A class of Hamilton-Jacobi equations on Banach-Finsler manifolds

The concept of subdifferentiability is studied in the context of $C^1$ Finsler manifolds (modeled on a Banach space with a Lipschitz $C^1$ bump function). A class of Hamilton-Jacobi equations defined on $C^1$ Finsler manifolds is studied and several results related to the existence and uniqueness of viscosity solutions are obtained.Comment: 24 page

Tests for primordial non-Gaussianity

We investigate the relative sensitivities of several tests for deviations from Gaussianity in the primordial distribution of density perturbations. We consider models for non-Gaussianity that mimic that which comes from inflation as well as that which comes from topological defects. The tests we consider involve the cosmic microwave background (CMB), large-scale structure (LSS), high-redshift galaxies, and the abundances and properties of clusters. We find that the CMB is superior at finding non-Gaussianity in the primordial gravitational potential (as inflation would produce), while observations of high-redshift galaxies are much better suited to find non-Gaussianity that resembles that expected from topological defects. We derive a simple expression that relates the abundance of high-redshift objects in non-Gaussian models to the primordial skewness.Comment: 6 pages, 2 figures, MNRAS in press (minor changes to match the accepted version

Powering AGNs with super-critical black holes

We propose a novel mechanism for powering the central engines of Active Galactic Nuclei through super-critical (type II) black hole collapse. In this picture, ~$10^3 M_\odot$ of material collapsing at relativistic speeds can trigger a gravitational shock, which can eject a large percentage of the collapsing matter at relativistic speeds, leaving behind a "light" black hole. In the presence of a poloidal magnetic field, the plasma collimates along two jets, and the associated electron synchrotron radiation can easily account for the observed radio luminosities, sizes and durations of AGN jets. For Lorentz factors of order 100 and magnetic fields of a few hundred $\mu G$, synchrotron electrons can shine for $10^6$ yrs, producing jets of sizes of order 100 kpc. This mechanism may also be relevant for Gamma Ray Bursts and, in the absence of magnetic field, supernova explosions.Comment: 4 pages, 1 figur

A long hard look at the minimum state of PG 2112+059 with XMM-Newton

XMM-Newton successfully detected the minimum state of PG 2112+059 during a short snapshot observation and performed a long follow-up observation. The high signal-to-noise spectra are modelled assuming different emission scenarios and compared with archival spectra taken by XMM-Newton and Chandra. The PG 2112+059 X-ray spectra acquired in May 2007 allowed the detection of a weak iron fluorescent line, which is interpreted as being caused by reflection from neutral material at some distance from the primary X-ray emitting source. The X-ray spectra of PG 2112+059 taken at five different epochs during different flux states can be interpreted within two different scenarios. The first consists of two layers of ionised material with column densities of N_H ~5 x 10^22 cm^-2 and N_H ~3.5 x 10^23 cm^-2, respectively. The first layer is moderately ionised and its ionisation levels follow the flux changes, while the other layer is highly ionised and does not show any correlation with the flux of the source. The spectra can also be interpreted assuming reflection by an ionised accretion disk seen behind a warm absorber. The warm absorber ionisation is consistent with being correlated with the flux of the source, which provides an additional degree of self-consistency with the overall reflection-based model. We explain the spectral variability with light bending according to the models of Miniutti and Fabian and constrain the black hole spin to be a/M > 0.86. Both scenarios also assume that a distant cold reflector is responsible for the Fe K \alpha emission line. Light bending provides an attractive explanation of the different states of PG 2112+059 and may also describe the physical cause of the observed properties of other X-ray weak quasars.Comment: 15 pages, 12 figures, A&A latex, accepted for publication in Astronomy & Astrophysic

Changes in organic aerosol composition with aging inferred from aerosol mass spectra

Organic aerosols (OA) can be separated with factor analysis of aerosol mass spectrometer (AMS) data into hydrocarbon-like OA (HOA) and oxygenated OA (OOA). We develop a new method to parameterize H:C of OOA in terms of f_(43)(ratio of m/z 43, mostly C_2H_3O^+, to total signal in the component mass spectrum). Such parameterization allows for the transformation of large database of ambient OOA components from the f_(44) (mostly CO^+_2, likely from acid groups) vs. f_(43) space ("triangle plot") (Ng et al., 2010) into the Van Krevelen diagram (H:C vs. O:C) (Van Krevelen, 1950). Heald et al. (2010) examined the evolution of total OA in the Van Krevelen diagram. In this work total OA is deconvolved into components that correspond to primary (HOA and others) and secondary (OOA) organic aerosols. By deconvolving total OA into different components, we remove physical mixing effects between secondary and primary aerosols which allows for examination of the evolution of OOA components alone in the Van Krevelen space. This provides a unique means of following ambient secondary OA evolution that is analogous to and can be compared with trends observed in chamber studies of secondary organic aerosol formation. The triangle plot in Ng et al. (2010) indicates that f_(44) of OOA components increases with photochemical age, suggesting the importance of acid formation in OOA evolution. Once they are transformed with the new parameterization, the triangle plot of the OOA components from all sites occupy an area in Van Krevelen space which follows a ΔH:C/ΔO:C slope of ~ −0.5. This slope suggests that ambient OOA aging results in net changes in chemical composition that are equivalent to the addition of both acid and alcohol/peroxide functional groups without fragmentation (i.e. C-C bond breakage), and/or the addition of acid groups with fragmentation. These results provide a framework for linking the bulk aerosol chemical composition evolution to molecular-level studies