G050504 00

GRAVITATIONAL WAVESFROM ACCRETING NS: 

GRAVITATIONAL WAVES FROM 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

NS SPINS IN LMXBs: 

NS SPINS IN LMXBs 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) breakup narrow range RXTE timing fNS LX

GW “STALLING”: 

GW “STALLING” GW torque  e2 f 5 balances 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!

I. THERMAL MOUNTAIN: 

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

Slide5: 

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

II. r-MODES: 

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)

Slide7: 

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

III. MAGNETIC BURIAL: 

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

GW SIGNAL: 

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

Slide10: 

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

MHD OSCILLATIONS: 

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

GW SPECTRUM: 

GW SPECTRUM f h+ h LIGO I LIGO II 2f f  d3Ixz/dt3 2f  d3Ixy/dt3

PRECESSION: 

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)

IV. SUPERFLUID CIRCULATION: 

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

Slide15: 

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

SUMMARY: 

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)

Slide17: 

Gone!