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?