Uncovering Local Absorbed Active Galactic Nuclei with Swift and Suzaku

Detection of absorbed active galactic nuclei and their properties remains an elusive and important problem in understanding the evolution and activation of black holes. With the very hard X-ray survey conducted by Swift's Burst Alert Telescope - the first all-sky survey in 30 years - we are beginning to uncover the characteristics of obscured AGN. The synergy between Suzaku and Swift has been crucial in pinning down the X-ray properties of newly detected heavily obscured but bright hard X-ray sources. We review the X-ray and optical spectroscopic properties of obscured AGN in the local Universe, as detected in the Swift survey. We discuss the relative distribution of absorbed/unabsorbed sources, including "hidden" and Compton thick AGN populations. Among the results from the survey, we find that absorbed AGN are less luminous than unabsorbed sources. Optical spectra reveal that sources with emission line ratios indicative of LINERs/H II galaxies/composites are the least luminous objects in the sample, while optical absorbed and unabsorbed Seyferts have the same luminosity distributions. Thus, the least luminous sources are likely accreting in a different mode than the Seyferts.Comment: 8 pages, 5 figures, To appear in the conference proceedings for "Exploring the X-ray Universe: Suzaku and Beyond", the July 2011 Suzaku Science Conferenc

Multi-Peak Solutions for a Wide Class of Singular Perturbation Problems

In this paper we are concerned with a wide class of singular perturbation problems arising from such diverse fields as phase transitions, chemotaxis, pattern formation, population dynamics and chemical reaction theory. We study the corresponding elliptic equations in a bounded domain without any symmetry assumptions. We assume that the mean curvature of the boundary has \overline{M} isolated, non-degenerate critical points. Then we show that for any positive integer m\leq \overline{M} there exists a stationary solution with M local peaks which are attained on the boundary and which lie close to these critical points. Our method is based on Liapunov-Schmidt reduction

Existence and stability of multiple spot solutions for the gray-scott model in R^2

We study the Gray-Scott model in a bounded two dimensional domain and establish the existence and stability of {\bf symmetric} and {\bf asymmetric} multiple spotty patterns. The Green's function and its derivatives together with two nonlocal eigenvalue problems both play a major role in the analysis. For symmetric spots, we establish a threshold behavior for stability: If a certain inequality for the parameters holds then we get stability, otherwise we get instability of multiple spot solutions. For asymmetric spots, we show that they can be stable within a narrow parameter range

Young measures in a nonlocal phase transition problem

A nonlocal variational problem modelling phase transitions is studied in the framework of Young measures. The existence of global minimisers among functions with internal layers on an infinite tube is proved by combining a weak convergence result for Young measures and the principle of concentration-compactness. The regularity of such global minimisers is discussed, and the nonlocal variational problem is also considered on asymptotic tubes

The Complex X-ray Spectrum of the Sefyert 1.5 Source NGC 6860

The X-ray spectrum of the Seyfert 1.5 source NGC 6860 is among the most complex of the sources detected in the Swift Burst Alert Telescope all-sky survey. A short XMM-Newton follow-up observation of the source revealed a flat spectrum both above and below 2 keV. To uncover the complexity of the source, in this paper we analyze both a 40 ks Suzaku and a 100 ks XMM-Newton observation of NGC 6860. While the spectral state of the source changed between the newer observations presented here and the earlier short XMM-Newton spectrum - showing a higher flux and steeper power law component - the spectrum of NGC 6860 is still complex with clearly detected warm absorption signatures. We find that a two component warm ionized absorber is present in the soft spectrum, with column densities of about 10^20 and 10^21 cm$^-2, ionization parameters of xi = 180 and 45 ergs cm s^-1, and outflow velocities for each component in the range of 0-300 km s^-1. Additionally, in the hard spectrum we find a broad (approx 11000 km s^-1) Fe K-alpha emission line, redshifted by approx 2800 km s^-1.Comment: 35 pages, 9 figures, Accepted to Ap

Solutions for the Cahn-Hilliard Equation With Many Boundary Spike Layers

In this paper we construct new classes of stationary solutions for the Cahn-Hilliard equation by a novel approach. One of the results is as follows: Given a positive integer K and a (not necessarily nondegenerate) local minimum point of the mean curvature of the boundary then there are boundary K-spike solutions whose peaks all approach this point. This implies that for any smooth and bounded domain there exist boundary K-spike solutions. The central ingredient of our analysis is the novel derivation and exploitation of a reduction of the energy to finite dimensions (Lemma 3.5), where the variables are closely related to the peak loations

Stationary solutions for the Cahn-Hilliard equation

We study the Cahn-Hilliard equation in a bounded domain without any symmetry assumptions. We assume that the mean curvature of the boundary has a nongenerate critical point. Then we show that there exists a spike-like stationary solution whose global maximum lies on the boundary. Our method is based on Lyapunov-Schmidt reduction and the Brouwer fixed-point theorem

Higher-Order Energy Expansions and Spike Locations

We consider the following singularly perturbed semilinear elliptic problem: (I)\left\{ \begin{array}{l} \epsilon^{2} \Delta u - u + f(u)=0 \ \ \mbox{in} \ \Omega, \\ u>0 \ \ \mbox{in} \ \ \Omega \ \ \mbox{and} \ \frac{\partial u}{\partial \nu} =0 \ \mbox{on} \ \partial \Omega, \end{array} \right. where \Om is a bounded domain in R^N with smooth boundary \partial \Om, \ep>0 is a small constant and f is some superlinear but subcritical nonlinearity. Associated with (I) is the energy functional J_\ep defined by J_\ep [u]:= \int_\Om \left(\frac{\ep^2}{2} |\nabla u|^2 + \frac{1}{2} u^2- F(u)\right) dx \ \ \ \ \ \mbox{for} \ u \in H^1 (\Om), where F(u)=\int_0^u f(s)ds. Ni and Takagi proved that for a single boundary spike solution u_\ep, the following asymptotic expansion holds: J_\ep [u_\ep] =\ep^{N} \Bigg[ \frac{1}{2} I[w] -c_1 \ep H(P_\ep) + o(\ep)\Bigg], where c_1>0 is a generic constant, P_\ep is the unique local maximum point of u_\ep and H(P_\ep) is the boundary mean curvature function at P_\ep \in \partial \Om. In this paper, we obtain a higher-order expansion of J_\ep [u_\ep]: J_\ep [u_\ep] =\ep^{N} \Bigg[ \frac{1}{2} I[w] -c_1 \ep H(P_\ep) + \ep^2 [c_2 (H(P_\ep))^2 + c_3 R (P_\ep)]+ o(\ep^2)\Bigg] where c_2, c_3 are generic constants and R(P_\ep) is the Ricci scalar curvature at P_\ep. In particular c_3 >0. Some applications of this expansion are given

Mutually exclusive spiky pattern and segmentation modelled by the five-component meinhardt-gierer system

We consider the five-component Meinhardt-Gierer model for mutually exclusive patterns and segmentation. We prove rigorous results on the existence and stability of mutually exclusive spikes which are located in different positions for the two activators. Sufficient conditions for existence and stability are derived, which depend in particular on the relative size of the various diffusion constants. Our main analytical methods are the Liapunov-Schmidt reduction and nonlocal eigenvalue problems. The analytical results are confirmed by numerical simulations