1. Probing Neutron Star interiors with ET ?
Kostas Glampedakis
University of Tuebingen
Joint ILIAS-ET meeting, Cascina, Italy, Nov. 2008

2. This talk
We review the expected GW observability of isolated and accreting neutron stars.
We address two key issues:
(i) Which mechanisms hold promise for a “detectable”
GW signal ?
(ii) What are the main theoretical challenges ?
We provide rough estimates for the GW strain h.

3. Key mechanisms for GW emission
‘Mountains’ & Precession
Pulsar glitches
Fluid instabilities
Magnetars

4. Neutron star mountains
Any mechanism leading to deformation is potentially relevant for GWs.
— Deformation is represented by the ellipticity:
 = ∆I/Izz, (Iij = moment of inertia tensor)
GW strain & frequency:
h = (f/10Hz)2 (1kpc/d) (/10-6)
fGW = f, 2f (f is spin frequency)
Link with precession:
— GW emission requires misalignment
between spin axis and deformation axis:
(i) precession
(ii) or ‘orthogonal rotator’ , provided  < 0
(Mestel-Jones mechanism).

5. Building neutron star mountains
Strained crust :
— Maximum deformation: max ≈ 10-6 (br/10-2)
— uncertain breaking strain, br = for terrestrial materials.
— unclear whether max is attainable.
Magnetic deformation by interior B-field: B ≈ ± (H/1015G) (B/1012G)
— Superconducting core: H = 1015G, H = B otherwise .
— B-field geometry, EoS: could change B by a factor ~
Exotic cores:
— quark matter in CFL superconducting “crystalline” phase ?
— uncertain physics, max ≈ 10-3 (br/10-2) (already constrained by LIGO).
Magnetically confined matter in accreting neutron stars: max ≈ 10-7

6. Mountain observability
Most pulsars too slow,
f=10-30Hz &
f= Hz
most promising bands.
Magnetic mountains:
Marginally detectable
even in the most
favourable scenario.
Newborn millisecond-
period magnetars:
Few days worth of signal,
could be observable.
(Figure credit: B. Haskell & B.S. Sathyaprakash)

7. Glitches
Glitch trigger mechanism still unknown, related to transfer of angular momentum due to ‘pinned’ vortices.
— Recent hydrodynamical treatment suggests superfluid
‘two-stream’ instability.
Estimate h by feeding the glitch energy into a single mode:
h ≈ 8 x 10-22(1kpc/d) (10Hz/f)[(∆E/10-12)(1s/)]1/2
Relaxation due to mutual friction
coupling:  ≈ 20 P(s)
Which modes could be excited ?

8. Glitch observability Vela-like glitches: ∆Eglitch = IΩ∆Ω ≈ 10-12 M c2
Glitch physics poorly known,
we can only make an educated
guess for the GW h-strain:
— Assume excitation of an
inertial mode fmode ≈ f
during relaxation.
— Mode energy unknown, assume:
Emode = 10-3 ∆Eglitch
h ≈ (f/10Hz)1/2 (1kpc/d)

9. Fluid instabilities: r-modes
Secular, GW-driven:
— grow ≈ 50 (P/1ms)6 s
— active for every Ω.
Instability window depends on
uncertain core-physics:
— hyperon & quark bulk viscosity
- suppressed by superfluidity
— Ekman layer friction
- modified by crust superfluid ?
Low amplitude due to non-linear saturation.
(Figure credit: N. Andersson)

10. Fluid instabilities: f-mode
f-mode instability “forgotten” for a decade or so …
— requires spin close to
break-up limit: Ω > 0.85 ΩK
Stabilised by superfluid mutual
friction (vortex drag) for
T «Tc ~ 109 K, and by bulk viscosity
for T > few x 1010 K
Unknown non-linear saturation.
Viscosity due to exotic matter phases ?
Instability window likely to change ?

11. Mode observability Newborn stars: — r-mode signal too weak beyond
the Galaxy (low saturation
amplitude).
— f-modes may stand a chance,
provided spin period ~ 1ms and
saturation amplitude is large.
LMXBs:
— exotic core could lead to
persistent r-mode radiation.
— Coupling to accretion disk could
easily set the spin limit, without the need for GWs …

12. Magnetars Recently discovered QPOs during flares
suggest mode excitation.
fqpo = Hz, duration  ≈ 1 min,
most of them associated with seismic crust modes.
— Magnetic field couples crust & core.
Most promising QPO for GWs:
l=2 mode at f ≈ 30 Hz.
Flare mechanism poorly known,
we estimate h assuming: Emode ≈ 10-3 Eburst
Event rate uncertain, possibly too low …
GW emission by flare-trigger instability?

13. Theory assignments — Superconductivity.
Progress on GW modelling is linked to our understanding of neutron star dynamics. Main directions for future work:
Multifluid hydrodynamics:
— Dynamics of exotic matter cores (mountains, glitches,…).
— New instabilities, extended mode families, extra dissipation processes.
— Superconductivity.
Numerics:
— f-mode non-linear saturation.
— Glitch physics (requires two-fluid model).
— B-field equilibria/topology/instabilities.
Magnetars:
— Oscillations (unstable modes ?).
— flare trigger mechanism.
Dynamics of newborn ‘hot’ neutron stars.

14. Executive summary
Several mechanisms for GW emission, but none really outstanding.
A secure assessment is hindered by the currently limited (or even rudimentary…) theoretical understanding.
Advances in the theoretical modelling in the next 5-10 years
should help us identify the most prominent GW-related aspects of neutron star dynamics.
Opt for narrow-banding ?
— Hz for LMXBs,
unstable modes (and supernovae!)