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Structure and stability of accretion moundson the polar caps of strongly magnetized
Neutron Stars
Dipankar Bhattacharya, Dipanjan Mukherjee(IUCAA, Pune)
andAndrea Mignone
(University of Torino, Italy)
Romanova, Kulkarni and Lovelace 2008
From Accretion Disk to the polar cap
Primary Sources: HMXB Pulsars
Heindl et al 2004
Ec1 ~ 12 B12 keV
Accreted matter forms magneticallysupported mound at polar cap
Cyclotron lines arisingin the mound provideestimate of localmagnetic field strength
Trumper et al 1978Gruber et al 2001
Her X-1:Neutron Starwith a 2 Msuncompanionin beginningatmosphericRoche lobeoverflow
Heindl et al 2004
Building a Physical Model of the Accretion Mound
Incoming plasma is highly conductingFlux freezing is satisfied to the leading order
magnetostatic balance:
; ;
Polar Mountain
assume azimuthal symmetry at polar cap
Mukherjee & DB 2011
Mukherjee & DB 2011
Mukherjee & DB 2011
Mukherjee & DB 2011
Hotspot emissionviewing geometry
Mukherjee & DB 2011
0 5-5angular extent (deg)
photospheric B map (max col ht = 70 m)
Central traverseEdge traverse
α = 10 deg
α = 60 deg
B field at LOS cuts
Mukherjee & DB 2011
Mukherjee & DB 2011
Hotspot emissionviewing geometry
Light bending:cos α ≃ u + (1 - u) cos ψ ; u = 2GM/c2r(Beloborodov 2002)
Mukherjee & DB 2011
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Mukherjee & DB 2011
Mukherjee & DB 2011
Stability Limit of GS solutions
Mukherjee & DB 2011
Stability Limit of GS solutions
Mukherjee & DB 2011
Stability Limit of GS solutions
Zm B∝ 0.5 approx.
Ballooning instabilitythreshold:
Zm B∝ 4/7 approx.
Litwin et al 2001
Why is stability of the mound important?
Plays an important role in matter spreading and secular evolution of magnetic field
A popular scenario is that thespreading matter buries the magnetic field under it
But this process is controlled entirely by instabilities.
The effectiveness of the field screening is determined by the amount of matter in the mound before cross-field transport canoccur.
The mound height is also important forgravitational wave radiation
Macc = 10-5 Msun
Payne & Melatos 2004
Instabilitiesnotaccountedfor
Scaled problem
Stability Analysis with PLUTO
PLUTOPLUTOConservative form of the MHD equations :
The stable cocktail :
1. Time stepping : Runge-Kutta 3rd order.
2. Interpolation : Parabolic (PPM), 3rd order.
3. Riemann solvers : HLL, HLLC, TVDLF.
4. Extended Hyperbolic Divergence cleaning.
5. EOS : IDEAL
Inflow
Boundary ConditionsBoundary Conditions• Fixed Boundary : Boundary fixed to initial value.Fixed Boundary : Boundary fixed to initial value.
• Outflow :Outflow :
• Fixed gradient. (Outflow only on perturbations) :Fixed gradient. (Outflow only on perturbations) :
• Extrapolated boundary.Extrapolated boundary.
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PLUTO MHD simulations
Mukherjee, Mignone & DB 2012
65m equilibrium solution
zero-mean perturbation
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PLUTO MHD simulations
Mukherjee, Mignone & DB 2012
65m equilibrium solution
3% mass load
PLUTO MHD simulations
Mukherjee, Mignone & DB 2012
65m equilibrium solution
5% mass load
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3-D simulations for 70m mound3-D simulations for 70m mound
Random velocity field as perturbation (strength ~ 5x10-2)
Toroidal perturbations causes growth of finger like projections :
fluting mode instabilities?
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Mukherjee, Mignone & DB 2012
Mukherjee, Mignone & DB 2012
Mukherjee, Mignone & DB 2012
Summary
•Numerical solution of Grad-Shafranov equation provides a good description of magnetically confined static polar mound.
•Large distortion of magnetic field required to support mound weight. Would have observable signature in Cyclotron spectra.
•2D MHD simulations show ballooning instability if mass is added to mounds in equilibrium. Mounds become unstable beyond ~ 10-13 Msun.
•3D MHD simulations show easy excitation of fluting mode instability and consequent cross-field transport. This would greatly reduce the efficacy of field burial.
