yr-1. • very plausible that merger could have optical / X-ray counterpart, esp. if it produces BH with accretion disk. movie courtesy M. Shibata are short GRBs from NS coalescence??

  30. Short GRBs • origin of short GRBs is still unknown, but NS mergers are a leading candidate! • if NS merger ! GRB, they are ideal • afterglow/host galaxy gives z • known direction decreases distance errors • known time reduces required SNR threshold!

  31. unbeamed 20± beaming Cosmology with GW from GRBs • assume 4-element network of detectors (LIGO-H, LIGO-L, Virgo, AIGO) of comparable sensitivity • double NS merger detectable out to 600 Mpc. • distance errors improve • if sources are collimated • GRB trigger may not be • necessary! Can get minutes • to hrs warning from GW, • ~degree localization, good • enough for follow-up?

  32. Cosmology with GW from GRBs How well does this constrain cosmological parameters e.g. dark energy equation of state parameter w? unbeamed 100 GRBs unbeamed 20± beaming But how is this possible? We’re using GRBs only out to 600 Mpc, z . 0.15. How can  or w be constrained?

  33. Absolute distances! • this works because GW measure absolute distances to sources, in Mpc, not h-1 Mpc. The CMB tells us distance to LSS also in Mpc, so combining the two can measure DE parameters! • put another way: for flat universe, only 3 parameters: {h, m, w}. CMB provides 2 constraints, on m h2, and on lA= dA(LSS)/rs. A 3rd constraint, like a measurement of H0, determines all three. • works for any H0 determination, e.g. using water masers. Measuring H0 = measuring w ! • more precisely, measures integral constraint on w(z), assuming flat universe.

  34. other GW sources • focused on GRBs since they have afterglows and a (reasonably) known rate from BATSE, Swift. • other stellar mass inspirals in LIGO bands, like NS-BH, BH-BH, could also serve as standard sirens, if they have EM counterparts. • if g-rays beamed, but afterglows less so, then even off-axis GRBs could be useful! • what about LISA?

  35. Overview of expected gravitational wave sources Pulsar timing LISA LIGO/… Bar detectors CMB anisotropy >106 M๏ BH/BH mergers 102-106 M๏ BH/BH mergers source “strength” 1-10 M๏ BH/BH mergers NS/BH mergers NS/NS mergers pulsars, supernovae EMR inspiral NS binaries WD binaries exotic physics in the early universe: phase transitions, cosmic strings, domain walls, … relics from the big bang, inflation 10-12 10-8 10-4 1 104 source frequency (Hz)

  36. Binary black holes in the Universe • Strong circumstantial evidence that black holes are ubiquitous objects in the universe • supermassive black holes (106 M๏ - 109 M๏)thought to exist at centers of most galaxies • high stellar velocities near the centers of galaxies, jets in active galactic nuclei, x-ray emission, … • more massive stars are expected to form BH’s at the end of their lives VLA image of the galaxy NGC 326, with HST image of jets inset. CREDIT: NRAO/AUI, STScI (inset) • Galaxy mergers are observed commonly, suggesting SMBH mergers may also be common. • LISA can detect all SMBH mergers within the horizon (e.g out to z=10) ! Two merging galaxies in Abell 400. Credits: X-ray, NASA/CXC/ AIfA/D.Hudson & T.Reiprich et al.; Radio: NRAO/VLA/NRL)

  37. Cosmology with LISA 100 GW sources, 0<z<2 • for LISA standard sirens to be useful, must have ~100 to average out lensing • merger rates, EM counterparts still uncertain!

  38. Conclusions! • exciting times for GW astronomy • waveforms from inspirals of compact object binaries are well-understood • these provide a self-calibrating distance indicator • the number of sources detectable with ground-based detectors is large enough to provide interesting constraints on cosmology!

  39. upcoming experiments • LIGO • operating at target sensitivity • began science run Nov 2005, expect to continue through 2007 • 2008, begin upgrade to LIGO-II (10£ increase in sensitivity!) • LIGO-II begins operations around 2009 • Virgo • European observatory, similar sensitivity, expect to follow LIGO by 2-3 yrs • AIGO • Australian observatory, funding uncertain LISA: ???

  40. slide from Keith Riles

  41. LIGO-II • Collaboration between LIGO and GEO600, to upgrade to advanced sensitivity (10£ increase). • increased laser power (10W ! 100W) • new test mass material (sapphire), lower internal thermal noise in bandwidth • increased test mass (10kg ! 40kg) • new suspension: single ! quadruple pendulum • improved seismic isolation (passive ! active) 10£ increase in sensitivity gives 1000£ in volume!

  42. LISA - The Overview • Mission Description • 3 spacecraft in Earth-trailing solar orbit separated by 5 x106 km. • Gravitational waves are detected by measuring changes in distance between fiducial masses in each spacecraft using laser interferometry • Partnership between NASA and ESA • Launch date ~2015+ • Observational Targets • Mergers of massive black holes • Inspiral of stellar-mass compact objects into massive black holes • Gravitational radiation from thousands of compact binary systems in our galaxy • Possible gravitational radiation from the early universe

  43. Orbits • Three spacecraft in triangular formation; separated by 5 million km • Spacecraft have constant solar illumination • Formation trails Earth by 20°; approximately constant arm-lengths 1 AU = 1.5x108 km

  44. Determining Source Directions • Directions (to about 1 degree) : 2 methods: AM & FM • FM: Frequency modulation due to LISA orbital doppler shifts • Analagous to pulsar timing over 1 year to get positions • FM gives best resolution for f > 1 mHz • AM: Amplitude modulation due to change in orientation of array with respect to source over the LISA orbit • AM gives best resolution for f < 1 mHz • Summary: LISA will have degree level angular resolution for many sources (sub-degree resolution for strong, high-frequency sources) • See e.g. Cutler (98), Cutler and Vecchio (98), Moore and Hellings (00), also Hughes (02) (Cornish and Larson, ’01) (F+ & Fx)

  45. Determining Source Distances • Distances(to about 1%) • Binary systems with orbital evolution (df/dt) • “Chirping” sources • Determine the luminosity distance to the system by comparing amplitude, h, and period derivative, df/dt, of the gravitational wave emission • Quadrupole approximation: • Luminosity distance (DL) can be estimated directly from the detected waveform • See e.g. work by Hughes, Vecchio for quantitative estimates

  46. Determining Polarization • LISA has 3 arms and thus can measure both polarizations • Gram-Schmidt orthogonalization of combinations that eliminate laser frequency noise yield polarization modes • Paper by Prince et al. (2002) • gr-qc/0209039 Y L2 L3 L1 X (notation from Cutler,Phinney)

  47. 2-arm “Michelson” sensitivity Acceleration Noise (Disturbance Level) Short- Limit Shot Noise (Measurement Sensitivity) 1 Hz 0.1 mHz frequency LISA Sensitivity 2-arm “Michelson” sensitivity + White Dwarf binary background White Dwarf Background (Includes gravitational wave transfer function averaged over sky position and polarization). Source sensitivities plotted as hSqrt(Tobs).

  48. Rate Estimates for Massive Black Hole Mergers • Use hierarchical merger trees • Rate estimates depend on several factors • In particular space density of MBHs with MBH<106 M • Depends on assumptions of formation of MBHs in lower mass structures at high-z • Some recent estimates • Sesana et al. (2004): about 1 per month • Menou (2003): few to hundreds per year depending on assumptions • Haehnelt (2003): 0.1 to 100 per year depending on assumptions 3 year mission [Sesana et al, astro-ph/0401543] courtesy T. Prince

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