halox.lss: Large-scale structure calculations

halox.lss: Large-scale structure calculations#

halox provides a JAX implementation of large-scale structure calculations including RMS variance computations, mass-to-radius conversions, and overdensity transformations. Cosmology calculations (e.g. power spectra) rely on jax-cosmo. For examples, see Large-Scale Structure quantities.

sigma_R(R, z, cosmo[, k_min, k_max, n_k_int])

Compute RMS variance of density fluctuations in spheres of radius R at redshift z.

sigma_M(M, z, cosmo[, k_min, k_max, ...])

Compute RMS variance of density fluctuations within the Lagrangian radius of a halo with mass M at redshift z.

overdensity_c_to_m(delta_c, z, cosmo)

Convert critical overdensity to mean overdensity.

overdensity_m_to_c(delta_m, z, cosmo)

Convert mean overdensity to critical overdensity.

mass_to_lagrangian_radius(M, cosmo)

Convert mass to Lagrangian radius.

peak_height(M, z, cosmo[, n_k_int, k_min, ...])

Peak height \(\nu = \delta_{sc} / \sigma(M, z)\).
halox.lss.sigma_R(R, z, cosmo, k_min=1e-05, k_max=100.0, n_k_int=5000)[source]#

Compute RMS variance of density fluctuations in spheres of radius R at redshift z.

Parameters:

  • R (Array) – Radius [h-1 Mpc]

  • z (Array) – Redshift

  • cosmo (jc.Cosmology) – Underlying cosmology

  • k_min (float) – Minimum k for integration [h Mpc-1], default 1e-5

  • k_max (float) – Maximum k for integration [h Mpc-1], default 1e2

  • n_k_int (int) – Number of k-space integration points for \(\sigma(R,z)\), default 5000

Returns:

RMS variance \(\sigma(R,z)\)

Return type:

Array

halox.lss.sigma_M(M, z, cosmo, k_min=1e-05, k_max=100.0, n_k_int=5000, emu=None)[source]#

Compute RMS variance of density fluctuations within the Lagrangian radius of a halo with mass M at redshift z.

When emu is provided, the emulator is used instead of the analytical integral and the k_min, k_max, n_k_int parameters are ignored.

Parameters:

  • M (Array) – Mass [h-1 Msun]

  • z (Array) – Redshift

  • cosmo (jc.Cosmology) – Underlying cosmology

  • k_min (float) – Minimum k for integration [h Mpc-1], default 1e-5

  • k_max (float) – Maximum k for integration [h Mpc-1], default 1e2

  • n_k_int (int) – Number of k-space integration points for \(\sigma(R,z)\), default 5000

  • emu (SigmaMEmulator, optional) – Trained emulator for \(\sigma(M)\). If provided, the emulator is used instead of the analytical integral.

Returns:

RMS variance \(\sigma(M,z)\)

Return type:

Array

See also

halox.emus.SigmaMEmulator

Emulator for \(\sigma(M,z)\).

halox.lss.overdensity_c_to_m(delta_c, z, cosmo)[source]#

Convert critical overdensity to mean overdensity.

Parameters:

  • delta_c (float) – Overdensity with respect to critical density

  • z (float) – Redshift

  • cosmo (jc.Cosmology) – Underlying cosmology

Returns:

Overdensity with respect to mean matter density

Return type:

float

halox.lss.overdensity_m_to_c(delta_m, z, cosmo)[source]#

Convert mean overdensity to critical overdensity.

Parameters:

  • delta_m (float) – Overdensity with respect to mean matter density

  • z (float) – Redshift

  • cosmo (jc.Cosmology) – Underlying cosmology

Returns:

Overdensity with respect to critical density

Return type:

float

halox.lss.mass_to_lagrangian_radius(M, cosmo)[source]#

Convert mass to Lagrangian radius.

Computes the radius of a sphere containing mass M at the mean matter density of the universe at z=0.

Parameters:

  • M (Array) – Mass [h-1 Msun]

  • cosmo (jc.Cosmology) – Underlying cosmology

Returns:

Lagrangian radius [h-1 Mpc]

Return type:

Array

halox.lss.peak_height(M, z, cosmo, n_k_int=5000, k_min=1e-05, k_max=100.0, delta_sc=1.68647, emu=None)[source]#

Peak height \(\nu = \delta_{sc} / \sigma(M, z)\).

Parameters:

  • M (Array) – Mass [h-1 Msun]

  • z (Array) – Redshift

  • cosmo (jc.Cosmology) – Underlying cosmology

  • n_k_int (int) – Number of k-space integration points for \(\sigma(R,z)\), default 5000

  • k_min (float) – Minimum k for integration [h Mpc-1], default 1e-5

  • k_max (float) – Maximum k for integration [h Mpc-1], default 1e2

  • delta_sc (float) – Spherical collapse overdensity, default 1.68647

  • emu (SigmaMEmulator, optional) – Trained emulator for \(\sigma(M)\).

Returns:

Peak height \(\nu\)

Return type:

Array

See also

halox.emus.SigmaMEmulator

Emulator for \(\sigma(M,z)\).