Fixed-density Structure¶

There are several ways to setup the disk structure in ProDiMo. The simplest one is to use a parameterized fixed density structure see Woitke+ (2016) for details.

In this case, ProDiMo will use a prescribed fixed 2D density structure for the disk, and then will calculate only once the dust radiative transfer, chemistry and thermal balance. In particular, ProDiMo will avoid to use the calculated gas temperatures and sound speeds to re-calculate the vertical disk structure (no disk structure iteration loop).are also described in.

Power-law disk structure¶

The simplest parameterized mode is to use power-laws for the radial surface density and the vertical scale-height of the disk.

The radial surface density profile $\Sigma$ given by

$$\Sigma(r) \propto r^{-\epsilon}$$

defined between Rin and Rout. The vertical scale height of the disk is given by

$$H(r)=H_0 \left(\frac{r}{\mathrm{R_\mathrm{ref}}}\right)^\beta$$

where the flaring index $\beta$ determines how the scale height H(r) increases with radius r. $\beta=1$ means constant H(r)/r. $\beta>1$ means H(r)/r increases with r ("flaring disk").

This results in a 2D density structure of the form:

$$\rho(r,z) \propto \exp\left(-\frac{z^2}{2 H(r)^2}\right)$$

where $\rho(r,z)$ is the 2D gas density distribution. This density distribution is than normalized by using the given total disk mass (i.e. integrating this density structure give the disk mass).

To activate this mode and setup the density structure the following parameters are required in Parameter.in

.false.     ! solve_diskstruc   : solve the vertical hydrostatic eq.?
.false.     ! conserve_pressure : conserve pressure in hydrostatic eq.?
.true.      ! MCFOST_LIKE       : fixed disk structure like in MCFOST?
0.02        ! Mdisk       [Msun]  : disk mass
.true.      ! MCFOST_LIKE         : parametric disk structure like in MCFOST?
0.05        ! Rin         [AU]    : inner disk radius
350.0       ! Rout        [AU]    : outer disk radius 
1.0         ! epsilon     [-]     : column density exponent
10.0        ! MCFOST_H0   [AU]    : reference scale height
100.0       ! MCFOST_RREF [AU]    : ... belonging to reference radius
1.13        ! MCFOST_BETA         : flaring index

The picture below shows an example for MCFOST_H0=10 AU at MCFOST_RREF=100 AU and MCFOST_BETA=1.13.

Tapered outer edge¶

It is also possible to used a radial disk structure with a tapered outer edge with an exponential drop of the vertical column density with radius (for details see Woitke+ 2016).

To activate it use

100.0       ! Rtaper      [AU]  : radius where disk start to taper off

For this case the ! Rout parameter is ignored and the outer disk radius is automatically set where the total vertical hydrogen number density reaches $N_\mathrm{H}(\mathrm{Rout})=10^{20}\,\mathrm{cm^{-2}}$. To still force a certain outer disk radius and use a tapered edge one has to use

100.0       ! Rtaper      [AU]  : radius where disk start to taper off
300.0       ! Rout        [AU]  : the outer radius of the disk
.false.     ! adjustRout        : do not automatically adjust the outer disk radius.