GRAVITATIONAL WAVES FROM NS INTERIORS C. Peralta, M. Bennett, M. - - PowerPoint PPT Presentation

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 ≈ 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
• scillating

hydro torque Re=104 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)

• TEkman = (2E1/2Ω)−1 with E = ν(2ΩR2)−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(imφ)
• Wave strain:

(van Eysden & Melatos 07, Bennett & Melatos 07)

GW SPECTRUM

• Lorentzian: measure width & peak frequency
• Extract two of E, N, K if Ω known (X-rays)
• Width ratio independent of E (i.e. viscosity)
• Amplitude depends on distance, orientation, ∆Ω, and

compressibilities… but not E

• Pol’n ratio: orientation to line of sight (also N, K)

2 2 11

) ( ) ( Ω − + =

2 ×

f E f f h ω

2 2 21

) 2 ( ) ( Ω − + =

2 +

f E f f h ω

EQUATORIAL OBSERVER (van Eysden & Melatos 07, Bennett & Melatos 07)

h+(f) h×(f) f f

Ν = 1 K = 1

K = 0.1 K = 3 K = 1 K = 0.3 N = 0.3 N = 0.1 N = 1 N = 3

(van Eysden & Melatos 07)

EXTRACTING NUCLEAR PHYSICS

N i E K

Total signal including current quadrupole

i i E N N K K E

(Bennett & Melatos 07)

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?

(Peralta et al 05, 06; Andersson et al 06, 07)

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!