Where is a Marginally Stable Last Circular Orbit in Super-Critical Accretion Flow?

Impressed by the widespread misunderstanding of the issue, we return to the old question of the location of the inner edge of accretion disk around black hole. We recall the fundamental results obtained in the 1970's and 1980's by Warsaw and Kyoto research groups that proved, in particular, that the inner edge does not coincide with the location of the innermost stable Keplerian circular orbit. We give some novel illustrations of this particular point and of some other fundamental results obtained by Warsaw and Kyoto groups. To investigate the flow dynamics of the inner edge of accretion disk, we carefully solve the structure of the transonic flow and plot the effective potential profile based on the angular-momentum distribution calculated numerically. We show that the flow does not have a potential minimum for accretion rates, {\dot M} > 10 L_E/c^2 (with L_E being the Eddington luminosity and $c$ being the speed of light). This property is realized even in relatively small viscosity parameters (i.e., \alpha ~ 0.01), because of the effect of pressure gradient. In conclusion, the argument based on the last circular orbit of a test particle cannot give a correct inner boundary of the super-critical flow and the inner edge should be determined in connection with radiation efficiency. The same argument can apply to optically thin ADAF. The interpretation of the observed QPO frequencies should be re-considered, since the assumption of Kepler rotation velocity can grossly over- or underestimate the disk rotation velocity, depending on the magnitude of viscosity.Comment: 7 pages, 3 figures, accepted for PAS

Codensity Lifting of Monads and its Dual

We introduce a method to lift monads on the base category of a fibration to its total category. This method, which we call codensity lifting, is applicable to various fibrations which were not supported by its precursor, categorical TT-lifting. After introducing the codensity lifting, we illustrate some examples of codensity liftings of monads along the fibrations from the category of preorders, topological spaces and extended pseudometric spaces to the category of sets, and also the fibration from the category of binary relations between measurable spaces. We also introduce the dual method called density lifting of comonads. We next study the liftings of algebraic operations to the codensity liftings of monads. We also give a characterisation of the class of liftings of monads along posetal fibrations with fibred small meets as a limit of a certain large diagram.Comment: Extended version of the paper presented at CALCO 2015, accepted for publication in LMC

Transonic Galactic Outflows and Their Influences to the Chemical Evolution of Galaxies and Intergalactic Space

We have categorized possible transonic solutions of galactic outflows in the gravitational potential of DMH and SMBH using the isothermal, spherically symmetric and steady model. We conclude that the gravitational potential of SMBH generates a new transonic branch while Tsuchiya et al. (2013) concluded that the gravitational potential of DMH forms one transonic solution. Because these two transonic solutions have different mass fluxes and starting points, these solutions will make different influences to the star formation rate, the evolution of galaxies, and the chemical evolution of the intergalactic medium. Therefore, we conclude that the influence of galactic outflows to the intergalactic medium depends not only on the mass distribution but also on the selected transonic solution. In addition, we have estimated range of parameters (KDMH; KBH) for actual galaxies. Moreover, it may be possible to estimate the galactic mass distributions of DMH and SMBH applying the model to the observed profile of the outflow velocity. Although it is difficult to determine the velocity of hot gas in the galactic halos from the current X-ray observations, but the next-generation X-ray observatory will be able to detect the detailed profiles of outflow velocities.Comment: 6 pages, 3 figures, accepted for publication in AIP Conference Proceeding