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

Thin Animals

Lattice animals provide a discretized model for the theta transition displayed by branched polymers in solvent. Exact graph enumeration studies have given some indications that the phase diagram of such lattice animals may contain two collapsed phases as well as an extended phase. This has not been confirmed by studies using other means. We use the exact correspondence between the q --> 1 limit of an extended Potts model and lattice animals to investigate the phase diagram of lattice animals on phi-cubed random graphs of arbitrary topology (``thin'' random graphs). We find that only a two phase structure exists -- there is no sign of a second collapsed phase. The random graph model is solved in the thermodynamic limit by saddle point methods. We observe that the ratio of these saddle point equations give precisely the fixed points of the recursion relations that appear in the solution of the model on the Bethe lattice by Henkel and Seno. This explains the equality of non-universal quantities such as the critical lines for the Bethe lattice and random graph ensembles.Comment: Latex, 10 pages plus 6 ps/eps figure

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

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

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

Probing the Ionizing Continuum of Narrow-Line Seyfert 1 Galaxies. I.Observational Results

We present optical spectra and emission-line ratios of 12 Narrow-Line Seyfert 1 (NLS1) galaxies that we observed to study the ionizing EUV continuum. A common feature in the EUV continuum of active galactic nuclei is the big blue bump (BBB), generally associated with thermal accretion disk emission. While Galactic absorption prevents direct access to the EUV range, it can be mapped by measuring the strength of a variety of forbidden optical emission lines that respond to different EUV continuum regions. We find that narrow emission-line ratios involving [OII]3727, Hbeta, [OIII]5007, [OI]6300, Halpha,[NII]6583, and [SII]6716,6731 indicate no significant difference between NLS1s and Broad-Line Seyfert 1 (BLS1) galaxies, which suggests that the spectral energy distributions of their ionizing EUV - soft X-ray continua are similar. The relative strength of important forbidden high ionization lines like [NeV]3426 compared to HeII4686 and the relative strength of [FeX]6374 appear to show the same range as in BLS1 galaxies. However, a trend of weaker F([OI]6300)/F(Halpha) emission-line ratios is indicated for NLS1s compared to BLS1s. To recover the broad emission-line profiles we used Gaussian components. This approach indicates that the broad Hbeta profile can be well described with a broad component (FWHM = 3275 +- 800 km/s) and an intermediate broad component (FWHM = 1200 +- 300 km/s). The width of the broad component is in the typical range of normal BLS1s. The emission-line flux that is associated with the broad component in these NLS1s amounts to at least 60% of the total flux. Thus it dominates the total line flux, similar to BLS1 galaxies.Comment: 34 pages, 9 figures. accepted for publication in the Astrophys.Journa

The origin of the Narrow Line Region of Mrk 3: an overpressured jet cocoon

We have obtained HST FOC long-slit optical spectroscopy of the Narrow Line Region of the Seyfert 2 galaxy Mrk 3. In the region cospatial with the radio-jet the velocity field is highly perturbed and shows two velocity systems separated by as much as 1700 km/s. We interpret this to be the consequence of the rapid expansion of a cocoon of hot gas, shocked and heated by the radio-emitting outflow, which compresses and accelerates the ambient gas. The NLR itself is essentially a cylindrical shell expanding supersonically. From the size and velocity of the expanding region, we derive an upper limit to the radio-source age, ~ 2 E42 erg/s required to inflate the cocoon and estimate that the jet minimum advance speed is 3 E-3 pc per year. The total kinetic energy of the high velocity NLR gas can be estimated as ~6 E54 erg, comparable to the total energy carried by the jet over its lifetime and this quantitatively supports the idea that the NLR gas is accelerated by the jet. If the advance speed of Mrk 3 is representative of the Seyfert population then these sources must also be short lived and probably recurrent. The jet kinetic luminosity of Mrk 3 is between 2 and 3 orders of magnitude smaller than that derived for radio-loud AGNs with similar emission-line luminosity. On the other hand, the fraction of jet power dissipated in radio-emission is similar. We speculate that the main distinction between radio-quiet and radio-loud AGN is ascribed to a difference in jet power rather than to a different efficiency in synchrotron emission production.Comment: 13 pages, 8 figures, Astrophysical Journal in pres

Multivariate Granger Causality and Generalized Variance

Granger causality analysis is a popular method for inference on directed interactions in complex systems of many variables. A shortcoming of the standard framework for Granger causality is that it only allows for examination of interactions between single (univariate) variables within a system, perhaps conditioned on other variables. However, interactions do not necessarily take place between single variables, but may occur among groups, or "ensembles", of variables. In this study we establish a principled framework for Granger causality in the context of causal interactions among two or more multivariate sets of variables. Building on Geweke's seminal 1982 work, we offer new justifications for one particular form of multivariate Granger causality based on the generalized variances of residual errors. Taken together, our results support a comprehensive and theoretically consistent extension of Granger causality to the multivariate case. Treated individually, they highlight several specific advantages of the generalized variance measure, which we illustrate using applications in neuroscience as an example. We further show how the measure can be used to define "partial" Granger causality in the multivariate context and we also motivate reformulations of "causal density" and "Granger autonomy". Our results are directly applicable to experimental data and promise to reveal new types of functional relations in complex systems, neural and otherwise.Comment: added 1 reference, minor change to discussion, typos corrected; 28 pages, 3 figures, 1 table, LaTe

Optimal control of a linear system subject to partially specified input noise

One of the most basic problems in control theory is that of controlling a discrete-time linear system subject to uncertain noise with the objective of minimising the expectation of a quadratic cost. If one assumes the noise to be white, then solving this problem is relatively straightforward. However, white noise is arguably unrealistic: noise is not necessarily independent and one does not always precisely know its expectation. We first recall the optimal control policy without assuming independence, and show that in this case computing the optimal control inputs becomes infeasible. In a next step, we assume only knowledge of lower and upper bounds on the conditional expectation of the noise, and prove that this approach leads to tight lower and upper bounds on the optimal control inputs. The analytical expressions that determine these bounds are strikingly similar to the usual expressions for the case of white noise