A Magnetic α ω Dynamo in Active Galactic Nuclei Disks - NMT Physics

– 23 –VP is pleased to thank Richard Lovelace and Eric Blackman for helpful discussions. EricBlackman is thanked again for his support during the late stages of this work. SC particularlyrecognizes Hui Li of LANL for support through the Director funded Research on the MagnetizedUniverse and New Mexico Tech for support of the plume rotation experiments as well as thedynamo experiment. The facilities and interactions of Aspen Center for Physics during two summervisits by VP and more by SAC are gratefully acknowledged. This work has been supportedby the U.S. Department of Energy through the LDRD program at Los Alamos National Laboratory.VP also acknowledges partial support by DOE grant DE-FG02-00ER54600 and by theCenter for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas at the Universityof Wisconsin-Madison.A. Parameters of Shakura–Sunyaev DiskIn the subsequent estimates of the disk physical parameters we will keep the radius of the diskr, where the star-disk collisions happen, Shakura–Sunyaev viscosity parameter α ss , ratio of the diskluminosity to the Eddington luminosity l E , fraction ǫ of the rest mass accretion flux Ṁc2 , which isradiated away, as parameters. We will assume them to be within an order of magnitude from theirtypical values of importance for the dynamo problem, which are the followingα ss = 0.01, l E = 0.1, ǫ = 0.1, r = 10 −2 pc. (A1)The flux of the stars through the disk, nv/4, peaks at the radii inside r = 10 −2 pc (see section 3.2),therefore we need to know the physics of the accretion disk at r ∼ 10 −2 pc. Below, we will definethe gravitational radius as r g = 2GM/c 2 = 3.0 · 10 13 M 8 cm = 9.5 · 10 −6 M 8 pc. All formulae forthe structure of Shakura–Sunyaev disk are written for an arbitrary value of the black hole massM = 10 8 M 8 M ⊙ . However, we will consider only M = 10 8 M ⊙ whenever we invoke the model forthe star distribution in the central cluster, because the best available model of the central starcluster was calculated for the M = 10 8 M ⊙ (section 2.1). Finally, the accuracy of expressions forthe disk parameters is only one significant figure in all cases, and we keep two or even three figuresonly to avoid introducing additional round off errors, when using our expressions. Similarly, oneshould not be concerned about small jumps of values across the boundaries with different physicalapproximations: a more elaborate treatment is needed to find exact matching solutions there,although the physical principles are unchanged.We use formulae from the Shakura & Sunyaev (1973) article to obtain estimate of the state ofthe accretion disk. We assume the Schwarzschild black hole with the inner edge of the disk beingat 3r g . However, since we consider star-disk collisions happening at ∼ 10 3 r g , general relativisticcorrections are only at a level less than few per cents and do not matter for our approximatetreatment of star-disk collision hydrodynamics. All expressions for disk quantities below were alsoverified in later textbooks by Shapiro & Teukolsky (1983) and Krolik (1999).The inner part of the disk (part (a) as in Shakura & Sunyaev (1973)) is radiation dominated