GRAVITATIONAL WAVES FROM ACCRETING NS

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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

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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)

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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 radn pressure ? Nacc lt 0 (Andersson et al.
  05)
• Promising sources (e.g. Sco X-1)
• known period, sinusoidal, persistent strong!

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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

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• Is e large enough?
• Elastic crust adjusts ? reduces e
• Need DT/T 5 at base of outer crust
• Slow conduction cracking (mshear lt NkT), so
  e persists
• GW correlated with thermal X-rays

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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)

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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)
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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 ? ? ds r/B
• Need 10-5MSun (cf. Brown Bildsten 98)

r
B
10-5MSun
r
B
(Payne Melatos 04)
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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)
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DRAINAGE
PARKER BLISTER
mass flux loss lt 1
Is this (distorted) magnetic field unstable? No!
Parker instability already happened (and
line tying)
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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

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GW SPECTRUM
h
h?
LIGO I
LIGO II
f? ? d3Ixz/dt3 2f? ? d3Ixy/dt3
f?
2f?
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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)

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IV. SUPERFLUID CIRCULATION
torque
EKMAN PUMPING
Re104

• Rotation in sphere drives meridional circulation
• Time-dependent asymmetric at high Re 1011
• Precession asymmetric KE of fluid ? GW

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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

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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)

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Gone!