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!
