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A practical method is proposed to achieve high-order finite-difference schemes on grids that are quasi-homogeneous on the sphere. A family of grids is used that are characterized by the parameter NP, which can take on values of 3, 4, and 5, etc. The parameter NP is the number of grid patches meeting at the Poles. For NP = 3 the cube sphere grid is obtained and for NP = 5 the icosahedron is obtained. While the grid construction method is valid for all values of NP, the tests performed in this paper concern only the case NP = 5 (i.e., the icosahedron). For each of the rhomboidal patches, the grid is created by connecting points on opposing sides of the rhomboid by great circles. This offers the possibility to obtain derivatives for a line of grid points along a great circle in the classical way. Therefore, it becomes possible to use well-known spatial discretizations from limited-area models. Local models can be transferred to the sphere with rather limited effort. The method was tested using the fourth-order Runge–Kutta integration method and fourth-order spatial differencing. At patch limits, boundary values are obtained using third-order serendipity interpolation, giving the scheme an overall space–time accuracy of 3. The serendipity interpolation is quite efficient. Third-order interpolation in two dimensions is achieved by a set of linear interpolations and a number of function evaluations. All coefficients can be precomputed. The third-order convergence is demonstrated by numerical experiments using Williamson’s test cases 2 and 6.

Aims. We present a comparison between independent computer codes, modeling the physics and chemistry of interstellar photon dominated regions (PDRs). Our goal was to understand the mutual differences in the PDR codes and their effects on the physical and chemical structure of the model clouds, and to converge the output of different codes to a common solution. Methods. A number of benchmark models have been created, covering low and high gas densities n = 10^3, 10^(5.5) cm^(-3) and far ultraviolet intensities χ = 10, 10^5 in units of the Draine field (FUV: 6 < h υ < 13.6 eV). The benchmark models were computed in two ways: one set assuming constant temperatures, thus testing the consistency of the chemical network and photo-processes, and a second set determining the temperature self consistently by solving the thermal balance, thus testing the modeling of the heating and cooling mechanisms accounting for the detailed energy balance throughout the clouds. Results. We investigated the impact of PDR geometry and agreed on the comparison of results from spherical and plane-parallel PDR models. We identified a number of key processes governing the chemical network which have been treated differently in the various codes such as the effect of PAHs on the electron density or the temperature dependence of the dissociation of CO by cosmic ray induced secondary photons, and defined a proper common treatment. We established a comprehensive set of reference models for ongoing and future PDR model bench-marking and were able to increase the agreement in model predictions for all benchmark models significantly. Nevertheless, the remaining spread in the computed observables such as the atomic fine-structure line intensities serves as a warning that there is still a considerable uncertainty when interpreting astronomical data with our models.

Aims: To calculate chemistry and gas temperature of evolving protoplanetary disks with decreasing mass or dust settling, and to explore the sensitivity of gas-phase tracers. Methods: The density and dust temperature profiles for a range of models of flaring and self-shadowed disks around a typical Herbig Ae star are used together with 2-dimensional ultraviolet (UV) radiative transfer to calculate the chemistry and gas temperature. In each model the line profiles and intensities for the fine structure lines of [O I], [C II] and [C I] and the pure rotational lines of CO, CN, HCN and HCO+ are determined. Results: The chemistry shows a strong correlation with disk mass. Molecules that are easily dissociated, like HCN, require high densities and large extinctions before they can become abundant. The products of photodissociation, like CN and C2H, become abundant in models with lower masses. Dust settling mainly affects the gas temperature, and thus high temperature tracers like the O and C+ fine structure lines. The carbon chemistry is found to be very sensitive to the adopted PAH abundance. The line ratios CO/13CO, CO/HCO+ and [O I] 63 um/146 um can be used to distinguish between disks where dust growth and settling takes place, and disks that undergo overall mass loss., 14 pages, 12 figures. Accepted for publication in A&A

Circumstellar disks are exposed to intense ultraviolet radiation from the young star. In the inner disks, the UV radiation can be enhanced by more than seven orders of magnitude compared with the average interstellar field, resulting in a physical and chemical structure that resembles that of a dense photon-dominated region (PDR). This intense UV field affects the chemistry, the vertical structure of the disk, and the gas temperature, especially in the surface layers of the disk. The parameters which make disks different from traditional PDRs are discussed, including the shape of the UV radiation field, grain growth, the absence of PAHs, the gas/dust ratio and the presence of inner holes. New photorates for selected species, including simple ions, are presented. Also, a summary of available cross sections at Lyman alpha 1216 A is made. Rates are computed for radiation fields with color temperatures ranging from 4000 to 30,000 K, and can be applied to a wide variety of astrophysical regions including exo-planetary atmospheres. The importance of photoprocesses is illustrated for a number of representative disk models, including disk models with grain growth and settling., Comment: A website with the final published version and all photodissociation cross sections and rates can be found at http://www.strw.leidenuniv.nl/~ewine/photo

Aims: The chemistry, distribution and mass of the gas in the transitional disk around the 5 Myr old B9.5 V star HD 141569A are constrained. Methods: A quasi 2-dimensional (2D) chemistry code for photon dominated regions (PDR) is used to calculate the chemistry and gas temperatures in the disk. The calculations are performed for several gas distributions, PAH abundances and values of the total gas mass. The resulting CO J=2-1 and J=3-2 emission lines are computed with a 2D radiative transfer code and are compared to observations. Results: The CO abundance is very sensitive to the total disk mass because the disk is in a regime where self-shielding just sets in. The observed CO emission lines are best fit by a power-law gas distribution of 80 M_earth starting at 80 AU from the central star, indicating that there is some gas in the inner hole. Predictions are made for intensities of atomic fine-structure lines. [C I], which is the dominant form of carbon in large parts of the disk, is found to be a good alternative tracer of the gas mass., 11 pages, 9 figures. Accepted for publication in A&A

A model is presented which calculates the gas temperature and chemistry in the surface layers of flaring circumstellar disks using a code developed for photon-dominated regions. Special attention is given to the influence of dust settling. It is found that the gas temperature exceeds the dust temperature by up to several hundreds of Kelvins in the part of the disk that is optically thin to ultraviolet radiation, indicating that the common assumption that Tgas=Tdust is not valid throughout the disk. In the optically thick part, gas and dust are strongly coupled and the gas temperature equals the dust temperature. Dust settling has little effect on the chemistry in the disk, but increases the amount of hot gas deeper in the disk. The effects of the higher gas temperature on several emission lines arising in the surface layer are examined. The higher gas temperatures increase the intensities of molecular and fine-structure lines by up to an order of magnitude, and can also have an important effect on the line shapes., 14 pages, 10 figures, accepted for publication in A&A