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GRAVITATIONAL WAVES FROM NS INTERIORS

Explore superfluid turbulence, post-glitch relaxation, and continuous source rotation within neutron stars to understand nuclear physics and macroscopic phenomena. Dive into the complexities of superfluid circulation, turbulence relaxation mechanisms, and the impact on gravitational wave signals. Discover how LIGO observations can illuminate the secrets of neutron star interiors.

jamesdanderson
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GRAVITATIONAL WAVES FROM NS INTERIORS

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  1. GRAVITATIONAL WAVESFROM NS INTERIORS C. Peralta, M. Bennett, M. Giacobello, A. Melatos, A. Ooi, A. van Eysden, S. Wyithe (U. Melbourne and AEI) • Superfluid turbulence • Post-glitch relaxation • Rigorous model → parametrised template→ nuclear physics (viscosity, compressibility)

  2. CONTINUOUS SOURCE C-C diff. rotation (glitches)→ nonaxisymmetric superfluid flows Long-lived (days → years) periodic signal • Superfluid turbulence as pulsar spins down (Re ≈1011) • Post-glitch relaxation (Ekman pumping) • Follows burst signal of glitch itself (msec?) Not discussed here... • R-modes continuously excited in core (Andersson et al. 99; Nayyar & Owen 06); cf. ocean r-modes (Heyl 04) • Amplitude and threshold probe superfluid core and viscous crust-core boundary layer(Lindblom & Mendell 99; Bildsten & Ushomirsky 00;Levin & Ushomirsky 01)

  3. SUPERFLUID CIRCULATION oscillating hydro torque EKMAN PUMPING Re=104 (Peralta et al. 05, 06, 07) Differential rotation → meridional circulation • superfluid→ HVBK two-fluid model (3D) • Quantised vortices ↔ mutual friction

  4. MACRO SF TURBULENCE TAYLOR VORTEX HERRINGBONE & SPIRAL TURBULENCE

  5. POST-GLITCH RELAXATION • Ekman: fluid spun up in radially expanding boundary layer (meridional → Coriolis) • TEkman = (2E1/2W)-1with E =n(2WR2)-1≈ Re-1 • Buoyancy inhibits meridional flow less/more according to compressibility K • Brunt-Vaisala frequency: N2=g2(ceq-2-K-2) • Incompressible: K→ ∞.Unstratified: N→ 0 • Nonaxisymmetric perturbation  exp(imf) • Wave strain:

  6. GW SPECTRUM • Lorentzian: measure width & peak frequency • Extract two of E, N, Kif W known(X-rays) • Width ratio independent of E (i.e. viscosity) • Amplitude depends on distance, orientation, DW, and compressibilities… but not E • Pol’n ratio: orientation to line of sight (also N, K) EQUATORIAL OBSERVER

  7. K= 0.1 N= 1 K= 0.3 h+(f) K= 1 K= 3 f N= 0.1 K = 1 h×(f) N= 0.3 N= 3 f N= 1

  8. EXTRACTING NUCLEAR PHYSICS E K N i i i E E K N K N Total signal including current quadrupole

  9. PHYSICS TO WORRY ABOUT • Microscopic turbulence • DGI →tangle of quantized vortices • Affects the mutual friction coupling ↓ • Macroscopic turbulence (Kolmogorov “eddies”) • Do large or small eddies dominate the GW signal?

  10. WHAT WILL LIGO TEACH US? SF turbulence • Is the core superfluid? • Mutual friction & entrainment parameter • Viscosity • Crust-core coupling

  11. Glitches • Measure ceqandKfor nuclear matter • Do glitches happen faster or slower than one rotation period? • Probe “seismic” (avalanche) dynamics • Spectrum of non-axisymmetric excitation NO OTHER GOOD WAY TO LEARN SUCH THINGS!

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