GRAVITATIONAL WAVES FROM ACCRETING NS

1. GRAVITATIONAL WAVESFROM ACCRETING NS A. Melatos, D. Payne, C. Peralta, M. Vigelius (U. Melbourne) • X-ray timing → LMXB spins → GW “stalling” → promising kHz sources! • Thermal mountains & r-modes • Magnetic mountains: GW spectrum • Precession & superfluid circulation

2. NS SPINS IN LMXBs narrow range RXTE timing breakup fNS LX • Low-mass ~ MSun X-ray binaries: disk accretion • kHz oscillations in thermonuclear X-ray bursts • Simultaneous pulses → stellar spin • Much slower than breakup (Chakrabarty et al. 03)

3. GW “STALLING” • GW torque e2 f 5balances accretion torque (dM/dt)Rdisk1/2(Wagoner 84; Bildsten 98) • Minimum quadrupole moment • Narrow range of f since NGW  f 5 (steep!) • BUT rad’n pressure → Nacc < 0(Andersson et al. 05) Promising sources(e.g. Sco X-1): known period, sinusoidal, persistent & strong!

4. I. THERMAL MOUNTAIN • Lateral T • e-capture (A,Z) → (A,Z-1) • Occurs at lower r in hot spots (Bildsten 98) • “Wavy” capture layers → e • (A,Z) & heating gradient ↔ T ↔ thermal conductivity & nuclear reaction rate

5. e = 10-8 LMXB data SF core N core (heat) (A,Z) (Ushomirsky et al. 00) • Is e large enough? • Elastic crust adjusts → reduces e • Need DT/T ≈ 5% at base of outer crust • Slow conduction & cracking (mshear< NkT), so e persists GW correlated with thermal X-rays

6. II. r-MODES • Rossby waves continuously excited in core (Andersson et al. 99); cf. ocean r-modes (Heyl 04) • Amplitude (→ e) set by shear modulus, normal-superfluid friction(Lindblom & Mendell 99), boundary layer viscosity (Bildsten & Ushomirsky 00), radial crust-core coupling (Levin & Ushomirsky 01) • Thermal instability(Levin 99) Quiescent LX~ 1034 erg s-1 from NS transients, e.g. Aql X-1… not seen!(Brown & Ushomirsky 00)

7. VBL + superfluid core newly born NS VBL + normal core accreting NS r-mode grows 2 MSPs 3 GW losses 1 4 no VBL Thermal runaway cycle (Levin 99) Onset of instability (Bildsten & Ushomirsky 00)

8. III. MAGNETIC BURIAL 10-8MSun • Polar accretion • Equatorward spreading • Hydro pressure balanced by tension in compressed equatorial B: (×B)×B-rF-P = 0 • Flux freezing →  dsr/|B| • Need 10-5MSun(cf. Brown & Bildsten 98) r B 10-5MSun r B (Payne & Melatos 04)

9. GW SIGNAL • Magnetic mountain → e → wave strain hc • Integrate for one yr • Resistivity, sinking… • Magnetic moment ↓ (see NS binaries) • Predict h m-1 LIGO I LIGO II 10-2MSun 10-8MSun (Melatos & Payne 05)

10. “DRAINAGE” PARKER “BLISTER” mass & flux loss < 1% Is this (distorted) magnetic field unstable? No! Parker instability “already” happened (and line tying)

11. MHD OSCILLATIONS 10-4MSun • Perturb in Zeus 3D: “sloshes” stably for 2500 TAlfven • Alfvén mode (slow) frequency depends on Ma • Sound mode (fast) frequency independent of Ma

12. ☺ z Wt ☺ y x GW SPECTRUM h+ h LIGO I LIGO II f  d3Ixz/dt3 2f  d3Ixy/dt3 f 2f

13. PRECESSION Magnetic mountain inclined to W • Precession undamped: GW near f and 2f • Precession damped:e3 →W, no X-ray pulses,GW at 2f only (if triaxial) Excitation • Disk-magnetosphere torque (Jones & Andersson 02) • Near-zone magnetic dipole torque (Melatos 00)

14. IV. SUPERFLUID CIRCULATION torque EKMAN PUMPING Re=104 • Rotation in sphere drives meridional circulation • Time-dependent & asymmetric at high Re~ 1011 • Precession: asymmetric KE of fluid → GW

15. KE SURFACE ruaub= const STREAM LINES QUADRUPOLE e(t) FFT → e(f) • 3-dim superfluid hydro code (HVBK theory) • GW near 2f broadened by Ekman & precession

16. SUMMARY • LMXB spins → GW “stalling” if e ≈ 10-8 • Thermal & magnetic mountains & r-modes • Detectable by LIGO II • Spectrum broadened by (MHD) oscillations • Precession • Accretion by SN fallback?(Watts & Andersson 03) • Surface asymmetry after r-p burning? (Jones 05)

17. Gone!