hyperion.densities.FlaredDisk#

class hyperion.densities.FlaredDisk(mass=None, rho_0=None, rmin=None, rmax=None, p=-1, beta=-1.25, h_0=None, r_0=None, cylindrical_inner_rim=True, cylindrical_outer_rim=True, star=None, dust=None)#

This class implements the density structure for a flared axisymmatric disk, with a density given by:

$\rho(R,z,\phi) = \rho_0^{\rm disk}\,\left(\frac{R_0}{R}\right)^{\beta - p}\,\exp{\left[-\frac{1}{2}\left(\frac{z}{h(R)}\right)^2\right]} \\$

where

$h(R) = h_0\left(\frac{R}{R_0}\right)^\beta$

The $\rho_0^{\rm disk}$ parameter does not need to be set directly (although it can be), and is instead automatically calculated when you set the disk mass. The exact equation relating $\rho_0^{\rm disk}$ to the disk mass can be found by integrating the equation for $\rho(R,z,\phi)$ over three dimensions and setting the result equal to the disk mass.

Once the FlaredDisk class has been instantiated, the parameters for the density structure can be set via attributes:

>>> from hyperion.util.constants import msun, au
>>> from hyperion.densities.flared_disk import FlaredDisk
>>> disk = FlaredDisk()
>>> disk.mass = 2. * msun
>>> disk.rmin = 0.1 * au
>>> disk.rmax = 100 * au

Attributes

`mass`	Total disk mass (g)
`rho_0`	Scale-factor for the disk density (g/cm^3)
`rmin`	inner radius (cm)
`rmax`	outer radius (cm)
`p`	surface density power-law exponent
`beta`	scaleheight power-law exponent
`h_0`	scaleheight of the disk at `r_0` (cm)
`r_0`	radius at which `h_0` is defined (cm)
`cylindrical_inner_rim`	Whether the inner edge of the disk should be defined as a truncation in cylindrical or spherical polar coordinates
`cylindrical_outer_rim`	Whether the outer edge of the disk should be defined as a truncation in cylindrical or spherical polar coordinates
`dust`	dust properties (filename or dust object)

Methods

`density`(grid)	Return the density grid
`midplane_cumulative_density`(r)	Find the cumulative column density as a function of radius.
`vertical_cumulative_density`(r, theta)	Find the cumulative column density as a function of theta.

Methods (detail)

density(grid)#

Return the density grid

Parameters:

gridSphericalPolarGrid or CylindricalPolarGrid instance.: The spherical or cylindrical polar grid object containing information about the position of the grid cells.

Returns:

rhonp.ndarray: A 3-dimensional array containing the density of the disk inside each cell. The shape of this array is the same as grid.shape.

midplane_cumulative_density(r)#

Find the cumulative column density as a function of radius.

The cumulative density is measured outwards from the origin, and in the midplane.

Parameters:

rnp.ndarray: Array of values of the radius up to which to tabulate the cumulative density.

Returns:

rhonp.ndarray: Array of values of the cumulative density.

vertical_cumulative_density(r, theta)#

Find the cumulative column density as a function of theta.

Parameters:

rfloat: The spherical radius at which to calculate the cumulative density.
thetanp.ndarray: The theta values at which to tabulate the cumulative density.

Returns:

rhonp.ndarray: Array of values of the cumulative density.

hyperion.densities.FlaredDisk

Contents

hyperion.densities.FlaredDisk#