BaryonForge.Profiles.Schneider19 module

class BaryonForge.Profiles.Schneider19.SchneiderProfiles(self, mass_def=<function MassDef200c>, c_M_relation=None, use_fftlog_projection=False, padding_lo_proj=0.1, padding_hi_proj=10, n_per_decade_proj=10, r_min_int=1e-06, r_max_int=1000.0, r_steps=500, xi_mm=None, **kwargs)

Bases: BaseBFGProfiles

Base class for defining halo density profiles based on Schneider et al. models.

This class extends the ccl.halos.profiles.HaloProfile class and provides additional functionality for handling different halo density profiles. It allows for custom real-space projection methods, control over parameter initialization, and adjustments to the Fourier transform settings to minimize artifacts.

Parameters:

• use_fftlog_projection (bool, optional) – If True, the default FFTLog projection method is used for the projected method. If False, a custom real-space projection is employed. Default is False.

• padding_lo_proj (float, optional) – The lower padding factor for the projection integral in real-space. Default is 0.1.

• padding_hi_proj (float, optional) – The upper padding factor for the projection integral in real-space. Default is 10.

• n_per_decade_proj (int, optional) – Number of integration points per decade in the real-space projection integral. Default is 10.

• xi_mm (callable, optional) – A function that returns the matter-matter correlation function at different radii. Default is None, in which case we use the CCL inbuilt model.

• **kwargs – Additional keyword arguments for setting specific parameters of the profile. If a parameter is not specified, defaults are assigned based on its type (e.g., mass/redshift/conc-dependence).

model_params

A dictionary containing all model parameters and their values.

Type:

dict

precision_fftlog

Dictionary with precision settings for the FFTLog convolution. Can be modified directly or using the update_precision_fftlog() method.

Type:

dict

real(cosmo, r, M, a)

Computes the real-space density profile.

projected(cosmo, r, M, a)

Computes the projected density profile.

model_param_names = ['cdelta', 'epsilon', 'a', 'n', 'q', 'p', 'cutoff', 'proj_cutoff', 'theta_ej', 'theta_co', 'M_c', 'gamma', 'delta', 'mu_theta_ej', 'mu_theta_co', 'mu_beta', 'mu_gamma', 'mu_delta', 'M_theta_ej', 'M_theta_co', 'M_gamma', 'M_delta', 'nu_theta_ej', 'nu_theta_co', 'nu_M_c', 'nu_gamma', 'nu_delta', 'zeta_theta_ej', 'zeta_theta_co', 'zeta_M_c', 'zeta_gamma', 'zeta_delta', 'A', 'M1', 'eta', 'eta_delta', 'tau', 'tau_delta', 'epsilon_h', 'mu_epsilon_h', 'M_epsilon_h', 'nu_A', 'nu_M1', 'nu_eta', 'nu_eta_delta', 'nu_tau', 'nu_tau_delta', 'nu_epsilon_h', 'zeta_A', 'zeta_M1', 'zeta_eta', 'zeta_eta_delta', 'zeta_tau', 'zeta_tau_delta', 'zeta_epsilon_h', 'alpha_nt', 'nu_nt', 'gamma_nt', 'mean_molecular_weight']

hyper_param_names = ['mass_def', 'c_M_relation', 'use_fftlog_projection', 'padding_hi_proj', 'padding_hi_proj', 'n_per_decade_proj', 'r_min_int', 'r_max_int', 'r_steps', 'xi_mm']

get_f_star(M_use, a, cosmo)

get_f_star_cen(M_use, a, cosmo)

get_f_star_sat(M_use, a, cosmo)

get_f_gas(M_use, a, cosmo)

class BaryonForge.Profiles.Schneider19.DarkMatter(self, mass_def=<function MassDef200c>, c_M_relation=None, use_fftlog_projection=False, padding_lo_proj=0.1, padding_hi_proj=10, n_per_decade_proj=10, r_min_int=1e-06, r_max_int=1000.0, r_steps=500, xi_mm=None, **kwargs)

Bases: SchneiderProfiles

Class representing the total Dark Matter (DM) profile using the NFW (Navarro-Frenk-White) profile.

This class is derived from the SchneiderProfiles class and provides an implementation of the dark matter profile based on the NFW model. It includes a custom _real method for calculating the real-space dark matter density profile, considering factors like the concentration-mass relation and truncation radius.

See SchneiderProfiles for more docstring details.

Notes

The DarkMatter class calculates the dark matter density profile using the NFW model with a modification for truncation at a specified radius set by epsilon. This profile accounts for the concentration-mass relation, which can be provided as cdelta during class init. If none is provided, we use the ConcentrationDiemer15 model.

The profile also includes an additional exponential cutoff to prevent numerical overflow and artifacts at large radii.

The dark matter density profile is given by:

\[\rho_{\text{DM}}(r) = \frac{\rho_c}{\frac{r}{r_s} \left(1 + \frac{r}{r_s}\right)^2} \cdot \frac{1}{\left(1 + \frac{r}{r_t}\right)^2}\]

where:

• \(\rho_c\) is the characteristic density of the halo.

• \(r_s\) is the scale radius of the halo, defined as \(r_s = R/c\).

• \(r_t = \epsilon \cdot R\) is the truncation radius, controlled by the parameter epsilon.

• \(r\) is the radial distance.

Examples

Create a DarkMatter profile and compute the density at specific radii:

>>> dm_profile = DarkMatter(**parameters)
>>> cosmo = ...  # Define or load a cosmology object
>>> r = np.logspace(-2, 1, 50)  # Radii in comoving Mpc
>>> M = 1e14  # Halo mass in solar masses
>>> a = 0.5  # Scale factor corresponding to redshift z
>>> density_profile = dm_profile.real(cosmo, r, M, a)

class BaryonForge.Profiles.Schneider19.TwoHalo(self, mass_def=<function MassDef200c>, c_M_relation=None, use_fftlog_projection=False, padding_lo_proj=0.1, padding_hi_proj=10, n_per_decade_proj=10, r_min_int=1e-06, r_max_int=1000.0, r_steps=500, xi_mm=None, **kwargs)

Bases: SchneiderProfiles

Class representing the two-halo term profile.

This class is derived from the SchneiderProfiles class and provides an implementation of the two-halo term profile. It utilizes the 2-point correlation function directly, rather than employing the full halo model.

See SchneiderProfiles for more docstring details.

Notes

The TwoHalo class calculates the two-halo term profile using the linear matter power spectrum to ensure the correct large-scale clustering behavior. The profile is defined using the matter-matter correlation function, \(\xi_{\text{mm}}(r)\), and a mass-dependent bias term.

The two-halo term density profile is given by:

\[\rho_{\text{2h}}(r) = \left(1 + b(M) \cdot \xi_{\text{mm}}(r)\right) \cdot \rho_{\text{m}}(a) \cdot \text{kfac}\]

where:

• \(b(M)\) is the linear halo bias, defined as:

  \[b(M) = 1 + \frac{q \nu_M^2 - 1}{\delta_c} + \frac{2p}{\delta_c \left(1 + (q \nu_M^2)^p\right)}\]

• \(\nu_M\) is the peak height parameter, \(\nu_M = \delta_c / \sigma(M)\).

• \(\delta_c\) is the critical density for spherical collapse.

• \(\xi_{\text{mm}}(r)\) is the matter-matter correlation function.

• \(\rho_{\text{m}}(a)\) is the mean matter density at scale factor a.

• \(\text{kfac}\) is an additional exponential cutoff factor to prevent numerical overflow.

See Sheth & Tormen 1999 for more details on the bias prescription.

The two-halo term is only valid when the cosmology object’s matter power spectrum is set to ‘linear’. An assertion check is included to ensure this.

Examples

Create a TwoHalo profile and compute the density at specific radii:

>>> two_halo_profile = TwoHalo(**parameters)
>>> cosmo = ...  # Define or load a cosmology object with linear matter power spectrum
>>> r = np.logspace(-2, 1, 50)  # Radii in comoving Mpc
>>> M = 1e14  # Halo mass in solar masses
>>> a = 0.5  # Scale factor corresponding to redshift z
>>> density_profile = two_halo_profile.real(cosmo, r, M, a)

class BaryonForge.Profiles.Schneider19.Stars(self, **kwargs)

Bases: SchneiderProfiles

Class representing the exponential stellar mass profile.

This class is derived from the SchneiderProfiles class and provides an implementation of an exponential stellar mass profile. It calculates the real-space stellar mass density profile, using parameters to account for factors like stellar mass fraction and halo radius.

See SchneiderProfiles for more docstring details.

Notes

The Stars class models the stellar mass distribution with an exponential profile, modulated by parameters such as eta, tau, A, and M1. These parameters adjust the stellar mass fraction as a function of halo mass. The profile also applies an exponential cutoff controlled by the epsilon_h parameter to define the characteristic radius of the stellar distribution.

The stellar mass density profile is given by:

\[\rho_\star(r) = \frac{f_{\text{cga}} M_{\text{tot}}}{4 \pi^{3/2} R_h} \frac{1}{r^2} \exp\left(-\frac{r^2}{4 R_h^2}\right)\]

where:

• \(f_{\text{cga}}\) is the stellar mass fraction, defined as:

  \[f_{\text{cga}} = 2 A \left(\left(\frac{M}{M_1}\right)^{\tau + \tau_\delta} + \left(\frac{M}{M_1}\right)^{\eta + \eta_\delta}\right)^{-1}\]

• \(M_{\text{tot}}\) is the total halo mass.

• \(R_h = \epsilon_h R\) is the characteristic scale radius of the stellar distribution.

• \(r\) is the radial distance.

The class overrides specific precision_fftlog settings to prevent ringing artifacts in the profiles. This is achieved by setting extreme padding values.

An additional exponential cutoff is included to prevent numerical overflow and artifacts at large radii.

Examples

Create a Stars profile and compute the density at specific radii:

>>> stars_profile = Stars(**parameters)
>>> cosmo = ...  # Define or load a cosmology object
>>> r = np.logspace(-2, 1, 50)  # Radii in comoving Mpc
>>> M = 1e14  # Halo mass in solar masses
>>> a = 0.5  # Scale factor corresponding to redshift z
>>> density_profile = stars_profile.real(cosmo, r, M, a)

class BaryonForge.Profiles.Schneider19.SatelliteStars(self, gas=None, stars=None, darkmatter=None, max_iter=10, reltol=0.01, r_min_int=1e-08, r_max_int=100000.0, r_steps=5000, **kwargs)

Bases: CollisionlessMatter

Class representing the matter density profile of stars in satellites.

It uses the CollisionlessMatter profiles with a simple rescaling to get just the SG (satellite galaxies) term alone. See that class for more details.

class BaryonForge.Profiles.Schneider19.Gas(self, mass_def=<function MassDef200c>, c_M_relation=None, use_fftlog_projection=False, padding_lo_proj=0.1, padding_hi_proj=10, n_per_decade_proj=10, r_min_int=1e-06, r_max_int=1000.0, r_steps=500, xi_mm=None, **kwargs)

Bases: SchneiderProfiles

Class representing the gas density profile.

This class is derived from the SchneiderProfiles class and provides an implementation of a gas density profile. It calculates the real-space gas density profile, using the general NFW (GNFW) model of Nagai, Kravtsov & Vikhlinin 2009.

See SchneiderProfiles for more docstring details.

Notes

The Gas class models the gas distribution in halos by considering the gas fraction, which is computed based on the total baryonic fraction minus the stellar fraction. The gas density profile is defined using parameters such as beta, delta, gamma, theta_co, and theta_ej. These parameters characterize the core and ejection properties of the gas distribution.

The gas density profile is given by:

\[\rho_{\text{gas}}(r) = \frac{f_{\text{gas}} M_{\text{tot}}}{N} \cdot \frac{1}{(1 + u)^{\beta}} \cdot \frac{1}{(1 + v)^{(\delta - \beta)/\gamma}}\]

where:

• \(f_{\text{gas}} = f_{\text{bar}} - f_{\star}\) is the gas fraction.

• \(f_{\text{bar}}\) is the cosmic baryon fraction.

• \(f_{\star}\) is the stellar mass fraction, defined as:

  \[f_{\star} = 2A \left(\left(\frac{M}{M_1}\right)^{\tau} + \left(\frac{M}{M_1}\right)^{\eta}\right)^{-1}\]

• \(M_{\text{tot}}\) is the total halo mass.

• \(N\) is the normalization factor to ensure mass conservation.

• \(u = \frac{r}{R_{\text{co}}}\) and \(v = \frac{r}{R_{\text{ej}}}\) are dimensionless radii.

• \(\beta\) is the power-law slope for \(R_{\text{co}} \lesssim r \lesssim R_{\text{ej}}\)

• \(\delta\) is the power-law slope at \(r \sim \lesssim R_{\text{ej}}\)

• \(\gamma\) is the power-law slope for \(r \gg R_{\text{ej}}\)

• \(R_{\text{co}} = \theta_{\text{co}} R\) is the core radius.

• \(R_{\text{ej}} = \theta_{\text{ej}} R\) is the ejection radius.

• \(r\) is the radial distance.

Examples

Create a Gas profile and compute the density at specific radii:

>>> gas_profile = Gas(**parameters)
>>> cosmo = ...  # Define or load a cosmology object
>>> r = np.logspace(-2, 1, 50)  # Radii in comoving Mpc
>>> M = 1e14  # Halo mass in solar masses
>>> a = 0.5  # Scale factor corresponding to redshift z
>>> density_profile = gas_profile.real(cosmo, r, M, a)

class BaryonForge.Profiles.Schneider19.ShockedGas(self, epsilon_shock, width_shock, **kwargs)

Bases: Gas

Class representing a shocked gas profile.

This class is derived from the Gas class and provides an implementation of a shocked gas profile, assuming Rankine-Hugoniot conditions. It models the effect of a high Mach-number shock, leading to a density suppression by a factor of 4. This suppression is implemented using a logistic function based on the radial distance.

Parameters:

• epsilon_shock (float) – A scaling factor that sets the shock radius as a fraction of the halo radius.

• width_shock (float) – The width of the shock transition, controlling how sharply the gas density changes across the shock front.

• **kwargs – Additional keyword arguments passed to the Gas class.

Notes

The ShockedGas class modifies the gas density profile inherited from the Gas class by applying a shock model. The shock is characterized by the epsilon_shock and width_shock parameters. The density is reduced by a factor of 4 at the shock front, a result that assumes a high Mach-number shock under Rankine-Hugoniot conditions.

The gas density profile is calculated as:

\[\rho_{\text{shocked}}(r) = \rho_{\text{gas}}(r) \cdot \left[ \frac{1 - 0.25}{1 + \exp\left(\frac{\log(r) - \log(\epsilon_{\text{shock}} R)}{\text{width}_{\text{shock}}}\right)} + 0.25 \right]\]

where:

• \(\rho_{\text{gas}}(r)\) is the gas density profile from the Gas class.

• \(\epsilon_{\text{shock}}\) sets the location of the shock.

• \(\text{width}_{\text{shock}}\) determines the sharpness of the transition.

• \(r\) is the radial distance from the halo center.

• The factor of 0.25 represents the maximum possible density drop due to the shock.

See the Gas class for more details on the base gas profile and additional parameters.

class BaryonForge.Profiles.Schneider19.CollisionlessMatter(self, gas=None, stars=None, darkmatter=None, max_iter=10, reltol=0.01, r_min_int=1e-08, r_max_int=100000.0, r_steps=5000, **kwargs)

Bases: SchneiderProfiles

Class representing the collisionless matter density profile.

This class is derived from the SchneiderProfiles class and provides an implementation for the collisionless matter density profile. It combines contributions from gas, stars, and dark matter to compute the total density profile, using an iterative method to solve for the collisionless matter (dark matter and galaxies) after adiabatic relaxation.

Parameters:

• gas (Gas, optional) – An instance of the Gas class defining the gas profile. If not provided, a default Gas object is created using kwargs.

• stars (Stars, optional) – An instance of the Stars class defining the stellar profile. If not provided, a default Stars object is created using kwargs.

• darkmatter (DarkMatter, optional) – An instance of the DarkMatter class defining the dark matter profile. If not provided, a default DarkMatter object is created using kwargs.

• max_iter (int, optional) – Maximum number of iterations for the relaxation method. Default is 10.

• reltol (float, optional) – Relative tolerance for convergence in the relaxation method. Default is 1e-2.

• r_min_int (float, optional) – Minimum radius for integration during the iterative relaxation. Default is 1e-8.

• r_max_int (float, optional) – Maximum radius for integration during the iterative relaxation. Default is 1e5.

• r_steps (int, optional) – Number of steps in the radius for integration. Default is 5000.

• **kwargs – Additional keyword arguments passed to initialize the Gas, Stars, and DarkMatter profiles, as well as other parameters from SchneiderProfiles.

Notes

The CollisionlessMatter class computes the total density profile by combining the contributions from gas, stars, and dark matter profiles. The relaxation method iteratively adjusts these profiles to achieve equilibrium, ensuring mass conservation. This approach accounts for different physical components and their interactions within the halo.

Calculation Steps:

1. Initial Profiles: The class starts by calculating the individual density profiles for dark matter, gas, and stars:

   \[\rho_{\text{DM}}(r), \; \rho_{\text{gas}}(r), \; \rho_{\text{stars}}(r)\]

2. Cumulative Mass Profiles: The cumulative mass profiles are calculated by integrating the density profiles:

   \[M_{\text{DM}}(r) = 4\pi \int_0^r \rho_{\text{DM}}(r') r'^2 dr'\]
   \[M_{\text{gas}}(r) = 4\pi \int_0^r \rho_{\text{gas}}(r') r'^2 dr'\]
   \[M_{\text{stars}}(r) = 4\pi \int_0^r \rho_{\text{stars}}(r') r'^2 dr'\]

3. Relaxation Iteration: The relaxation method iteratively adjusts the mass profile to achieve equilibrium. The adjusted mass profile is calculated as:

   \[M_{\text{CLM}}(r) = f_{\text{clm}}(M_{\text{DM}} + M_{\text{gas}} + M_{\text{stars}})\]

   where \(f_{\text{clm}}\) is calculated using:

   \[f_{\text{clm}} = 1 - \frac{\Omega_b}{\Omega_m} + f_{\text{sga}}\]

   Here, \(f_{\text{sga}}\) is the satellite galaxy mass fraction

4. Relaxation Factor Update: During each iteration, the relaxation factor ( zeta ) is updated using:

   \[\zeta_{\text{new}} = a \left( \left(\frac{M_{\text{DM}}}{M_{\text{CLM}}}\right)^n - 1 \right) + 1\]

   This equation ensures that the mass distribution relaxes towards equilibrium over successive iterations, where ( a ) and ( n ) are parameters controlling the relaxation process.

5. Density Profile Calculation: The final collisionless matter density profile is derived from the adjusted cumulative mass:

   \[\rho_{\text{CLM}}(r) = \frac{1}{4\pi r^2} \frac{d}{dr} M_{\text{CLM}}(r)\]

Integration Range and Convergence: The relaxation method uses a logarithmic integration range defined by r_min_int, r_max_int, and r_steps. The method iterates until the relative difference falls below reltol or the maximum number of iterations (max_iter) is reached.

See SchneiderProfiles and associated classes (Gas, Stars, DarkMatter) for more details on the underlying profiles and parameters.

Warning

The method checks if the provided radius values fall within the integration limits. Warnings are issued if adjustments to r_min_int or r_max_int are recommended to cover the full range of the input radii. Note that sometimes warnings occur because the FFTlog asks for a ridiculously high/low radius, and the profile calculation will just return 0s there. In this case the warning is benign and can be safely ignored

class BaryonForge.Profiles.Schneider19.DarkMatterOnly(self, darkmatter=None, twohalo=None, **kwargs)

Bases: SchneiderProfiles

Class representing a combined dark matter profile using the NFW profile and the two-halo term.

This class is derived from the SchneiderProfiles class and provides an implementation that combines the contributions from the Navarro-Frenk-White (NFW) profile (representing dark matter within the halo) and the two-halo term (representing the contribution of neighboring halos). This approach models the total dark matter distribution by considering both the one-halo and two-halo terms.

Parameters:

• darkmatter (DarkMatter, optional) – An instance of the DarkMatter class defining the NFW profile for dark matter within a halo. If not provided, a default DarkMatter object is created using kwargs.

• twohalo (TwoHalo, optional) – An instance of the TwoHalo class defining the two-halo term profile, representing the contribution from neighboring halos. If not provided, a default TwoHalo object is created using kwargs.

• **kwargs – Additional keyword arguments passed to initialize the DarkMatter and TwoHalo profiles, as well as other parameters from SchneiderProfiles.

Notes

The DarkMatterOnly class models the total dark matter density profile by summing the contributions from a one-halo term (using the NFW profile) and a two-halo term. This provides a more complete description of the dark matter distribution, accounting for both the mass within individual halos and the influence of surrounding structure.

The total dark matter density profile is calculated as:

\[\rho_{\text{DMO}}(r) = \rho_{\text{NFW}}(r) + \rho_{\text{2h}}(r)\]

where:

• \(\rho_{\text{NFW}}(r)\) is the NFW profile for the dark matter halo.

• \(\rho_{\text{2h}}(r)\) is the two-halo term representing contributions from neighboring halos.

• \(r\) is the radial distance from the center of the halo.

This class provides a way to model dark matter distribution that includes the impact of both the immediate halo and the larger-scale structure, which is important for understanding clustering and cosmic structure formation.

See the DarkMatter and TwoHalo classes for more details on the underlying profiles and their parameters.

class BaryonForge.Profiles.Schneider19.DarkMatterBaryon(self, gas=None, stars=None, collisionlessmatter=None, darkmatter=None, twohalo=None, r_min_int=1e-05, r_max_int=100, r_steps=500, **kwargs)

Bases: SchneiderProfiles

Class representing a combined dark matter and baryonic matter profile.

This class is derived from the SchneiderProfiles class and provides an implementation that combines the contributions from dark matter, gas, stars, and collisionless matter to compute the total density profile. It includes both one-halo and two-halo terms, ensuring mass conservation and accounting for both dark matter and baryonic components.

Parameters:

• gas (Gas, optional) – An instance of the Gas class defining the gas profile. If not provided, a default Gas object is created using kwargs.

• stars (Stars, optional) – An instance of the Stars class defining the stellar profile. If not provided, a default Stars object is created using kwargs.

• collisionlessmatter (CollisionlessMatter, optional) – An instance of the CollisionlessMatter class defining the profile that combines dark matter, gas, and stars. If not provided, a default CollisionlessMatter object is created using kwargs.

• darkmatter (DarkMatter, optional) – An instance of the DarkMatter class defining the NFW profile for dark matter. If not provided, a default DarkMatter object is created using kwargs.

• twohalo (TwoHalo, optional) – An instance of the TwoHalo class defining the two-halo term profile, representing the contribution of neighboring halos. If not provided, a default TwoHalo object is created using kwargs.

• **kwargs – Additional keyword arguments passed to initialize the Gas, Stars, CollisionlessMatter, DarkMatter, and TwoHalo profiles, as well as other parameters from SchneiderProfiles.

Notes

The DarkMatterBaryon class models the total matter density profile by combining contributions from collisionless matter, gas, stars, dark matter, and the two-halo term. This comprehensive approach accounts for the interaction and distribution of both dark matter and baryonic matter within halos and across neighboring halos.

Calculation Steps:

1. Normalization of Dark Matter: To ensure mass conservation, the one-halo term is normalized so that the dark matter-only profile matches the dark matter-baryon profile at large radii. The normalization factor is calculated as:

   \[\text{Factor} = \frac{M_{\text{DMO}}}{M_{\text{DMB}}}\]

   where:

   • \(M_{\text{DMO}}\) is the total mass from the dark matter-only profile.

   • \(M_{\text{DMB}}\) is the total mass from the combined dark matter and baryon profile.

2. Total Density Profile: The total density profile is computed by summing the contributions from the collisionless matter, stars, gas, and two-halo term, scaled by the normalization factor:

   \[\rho_{\text{total}}(r) = \rho_{\text{CLM}}(r) \cdot \text{Factor} + \rho_{\text{stars}}(r) \cdot \text{Factor} + \rho_{\text{gas}}(r) \cdot \text{Factor} + \rho_{\text{2h}}(r)\]

   where:

   • \(\rho_{\text{CLM}}(r)\) is the density from the collisionless matter profile.

   • \(\rho_{\text{stars}}(r)\) is the stellar density profile.

   • \(\rho_{\text{gas}}(r)\) is the gas density profile.

   • \(\rho_{\text{2h}}(r)\) is the two-halo term density profile.

This method ensures that both dark matter and baryonic matter are accounted for, providing a realistic representation of the total matter distribution.

See SchneiderProfiles, Gas, Stars, CollisionlessMatter, DarkMatter, and TwoHalo classes for more details on the underlying profiles and parameters.