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Observing Gravitational Waves from Spinning Neutron Stars LIGO-G060662-00-Z Reinhard Prix (Albert-Einstein-Institut)

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Observing Gravitational Waves from Spinning Neutron Stars LIGO-G060662-00-Z Reinhard Prix (Albert-Einstein-Institut) Astrophysical Motivation Detecting Gravitational Waves from NS Observing Gravitational Waves from Spinning Neutron Stars LIGO-G060662-00-Z Reinhard Prix (Albert-Einstein-Institut) for the LIGO Scientific Collaboration Toulouse, 6 July 2006 R. Prix Gravitational Waves from Neutron Stars Astrophysical Motivation Detecting Gravitational Waves from NS Outline 1 Astrophysical Motivation Gravitational Waves from Neutron Stars? Emission Mechanisms (Mountains, Precession, Oscillations, Accretion) Gravitational Wave Astronomy of NS 2 Detecting Gravitational Waves from NS Status of LIGO (+GEO600) Data-analysis of continous waves Observational Results R. Prix Gravitational Waves from Neutron Stars Gravitational Waves from Neutron Stars? Astrophysical Motivation Emission Mechanisms Detecting Gravitational Waves from NS Gravitational Wave Astronomy of NS Orders of Magnitude Quadrupole formula (Einstein 1916). GW luminosity (: deviation from axisymmetry): 2 G MV 3 O(10−53) L ∼ 2 GW c5 R c5 R 2 V 6 O(1059) erg = 2 s s G R c 2 Schwarzschild radius Rs = 2GM/c Need compact objects in relativistic motion: Black Holes, Neutron Stars, White Dwarfs R. Prix Gravitational Waves from Neutron Stars Gravitational Waves from Neutron Stars? Astrophysical Motivation Emission Mechanisms Detecting Gravitational Waves from NS Gravitational Wave Astronomy of NS What is a neutron star? −1 Mass: M ∼ 1.4 M Rotation: ν . 700 s Radius: R ∼ 10 km Magnetic field: B ∼ 1012 − 1014 G =⇒ density: ρ¯ & ρnucl =⇒ Rs = 2GM ∼ . relativistic: R c2R 0 4 R. Prix Gravitational Waves from Neutron Stars Gravitational Waves from Neutron Stars? Astrophysical Motivation Emission Mechanisms Detecting Gravitational Waves from NS Gravitational Wave Astronomy of NS Gravitational Wave Strain h(t) + Plane gravitational wave hµν along z-direction: Lx −Ly Strain h(t) ≡ 2L : y Ly Lx x h(t) t R. Prix Gravitational Waves from Neutron Stars Gravitational Waves from Neutron Stars? Astrophysical Motivation Emission Mechanisms Detecting Gravitational Waves from NS Gravitational Wave Astronomy of NS Triaxial Spinning Neutron Stars Rotating neutron star: - non-axisymmetric = Ixx −Iyy Izz - rotation rate ν GW with frequency f = 2 ν Strain-amplitude h0 on earth: 16π2 G I ν2 h = zz 0 c4 d I ν 2 100 pc = 4 × 10−25 zz 10−6 1045 g cm2 100 Hz d √ −23 −1/2 Current LIGO sensitivity (S5): Sn ∼ 4 × 10 Hz NS signals buried in the noise =⇒ need “matched filtering” R. Prix Gravitational Waves from Neutron Stars Gravitational Waves from Neutron Stars? Astrophysical Motivation Emission Mechanisms Detecting Gravitational Waves from NS Gravitational Wave Astronomy of NS Possible Emission Mechanisms “Mountains” Oscillations Free precession Accretion (driver) R. Prix Gravitational Waves from Neutron Stars Gravitational Waves from Neutron Stars? Astrophysical Motivation Emission Mechanisms Detecting Gravitational Waves from NS Gravitational Wave Astronomy of NS Neutron Star “Mountains” Conventional NS crustal shear mountains: −7 −6 crust . 10 − 10 (Ushomirsky, Cutler, Bildsten) Superfluid vortices: Magnus-strain deforming crust −7 Magnus ∼ 5 × 10 (D.I. Jones; Ruderman) Exotic EOS: strange-quark solid cores −5 −4 strange . 10 − 10 (B. Owen) Magnetic mountains: 15 large toroidal field Bt ∼ 10 G ⊥ to rotation: −6 toroidal ∼ 10 (C. Cutler) accretion along B-lines =⇒“bottled” mountains −6 −5 bottle . 10 − 10 (Melatos, Payne) non-aligned poloidal magnetic field B ∼ 1013 G, type-I or type-II superconducting interior, −6 B . 10 (Bonazzola&Gourgoulhon) R. Prix Gravitational Waves from Neutron Stars Gravitational Waves from Neutron Stars? Astrophysical Motivation Emission Mechanisms Detecting Gravitational Waves from NS Gravitational Wave Astronomy of NS Oscillation Modes Chandrasekhar-Friedman-Schutz instability: counter-rotating mode “dragged forward” =⇒negative energy and angular momentum emission of GW amplifies the mode counteracted by dissipation r-mode instability window: Open questions: Dissipation mechanisms: vortex friction, hyperons, crust-core coupling,... saturation amplitude, mode-mode coupling, evolution timescales R. Prix Gravitational Waves from Neutron Stars Gravitational Waves from Neutron Stars? Astrophysical Motivation Emission Mechanisms Detecting Gravitational Waves from NS Gravitational Wave Astronomy of NS Free Precession “Most general motion of a rigid body” (Landau&Lifshitz 1976) NS are not rigid: coupled crust - core (viscosity + superfluid vortex pinning) likely to be damped rapidly no obvious instability or “pumping mechanism” θ 100 pc ν 2 h ∼ 10−26 w 0 0.1 d 500 Hz R. Prix Gravitational Waves from Neutron Stars Gravitational Waves from Neutron Stars? Astrophysical Motivation Emission Mechanisms Detecting Gravitational Waves from NS Gravitational Wave Astronomy of NS Accretion Breakup-limit νK ∼ 1.5 kHz What limits the NS-spin? Bildsten, Wagoner: Accretion-torque = GW torque (∝ ν5) −26 1/2 Observed X-ray flux Sco X-1: h0 ∼ 3 × 10 (270 Hz/ν) R. Prix Gravitational Waves from Neutron Stars Gravitational Waves from Neutron Stars? Astrophysical Motivation Emission Mechanisms Detecting Gravitational Waves from NS Gravitational Wave Astronomy of NS Astrophysics Summary NS are plausible sources for LIGO I, II or VIRGO Whether or not they are detectable depends on many poorly-understood aspects of NS physics Any GW-detection from rotating NS will be extremely valuable for NS physics Even the absence of detection can yield astrophysically interesting information (crust deformation, B, instabilities) NS physics producing GWs is very different and complementary to electromagnetic emission (bulk-mass motion vs magnetosphere-electron motion) R. Prix Gravitational Waves from Neutron Stars Gravitational Waves from Neutron Stars? Astrophysical Motivation Emission Mechanisms Detecting Gravitational Waves from NS Gravitational Wave Astronomy of NS Gravitational Wave Astronomy “Astero-Seismology” (Andersson, Kokkotas 1998): f-mode Measurement of (ωf , τf ) =⇒ deduce (M, R) =⇒ EOS R. Prix Gravitational Waves from Neutron Stars Status of LIGO (+GEO600) Astrophysical Motivation Data-analysis of continous waves Detecting Gravitational Waves from NS Observational Results LSC detectors: LIGO + GEO600 R. Prix Gravitational Waves from Neutron Stars Status of LIGO (+GEO600) Astrophysical Motivation Data-analysis of continous waves Detecting Gravitational Waves from NS Observational Results Current LIGO noise performance ∆L −23 −19 −4 h0 = L ∼ 3 × 10 =⇒ ∆L ∼ 10 m = 10 fm!! R. Prix Gravitational Waves from Neutron Stars Status of LIGO (+GEO600) Astrophysical Motivation Data-analysis of continous waves Detecting Gravitational Waves from NS Observational Results LSC Data Analysis LIGO (H1, H2, L1) and GEO600 data analyzed within the LIGO Scientific Collaboration (LSC): ∼ 40 institutions, ∼ 320 authors (S3) 4 major search groups (different targets and methods): Binary inspirals: short inspiral signals (modeled) Bursts: short unmodeled signals (supernovae, merger) Stochastic background: cosmological background GWs “Continuous waves”: spinning NS signals (long-lived) R. Prix Gravitational Waves from Neutron Stars Status of LIGO (+GEO600) Astrophysical Motivation Data-analysis of continous waves Detecting Gravitational Waves from NS Observational Results Nature of GW from Rotating Neutron Stars J NS frame: monochromatic wave, slowly varying frequency 1 ˙ 2 Phase Φ(τ) = φ0 + 2π f τ + 2 f τ + ... GW frequency for triaxial NS: f = 2 ν , r-modes: f = 4/3 ν, precession: f ≈ ν 2 polarization amplitudes: A+, A× =⇒ Wave-components in NS frame: h×(τ) = A+ cos Φ(τ) h+(τ) = A× sin Φ(τ) J Detector frame t: sky-position (α, δ) dependent modulations: Phase: Doppler-effect due to earth’s motion τ = τ(t; α, δ) Amplitude: rotating Antenna-pattern F+,×(t, ψ; α, δ) R. Prix Gravitational Waves from Neutron Stars Status of LIGO (+GEO600) Astrophysical Motivation Data-analysis of continous waves Detecting Gravitational Waves from NS Observational Results Signal Received at the Detector GW strain at the detector: h(t) = F+(t) h+(t) + F×(t) h×(t) Signal dependencies h ˙ i h(t) = F+(t, ψ; α, δ) A+ cos φ0 + φ(t; α, δ, f , f , ..) h ˙ i + F×(t, ψ; α, δ) A× sin φ0 + φ(t; α, δ, f , f , ..) Signal parameters: µ µ 4 “Amplitude parameters”: A = A (A+, A×, ψ, φ0) “Doppler parameters”: λ = {α, δ, f , f˙, ... (+ orbital parameters) } R. Prix Gravitational Waves from Neutron Stars Status of LIGO (+GEO600) Astrophysical Motivation Data-analysis of continous waves Detecting Gravitational Waves from NS Observational Results Optimal detection statistic: “Matched filtering” data noise signal z}|{ z}|{ z }| { Measured strain: x(t) = n(t) + s(t; A, λ) Z x(f ) y ∗(f ) scalar product: (x|y) ≡ e e df Sn(f ) − 1 (n|n) pdf for Gaussian noise n(t): P(n(t)|Sn) = k e 2 =⇒ likelihood of x(t) in presence of signal s(t; A, λ): − 1 (x|x) (x|s)− 1 (s|s) P(x(t)|A, λ; Sn) = k e 2 e 2 Bayesian posterior probability for signal {A, λ} in data x(t): 0 (x|s)− 1 (s|s) P(A, λ|x(t); Sn) = k P(A, λ) e 2 | {z } ”prior”probability R. Prix Gravitational Waves from Neutron Stars Status of LIGO (+GEO600) Astrophysical Motivation Data-analysis of continous waves Detecting Gravitational Waves from NS Observational Results Matched filtering II: the F-statistic 1 detection statistic: Q(A, λ) ≡ (x|s) − 2 (s|s) find maximum of Q in parameter space {A, λ}. 4 X µ s(t; A, λ) = A hµ(t; λ) (Jaranowski, Krolak, Schutz, PRD 1998) µ=1 µ ∂Q µ =⇒ analytically maximize Q over A : ∂Aµ = 0 =⇒ A MLE Definition of the “F-statistic”: F = Q(AMLE , λ) µν 2F(λ) = xµ M xν µν −1 where xµ(λ) ≡ (x|hµ(λ)), and M (λ) = (hµ(λ)|hν(λ)) find maximum of F in reduced parameter-space {λ}. R. Prix Gravitational Waves from Neutron Stars Status of LIGO (+GEO600) Astrophysical Motivation Data-analysis of continous waves Detecting Gravitational Waves from NS Observational Results Matched filtering III: multi-detector generalization multi-detector vector {x(t)}X = xX(t) with X ∈ {H1, L1, V1...} Z X −1 Y∗ (x|y) = xe (f ) SXY ye (f ) df µν −1 xµ(λ) = (x|hµ), M (λ) = (hµ|hν ) µν =⇒ 2F(λ) = xµ M xν (Cutler&Schutz, PRD 2005) Signal-to-noise ratio @ perfect match √ p h0 SNR = (s|s) ∝ √ T N T ..
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