Gas disk

The gas disk is implemented according to [MorishimaStadelMoore10]. It supports gas drag, Type I migration and drag enhancement for small particles. The parameters for the gas disk can be set with the following arguments:

In the param.dat file

  • Use gas disk

  • Use gas disk potential

  • Use gas disk enhancement

  • Use gas disk drag

  • Use gas disk tidal dampening

  • Gas dTau_diss

  • Gas disk inner edge:

  • Gas disk outer edge:

  • Gas disk grid outer edge:

  • Gas disk grid dr:

  • Gas Sigma_10

  • Gas alpha

  • Gas beta

  • Gas Mgiant

  • Gas file name

In the define.h file

  • def_Gasnz_g: Number of cells in z direction for gas grid

  • def_Gasnz_p: Number of cells in z direction for particle grid

  • def_h_1: scale height at 1AU for c = 1km/s

  • def_M_Enhance: factor for enhancement

  • def_Mass_pl: factor for enhancement

  • def_fMass_min: factor for enhancement

  • def_Gas_cd: numerical gas drag coefficient

Gas disk structure

The gas disk structure is implemented as a uniform disk in space, which decays exponentially in time ([MorishimaStadelMoore10]).

(2)\[\Sigma_{gas}(r,t) = \Sigma{gas,0} \left( \frac{r}{1 AU} \right)^{-\alpha} \exp \left( - \frac{t}{\tau_{decay}} \right),\]

with the gas surface density at 1 AU \(\Sigma{gas,0}\), the dissipation time \(\tau_{decay}\) and the power law exponent \(\alpha\).

The scale height of the gas disk is set to

(3)\[h(r) = h_0 \frac{r}{1 AU} \left( \frac{r}{1 AU} \right)^{\beta},\]

with the scale height at 1AU \(h_0\).

Gas disk physical range in r

The range of the gas disk can be set with the Gas disk inner edge: and Gas disk outer edge: parameters. Outside of these boundaries, the gas disk density is 0.

Gas disk grid

In order to calculate the gas disk gravitational effect on the particles, the gas disk gravitational force in r and z is tabulated and stored in a gas disk grid. While the tabulated values of the grid respect the entire gas disk, ranging from the inner edge to the outer edge, the gas disk itself can have a smaller range in r. This is especially useful, when the gas disk extends a broader range than the particles. Therefore, the outer range of the gas disk grid can be set by a different parameter Gas disk grid outer edge:. The inner edge of the gas disk grid corresponds to the physical inner edge of the disk, Gas disk inner edge:

The spacing of the gas disk grid in r can be set with the parameter Gas disk grid dr.

When a particle is located outside of the gas disk grid, then the effect of the gas disk potential on the particles is not applied by using the tabulated values, but with a simpler approach according to Ward(1981).

Gas drag force

The gas drag force is enabled with the Use gas disk drag parameter. The gas drag force is implemented as

(4)\[\mathbf{F}_{drag} = - \frac{1}{2m} c_D \pi r^2 \rho_{gas} | \mathbf{v}_{rel} | \mathbf{v}_{rel},\]

with the radius of the particle \(r\) and the mass of the particle \(m\). The numerical coefficient \(c_D\) is set to 2 ([MorishimaStadelMoore10]). The value of \(c_D\) can be changed in the define.h file.

Gas disk file

When a gas disk file name is specified in the Gas file name parameter. Then the gas disk structure is red from this file. The file must contain the following columns:

time0 r Sigma h
time1 r Sigma h
.
.
.

with:

  • time in years.

  • r the distance from the cell to the star in AU.

  • Sigma, the surface density at the cell location r,in in g/\(\text{cm}^3\).

  • h, the gas disk scale height at the cell location r, in AU.