Coupling a branching process to an infinite dimensional epidemic process

Branching process approximation to the initial stages of an epidemic process has been used since the 1950's as a technique for providing stochastic counterparts to deterministic epidemic threshold theorems. One way of describing the approximation is to construct both branching and epidemic processes on the same probability space, in such a way that their paths coincide for as long as possible. In this paper, it is shown, in the context of a Markovian model of parasitic infection, that coincidence can be achieved with asymptotically high probability until o(N^{2/3}) infections have occurred, where N denotes the total number of hosts.Comment: 16 page

HST Observations of the Double-Peaked Emission Lines in the Seyfert Galaxy Markarian 78: Mass Outflows from a Single AGN

Previous ground based observations of the Seyfert 2 galaxy Mrk 78 revealed a double set of emission lines, similar to those seen in several AGN from recent surveys. Are the double lines due to two AGN with different radial velocities in the same galaxy, or are they due to mass outflows from a single AGN?We present a study of the outflowing ionized gas in the resolved narrow-line region (NLR) of Mrk 78 using observations from Space Telescope Imaging Spectrograph (STIS) and Faint Object Camera (FOC) aboard the Hubble Space Telescope(HST) as part of an ongoing project to determine the kinematics and geometries of active galactic nuclei (AGN) outflows. From the spectroscopic information, we deter- mined the fundamental geometry of the outflow via our kinematics modeling program by recreating radial velocities to fit those seen in four different STIS slit positions. We determined that the double emission lines seen in ground-based spectra are due to an asymmetric distribution of outflowing gas in the NLR. By successfully fitting a model for a single AGN to Mrk 78, we show that it is possible to explain double emission lines with radial velocity offsets seen in AGN similar to Mrk 78 without requiring dual supermassive black holes.Comment: 22 pages, 7 figures (2 color), accepted for publication in The Astrophysical Journa

Ionization Mechanisms in Jet-Dominated Seyferts: A Detailed Case Study

For the past 10 years there has been an active debate over whether fast shocks play an important role in ionizing emission line regions in Seyfert galaxies. To investigate this claim, we have studied the Seyfert 2 galaxy Mkn 78, using HST UV/optical images and spectroscopy. Since Mkn 78 provides the archetypal jet-driven bipolar velocity field, if shocks are important anywhere they should be important in this object. Having mapped the emission line fluxes and velocity field, we first compare the ionization conditions to standard photoionization and shock models. We find coherent variations of ionization consistent with photoionization model sequences which combine optically thick and thin gas, but are inconsistent with either autoionizing shock models or photoionization models of just optically thick gas. Furthermore, we find absolutely no link between the ionization of the gas and its kinematic state, while we do find a simple decline of ionization degree with radius. We feel this object provides the strongest case to date against the importance of shock related ionization in Seyferts.Comment: 4 pages, 1 figure, to appear in the proceedings of IAU Symposium 222 "The Interplay among Black Holes, Stars and ISM in Galactic Nuclei", T. Storchi Bergmann, L.C. Ho & H.R. Schmitt, ed

Clues to Quasar Broad Line Region Geometry and Kinematics

We present evidence that the high-velocity CIV lambda 1549 emission line gas of radio-loud quasars may originate in a disk-like configuration, in close proximity to the accretion disk often assumed to emit the low-ionization lines. For a sample of 36 radio-loud z~2 quasars we find the 20--30% peak width to show significant inverse correlations with the fractional radio core-flux density, R, the radio axis inclination indicator. Highly inclined systems have broader line wings, consistent with a high-velocity field perpendicular to the radio axis. By contrast, the narrow line-core shows no such relation with R, so the lowest velocity CIV-emitting gas has an inclination independent velocity field. We propose that this low-velocity gas is located at higher disk-altitudes than the high-velocity gas. A planar origin of the high-velocity CIV-emission is consistent with the current results and with an accretion disk-wind emitting the broad lines. A spherical distribution of randomly orbiting broad-line clouds and a polar high-ionization outflow are ruled out.Comment: 5 Latex pages, 1 figure, accepted for publication in ApJ Letter

The Spitzer View of Low-Metallicity Star Formation: II. Mrk 996, a Blue Compact Dwarf Galaxy with an Extremely Dense Nucleus

(abridged) We present new Spitzer, UKIRT and MMT observations of the blue compact dwarf galaxy (BCD) Mrk 996, with an oxygen abundance of 12+log(O/H)=8.0. This galaxy has the peculiarity of possessing an extraordinarily dense nuclear star-forming region, with a central density of ~10^6 cm^{-3}. The nuclear region of Mrk 996 is characterized by several unusual properties: a very red color J-K = 1.8, broad and narrow emission-line components, and ionizing radiation as hard as 54.9 eV, as implied by the presence of the OIV 25.89 micron line. The nucleus is located within an exponential disk with colors consistent with a single stellar population of age >1 Gyr. The infrared morphology of Mrk 996 changes with wavelength. The IRS spectrum shows strong narrow Polycyclic Aromatic Hydrocarbon (PAH) emission, with narrow line widths and equivalent widths that are high for the metallicity of Mrk 996. Gaseous nebular fine-structure lines are also seen. A CLOUDY model requires that they originate in two distinct HII regions: a very dense HII region of radius ~580 pc with densities declining from ~10^6 at the center to a few hundreds cm^{-3} at the outer radius, where most of the optical lines arise; and a HII region with a density of ~300 cm^{-3} that is hidden in the optical but seen in the MIR. We suggest that the infrared lines arise mainly in the optically obscured HII region while they are strongly suppressed by collisional deexcitation in the optically visible one. The hard ionizing radiation needed to account for the OIV 25.89 micron line is most likely due to fast radiative shocks propagating in an interstellar medium. A hidden population of Wolf-Rayet stars of type WNE-w or a hidden AGN as sources of hard ionizing radiation are less likely possibilities.Comment: 48 pages, 13 figures, accepted for publication in the Astrophysical Journa

The Nuclear Outflow in NGC 2110

We present a HST/STIS spectroscopic and optical/radio imaging study of the Seyfert NGC 2110 aiming to measure the dynamics and understand the nature of the nuclear outflow in the galaxy. Previous HST studies have revealed the presence of a linear structure in the Narrow-Line Region (NLR) aligned with the radio jet. We show that this structure is strongly accelerated, probably by the jet, but is unlikely to be entrained in the jet flow. The ionisation properties of this structure are consistent with photoionisation of dusty, dense gas by the active nucleus. We present a plausible geometrical model for the NLR, bringing together various components of the nuclear environment of the galaxy. We highlight the importance of the circum-nuclear disc in determining the appearance of the emission line gas and the morphology of the jet. From the dynamics of the emission line gas, we place constraints on the accelerating mechanism of the outflow and discuss the relative importance of radio source synchrotron pressure, radio jet ram pressure and nuclear radiation pressure in accelerating the gas. While all three mechanisms can account for the energetics of the emission line gas, gravitational arguments support radio jet ram pressure as the most likely source of the outflow.Comment: 15 pages, 7 figures; accepted to MNRA

A Potts/Ising Correspondence on Thin Graphs

We note that it is possible to construct a bond vertex model that displays q-state Potts criticality on an ensemble of phi3 random graphs of arbitrary topology, which we denote as ``thin'' random graphs in contrast to the fat graphs of the planar diagram expansion. Since the four vertex model in question also serves to describe the critical behaviour of the Ising model in field, the formulation reveals an isomorphism between the Potts and Ising models on thin random graphs. On planar graphs a similar correspondence is present only for q=1, the value associated with percolation.Comment: 6 pages, 5 figure

The Yang Lee Edge Singularity on Feynman Diagrams

We investigate the Yang-Lee edge singularity on non-planar random graphs, which we consider as the Feynman Diagrams of various d=0 field theories, in order to determine the value of the edge exponent. We consider the hard dimer model on phi3 and phi4 random graphs to test the universality of the exponent with respect to coordination number, and the Ising model in an external field to test its temperature independence. The results here for generic (``thin'') random graphs provide an interesting counterpoint to the discussion by Staudacher of these models on planar random graphs.Comment: LaTeX, 6 pages + 3 figure

ISO-SWS spectroscopy of NGC 1068

We present ISO-SWS spectroscopy of NGC 1068 for the wavelength range 2.4 to 45um, detecting a total of 36 emission lines. Most of the observed transitions are fine structure and recombination lines originating in the narrow line region. We compare the line profiles of optical lines and reddening-insensitive infrared lines to constrain the dynamical structure and extinction properties of the NLR. The considerable differences found are most likely explained by two effects. (1) The spatial structure of the NLR is a combination of a highly ionized outflow cone and lower excitation extended emission. (2) Parts of the NLR, mainly in the receding part at velocities above systemic, are subject to extinction that is significantly suppressing optical emission. Line asymmetries and net blueshifts remain, however, even for infrared fine structure lines suffering very little obscuration. This may be either due to an intrinsic asymmetry of the NLR, or due to a very high column density obscuring component which is hiding part of the NLR even from infrared view. Mid-infrared emission of molecular hydrogen in NGC 1068 arises in a dense molecular medium at temperatures of a few hundred Kelvin that is most likely closely related to the warm and dense components seen in the near-infrared H2 transitions, and in millimeter wave tracers of molecular gas. Any emission of the putative pc-scale molecular torus is likely overwhelmed by this larger scale emission.Comment: aastex (V4), 9 eps figures. Accepted by Ap