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Neutron Star Magnetic Mountains: An Improved Model

Neutron Star Magnetic Mountains: An Improved Model. Orange 2009: Pulsar Meeting. Maxim Priymak Supervisor: Dr. A. Melatos. Overview. Accreting Neutron Stars (NS) as Gravitational Wave (GW) sources Magnetic mountain mechanism Improved magnetic mountain model Implemented more realistic EoS

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Neutron Star Magnetic Mountains: An Improved Model

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  1. Neutron Star Magnetic Mountains: An Improved Model Orange 2009: Pulsar Meeting Maxim Priymak Supervisor: Dr. A. Melatos

  2. 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…)

  3. NOT a selection effect • 2 mechanisms explain this: • Gravitational Wave (GW) emission • Propeller effect • Dominant mechanism Inconclusive • both contribute X-ray pulsations Burst oscillations Quasi-Periodic Oscillations 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) ? XTE J1739-285 ? From tabulated data of Watts et al. 2008

  4. Magnetic Mountain • 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 • 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

  5. Initial State Final State ψ1 ψ2 ψ1 ψ3 ψ2 ψ3 ψ4 ψ4 ψ5 ψ5 ψ6 ψ6 ψ7 ψ7 ψ8 ψ9 ψ8 ψ10 ψ9 ψ10 Solving the MHS equilibrium Lorentz force (pressure + tension) • Supplemented with: • EoS: • Mass-flux Constraint: dM/dΨ|final = dM/dΨ|initial + dM/dΨ|accreted Pressure gradient Gravitational force Net Force

  6. 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 )

  7. MHS Equilibrium: |B|max and ρmax versus Maccreted • Attained ρmax realistic (cf. Ideal Isothermal EoS) • Above Bcracking plastic flow ?

  8. Magnetic Mountain: Ideal Isothermal EoS Maccreted = 3.3x10-5 Mסּ

  9. Magnetic Mountain: Adiabatic EoS Degenerate n EoS: Maccreted = 3.3x10-7 Mסּ Degenerate Relativistic e-EoS: Maccreted = 3.3x10-8 Mסּ

  10. LIGO locations LIGO/ALIGO detectability curves www.cs.unc.edu Vigelius et al. 2008 LIGO/ALIGO Estimates • GW strain h is: Ma = 10-4 Mסּ Ohmic diffusion arrests mountain growth Ma = 10-5 Mסּ Degenerate n EoS Ma = 10-6 Mסּ Relativistic Degenerate e- EoS Ma = 10-7 Mסּ Ma = 10-8 Mסּ Ma = 10-9 Mסּ No observed NS that spin fast enough

  11. 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…)

  12. The End Thank you for your attention. Any Questions?

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