1. 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

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. known period, sinusoidal, persistent & strong!
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!

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. GW correlated with thermal X-rays
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
e = 10-8
N core
SF core
LMXB data
(A,Z)
(heat)
(Ushomirsky et al. 00)

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

8. III. MAGNETIC BURIAL (×B)×B-rF-P = 0 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)
10-8MSun 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. Is this (distorted) magnetic field unstable? No!
“DRAINAGE”
PARKER
“BLISTER”
mass & flux
loss < 1%
Is this (distorted) magnetic field unstable? No!
Parker instability “already” happened (and line tying)

11. MHD OSCILLATIONS Perturb in Zeus 3D: “sloshes” stably for 2500 TAlfven
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. GW SPECTRUM h+ h 2f  d3Ixy/dt3 f 2f ☺ LIGO I LIGO II
f  d3Ixz/dt3
2f  d3Ixy/dt3 f x y z Wt ☺
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
EKMAN
PUMPING
torque
Re=104
Rotation in sphere drives meridional circulation
Time-dependent & asymmetric at high Re ~ 1011
Precession: asymmetric KE of fluid → GW

15. 3-dim superfluid hydro code (HVBK theory)
STREAM
LINES
KE SURFACE
ruaub = const
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!