Hernquist Light Profile

[Jammy2211]

The following seminar work of Hernquist details a light profile called the Hernquist profile:

https://ui.adsabs.harvard.edu/abs/1990ApJ...356..359H/abstract

The intensity calculation for a spherical model is given by equations (32-35):

It would be good to implement this light profile in the module autogalaxy.profiles.light_profiles:

https://github.com/Jammy2211/PyAutoGalaxy/blob/master/autogalaxy/profiles/light_profiles.py

A template for the profile is as follows:

class SpHernquist(LightProfile):
    def __init__(
        self,
        centre: Tuple[float, float] = (0.0, 0.0),
        another_parameter: float = 1.0,
    ):
        """
        The spherical Hernquist profile, used to fit the light of galaxies.

        Parameters
        ----------
        centre
            The (y,x) arc-second coordinates of the profile centre.
        """

        super().__init__(
            centre=centre,
            elliptical_comps=(0.0, 0.0),
        )

    def image_2d_from_grid_radii(self, grid_radii):
        """
        Calculate the intensity of the Hernquist light profile on a grid of radial coordinates.

        Parameters
        ----------
        grid_radii : float
            The radial distance from the centre of the profile. for each coordinate on the grid.
        """
        return expression_for_projected_intensity

   # For new users: These decorators perform geometric transformation of the input grid using its `centre`.

    @grid_decorators.grid_2d_to_structure
    @grid_decorators.transform
    @grid_decorators.relocate_to_radial_minimum
    def image_2d_from_grid(self, grid, grid_radial_minimum=None):
        """Calculate the intensity of the light profile on a grid of Cartesian (y,x) coordinates.

        If the coordinates have not been transformed to the profile's geometry, this is performed automatically.

        Parameters
        ----------
        grid
            The (y, x) coordinates in the original reference frame of the grid.
        """
        return self.image_2d_from_grid_radii(self.grid_to_eccentric_radii(grid))