Astrophysical Stochastic Gravitational WavesIntroductionIntroductionIntroductionWhat is the Astrophysical Background???CharacterizationMeasurement - IndirectMeasurement – IFO’s & BarsMeasurementSourcesEccentric Neutron StarsEccentric Neutron StarsEccentric Neutron StarsSupernovas (ka-pow!)Supernovas (ka-pow!)Neutron Star Coalescence Neutron Star Coalescence ScienceA Rough SketchReferencesAstrophysical StochasticAstrophysical StochasticGravitational WavesGravitational WavesJonah Kanner Jonah Kanner ––PHYS 798G PHYS 798G ––March 27, 2007March 27, 2007IntroductionIntroductionzzGravitational Waves come from spaceGravitational Waves come from spacezzRequire acceleration of dense mass Require acceleration of dense mass (Think black holes and neutron stars!)(Think black holes and neutron stars!)zzWill be detected with resonant bars and Will be detected with resonant bars and interferometers (both exist and are interferometers (both exist and are improving!)improving!)E-M Waves come from moving charges, flipping field lines back and forth.Gravitational quadra-pole fields lead to tidal forces. The “tidal forces” describe the field –ocean not required!GWs come from moving masses, flipping a tidal stretch back and forth across 2 orientations.IntroductionIntroductionIntroductionIntroductionzzCurrent detectors measure mainly Current detectors measure mainly ~50~50--3000 Hz 3000 Hz (In band of human hearing!)(In band of human hearing!)Merger (burst)Inspiral(~periodic)SN Stochastic (popcorn)http://www.ligo.caltech.edu/~mours/bh-no-noise.au http://www.physics.uwa.edu.au/~coward/SIMULATION.htmhttp://gmunu.mit.edu/sounds.htmlWhat is the Astrophysical What is the Astrophysical Background???Background???zzWhat: Many points sources overlapping in What: Many points sources overlapping in timetimezzQuick Math: Imagine a spherical shellQuick Math: Imagine a spherical shellzzNumber of sources/shell N ~ r^2Number of sources/shell N ~ r^2zzAmplitude per source A ~ 1/rAmplitude per source A ~ 1/rzzNet Amp ~ Random Walk ~ A*Net Amp ~ Random Walk ~ A*sqrtsqrt(N) ~ (N) ~ CONSTANT!CONSTANT!Result: A background fuzz from redshift z~1-5CharacterizationCharacterizationzzOmega!!!!!!Omega!!!!!!Ω(f) is roughly the normalized energy density in a given Ω(f) is roughly the normalized energy density in a given frequency band of the stochastic background frequency band of the stochastic background ∫∫Ω(f) d(Ω(f) d(lnln(f)) = ρ(f)) = ρGWGW//ρρccIn the same sense that a single temperature (2.7 K) In the same sense that a single temperature (2.7 K) completely describes the CMB, omega completely completely describes the CMB, omega completely describes the GW background if it’s stationary, describes the GW background if it’s stationary, Gaussian, and isotropicGaussian, and isotropicConvention: Bound ΩConvention: Bound Ω00Measurement Measurement --IndirectIndirectThe nucleosynthesisbound applies only to Cosmological signalsFor high freq, it’s a wide open field!Maggiore, M. 2000, Physics Reports. 331, 283Measurement Measurement ––IFO’sIFO’s& Bars& BarszzLIGO, TAMA, LIGO, TAMA, GEO,VIRGOGEO,VIRGOzzBar DetectorsBar DetectorszzAdvanced Advanced Detectors Detectors (LIGO, VIRGO) (LIGO, VIRGO) ~ 2013~ 2013Current bound on Ω of about 10^Ω of about 10^--5 at 505 at 50--150 Hz150 HzBounds around 10^Bounds around 10^--9 from “adv” 9 from “adv” IFOsIFOs(50(50--150Hz)150Hz)Bars + Bars + IFOsIFOsfor higher frequency boundsfor higher frequency boundsMeasurementMeasurementzzCross CorrelationCross CorrelationIdealization (Idealization (IFOsIFOsat same place): at same place): ∫∫s1(t) s2(t) s1(t) s2(t) dtdtLimitation: IFOs are usually not in the same place!! Wavelengths much shorter than 3000 km (100 Hz) will get “washed out” of cross correlation for L1-H1 pairAllen, B. 1996, gr-qc/9604033SourcesSourcesEstimationEstimation--Star Formation Rate (SFR)Star Formation Rate (SFR)--Galactic Population PropertiesGalactic Population Properties(Magnetic fields, freq, masses, etc…)(Magnetic fields, freq, masses, etc…)--GW strength per sourceGW strength per sourceEccentric Neutron StarsEccentric Neutron StarszzEccentricity may be any asymmetry with Eccentricity may be any asymmetry with respect to axis of rotation (potato or respect to axis of rotation (potato or mtmt.).)zzUse pulsar data to make estimates on the Use pulsar data to make estimates on the properties of the spinning neutron star properties of the spinning neutron star population (also population (also LMXB’sLMXB’sand and HMXB’sHMXB’s) ) zzεεis difficult to estimate is difficult to estimate ––existing upper existing upper bounds, but hard to get a good valuebounds, but hard to get a good valueEccentric Neutron StarsEccentric Neutron StarsT. Regimbau and J. A. de Freitas Pachecoestimate ΩΩbetween 10^between 10^--9 and 10^9 and 10^--1111-- Assume ε = 10^-6 (?)-- Wide range of ΩΩ0 0 comes from different comes from different models of SFR (corresponding to different models of SFR (corresponding to different models of cosmic dust)models of cosmic dust)----Freq ~1Freq ~1--1.5 kHz (from pulsar freq.)1.5 kHz (from pulsar freq.)Eccentric Neutron StarsEccentric Neutron StarsNot promising for IFO alone (high freq!)--Bars + IFO might do itR-modes might do betterTough estimate! Measurement probes SFRSupernovas Supernovas (ka(ka--powpow!)!)David M. Coward,P Ronald R. Burman and David G. Blair consider NS forming SNSN still not well understood – authors consider a mix of three different models – GW production depends on asymmetry of simulationSupernovas Supernovas (ka(ka--powpow!)!)zzPopcorn noisePopcorn noisez Get ΩΩabout 10^about 10^--12 peaked at 20012 peaked at 200--300 Hz300 Hzz With BH forming SN, could be closer to 10^-10Neutron Star CoalescenceNeutron Star CoalescencezzHard things to estimate: What fraction of Hard things to estimate: What fraction of massive stars exist as binaries??massive stars exist as binaries??zzOf those, what fraction are binaries after 2 Of those, what fraction are binaries after 2 SN’sSN’s????zzCan use eccentricity of pulsar orbits to Can use eccentricity of pulsar orbits to estimate “kick” from SNestimate “kick” from SNNeutron Star CoalescenceNeutron Star CoalescenceT. Regimbau and J. A. de Freitas PachecoShould be visible by Advanced IFOsRegimbau, T. & de Freitas Pacheco, J. A. 2006, The Astrophysical Journal.