neutron star magnetic mountains: an improved model maxim priymak supervisor: dr. a. melatos orange...
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Neutron Star Magnetic Mountains: An Improved Model
Maxim PriymakSupervisor: Dr. A. Melatos
Orange 2009: Pulsar Meeting
Overview• Accreting Neutron Stars (NS) as Gravitational
Wave (GW) sources• Magnetic mountain mechanism
• Improved magnetic mountain model– Implemented more realistic EoS• GW detectability decreases
Motivation – Quantify GW detectability of accreting NS by
LIGO/ALIGO– Construct GW search templates– Infer NS properties (Maccreted, conductivity etc…)
Accreting Neutron Stars
• Accreting Neutron Stars (NS) X-ray sources (LMXB/HMXB)
• NS spin up
• NS spin measurements: X-ray pulsations/Burst
oscillations/QPO
• Spin distribution cut off > 700 Hz None at ≈ Ωbreak up (~1500-3000 Hz)
• NOT a selection effect
• 2 mechanisms explain this:1) Gravitational Wave (GW) emission2) Propeller effect
• Dominant mechanism Inconclusive– both contribute
From tabulated data of Watts et al. 2008
? XTE J1739-285 ?
X-ray pulsations
Burst oscillations
Quasi-Periodic Oscillations
Magnetic Mountain• Accretion driven (LMXB/HMXB)
• B confines matter:
1) PHYDROSTATIC > PMAGNETIC Matter Spreads
2) B distorted Equilibrium NS asphericity
4) Spin/Dipole axes misaligned Q ≠ 0 GW
• Advantages (as GW emitter):
– Known position and/or signal f (X-ray / Optical / Radio) + Persistent
• Current Models:
– 2D (Payne & Melatos 2004)• Axisymmetric MHS equilibrium• Stable
– 3D (Vigelius & Melatos 2008)
• Non-ideal MHD• Stable
Time evolution of 3D magnetic mountain
Vigelius & Melatos 2008
• Current model deficiencies:– Rigid crust no sinking– Irrotational no FCORIOLIS
– Constant BC’s no crustal freezing– Isothermal no variable resistivity – No inclination unrealistic
– Ideal isothermal EoS (P = cs2ρ)
unrealistic
Solving the MHS equilibrium
ψ1
ψ5
ψ4
ψ3
ψ2
ψ6
ψ7
ψ8
ψ9
ψ10
ψ1
ψ7
ψ6
ψ5
ψ4
ψ3
ψ2
ψ10 ψ
9
ψ8
Initial State Final State
• Supplemented with:– EoS:
– Mass-flux Constraint: dM/dΨ|final = dM/dΨ|initial + dM/dΨ|accreted
Gravitational force
Lorentz force (pressure + tension)Pressure gradient
Net Force
MHS Equilibrium: Dipole Moment (μ) and Ellipticity (ε) versus Maccreted
• 2 Feasible EoS: (P = KρΓ)– Degenerate Neutron EoS [K = 5.4e4 (SI), Γ = 5/3]
– Relativistic Degenerate Electron EoS [K = 4.9e9 (SI), Γ = 4/3]
(cf. Ideal Isothermal EoS P = cs2ρ )
MHS Equilibrium: |B|max and ρmax versus Maccreted
1) Attained ρmax realistic (cf. Ideal Isothermal EoS)
2) Above Bcracking plastic flow ?
Magnetic Mountain: Ideal Isothermal EoS
Maccreted = 3.3x10-5 Mּס
Maccreted = 3.3x10-7 Mּס
Maccreted = 3.3x10-8 Mּס
Degenerate n EoS:
Degenerate Relativistic e- EoS:
Magnetic Mountain: Adiabatic EoS
LIGO/ALIGO Estimates
• GW strain h is:
www.cs.unc.edu
LIGO locations
Vigelius et al. 2008
LIGO/ALIGO detectability curves
Relativistic Degenerate e- EoS
Degenerate n EoS
Ma = 10-7 Mּס
Ma = 10-9 Mּס
Ma = 10-6 Mּס
Ma = 10-8 Mּס
Ma = 10-5 Mּס
Ma = 10-4 Mּס
No observed NS that spin fast enough
Ohmic diffusion arrests mountain growth
Current Work
• Extend to realistic Maccreted
• Implement Realistic Nuclear EoS
Future Work• Crustal freezing / sinking• Compute feedback b/w mountain and magnetosphere
Cornell Collaboration• Application to X-ray bursts– Light curves & cyclones / Episodic decay of the
mountain
WHY? – Quantify the effects on GW detectability by
LIGO/ALIGO– Construct GW search templates– Infer NS properties (Maccreted, conductivity etc…)
The End
Thank you for your attention.
Any Questions?
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