Rounded inner walls¶

Setup¶

Instead of sharp edges, one can choose to have walls with exponentially increasing column density according to

$$\Sigma(r) \propto r^{(-\epsilon)} \exp\left[-\left(\frac{r}{R_{taper}}\right)^{(2-\gamma)}\right] \exp\left[-\left(\frac{R_{soft}}{r}\right)^{sharp}\right] \qquad (1)$$

where the first exponential factor causes a tapering-off for the outer edge, and the second exponential factor leads to a rounded appearance of the inner rim, and of the inner walls of further outer zones. The second exponential factor reduces the column density Sigma inside of r<R_{soft}.

To activate this option, set reduc and raduc parameters in Parameter.in. reduc tells ProDiMo which maximum reduction factor to apply for the column density at $r=R_\mathrm{in}$, and raduc positions $R_\mathrm{soft}$ as

$$raduc = \frac{R_{soft}}{R_{in}} \qquad (2)$$

$$reduc = \exp\left[-\left(\frac{R_{soft}}{R_{in}}\right)^{sharp}\right] . \qquad (3)$$

Internally, $R_\mathrm{soft}$ and $sharp$ are calculated from reduc and raduc using Eqs.(2) and (3).

If you set reduc and raduc in Parameter.in, they apply to all zones. You can set more specific zone parameter using r1educ, r2educ, r3educ, r4educ, and r1aduc, r2aduc, r3aduc, r4aduc, respectively.

The following plots show the column densities and densities in two models with sharp inner edges (left, standard) and with exponentially increasing column densities at walls (right, parameters reduc=1.E-6 and raduc=2.0)

The red and black dashed lines show radial and vertical optical depths, $A_\mathrm{V,rad} = [0.01,1]$ and $A_\mathrm{V,ver} = [1,10]$, respectively. Note the more rounded shape of the inner walls. The reduc/raduc approach avoids numerical artefacts due to insufficient wall resolution, see spatial_grid_resolution, so you don't need to fiddle with Ninner and NnewWall when using the reduc/raduc approach.

Impact on observables¶

The rounded-off inner rim looks more ring-like at 6.5um continuum (right), whereas the sharp edge is more dominated by the far side (the visible part) of the inner wall.

The rounded-off inner rim appears more ring-like in CO ro-vibrational lines (right), whereas the appearance of the sharp edge is dominated by the far side (the visible part) of the inner wall. The two-layer emission on the l.h.s. (sharp edge) is gone on the r.h.s. (rounded-off edge). The rounded-off inner rim appears a bit bigger in CO ro-vibrational lines, and more double-peaked. Note that the peak signal of the rounded-off inner rim is down by a factor 10, the total fine flux by factor 1.6. Possibly some resolution problems on the r.h.s.

Peter Woitke, May 22, 2015