Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune) and Andrea 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 E c1 ~ 12 B 12 keV Accreted matter forms magnetically supported mound at polar cap Cyclotron lines arising in the mound provide estimate of local magnetic field strength

Trumper et al 1978 Gruber et al 2001 Her X-1: Neutron Star with a 2 Msun companion in beginning atmospheric Roche lobe overflow

Heindl et al 2004 Building a Physical Model of the Accretion Mound

Incoming plasma is highly conducting Flux freezing is satisfied to the leading order magnetostatic balance: ; ; Polar Mountain assume azimuthal symmetry at polar cap

Mukherjee & DB 2011

Hotspot emission viewing geometry

Mukherjee & DB angular extent (deg) photospheric B map (max col ht = 70 m) Central traverse Edge traverse

α = 10 deg α = 60 deg B field at LOS cuts Mukherjee & DB 2011

Hotspot emission viewing geometry Light bending: cos α ≃ u + (1 - u) cos ψ ; u = 2GM/c 2 r (Beloborodov 2002)

Mukherjee & DB 2011

Stability Limit of GS solutions

Mukherjee & DB 2011 Stability Limit of GS solutions

Mukherjee & DB 2011 Stability Limit of GS solutions Z m ∝ B 0.5 approx.

Ballooning instability threshold: Z m ∝ 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 the spreading 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 can occur. The mound height is also important for gravitational wave radiation

M acc = M sun Payne & Melatos 2004 Instabilities not accounted for Scaled problem

Stability Analysis with PLUTO

PLUTO Conservative form of the MHD equations : The stable cocktail : 1.Time stepping : Runge-Kutta 3 rd order. 2. Interpolation : Parabolic (PPM), 3 rd order. 3.Riemann solvers : HLL, HLLC, TVDLF. 4.Extended Hyperbolic Divergence cleaning. 5.EOS : IDEAL Inflow

Boundary Conditions Fixed Boundary : Boundary fixed to initial value. Outflow : Fixed gradient. (Outflow only on perturbations) : Extrapolated boundary. Extrapolated boundary.

PLUTO MHD simulations Mukherjee, Mignone & DB m equilibrium solution zero-mean perturbation

PLUTO MHD simulations Mukherjee, Mignone & DB m equilibrium solution 3% mass load

PLUTO MHD simulations Mukherjee, Mignone & DB m equilibrium solution 5% mass load

3-D simulations for 70m mound Random velocity field as perturbation (strength ~ 5x10 -2 ) Toroidal perturbations causes growth of finger like projections : fluting mode instabilities?

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 ~ M sun. 3D MHD simulations show easy excitation of fluting mode instability and consequent cross-field transport. This would greatly reduce the efficacy of field burial.