Boltzmann Collision Term

We derive the Boltzmann equation for scalar fields using the Schwinger-Keldysh formalism. The focus lies on the derivation of the collision term. We show that the relevant self-energy diagrams have a factorization property. The collision term assumes the Boltzmann-like form of scattering probability times statistical factors for those self-energy diagrams which correspond to tree level scattering processes. Our proof covers scattering processes with any number of external particles, which come from self-energy diagrams with any number of loops.Comment: 17 pages, 4 figure

Jet-cloud interations and the brightening of the narrow line region in Seyfert galaxies

We study the kinematical and brightness evolution of emission line clouds in the narrow line region (NLR) of Seyfert galaxies during the passage of a jet. We derive a critical density above which a cloud remains radiative after compression by the jet cocoon. The critical density depends mainly on the cocoon pressure. Super-critical clouds increase in emission line brightness, while sub-critical clouds generally are highly overheated reducing their luminosity below that of the inter-cloud medium. Due to the pressure stratification in the bow-shock of the jet, a cylindrical structure of nested shells develops around the jet. The most compact and brightest compressed clouds surround the cloud-free channel of the radio jet. To support our analytical model we present a numerical simulation of a supersonic jet propagating into a clumpy NLR. The position-velocity diagram of the simulated H_alpha emission shows total line widths of the order of 500 km/s with large-scale variations in the radial velocities of the clouds due to the stratified pressure in the bow-shock region of the jet. Most of the luminosity is concentrated in a few dense clouds surrounding the jet. These morphological and kinematic signatures are all found in the well observed NLR of NGC1068 and other Seyfert galaxies.Comment: 11 pages, 3 figures, accepted for publication in The Astrophysical Journal Letter

ALMA data suggest the presence of a spiral structure in the inner wind of CW Leo

(abbreviated) We aim to study the inner wind of the well-known AGB star CW Leo. Different diagnostics probing different geometrical scales have pointed toward a non-homogeneous mass-loss process: dust clumps are observed at milli-arcsec scale, a bipolar structure is seen at arcsecond-scale and multi-concentric shells are detected beyond 1". We present the first ALMA Cycle 0 band 9 data around 650 GHz. The full-resolution data have a spatial resolution of 0".42x0".24, allowing us to study the morpho-kinematical structure within ~6". Results: We have detected 25 molecular lines. The emission of all but one line is spatially resolved. The dust and molecular lines are centered around the continuum peak position. The dust emission has an asymmetric distribution with a central peak flux density of ~2 Jy. The molecular emission lines trace different regions in the wind acceleration region and suggest that the wind velocity increases rapidly from about 5 R* almost reaching the terminal velocity at ~11 R*. The channel maps for the brighter lines show a complex structure; specifically for the 13CO J=6-5 line different arcs are detected within the first few arcseconds. The curved structure present in the PV map of the 13CO J=6-5 line can be explained by a spiral structure in the inner wind, probably induced by a binary companion. From modeling the ALMA data, we deduce that the potential orbital axis for the binary system lies at a position angle of ~10-20 deg to the North-East and that the spiral structure is seen almost edge-on. We infer an orbital period of 55 yr and a binary separation of 25 au (or ~8.2 R*). We tentatively estimate that the companion is an unevolved low-mass main-sequence star. The ALMA data hence provide us for the first time with the crucial kinematical link between the dust clumps seen at milli-arcsecond scale and the almost concentric arcs seen at arcsecond scale.Comment: 22 pages, 18 Figures, Astronomy & Astrophysic

Jets and the shaping of the giant bipolar envelope of the planetary nebula KjPn 8

A hydrodynamic model involving cooling gas in the stagnation region of a collimated outflow is proposed for the formation of the giant parsec-scale bipolar envelope that surrounds the planetary nebula KjPn 8. Analytical calculations and numerical simulations are presented to evaluate the model. The envelope is considered to consist mainly of environmental gas swept-up by shocks driven by an episodic, collimated, bipolar outflow. In this model, which we call the ``free stagnation knot'' mechanism, the swept-up ambient gas located in the stagnation region of the bow-shock cools to produce a high density knot. This knot moves along with the bow-shock. When the central outflow ceases, pressurization of the interior of the envelope stops and its expansion slows down. The stagnation knot, however, has sufficient momentum to propagate freely further along the axis, producing a distinct nose at the end of the lobe. The model is found to successfully reproduce the peculiar shape and global kinematics of the giant bipolar envelope of KjPn 8.Comment: 20 pages + 8 figures (in 1 tar-file 0.67 Mb

Towards a global quantification of volcanogenic aluminosilicate alteration rates through the mass balance of strontium in marine sediments

Despite the important role that volcanogenic aluminosilicate (VA) alteration has on elemental cycles in marine sediments, there is no mechanism to arrive at a global assessment of this process. To quantify the VA alteration rates from Japan, New Zealand (NZ), and Costa Rica, we developed a mass balance approach that is constrained by the strontium concentration and 87Sr/86Sr ratios in pore fluid, authigenic carbonates, and VA. We derived VA alteration rates ranging from 101 to 103 nmole Sr/m3 bulk sediment/yr with the highest rate obtained for Tuaheni, NZ (Site GeoB80202), which has the youngest sediment. We showed that 87Sr/86Sr ratios of VA derived from this mass balance approach are significantly higher than the reported ratios from volcanic glass samples, indicating a concomitant role of volcanogenic feldspar dissolution and/or authigenic clay formation. Most of the strontium released during VA alteration is precipitated as authigenic carbonate, with important implications for carbon inventories. The VA alteration rates derived from this approach can also be used to quantify the release of other critical elements, such as release of iron that can stimulate formation of Fe‑carbonates and/or fuel microbial activity at depth

Structure, Scaling and Phase Transition in the Optimal Transport Network

We minimize the dissipation rate of an electrical network under a global constraint on the sum of powers of the conductances. We construct the explicit scaling relation between currents and conductances, and show equivalence to a a previous model [J. R. Banavar {\it et al} Phys. Rev. Lett. {\bf 84}, 004745 (2000)] optimizing a power-law cost function in an abstract network. We show the currents derive from a potential, and the scaling of the conductances depends only locally on the currents. A numerical study reveals that the transition in the topology of the optimal network corresponds to a discontinuity in the slope of the power dissipation.Comment: 4 pages, 3 figure