The gas temperature in the surface layers of protoplanetary disks

Models for the structure of protoplanetary disks have so far been based on the assumption that the gas and the dust temperature are equal. The gas temperature, an essential ingredient in the equations of hydrostatic equilibrium of the disk, is then determined from a continuum radiative transfer calculation, in which the continuum opacity is provided by the dust. It has been long debated whether this assumption still holds in the surface layers of the disk, where the dust infrared emission features are produced. In this paper we compute the temperature of the gas in the surface layers of the disk in a self-consistent manner. The gas temperature is determined from a heating-cooling balance equation in which processes such as photoelectric heating, dissociative heating, dust-gas thermal heat exchange and line cooling are included. The abundances of the dominant cooling species such as CO, C, C+ and O are determined from a chemical network based on the atomic species H, He, C, O, S, Mg, Si, Fe (Kamp & Bertoldi 2000). The underlying disk models to our calculations are the models of Dullemond, van Zadelhoff & Natta (2002). We find that in general the dust and gas temperature are equal to withing 10% for A_V >~ 0.1, which is above the location of the `super-heated surface layer' in which the dust emission features are produced (e.g. Chiang & Goldreich 1997). High above the disk surface the gas temperature exceeds the dust temperature and can can become -- in the presence of polycyclic aromatic hydrocarbons -- as high as 600 K at a radius of 100 AU. This is a region where CO has fully dissociated, but a significant fraction of hydrogen is still in molecular form. The densities are still high enough for non-negligible H_2 emission to be produced.....(see paper for full abstract)Comment: 28 pages, 8 figures, accepted for publication in Ap

Automated Termination Proofs for Logic Programs by Term Rewriting

There are two kinds of approaches for termination analysis of logic programs: "transformational" and "direct" ones. Direct approaches prove termination directly on the basis of the logic program. Transformational approaches transform a logic program into a term rewrite system (TRS) and then analyze termination of the resulting TRS instead. Thus, transformational approaches make all methods previously developed for TRSs available for logic programs as well. However, the applicability of most existing transformations is quite restricted, as they can only be used for certain subclasses of logic programs. (Most of them are restricted to well-moded programs.) In this paper we improve these transformations such that they become applicable for any definite logic program. To simulate the behavior of logic programs by TRSs, we slightly modify the notion of rewriting by permitting infinite terms. We show that our transformation results in TRSs which are indeed suitable for automated termination analysis. In contrast to most other methods for termination of logic programs, our technique is also sound for logic programming without occur check, which is typically used in practice. We implemented our approach in the termination prover AProVE and successfully evaluated it on a large collection of examples.Comment: 49 page

Cenozoic sedimentary and volcanic rocks of New Zealand: A reference volume of lithology, age and paleoenvironments with maps (PMAPs) and database.

This volume presents descriptive geological data and text about each Cenozoic sedimentary and volcanic geological unit to formation and member level (in some cases) exposed on land in New Zealand, including their lithology, stratigraphic age and inferred environment of deposition or emplacement. These data are illustrated as two types of PMAPS: a present-day paleoenvironment map of New Zealand; and as restored paleoenvironment maps, one for each million years from 65 Ma to the present. These information and data underpin the development of a new Cenozoic paleogeographical model of New Zealand

Patterns of Late Cenozoic exhumation deduced from apatite and zircon U-He ages from Fiordland, New Zealand

New apatite and zircon (U-Th)/He ages from the Fiordland region of New Zealand's South Island expand on earlier results and provide new constraints on patterns of Late Cenozoic exhumation and cooling across this region. Zircon (U-Th)/He cooling ages, in combination with increased density of apatite ages, show that in addition to a gradual northward decrease in cooling ages that was seen during an earlier phase of this study, there is also a trend toward younger cooling ages to the east. Distinct breaks in cooling age patterns on southwestern Fiordland appear to be correlated to the location of previously mapped faults. The northward decrease in ages may reflect asynchronous cooling related to migration in the locus of exhumation driven by subduction initiation, or it may reflect synchronous regional exhumation that exposed different structural levels across Fiordland, or some combination of these effects. In either case, differential exhumation accommodated by major and minor faults that dissect Fiordland basement rocks apparently played an important role in producing the resulting age patterns

Involutivity of integrals for sine-Gordon, modified KdV and potential KdV maps

Closed form expressions in terms of multi-sums of products have been given in \cite{Tranclosedform, KRQ} of integrals of sine-Gordon, modified Korteweg-de Vries and potential Korteweg-de Vries maps obtained as so-called $(p,-1)$-traveling wave reductions of the corresponding partial difference equations. We prove the involutivity of these integrals with respect to recently found symplectic structures for those maps. The proof is based on explicit formulae for the Poisson brackets between multi-sums of products.Comment: 24 page

A Resolved Molecular Gas Disk around the Nearby A Star 49 Ceti

The A star 49 Ceti, at a distance of 61 pc, is unusual in retaining a substantial quantity of molecular gas while exhibiting dust properties similar to those of a debris disk. We present resolved observations of the disk around 49 Ceti from the Submillimeter Array in the J=2-1 rotational transition of CO with a resolution of 1.0x1.2 arcsec. The observed emission reveals an extended rotating structure viewed approximately edge-on and clear of detectable CO emission out to a distance of ~90 AU from the star. No 1.3 millimeter continuum emission is detected at a 3-sigma sensitivity of 2.1 mJy/beam. Models of disk structure and chemistry indicate that the inner disk is devoid of molecular gas, while the outer gas disk between 40 and 200 AU from the star is dominated by photochemistry from stellar and interstellar radiation. We determine parameters for a model that reproduces the basic features of the spatially resolved CO J=2-1 emission, the spectral energy distribution, and the unresolved CO J=3-2 spectrum. We investigate variations in disk chemistry and observable properties for a range of structural parameters. 49 Ceti appears to be a rare example of a system in a late stage of transition between a gas-rich protoplanetary disk and a tenuous, virtually gas-free debris disk.Comment: 11 pages, 6 figures, accepted for publication in Ap

The staircase method: integrals for periodic reductions of integrable lattice equations

We show, in full generality, that the staircase method provides integrals for mappings, and correspondences, obtained as traveling wave reductions of (systems of) integrable partial difference equations. We apply the staircase method to a variety of equations, including the Korteweg-De Vries equation, the five-point Bruschi-Calogero-Droghei equation, the QD-algorithm, and the Boussinesq system. We show that, in all these cases, if the staircase method provides r integrals for an n-dimensional mapping, with 2r<n, then one can introduce q<= 2r variables, which reduce the dimension of the mapping from n to q. These dimension-reducing variables are obtained as joint invariants of k-symmetries of the mappings. Our results support the idea that often the staircase method provides sufficiently many integrals for the periodic reductions of integrable lattice equations to be completely integrable. We also study reductions on other quad-graphs than the regular 2D lattice, and we prove linear growth of the multi-valuedness of iterates of high-dimensional correspondences obtained as reductions of the QD-algorithm.Comment: 40 pages, 23 Figure