The large scale magnetic fields of advection dominated accretion flows

We calculate the advection/diffusion of the large-scale magnetic field threading an ADAF, and find that the magnetic field can be dragged inward by the accretion flow efficiently, if the magnetic Prandtl number P~1. This is due to the large radial velocity of the ADAF. It is found that the magnetic pressure can be as high as ~50% of the gas pressure in the inner region of the ADAF close to the black hole horizon, even if the external imposed vertical field strength is <5% of the gas pressure at the outer radius of the ADAF, which is caused by the gas plunging rapidly to the black hole within the marginal stable circular orbit. In the inner region of the ADAF, the flow is significantly pressured in the vertical direction by the magnetic field, and therefore its gas pressure can be two orders of magnitude higher than that in the ADAF without magnetic fields. This means that the magnetic field strength near the black hole is underestimated by assuming equipartition between magnetic and gas pressure with the conventional ADAF model. Our results show that the magnetic field strength of the flow near the black hole horizon can be more than one order of magnitude higher than that in the ADAF at 6GM/c^2, which implies the Blandford-Znajek mechanism could be more important than the Blandford-Payne mechanism for ADAFs. We find that the accretion flow is decelerated near the black hole by the magnetic field when the external imposed field is strong enough or the gas pressure of the flow is low at the outer radius, or both. This corresponds to a critical accretion rate, below which the accretion flow will be arrested by the magnetic field near the black hole for a given external imposed field. In this case, the gas may accrete as magnetically confined blobs diffusing through field lines in the region very close to the black hole horizon, which is similar to those in compact stars.