Discovery of Enhanced Radiative Recombination Continua of He-like Iron and Calcium from IC 443 and Its Implications

We present deep observations of the Galactic supernova remnant IC 443 with the {\it Suzaku X-ray satellite}. We find prominent K-shell lines from iron and nickel, together with a triangle residual at 8--10~keV, which corresponds to the energy of the radiative recombination continuum (RRC) of He-like iron. In addition, the wavy residuals have been seen at $\sim$5.1 and $\sim$5.5~keV. We confirm that the residuals show the first enhanced RRCs of He- and H-like calcium found in supernova remnants. These facts provide robust evidence for the recombining plasma. We reproduce the plasma in the 3.7--10~keV band using a recombining plasma model at the electron temperature 0.65~keV. The recombination parameter $n_{\rm e}t$ ($n_{\rm e}$ is electron density and $t$ is elapsed time after formation of a recombining plasma) and abundances of iron and nickel are strongly correlated, and hence the errors are large. On the other hand, the ratio of nickel to iron relative to the solar abundances is well constrained to 11$^{+4}_{-3}$ (1$\sigma$). A possibility is that the large abundance ratio is a result of an asymmetric explosion of the progenitor star.Comment: 4 pages, 5 figures, published in Ap

Heat equation on the hypergraph containing vertices with given data

This paper is concerned with the Cauchy problem of a multivalued ordinary differential equation governed by the hypergraph Laplacian, which describes the diffusion of ``heat'' or ``particles'' on the vertices of hypergraph. We consider the case where the heat on several vertices are manipulated internally by the observer, namely, are fixed by some given functions. This situation can be reduced to a nonlinear evolution equation associated with a time-dependent subdifferential operator, whose solvability has been investigated in numerous previous researches. In this paper, however, we give an alternative proof of the solvability in order to avoid some complicated calculations arising from the chain rule for the time-dependent subdifferential. As for results which cannot be assured by the known abstract theory, we also discuss the continuous dependence of solution on the given data and the time-global behavior of solution.Comment: 19 pages, 3 figure

Time Variability of Nonthermal X-ray Stripes in Tycho's Supernova Remnant with Chandra

Analyzing Chandra data of Tycho's supernova remnant (SNR) taken in 2000, 2003, 2007, 2009, and 2015, we search for time variable features of synchrotron X-rays in the southwestern part of the SNR, where stripe structures of hard X-ray emission were previous found. By comparing X-ray images obtained at each epoch, we discover a knot-like structure in the northernmost part of the stripe region became brighter particularly in 2015. We also find a bright filamentary structure gradually became fainter and narrower as it moved outward. Our spectral analysis reveal that not only the nonthermal X-ray flux but also the photon indices of the knot-like structure change from year to year. During the period from 2000 to 2015, the small knot shows brightening of $\sim 70\%$ and hardening of $\Delta \Gamma \sim 0.45$. The time variability can be explained if the magnetic field is amplified to $\sim 100~\mathrm{\mu G}$ and/or if magnetic turbulence significantly changes with time.Comment: 8 pages, 3 figures, 2 tables, accepted for publication in Ap