halox.halo.nfw: The NFW profile

halox.halo.nfw: The NFW profile#

halox provides utility functions to compute properties of halos with a Navarro-Frenk-White (NFW) profile. For examples, see NFW Profiles.

Note

halox.halo.nfw is also accessible as halox.nfw for backward compatibility with older code.

NFWHalo(m_delta, c_delta, z, cosmo[, delta])

Properties of a dark matter halo following a Navarro-Frenk-White density profile.

delta_delta(M, c, z, cosmo, delta_old, delta_new)

Convert between overdensity definitions assuming an NFW profile.
class halox.halo.nfw.NFWHalo(m_delta, c_delta, z, cosmo, delta=200.0)[source]#

Properties of a dark matter halo following a Navarro-Frenk-White density profile.

Parameters:

  • m_delta (float) – Mass at overdensity delta [h-1 Msun]

  • c_delta (float) – Concentration at overdensity delta

  • z (float) – Redshift

  • cosmo (jc.Cosmology) – Underlying cosmology

  • delta (float) – Density contrast in units of critical density at redshift z, defaults to 200.

density(r)[source]#

NFW density profile \(\rho(r)\).

Parameters:

r (Array [h-1 Mpc]) – Radius

Returns:

Density at radius r

Return type:

Array [h2 Msun Mpc-3]

enclosed_mass(r)[source]#

Enclosed mass profile \(M(<r)\).

Parameters:

r (Array [h-1 Mpc]) – Radius

Returns:

Enclosed mass at radius r

Return type:

Array [h-1 Msun]

potential(r)[source]#

Potential profile \(\phi(r)\).

Parameters:

r (Array [h-1 Mpc]) – Radius

Returns:

Potential at radius r

Return type:

Array [km2 s-2]

circular_velocity(r)[source]#

Circular velocity profile \(v_c(r)\).

The circular velocity is related to the enclosed mass by: \(v_c^2(r) = GM(<r)/r\)

Parameters:

r (Array [h-1 Mpc]) – Radius

Returns:

Circular velocity at radius r

Return type:

Array [km s-1]

velocity_dispersion(r)[source]#

Radial velocity dispersion profile \(\sigma_r(r)\).

Uses the Jeans equation assuming isotropic orbits: \(\sigma_r^2(r) = \frac{1}{\rho(r)} \int_r^{\infty} \rho(s) \frac{GM(<s)}{s^2} ds\)

For NFW halos, this has an analytical solution.

Parameters:

r (Array [h-1 Mpc]) – Radius

Returns:

Radial velocity dispersion at radius r

Return type:

Array [km s-1]

surface_density(r)[source]#

Projected surface density profile \(\Sigma(r)\).

The projected surface density is obtained by integrating the 3D density profile along the line of sight: \(\Sigma(r) = 2 \int_r^{\infty} \frac{\rho(s) s ds} {\sqrt{s^2 - r^2}}\)

For NFW halos, this has an analytical solution.

Parameters:

r (Array [h-1 Mpc]) – Projected radius

Returns:

Surface density at projected radius r

Return type:

Array [h Msun Mpc-2]

to_delta(delta_new)[source]#

Convert halo properties to a different overdensity definition.

Parameters:

delta_new (float) – New density contrast in units of critical density at redshift z

Return type:

tuple[Array, Array, Array]

Returns:

  • Array [h-1 Msun] – Mass at new overdensity

  • Array [h-1 Mpc] – Radius at new overdensity

  • Array – Concentration at new overdensity

halox.halo.nfw.delta_delta(M, c, z, cosmo, delta_old, delta_new)[source]#

Convert between overdensity definitions assuming an NFW profile.

Parameters:

  • M (Array) – Halo mass at delta_old overdensity [h-1 Msun]

  • c (Array) – Concentration at delta_old overdensity

  • z (Array) – Redshift

  • cosmo (jc.Cosmology) – Underlying cosmology

  • delta_old (float) – Input overdensity in units of critical density at redshift z

  • delta_new (float) – Output overdensity in units of critical density at redshift z

Return type:

tuple[Array, Array, Array]

Returns:

  • Array [h-1 Msun] – Halo mass at delta_new overdensity

  • Array [h-1 Mpc] – Halo radius at delta_new overdensity

  • Array – Concentration at delta_new overdensity