Benchmark Test Nr. 1

The test described here is a one-radial-zone test. The test setup uses a grazing angle recipe for the incoming flux. In this approach the vertical (1-D) disk structure is computed in a plane-parallel way (as a function of Z or tau_V), and the incoming flux is inserted at the top with a certain grazing angle with respect to the surface of the disk (usually a small number of order 0.05 or so). If your code does not use this recipe, but instead needs the entire disk structure (as a function of R and Z), then please be patient: in a few weeks some "full disk structure" tests will be installed.

In the present test, the grazing angle is specified as a fixed value, so it is not computed here. The parameters of the setup are:

The spectrum of the star is assumed to be a perfect blackbody with the temperature given above. The parameter "starvisfrac=0.5" means that it is assumed that the disk somehow extends down to the stellar surface (although we model here only this tiny annulus), so that it obscures half of the stellar surface, i.e. the surface on the sky of an observer standing on the surface of disk. Effectively this means that only half of the usual stellar flux reaches the disk.

The opacity table to use for this test setup has been computed by E. Kruegel, and is the opacity per gram gas+dust for silicate dust. A plot of the opacity table can be found here.

If everything goes alright, the outcoming flux of the annulus (which equals the incoming flux) from one side of the disk is:

which is the flux at the disk's surface (i.e. not the observed flux at 1 pc).

Objective:
The objective is to compute the temperature as a function of vertical optical depth tau (at 550 nm). The tau coordinate is measured from above (i.e. from vertical height Z=infinity downwards). The vertical density structure is irrelevant for this problem, so that is why we specify everything in terms of tau. Once the temperature structure is found, the spectrum (spectral energy distribution) of the annulus should be computed for an inclination incl = 0 deg (i.e. face-on) and a distance of d = 1 parsec. The spectrum should include only the annulus, i.e. not the star.

We would be very grateful if you submit your results to us via Email. You would then do us a great favor if you submit your results in the following format, although we do not insist on this.

Remarks:
The parameters M_star and H_p are non-essential parameters. But the value of H_p can be used to convert tau_tot into the vertical coordinate z (height above the midplane), if one wishes to use format type 1 for the submission. The Density profile is then defined to be a Gaussian: rho = Sigma exp(-0.5*z^2/H_p^2) / sqrt(2 pi) H_p.

Results from previous authors:
The results from previous authors are shown in the results page. If you are an active participant in the test, please do not view this page before having your own independent results.