pisces.models.galaxy_clusters.spherical.SphericalGalaxyClusterModel.from_density_and_total_density#

classmethod SphericalGalaxyClusterModel.from_density_and_total_density(density_profile: BaseSphericalDensityProfile, total_density_profile: BaseSphericalDensityProfile, filename: str | Path, min_radius: unyt_quantity | str = unyt_quantity(1, 'kpc'), max_radius: unyt_quantity | str = unyt_quantity(1, 'Mpc'), num_points: int = 1000, overwrite: bool = False, stellar_density_profile: BaseSphericalDensityProfile = None, **kwargs)[source]#

Generate a spherical cluster model from analytic density profiles.

Parameters:

  • density_profile (BaseSphericalDensityProfile) – Profile object representing the radial gas density.

  • total_density_profile (BaseSphericalDensityProfile) – Profile object representing the total density.

  • filename (str or Path) –

    The file at which to save the model. If the file already exists, then it will raise an error unless overwrite=True.

    This should be an HDF5 file with a .h5 or .hdf5 extension.

  • min_radius (unyt_quantity or str, optional) – Minimum radius for sampling (default: 1 kpc).

  • max_radius (unyt_quantity or str, optional) – Maximum radius for sampling (default: 1 Mpc).

  • num_points (int, optional) – Number of radial samples (default: 1000).

  • overwrite (bool, optional) – Whether to overwrite existing file (default: False).

  • stellar_density_profile (BaseSphericalDensityProfile, optional) – Optional stellar density profile. If provided, the stellar density will be included in the model. Otherwise, the stellar density is assumed to be zero and no stellar component is included.

  • **kwargs – Additional keyword arguments passed to the density profile constructors.

Notes

Given gas density \(\rho_{\mathrm{gas}}(r)\), total density \(\rho_{\mathrm{tot}}(r)\), and an optional stellar density \(\rho_{\star}(r)\), we perform the following steps:

  1. Compute Dark Matter Density:

    Requiring that the total density is the sum of gas, stellar, and dark matter densities:

    \[\rho_{\mathrm{DM}}(r) = \rho_{\mathrm{tot}}(r) - \rho_{\mathrm{gas}}(r) - \rho_{\star}(r)\]

  1. Compute mass profiles via:

    \[M_i(<r) = 4\pi \int_0^r \rho_i(r') \, r'^2 \, dr'\]

for each component \(i \in \{\mathrm{gas}, \mathrm{tot}, {\rm dm}, \mathrm{stellar}\}\).

  1. Compute the gravitational field:

    \[\nabla \Phi(r) = \frac{G M_{\mathrm{tot}}(<r)}{r^2}\]

  2. Use hydrostatic equilibrium to integrate for pressure:

    \[\nabla P = - \rho_{\mathrm{gas}}(r) \nabla \Phi(r)\]

  3. Solve for temperature using the ideal gas law:

    \[T(r) = \frac{P(r)}{n(r)} = \frac{P(r)}{\rho_{\mathrm{gas}}(r)} \cdot \mu m_p\]