Investigating the Structure of the Windy Torus in Quasars

Thermal mid-infrared emission of quasars requires an obscuring structure that can be modeled as a magneto-hydrodynamic wind in which radiation pressure on dust shapes the outflow. We have taken the dusty wind models presented by Keating and collaborators that generated quasar mid-infrared spectral energy distributions (SEDs), and explored their properties (such as geometry, opening angle, and ionic column densities) as a function of Eddington ratio and X-ray weakness. In addition, we present new models with a range of magnetic field strengths and column densities of the dust-free shielding gas interior to the dusty wind. We find this family of models -- with input parameters tuned to accurately match the observed mid-IR power in quasar SEDs -- provides reasonable values of the Type 1 fraction of quasars and the column densities of warm absorber gas, though it does not explain a purely luminosity-dependent covering fraction for either. Furthermore, we provide predictions of the cumulative distribution of E(B-V) values of quasars from extinction by the wind and the shape of the wind as imaged in the mid-infrared. Within the framework of this model, we predict that the strength of the near-infrared bump from hot dust emission will be correlated primarily with L/L_Edd rather than luminosity alone, with scatter induced by the distribution of magnetic field strengths. The empirical successes and shortcomings of these models warrant further investigations into the composition and behaviour of dust and the nature of magnetic fields in the vicinity of actively accreting supermassive black holes.Comment: 11 pages, 6 figures, accepted for publication in MNRA

Nonisomorphic curves that become isomorphic over extensions of coprime degrees

We show that one can find two nonisomorphic curves over a field K that become isomorphic to one another over two finite extensions of K whose degrees over K are coprime to one another. More specifically, let K_0 be an arbitrary prime field and let r and s be integers greater than 1 that are coprime to one another. We show that one can find a finite extension K of K_0, a degree-r extension L of K, a degree-s extension M of K, and two curves C and D over K such that C and D become isomorphic to one another over L and over M, but not over any proper subextensions of L/K or M/K. We show that such C and D can never have genus 0, and that if K is finite, C and D can have genus 1 if and only if {r,s} = {2,3} and K is an odd-degree extension of F_3. On the other hand, when {r,s}={2,3} we show that genus-2 examples occur in every characteristic other than 3. Our detailed analysis of the case {r,s} = {2,3} shows that over every finite field K there exist nonisomorphic curves C and D that become isomorphic to one another over the quadratic and cubic extensions of K. Most of our proofs rely on Galois cohomology. Without using Galois cohomology, we show that two nonisomorphic genus-0 curves over an arbitrary field remain nonisomorphic over every odd-degree extension of the base field.Comment: LaTeX, 32 pages. Further references added to the discussion in Section 1

What Makes Educational Campaings Succeed?

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Percolation, depinning, and avalanches in capillary condensation of gases in disordered porous solids

We propose a comprehensive theoretical description of hysteresis in capillary condensation of gases in mesoporous disordered materials. Applying mean-field density functional theory to a coarse-grained lattice-gas model, we show that the morphology of the hysteresis loops is influenced by out-of-equilibrium transitions that are different on filling and on draining. In particular, desorption may be associated to a depinning process and be percolation-like without explicit pore-blocking effects.Comment: 4 pages, 5 figure

A Superluminal Subway: The Krasnikov Tube

The ``warp drive'' metric recently presented by Alcubierre has the problem that an observer at the center of the warp bubble is causally separated from the outer edge of the bubble wall. Hence such an observer can neither create a warp bubble on demand nor control one once it has been created. In addition, such a bubble requires negative energy densities. One might hope that elimination of the first problem might ameliorate the second as well. We analyze and generalize a metric, originally proposed by Krasnikov for two spacetime dimensions, which does not suffer from the first difficulty. As a consequence, the Krasnikov metric has the interesting property that although the time for a one-way trip to a distant star cannot be shortened, the time for a round trip, as measured by clocks on Earth, can be made arbitrarily short. In our four dimensional extension of this metric, a ``tube'' is constructed along the path of an outbound spaceship, which connects the Earth and the star. Inside the tube spacetime is flat, but the light cones are opened out so as to allow superluminal travel in one direction. We show that, although a single Krasnikov tube does not involve closed timelike curves, a time machine can be constructed with a system of two non-overlapping tubes. Furthermore, it is demonstrated that Krasnikov tubes, like warp bubbles and traversable wormholes, also involve unphysically thin layers of negative energy density, as well as large total negative energies, and therefore probably cannot be realized in practice.Comment: 20 pages, LATEX, 5 eps figures, uses \eps