Asymptotic stability of traveling wave solutions for nonlocal viscous conservation laws with explicit decay rates

We consider scalar conservation laws with nonlocal diffusion of Riesz-Feller type such as the fractal Burgers equation. The existence of traveling wave solutions with monotone decreasing profile has been established recently (in special cases). We show the local asymptotic stability of these traveling wave solutions in a Sobolev space setting by constructing a Lyapunov functional. Most importantly, we derive the algebraic-in-time decay of the norm of such perturbations with explicit algebraic-in-time decay rates

Mass Function of Binary Massive Black Holes in Active Galactic Nuclei

If the activity of active galactic nuclei (AGNs) is predominantly induced by major galaxy mergers, then a significant fraction of AGNs should harbor binary massive black holes in their centers. We study the mass function of binary massive black holes in nearby AGNs based on the observed AGN black-hole mass function and theory of evolution of binary massive black holes interacting with a massive circumbinary disk in the framework of coevolution of massive black holes and their host galaxies. The circumbinary disk is assumed to be steady, axisymmetric, geometrically thin, self-regulated, self-gravitating but non-fragmenting with a fraction of Eddington accretion rate, which is typically one tenth of Eddington value. The timescale of orbital decay is {then} estimated as ~10^8yr for equal mass black-hole, being independent of the black hole mass, semi-major axis, and viscosity parameter but dependent on the black-hole mass ratio, Eddington ratio, and mass-to-energy conversion efficiency. This makes it possible for any binary massive black holes to merge within a Hubble time by the binary-disk interaction. We find that (1.8+-0.6%) for the equal mass ratio and (1.6+-0.4%) for the one-tenth mass ratio of the total number of nearby AGNs have close binary massive black holes with orbital period less than ten years in their centers, detectable with on-going highly sensitive X-ray monitors such as Monitor of All-sky X-ray Image and/or Swift/Burst Alert Telescope. Assuming that all binary massive black holes have the equal mass ratio, about 20% of AGNs with black hole masses of 10^{6.5-7}M_sun has the close binaries and thus provides the best chance to detect them.Comment: 22 pages, 11 figures, accepted for publication in PASJ. The draft was significantly revised. The major differences from the previous version are as follows: (1)The circumbinary disk is assumed to be a steady, axisymmetric, geometrically thin, self-gravitating, self-regulated but non-fragmenting. (2)The stellar scattering process is taken account of in the merging process of binary black hole

NuSTAR and Swift observations of the ultraluminous X-ray source IC 342 X-1 in 2016: witnessing spectral evolution

We report on an X-ray observing campaign of the ultraluminous X-ray source IC 342 X-1 with NuSTAR and Swift in 2016 October, in which we captured the very moment when the source showed spectral variation. The Swift/XRT spectrum obtained in October 9--11 has a power-law shape and is consistent with those observed in the coordinated XMM-Newton and NuSTAR observations in 2012. In October 16--17, when the 3--10 keV flux became $\approx$4 times higher, we performed simultaneous NuSTAR and Swift observations. In this epoch, the source showed a more round-shaped spectrum like that seen with ASCA 23 years ago. Thanks to the wide energy coverage and high sensitivity of NuSTAR, we obtained hard X-ray data covering up to $\sim$30 keV for the first time during the high luminosity state of IC 342 X-1. The observed spectrum has a broader profile than the multi-color disk blackbody model. The X-ray flux decreased again in the last several hours of the NuSTAR observation, when the spectral shape approached those seen in 2012 and 2016 October 9--11. The spectra obtained in our observations and in 2012 can be commonly described with disk emission and its Comptonization in cool ($T_{\rm e} \approx 4$ keV), optically-thick ($\tau \approx 5$) plasma. The spectral turnover seen at around 5--10 keV shifts to higher energies as the X-ray luminosity decreases. This behavior is consistent with that predicted from recent numerical simulations of super-Eddington accretion flows with Compton-thick outflows. We suggest that the spectral evolution observed in IC 342 X-1 can be explained by a smooth change in mass accretion rate.Comment: 10 pages, 6 figures, accepted for publication in Ap