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

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.

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

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 = 10-28 (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).

Building neutron star mountains Strained crust : — Maximum deformation: max ≈ 10-6 (br/10-2) — uncertain breaking strain, br = 10-2 - 10-5 for terrestrial materials. — unclear whether max is attainable. Magnetic deformation by interior B-field: B ≈ ± 10-9 (H/1015G) (B/1012G) — Superconducting core: H = 1015G, H = B otherwise . — B-field geometry, EoS: could change B by a factor ~ 10-100. 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

Mountain observability Most pulsars too slow, f=10-30Hz & f= 300-1000 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)

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 ?

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 ≈ 10-22 (f/10Hz)1/2 (1kpc/d)

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)

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 ?

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 …

Magnetars Recently discovered QPOs during flares suggest mode excitation. fqpo = 20-1000 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?

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.

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 ? — 300-1000 Hz for LMXBs, unstable modes (and supernovae!)