Models

DiskJockey supports many different disk models, and is designed in such a way so as to be easily extensible to any new model you might like (pull requests welcome)!

The current models include

Standard

Keyword: standard

This is a standard model that is used in Czekala et al. 2015 and 2016, and Rosenfeld et al. 2012.

This model includes an adjustable exponential taper for the inner surface density profile. This is meant to mimic the appearance of large inner gas gaps in disks. Relevant notebook sketches of this idea can be found in notebooks/Cavity Surface Density.ipynb. The main difference from the standard model is the introduction of two new parameters: a cavity radius and decay profile exponent.

Vertical

Keyword: vertical

This model includes a more realistic temperature profile as outlined in Dartois et al. 2003, Rosenfeld et al. 2013, and Williams and Best 2014, among many others. We follow the specific parameterization in Williams and Best 2014.

The primary additional step for this model is the necessity to numerically solve the hydrostatic equilibrium equation (WB14 Eqn 1).

for a given radius, r, come up with a vertical grid of z points that stretches from the midplane to an appropriate height where the gas density is approximately zero.
calculate ln(rho(r,z)) as a function of (r, z) by integrating WB14 Eqn 1 using quadgk. This is the unnormalized density of the disk, which means the relative values at a fixed radius should be correct, but no guarantees about anything else. We will call the unnormalized density un_rho(r,z).
now, we know that Sigma(r) specifies the surface density of the disk, i.e., or the integral of rho(r, z) from z = -inf to +inf. Therefore, we can find rho(r,z) by vertically integrating un_rho(r,z) and finding the normalization constant, norm(r). Because we are dealing with integrals of very big and very small numbers, we need to do some tricks to avoid overflow and underflow errors.
finally, we know that CO is photodissociated when it is not shielded by enough gas, i.e., there is not enough gas column density above this height to block harmful radiation. Therefore, we need to find the photodissociation height, z_phot(r), above which the molecule CO can no longer exist. To do this requires integrating from z = +inf towards the midplane (z = 0) to find the height at which we have accumulated enough gas column density to be shielded.

This sounds like a lot of steps just to evaluate a single rho(r,z) point. Because RADMC-3D solves the radiative transfer on a spherical grid and the disk model is defined on a cylindrical grid, there is a careful order of operations necessary to achieve the appropriate accuracy in the shortest amount of computational time. We address this by first solving everything on a cylindrical grid to find norm(r) and z_phot(r) as a function of disk radius. Then, for a given (r_spherical, theta) point, we convert to cylindrical coordinates and solve WB14 Eqn 1 to find un_rho(r,z).

VerticalEta

Characterized with ParametersVerticalEta. In addition to the parameters described in the Vertical model, this extension has an additional parameter eta, designed to vary the height of the atmosphere with radius.

Conventions

Inclination

Disk inclination ranges from 0 to 180 degrees. 0 degrees means face on, angular momentum vector pointing at observer; 90 means edge on; and 180 means face on, angular momentum vector pointing away from observer. These are the same as the RADMC-3D conventions.

Position Angle

We also adopt the RADMC-3D convention for position angle, which defines position angle by the angular momentum vector. A positive PA angle means the disk angular momentum vector will be rotated counter clockwise (from North towards East).