structure and stability of accretion mounds on the polar caps of strongly magnetized neutron stars...
TRANSCRIPT
![Page 1: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/1.jpg)
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)
![Page 2: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/2.jpg)
Romanova, Kulkarni and Lovelace 2008
From Accretion Disk to the polar cap
![Page 3: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/3.jpg)
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
![Page 4: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/4.jpg)
Trumper et al 1978Gruber et al 2001
Her X-1:Neutron Starwith a 2 Msuncompanionin beginningatmosphericRoche lobeoverflow
![Page 5: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/5.jpg)
Heindl et al 2004
Building a Physical Model of the Accretion Mound
![Page 6: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/6.jpg)
Incoming plasma is highly conductingFlux freezing is satisfied to the leading order
magnetostatic balance:
; ;
Polar Mountain
assume azimuthal symmetry at polar cap
![Page 7: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/7.jpg)
Mukherjee & DB 2011
![Page 8: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/8.jpg)
Mukherjee & DB 2011
![Page 9: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/9.jpg)
Mukherjee & DB 2011
![Page 10: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/10.jpg)
Mukherjee & DB 2011
Hotspot emissionviewing geometry
![Page 11: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/11.jpg)
Mukherjee & DB 2011
0 5-5angular extent (deg)
photospheric B map (max col ht = 70 m)
Central traverseEdge traverse
![Page 12: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/12.jpg)
α = 10 deg
α = 60 deg
B field at LOS cuts
Mukherjee & DB 2011
![Page 13: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/13.jpg)
Mukherjee & DB 2011
Hotspot emissionviewing geometry
Light bending:cos α ≃ u + (1 - u) cos ψ ; u = 2GM/c2r(Beloborodov 2002)
![Page 14: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/14.jpg)
Mukherjee & DB 2011
![Page 15: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/15.jpg)
QuickTime™ and a decompressor
are needed to see this picture.
Mukherjee & DB 2011
![Page 16: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/16.jpg)
Mukherjee & DB 2011
Stability Limit of GS solutions
![Page 17: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/17.jpg)
Mukherjee & DB 2011
Stability Limit of GS solutions
![Page 18: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/18.jpg)
Mukherjee & DB 2011
Stability Limit of GS solutions
Zm B∝ 0.5 approx.
![Page 19: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/19.jpg)
Ballooning instabilitythreshold:
Zm B∝ 4/7 approx.
Litwin et al 2001
![Page 20: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/20.jpg)
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
![Page 21: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/21.jpg)
Macc = 10-5 Msun
Payne & Melatos 2004
Instabilitiesnotaccountedfor
Scaled problem
![Page 22: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/22.jpg)
Stability Analysis with PLUTO
![Page 23: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/23.jpg)
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
![Page 24: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/24.jpg)
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.
![Page 25: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/25.jpg)
QuickTime™ and a decompressor
are needed to see this picture.
PLUTO MHD simulations
Mukherjee, Mignone & DB 2012
65m equilibrium solution
zero-mean perturbation
![Page 26: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/26.jpg)
QuickTime™ and a decompressor
are needed to see this picture.
PLUTO MHD simulations
Mukherjee, Mignone & DB 2012
65m equilibrium solution
3% mass load
![Page 27: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/27.jpg)
PLUTO MHD simulations
Mukherjee, Mignone & DB 2012
65m equilibrium solution
5% mass load
QuickTime™ and a decompressor
are needed to see this picture.
![Page 28: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/28.jpg)
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?
![Page 29: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/29.jpg)
QuickTime™ and a decompressor
are needed to see this picture.
Mukherjee, Mignone & DB 2012
![Page 30: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/30.jpg)
Mukherjee, Mignone & DB 2012
![Page 31: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/31.jpg)
Mukherjee, Mignone & DB 2012
![Page 32: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/32.jpg)
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.
![Page 33: Structure and stability of accretion mounds on the polar caps of strongly magnetized Neutron Stars Dipankar Bhattacharya, Dipanjan Mukherjee (IUCAA, Pune)](https://reader035.vdocument.in/reader035/viewer/2022062321/56649e155503460f94aff35c/html5/thumbnails/33.jpg)