GRAVITATIONAL WAVESFROM 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 ≈ 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)

C-C diff. rotation (glitches)→ nonaxisymmetric superfluid flows

SUPERFLUID CIRCULATION

Differential rotation → meridional circulation• superfluid → HVBK two-fluid model (3D)• Quantised vortices ↔ mutual friction

oscillatinghydro torque

Re=104

EKMANPUMPING

(Peralta et al. 05, 06, 07)

MACRO SF TURBULENCE

HERRINGBONE& SPIRAL

TURBULENCE

TAYLORVORTEX

POST-GLITCH RELAXATION

• Ekman: fluid spun up in radially expanding boundary layer (meridional → Coriolis)

• TEkman = (2E1/2) with E = (2R2)≈ Re

• Buoyancy inhibits meridional flow less/more according to compressibility K

• Brunt-Vaisala frequency: N2=g2(ceqK)

• 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)

2211 )(

)(

fE

ffh

2221 )2(

)(

fE

ffh

EQUATORIAL OBSERVER

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

ii

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 ceq 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!