GRAVITATIONAL WAVES FROM NS INTERIORS C. Peralta, M. Bennett, M. Giacobello, A. Melatos, A. Ooi, A. van Eysden, S. Wyithe (U. Melbourne and AEI) 1.Superfluid turbulence 2.Post-glitch relaxation 3.Rigorous model → parametrised template → nuclear physics (viscosity, compressibility)

CONTINUOUS SOURCE Long-lived (days → years) periodic signal Superfluid turbulence as pulsar spins down ( Re ≈ ) 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) C-C diff. rotation (glitches)→ nonaxisymmetric superfluid flows

SUPERFLUID CIRCULATION Differential rotation → meridional circulation superfluid → HVBK two-fluid model (3D) Quantised vortices ↔ mutual friction oscillating hydro torque Re=10 4 EKMAN PUMPING (Peralta et al. 05, 06, 07)

MACRO SF TURBULENCE HERRINGBONE & SPIRAL TURBULENCE TAYLOR VORTEX

POST-GLITCH RELAXATION Ekman: fluid spun up in radially expanding boundary layer (meridional → Coriolis) T Ekman = (2E 1/2  )  with E = (2  R 2 )   ≈ Re  Buoyancy inhibits meridional flow less/more according to compressibility K Brunt-Vaisala frequency: N 2 =g 2 (c eq   K  ) Incompressible: K → ∞. Unstratified: N → 0 Nonaxisymmetric perturbation  exp(im  ) Wave strain :

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

h+(f)h+(f) h×(f)h×(f) f f  K  K  K  K  K  N  N  N  N 

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

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?

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

Glitches Measure c eq and K for 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!