Limit Theorems and Governing Equations for Levy Walks

The Levy Walk is the process with continuous sample paths which arises from consecutive linear motions of i.i.d. lengths with i.i.d. directions. Assuming speed 1 and motions in the domain of beta-stable attraction, we prove functional limit theorems and derive governing pseudo-differential equations for the law of the walker's position. Both Levy Walk and its limit process are continuous and ballistic in the case beta in (0,1). In the case beta in (1,2), the scaling limit of the process is beta-stable and hence discontinuous. This case exhibits an interesting situation in which scaling exponent 1/beta on the process level is seemingly unrelated to the scaling exponent 3-beta of the second moment. For beta = 2, the scaling limit is Brownian motion

Flux enhancement in the inner region of a geometrically and optically thick accretion disk

The surface flux (and the corresponding observed flux) of a geometrically thick ``funnel'' shaped disk is computed taking into account the radiation impinging on the surface from other parts of the disk. It is found that the ratio of the maximum apparent luminosity to the real luminosity of the disk is only a factor $\approx 5$ even when the opening angle of the disk is small ($\approx 15^o$). Thus, geometrically beamed emission from ``funnel'' shaped sub-Eddington disks around stellar mass black holes, cannot explain the Ultra-Luminous X-ray sources detected in nearby galaxies.Comment: accepted for publication in Ap

Subdiffusive transport in intergranular lanes on the Sun. The Leighton model revisited

In this paper we consider a random motion of magnetic bright points (MBP) associated with magnetic fields at the solar photosphere. The MBP transport in the short time range [0-20 minutes] has a subdiffusive character as the magnetic flux tends to accumulate at sinks of the flow field. Such a behavior can be rigorously described in the framework of a continuous time random walk leading to the fractional Fokker-Planck dynamics. This formalism, applied for the analysis of the solar subdiffusion of magnetic fields, generalizes the Leighton's model.Comment: 7 page

An extreme, blueshifted iron line profile in the Narrow Line Seyfert 1 PG 1402+261; an edge-on accretion disk or highly ionized absorption?

We report on a short XMM-Newton observation of the radio-quiet Narrow Line Seyfert 1 PG 1402+261. The EPIC X-ray spectrum of PG 1402+261 shows a strong excess of counts between 6-9 keV in the rest frame. This feature can be modeled by an unusually strong (equivalent width 2 keV) and very broad (FWHM velocity of 110000 km/s) iron K-shell emission line. The line centroid energy at 7.3 keV appears blue-shifted with respect to the iron Kalpha emission band between 6.4-6.97 keV, while the blue-wing of the line extends to 9 keV in the quasar rest frame. The line profile can be fitted by reflection from the inner accretion disk, but an inclination angle of >60 deg is required to model the extreme blue-wing of the line. Furthermore the extreme strength of the line requires a geometry whereby the hard X-ray emission from PG 1402+261 above 2 keV is dominated by the pure-reflection component from the disk, while little or none of the direct hard power-law is observed. Alternatively the spectrum above 2 keV may instead be explained by an ionized absorber, if the column density is sufficiently high (N_H > 3 x 10^23 cm^-2) and if the matter is ionized enough to produce a deep (tau~1) iron K-shell absorption edge at 9 keV. This absorber could originate in a large column density, high velocity outflow, perhaps similar to those which appear to be observed in several other high accretion rate AGN. Further observations, especially at higher spectral resolution, are required to distinguish between the accretion disk reflection or outflow scenarios.Comment: Accepted for publication in ApJ (18 pages, 5 figures, 1 table