structure and stability of accretion mounds on the polar caps of strongly magnetized neutron stars...

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

QuickTime™ and a decompressor

are needed to see this picture.

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.

QuickTime™ and a decompressor

are needed to see this picture.

PLUTO MHD simulations

Mukherjee, Mignone & DB 2012

65m equilibrium solution

zero-mean perturbation

QuickTime™ and a decompressor

are needed to see this picture.

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

QuickTime™ and a decompressor

are needed to see this picture.

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?

QuickTime™ and a decompressor

are needed to see this picture.

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.