SphericalGalaxyClusterModel

class pisces.models.galaxy_clusters.spherical.SphericalGalaxyClusterModel(filepath: str | Path, *args, **kwargs)

Spherical, hydrostatic galaxy cluster model.

This model represents a galaxy cluster composed of 3 components:

1. Gas: the hot, diffuse plasma filling the cluster.

2. Dark Matter: the dominant mass component, providing gravitational binding.

3. Stellar: the stellar component, if provided.

The model is fully spherical and assumes hydrostatic equilibrium, meaning the gas pressure balances the gravitational pull of the total mass (gas + dark matter + stellar). This model ignores the presence of non-thermal pressure components (e.g., cosmic rays, magnetic fields).

Fields

The following physical fields are computed and stored in the model:

Spherical Galaxy Cluster Model Fields

Field Name	Description	Symbol	Notes
radii	Radial coordinate grid	\(r\)
gas_density	Gas density profile	\(\rho_{\mathrm{gas}}(r)\)
stellar_density	Stellar density profile	\(\rho_\star(r)\)
total_density	Total density profile	\(\rho_{\mathrm{tot}}(r)\)
dark_matter_density	Dark matter density profile	\(\rho_{\mathrm{DM}}(r)\)
gas_mass	Enclosed gas mass	\(M_{\mathrm{gas}}(<r)\)
stellar_mass	Enclosed stellar mass	\(M_\star(<r)\)
total_mass	Enclosed total mass	\(M_{\mathrm{tot}}(<r)\)
dark_matter_mass	Enclosed dark matter mass	\(M_{\mathrm{DM}}(<r)\)
gravitational_field	Gravitational acceleration	\(g(r)\)
gravitational_potential	Gravitational potential	\(\Phi(r)\)
pressure	Gas pressure profile	\(P(r)\)
temperature	Gas temperature profile	\(T(r)\)
electron_density	Electron number density	\(n_e(r)\)
entropy	Entropy profile	\(K(r)\)
sound_speed	Adiabatic sound speed	\(c_s(r)\)
baryon_fraction	Baryonic mass fraction	\(M_{\rm bary} / M_{\rm tot}\)

Methodology

This model makes a number of assumptions across all of its construction methods:

• Spherical symmetry: all profiles depend only on radius \(r\).

• Fully thermal hydrostatic equilibrium (HE): non-thermal pressure components are ignored.

• Single-phase gas: temperature and density are well-defined scalars at each point.

• Ionic equilibrium: used for electron density and entropy computation.

• Ideal gas law: pressure and temperature are related via a constant mean molecular weight.

The process to generate a model follows one of three modes depending on the inputs.

Density & Total Density

Hint

This mode is available through from_density_and_total_density().

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

2. Compute the gravitational field:

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

3. Use hydrostatic equilibrium to integrate for pressure:

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

4. Solve for temperature using the ideal gas law:

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

Temperature + Density

Hint

This mode is available through from_temperature_and_density().

Given \(T(r)\) and \(\rho_{\mathrm{gas}}(r)\), we compute:

1. Pressure from the ideal gas law:

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

2. Gravitational field via hydrostatic equilibrium:

   \[g(r) = -\frac{1}{\rho_{\mathrm{gas}}(r)} \cdot \frac{dP}{dr}\]

3. Total mass profile:

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

4. Derive \(\rho_{\mathrm{tot}}(r)\) via:

   \[\rho_{\mathrm{tot}}(r) = \frac{1}{4\pi r^2} \frac{dM_{\mathrm{tot}}}{dr}\]

Entropy + Density

Hint

This mode is available through from_entropy_and_density().

Given entropy \(K(r)\) and gas density \(\rho_{\mathrm{gas}}(r)\), we use:

1. Entropy definition:

   \[K(r) = \frac{T(r)}{n_e(r)^{2/3}}\]

   with

   \[n_e(r) = \frac{\rho_{\mathrm{gas}}(r)}{\mu_e m_p}\]

2. Invert to get temperature:

   \[T(r) = K(r) \cdot \left(\frac{\rho_{\mathrm{gas}}(r)}{\mu_e m_p}\right)^{2/3}\]

3. Compute pressure from ideal gas law and proceed as in the temperature + density pathway.

Note

In all modes, the gravitational potential is computed via:

\[\Phi(r) = -G \left[ \frac{M(<r)}{r} + 4\pi \int_0^r \rho_{\mathrm{tot}}(r') \cdot r' \, dr' \right]\]

Methods

__init__(filepath, *args, **kwargs)	Load a Pisces model from an existing HDF5 file.
add_field(name[, element_shape, units, ...])	Add a new physical field to the model.
add_profile(name, profile[, overwrite])	Add a new analytic profile to the model.
compute_df(species[, num_points, scale, ...])	Compute the isotropic Eddington distribution function for a given species.
copy_field(old_name, new_name)	Create a duplicate of an existing field under a new name.
copy_profile(old_name, new_name)	Create a duplicate of an existing profile under a new name.
from_components(filepath, grid, fields, ...)	Create and save a Pisces model from in-memory components.
from_density_and_total_density(...[, ...])	Generate a spherical cluster model from analytic density profiles.
from_entropy_and_density(density_profile, ...)	Generate a spherical cluster model from gas density and entropy profiles.
from_temperature_and_density(...[, ...])	Generate a spherical galaxy cluster model from gas density and temperature profiles.
generate_particles(filename, num_particles)	Convert this galaxy cluster model into a particle dataset.
get_active_hooks([names])	Return all active hook classes mixed into the model.
get_all_hooks([names])	Return all hook classes mixed into the model, regardless of activation status.
get_df(species)	Retrieve the distribution function and energy grid for a given species.
get_field(name)	Retrieve a physical field by name.
get_hook_class(hook_name)	Return the hook class associated with a given hook name.
get_hook_description(hook_cls)	Return the human-readable description for a given hook class.
get_hook_name(hook_cls)	Return the symbolic name for a given hook class.
get_profile(name)	Retrieve an analytic profile by name.
has_hook(hook)	Check if a given hook is mixed into the model (regardless of activation status).
list_fields()	List all physical fields currently stored in the model.
list_profiles()	List all analytic profiles currently stored in the model.
remove_field(name)	Remove a physical field from the model.
remove_profile(name)	Remove an analytic profile from the model.
rename_field(old_name, new_name)	Rename an existing field in the model.
rename_profile(old_name, new_name)	Rename an existing profile in the model.

Attributes

active_grid_axes	List of active axes in the model's grid.
config	Model-specific configuration settings.
coordinate_system	The coordinate system of the model's grid.
dark_matter_df	Return (E, DF) for the dark matter component.
fields	Model field buffers.
grid	The spatial grid of the model.
handle	The open HDF5 file handle.
has_dark_matter_df	Check whether the dark matter DF is stored in the model file.
has_stellar_df	Check whether the stellar DF is stored in the model file.
logger	Logger interface for this model.
metadata	Model metadata dictionary.
path	The path to the model's HDF5 file.
profiles	Model profile objects.
stellar_df	Return (E, DF) for the stellar component.