X-Ray Line Profiles from Parameterized Emission Within an Accelerating Stellar Wind

Motivated by recent detections by the XMM and Chandra satellites of X-ray line emission from hot, luminous stars, we present synthetic line profiles for X-rays emitted within parameterized models of a hot-star wind. The X-ray line emission is taken to occur at a sharply defined co-moving-frame resonance wavelength, which is Doppler-shifted by a stellar wind outflow parameterized by a `beta' velocity law, $v(r)=v_{\infty} (1-\R_{\ast}/r)^\beta$. Above some initial onset radius $R_o$ for X-ray emission, the radial variation of the emission filling factor is assumed to decline as a power-law in radius, $f(r) \sim r^{-q}$. The computed emission profiles also account for continuum absorption within the wind, with the overall strength characterized by a cumulative optical depth $\tau_\ast$. In terms of a wavelength shift from line-center scaled in units of the wind terminal speed $v_{\infty}$, we present normalized X-ray line profiles for various combinations of the parameters $\beta$, $\tau_\ast$, $q$ and $R_o$, and including also the effect of instrumental broadening as characterized by a Gaussian with a parameterized width $\sigma$. We discuss the implications for interpreting observed hot-star X-ray spectra, with emphasis on signatures for discriminating between ``coronal'' and ``wind-shock'' scenarios. In particular, we note that in profiles observed so far the substantial amount of emission longward of line center will be difficult to reconcile with the expected attenuation by the wind and stellar core in either a wind-shock or coronal model.Comment: Submitted to Ap.J. 17 pages; includes 5 figures. Preprint also available at http://www.bartol.udel.edu/~owocki/preprint

Matter Mixing in Aspherical Core-collapse Supernovae: Three-dimensional Simulations with Single Star and Binary Merger Progenitor Models for SN 1987A

We perform three-dimensional hydrodynamic simulations of aspherical core-collapse supernovae focusing on the matter mixing in SN 1987A. The impacts of four progenitor (pre-supernova) models and parameterized aspherical explosions are investigated. The four pre-supernova models include a blue supergiant (BSG) model based on a slow merger scenario developed recently for the progenitor of SN 1987A (Urushibata et al. 2018). The others are a BSG model based on a single star evolution and two red supergiant (RSG) models. Among the investigated explosion (simulation) models, a model with the binary merger progenitor model and with an asymmetric bipolar-like explosion, which invokes a jetlike explosion, best reproduces constraints on the mass of high velocity $^{56}$Ni, as inferred from the observed [Fe II] line profiles. The advantage of the binary merger progenitor model for the matter mixing is the flat and less extended $\rho \,r^3$ profile of the C+O core and the helium layer, which may be characterized by the small helium core mass. From the best explosion model, the direction of the bipolar explosion axis (the strongest explosion direction), the neutron star (NS) kick velocity, and its direction are predicted. Other related implications and future prospects are also given

Evidence for <i>L</i>-dependence generated by channel coupling: ¹⁶O scattering from ¹²C at 115.9 MeV

Background: In earlier work, inversion of S matrix for 330 MeV 16O on 12C resulted in highly undulatory potentials; the S matrix resulted from the inclusion of strong coupling to states of projectile and target nuclei. L-independent S-matrix equivalent potentials for other explicitly L-dependent potentials have been found to be undulatory. Purpose: To investigate the possible implications of the undulatory dynamic polarization potential for an underlying L dependence of the 16O on 12C optical potential. Methods: S matrix to potential, SL → V (r), inversion which yields local potentials that reproduce the elastic channel S matrix of coupled channel (CC) calculations, will be applied to the S matrix for 115.9 MeV 16O on 12C. Further, SL for explicitly L-dependent potentials are inverted and the resulting L-independent potentials are characterized and compared with the undulatory potentials found for 16O on 12C. Results: Some of the undulatory features exhibited by the potentials modified by channel coupling for 115.9 MeV 16O on 12C can be simulated by simple parameterized L-dependent potentials. Conclusions: The elastic scattering of 16O by 12C is a particularly favorable case for revealing the effective L dependence of the potential modified by channel coupling. Nevertheless, there is no reason to suppose that undularity is not a generic property leading in many cases to the choice: nucleus-nucleus potentials are (i) smooth and L-dependent, (ii) L-independent and undulatory, or (iii) both

Parameterized Distributed Algorithms

In this work, we initiate a thorough study of graph optimization problems parameterized by the output size in the distributed setting. In such a problem, an algorithm decides whether a solution of size bounded by k exists and if so, it finds one. We study fundamental problems, including Minimum Vertex Cover (MVC), Maximum Independent Set (MaxIS), Maximum Matching (MaxM), and many others, in both the LOCAL and CONGEST distributed computation models. We present lower bounds for the round complexity of solving parameterized problems in both models, together with optimal and near-optimal upper bounds. Our results extend beyond the scope of parameterized problems. We show that any LOCAL (1+epsilon)-approximation algorithm for the above problems must take Omega(epsilon^{-1}) rounds. Joined with the (epsilon^{-1}log n)^{O(1)} rounds algorithm of [Ghaffari et al., 2017] and the Omega (sqrt{(log n)/(log log n)}) lower bound of [Fabian Kuhn et al., 2016], the lower bounds match the upper bound up to polynomial factors in both parameters. We also show that our parameterized approach reduces the runtime of exact and approximate CONGEST algorithms for MVC and MaxM if the optimal solution is small, without knowing its size beforehand. Finally, we propose the first o(n^2) rounds CONGEST algorithms that approximate MVC within a factor strictly smaller than 2

Hawking radiation from a spherical loop quantum gravity black hole

We introduce quantum field theory on quantum space-times techniques to characterize the quantum vacua as a first step towards studying black hole evaporation in spherical symmetry in loop quantum gravity and compute the Hawking radiation. We use as quantum space time the recently introduced exact solution of the quantum Einstein equations in vacuum with spherical symmetry and consider a spherically symmetric test scalar field propagating on it. The use of loop quantum gravity techniques in the background space-time naturally regularizes the matter content, solving one of the main obstacles to back reaction calculations in more traditional treatments. The discreteness of area leads to modifications of the quantum vacua, eliminating the trans-Planckian modes close to the horizon, which in turn eliminates all singularities from physical quantities, like the expectation value of the stress energy tensor. Apart from this, the Boulware, Hartle--Hawking and Unruh vacua differ little from the treatment on a classical space-time. The asymptotic modes near scri are reproduced very well. We show that the Hawking radiation can be computed, leading to an expression similar to the conventional one but with a high frequency cutoff. Since many of the conclusions concern asymptotic behavior, where the spherical mode of the field behaves in a similar way as higher multipole modes do, the results can be readily generalized to non spherically symmetric fields.Comment: 15 pages, no figures, several points clarifie