Supernova Resonance--scattering Line Profiles in the Absence of a Photosphere

In supernova spectroscopy relatively little attention has been given to the properties of optically thick spectral lines in epochs following the photosphere's recession. Most treatments and analyses of post-photospheric optical spectra of supernovae assume that forbidden-line emission comprises most if not all spectral features. However, evidence exists which suggests that some spectra exhibit line profiles formed via optically thick resonance-scattering even months or years after the supernova explosion. To explore this possibility we present a geometrical approach to supernova spectrum formation based on the "Elementary Supernova" model, wherein we investigate the characteristics of resonance-scattering in optically thick lines while replacing the photosphere with a transparent central core emitting non-blackbody continuum radiation, akin to the optical continuum provided by decaying 56Co formed during the explosion. We develop the mathematical framework necessary for solving the radiative transfer equation under these conditions, and calculate spectra for both isolated and blended lines. Our comparisons with analogous results from the Elementary Supernova code SYNOW reveal several marked differences in line formation. Most notably, resonance lines in these conditions form P Cygni-like profiles, but the emission peaks and absorption troughs shift redward and blueward, respectively, from the line's rest wavelength by a significant amount, despite the spherically symmetric distribution of the line optical depth in the ejecta. These properties and others that we find in this work could lead to misidentification of lines or misattribution of properties of line-forming material at post-photospheric times in supernova optical spectra.Comment: 37 pages, 24 figures; accepted for publication in ApJ Supplement Serie

BFKL, BK and the Infrared

The perturbative non-linear (NL) effects in the small-$x$ evolution of the gluon densities depend crucially on the infrared (IR) regularization. The IR regulator, $R_c$, is determined by the scale of the non-perturbative fluctuations of QCD vacuum. From the instanton models and from the lattice $R_c\sim 0.3$ fm. For perturbative gluons with the propagation length $R_c= 0.26$ fm the linear BFKL gives a good description of the proton structure function $F_2(x,Q^2)$ in a wide range of $x$ and $Q^2$. The NL effects turn out to be rather weak and amount to the 10% correction to $F_2(x,Q^2)$ for x\lsim 10^{-5}. Much more pronounced NL effects were found in the non-linear model, described in the literature, with a very soft IR regularization corresponding to the IR cutoff at $\simeq \Lambda^{-1}_{QCD}$. The latter issue is also commented below.Comment: 5 pages, LaTeX, Talk at the workshop Diffraction 2012, Puerto del Carmen, Lanzarote, Spain, Sept. 10-15, 201

A Dynamical Potential-Density Pair for Star Clusters With Nearly Isothermal Interiors

We present a potential-density pair designed to model nearly isothermal star clusters (and similar self-gravitating systems) with a central core and an outer turnover radius, beyond which density falls off as $r^{-4}$. In the intermediate zone, the profile is similar to that of an isothermal sphere (density $\rho \propto r^{-2}$), somewhat less steep than the King 62 profile, and with the advantage that many dynamical quantities can be written in a simple closed form. We derive new analytic expressions for the cluster binding energy and velocity dispersion, and apply these to create toy models for cluster core collapse and evaporation. We fit our projected surface brightness profiles to observed globular and open clusters, and find that the quality of the fit is generally at least as good as that for the surface brightness profiles of King 62. This model can be used for convenient computation of the dynamics and evolution of globular and nuclear star clusters.Comment: 6 pages, 5 figures. Published in ApJL; changes to match published versio

Holography at an Extremal De Sitter Horizon

Rotating maximal black holes in four-dimensional de Sitter space, for which the outer event horizon coincides with the cosmological horizon, have an infinite near-horizon region described by the rotating Nariai metric. We show that the asymptotic symmetry group at the spacelike future boundary of the near-horizon region contains a Virasoro algebra with a real, positive central charge. This is evidence that quantum gravity in a rotating Nariai background is dual to a two-dimensional Euclidean conformal field theory. These results are related to the Kerr/CFT correspondence for extremal black holes, but have two key differences: one of the black hole event horizons has been traded for the cosmological horizon, and the near-horizon geometry is a fiber over dS_2 rather than AdS_2.Comment: 15 page