The structure of thin accretion discs around magnetized stars

Solomon Belay Tessema & Ulf TorkelssonA&A, 509, A45 (2010) . arXiv:0911.2084

• Introduction

• Mathematical formulation

• Numerical solution

• Discussion & conclusions

Introduction

• Background– Standard model of Shakura & Sunyaev 1973– Effective angular momentum transport

mechanism introduced by Balbus & Hawley 1991 (MRI)

– Coupling of the magnetic field of the star and the disc surrounding. (Ghosh & Lamb 1979)

– Torque-reversals (TRs) of some X-ray pulsars 4U1626-67, Cen X-3, OAO 1657-415

• Nelson et al.(1997)– Transition of co-rotating and counter-rotating

accretion discs (only occur in wind fed accretion)

• Torkelsson(1998) – TRs maybe the results of reversals of the

magnetic field generated by dynamo

Mathematical formulation

• Conservation of mass

• Conservation of momentum

• Azimuthal component

• Conservation of energy

• Magnetic dissipation is negligible

M

Numerical solution

• Boundary conditions• Outer boundary--> SS model

• Inner boundary• Case D

• Case V

M=1.4Msolar,dotM=1013 kgs-1,αss=0.01,γ=1,γdyn=10,μ=1020 Tm-3

• The structure of an accretion disc

Discussion

• The angular momentum balance

Nadv

NdynNshear

Nvis

Discussion and conclusions• BATSE data of 7.6s X-ray pulsar 4U1626-67

(Bildsten et al. 1997)

The over estimate of the torque may explain by that the unidirection of Bφ,dyn through the disc was assumed in this model.

In the model of accretion disc supporting an internal dynamo, the resulting torque of interaction between the magnetosphere of the star and the disc is larger than the model by Ghosh & Lamb (1979) .

This extra torque can explain the large spin frequency variations of some sources (Cen X-3, OAO1657-415)

The reversal of the magnetic field that is generated by the internal dynamo could explain the TRs in these objects

The dynamo also leads to that the inner edge of the accretion disc occurs at a larger radius than RA

Thanks