Limiting Carleman weights and anisotropic inverse problems

In this article we consider the anisotropic Calderon problem and related inverse problems. The approach is based on limiting Carleman weights, introduced in Kenig-Sjoestrand-Uhlmann (Ann. of Math. 2007) in the Euclidean case. We characterize those Riemannian manifolds which admit limiting Carleman weights, and give a complex geometrical optics construction for a class of such manifolds. This is used to prove uniqueness results for anisotropic inverse problems, via the attenuated geodesic X-ray transform. Earlier results in dimension $n \geq 3$ were restricted to real-analytic metrics.Comment: 58 page

Companions of Bright Barred Shapley Ames Galaxies

Companion galaxy environment for a subset of 78 bright and nearby barred galaxies from the Shapley Ames Catalog is presented. Among spiral barred galaxies there are Seyfert galaxies, galaxies with circumnuclear structures, galaxies not associated with any large scale galaxy cloud structure, galaxies with peculiar disk morphology (crooked arms) and galaxies with normal disk morphology; the list includes all Hubble types. The companion galaxy list includes number of companion galaxies within 20 diameters (D25), their Hubble type and projected separation distance. Additionally, companion environment was searched for four known active spiral galaxies, three of them are Seyfert galaxies, namely, NGC 1068, NGC 1097, NGC 5548 and one is a starburst galaxy, M82. Among the results obtained it is noted that the only spiral barred galaxy classified as Sy 1 in our list has no companions within a projected distance of 20 diameters; 6 out of 10 Sy 2 bar galaxies have no companions within 10 diamters, 6 out of 10 Sy 2 galaxies have one or more companions at projected separation distances between 10 and 20 diameters; 6 out of 12 galaxies with circumnuclear structures have 2 or more companions within 20 diametersComment: Accepted for publication in the Astronomical Journal, 40 pages incl. 3 figure

Inverse problems with partial data for a magnetic Schr\"odinger operator in an infinite slab and on a bounded domain

In this paper we study inverse boundary value problems with partial data for the magnetic Schr\"odinger operator. In the case of an infinite slab in $R^n$, $n\ge 3$, we establish that the magnetic field and the electric potential can be determined uniquely, when the Dirichlet and Neumann data are given either on the different boundary hyperplanes of the slab or on the same hyperplane. This is a generalization of the results of [41], obtained for the Schr\"odinger operator without magnetic potentials. In the case of a bounded domain in $R^n$, $n\ge 3$, extending the results of [2], we show the unique determination of the magnetic field and electric potential from the Dirichlet and Neumann data, given on two arbitrary open subsets of the boundary, provided that the magnetic and electric potentials are known in a neighborhood of the boundary. Generalizing the results of [31], we also obtain uniqueness results for the magnetic Schr\"odinger operator, when the Dirichlet and Neumann data are known on the same part of the boundary, assuming that the inaccessible part of the boundary is a part of a hyperplane

Precursor flares in OJ 287

We have studied three most recent precursor flares in the light curve of the blazar OJ 287 while invoking the presence of a precessing binary black hole in the system to explain the nature of these flares. Precursor flare timings from the historical light curves are compared with theoretical predictions from our model that incorporate effects of an accretion disk and post-Newtonian description for the binary black hole orbit. We find that the precursor flares coincide with the secondary black hole descending towards the accretion disk of the primary black hole from the observed side, with a mean z-component of approximately z_c = 4000 AU. We use this model of precursor flares to predict that precursor flare of similar nature should happen around 2020.96 before the next major outburst in 2022.Comment: to appear in the Astrophysical Journa