On Lelong Numbers of Generalized Monge-Amp\`ere Products

We consider generalized (mixed) Monge-Amp\`ere products of quasiplurisubharmonic functions (with and without analytic singularities) as they were introduced and studied in several articles written by subsets of M. Andersson, E. Wulcan, Z. B{\l}ocki, R. L\"ark\"ang, H. Raufi, J. Ruppenthal, and the author. We continue these studies and present estimates for the Lelong numbers of pushforwards of such products by proper holomorphic submersions. Furthermore, we apply these estimates to Chern and Segre currents of pseudoeffective vector bundles. Among other corollaries, we obtain the following generalization of a recent result by X. Wu. If the non-nef locus of a pseudoeffective vector bundle $E$ on a K\"ahler manifold is contained in a countable union of $k$-codimensional analytic sets, and if the $k$-power of the first Chern class of $E$ is trivial, then $E$ is nef.Comment: 32 pages; minor corrections in the second versio

What is the Hidden Depolarization Mechanism in Low Luminosity AGN?

Millimeter wavelength polarimetry of accreting black hole systems can provide a tomographic probe of the accretion flow on a wide range of linear scales. We searched for linear polarization in two low luminosity active galactic nuclei (LLAGN), M81 and M84, using the Combined Array for Millimeter Astronomy (CARMA) and the Submillimeter Array (SMA). We find upper limits of $\sim 1 - 2\%$ averaging over the full bandwidth and with a rotation measure (RM) synthesis technique. These low polarization fractions, along with similar low values for LLAGN M87 and 3C84, suggest that LLAGN have qualitatively different polarization properties than radio-loud sources and Sgr A*. If the sources are intrinsically polarized and then depolarized by Faraday rotation then we place lower limits on the RM of a few times $10^7\, {\rm rad\, m^{-2}}$ for the full bandwidth case and $\sim 10^9\, {\rm rad\, m^{-2}}$ for the RM synthesis analysis. These limits are inconsistent with or marginally consistent with expected accretion flow properties. Alternatively, the sources may be depolarized by cold electrons within a few Schwarzschild radii from the black hole, as suggested by numerical models.Comment: Accepted for publication in ApJ

Determining the optimal locations for shock acceleration in magnetohydrodynamical jets

Observations of relativistic jets from black holes systems suggest that particle acceleration often occurs at fixed locations within the flow. These sites could be associated with critical points that allow the formation of standing shock regions, such as the magnetosonic modified fast point. Using the self-similar formulation of special relativistic magnetohydrodynamics by Vlahakis & K\"onigl, we derive a new class of flow solutions that are both relativistic and cross the modified fast point at a finite height. Our solutions span a range of Lorentz factors up to at least 10, appropriate for most jets in X-ray binaries and active galactic nuclei, and a range in injected particle internal energy. A broad range of solutions exists, which will allow the eventual matching of these scale-free models to physical boundary conditions in the analysis of observed sources.Comment: 9 pages, 4 figures, accepted for publication in Ap

The Fundamental Plane of Black Hole Accretion and its Use as a Black Hole-Mass Estimator

We present an analysis of the fundamental plane of black hole accretion, an empirical correlation of the mass of a black hole ($M$), its 5 GHz radio continuum luminosity ($\nu L_{\nu}$), and its 2-10 keV X-ray power-law continuum luminosity ($L_X$). We compile a sample of black holes with primary, direct black hole-mass measurements that also have sensitive, high-spatial-resolution radio and X-ray data. Taking into account a number of systematic sources of uncertainty and their correlations with the measurements, we use Markov chain Monte Carlo methods to fit a mass-predictor function of the form $\log(M/10^{8}\,M_{\scriptscriptstyle \odot}) = \mu_0 + \xi_{\mu R} \log(L_R / 10^{38}\,\mathrm{erg\,s^{-1}}) + \xi_{\mu X} \log(L_X / 10^{40}\,\mathrm{erg\,s^{-1}})$. Our best-fit results are $\mu_0 = 0.55 \pm 0.22$, $\xi_{\mu R} = 1.09 \pm 0.10$, and $\xi_{\mu X} = -0.59^{+0.16}_{-0.15}$ with the natural logarithm of the Gaussian intrinsic scatter in the log-mass direction $\ln\epsilon_\mu = -0.04^{+0.14}_{-0.13}$. This result is a significant improvement over our earlier mass scaling result because of the increase in active galactic nuclei sample size (from 18 to 30), improvement in our X-ray binary sample selection, better identification of Seyferts, and improvements in our analysis that takes into account systematic uncertainties and correlated uncertainties. Because of these significant improvements, we are able to consider potential influences on our sample by including all sources with compact radio and X-ray emission but ultimately conclude that the fundamental plane can empirically describe all such sources. We end with advice for how to use this as a tool for estimating black hole masses.Comment: ApJ Accepted. Online interactive version of Figure 7 available at http://kayhan.astro.lsa.umich.edu/supplementary_material/fp