rabacus.cosmology package¶

Subpackages¶

Submodules¶

rabacus.cosmology.general module¶

A general FLRW cosmology module. Assumes a spatially flat universe.

class rabacus.cosmology.general.Cosmology(cpdict, verbose=False, zlo=0.0, zhi=200.0, Nz=500)[source]¶

Bases: object

General Cosmology Class. Assumes a spatialy flat universe.

Args:

cpdict (dict) A dictionary of cosmological parameters. For example, see PlanckParameters.

The dictionray cpdict must include the following keys,

omegam -> current matter density in units of critical today
omegal -> current lambda density in units of critical today
omegab -> current baryon density in units of critical today
h -> Hubble parameter H0 = 100 h km/s/Mpc
sigma8 -> amplitude of fluctuations in spheres w/ R = 8 Mpc/h
ns -> slope of primordial power spectrum
Yp -> primordial mass fraction of helium

Attributes:

H0 (real): hubble parameter now, $H_0$ .

OmegaB (real): baryon density / critical density now, $\Omega_b$

OmegaC (real): cold dark matter density / critical density now, $\Omega_c$

OmegaL (real): dark energy density / critical density now, $\Omega_{\Lambda}$

OmegaM (real): matter density / critical density now, $\Omega_m$

Yp (real): primoridial helium mass fraction, $Y_p$

cu (CosmoUnits): cosmological units which are aware of the hubble parameter.

dH0 (real): hubble distance now, $d_{\rm H_0} = c / H_0$

tH0 (real): hubble time now, $t_{\rm H_0} = 1 / H_0$

rho_crit0 (real): critical density now, $\rho_{c,0} = (3 H_0^2) / (8 \pi G)$

eps_crit0 (real): critical energy density now, $\epsilon_{c,0} = \rho_{c,0} \, c^2$

nH_crit0 (real): critical hydrogen number density now, $n_{\rm H,c,0} = \rho_{c,0} \, \Omega_b \, (1-Y_p) \, / \, m_{\rm H}$

D1a(a)[source]¶

Linear growth function D1(a).

$D_1(a) \propto H(a) \int_0^a \frac{da'}{a'^3 H(a')^3}$

The normalization is such that D1a(1) = 1

D1z(z)[source]¶

Linear growth function D1(z)

$D_1(z) \propto H(z) \int_z^\infty \frac{1+z'}{H(z')^3} dz'$

The normalization is such that D1z(0) = 1

Dc_at_tL(tL)[source]¶: Comoving distance at a given lookback time, Dc(tL). First finds a redshift z by inverting the function tLz() using tabulated values. Second, calls Dcz() to get a comoving distance from z.

$z = {\rm Inverse}[ t_L(z) ] \\ D_C(z) = d_{\rm H_0} \int_{0}^{z} \frac{dz'}{E(z')}$

Dca(a)[source]¶: Comoving distance between a=1 and a, Dc(a). The scale factor a is converted to redshift z and then Dcz() is called.

$D_C(a) = d_{\rm H_0} \int_{a}^{1} \frac{da'}{a'^2 E(a')}$

Dcz(z)[source]¶: Comoving distance between z=0 and z, Dc(z)

$D_C(z) = d_{\rm H_0} \int_{0}^{z} \frac{dz'}{E(z')}$

Ea(a)[source]¶: Helper function H(a) = H0 * E(a)

$E(a) = ( \Omega_R a^{-4} + \Omega_M a^{-3} + \Omega_{\Lambda} )^{1/2}$

Ez(z)[source]¶: Helper function H(z) = H0 * E(z)

$E(z) = [ \Omega_R (1+z)^{4} + \Omega_M (1+z)^{3} + \Omega_{\Lambda} ]^{1/2}$

Ha(a)[source]¶: Hubble parameter at scale factor a, H(a) = H0 * E(a)

$H(a) = H_0 E(a)$

Hz(z)[source]¶: Hubble parameter at redshift z, H(z) = H0 * E(z)

$H(z) = H_0 E(z)$

X(z1, z2)[source]¶: Absorption distance between z1 and z2,

$X(z1,z2) = \int_{z1}^{z2} dz' (1+z')^2 / E(z')$

dHa(a)[source]¶: Hubble distance at scale factor a, dH(a)

$d_{\rm H(a)} = c / H(a)$

dHz(z)[source]¶: Hubble distance at redshift z, dH(z)

$d_{\rm H(z)} = c / H(z)$

da2dDc(a1, a2)[source]¶: Comoving distance between a1 and a2. The scale factors a1 and a2 are converted to redshifts z1 and z2 and then dz2dDc() is called. a1 < a2 produces positive comoving distance.

$D_C(a1,a2) = d_{\rm H_0} \int_{a1}^{a2} \frac{da'}{a'^2 E(a')}$

da2dtL(a1, a2)[source]¶: Lookback time between a1 and a2. Two calls to tLa() are made and the results subtracted. a1 < a2 produces positive lookback time.

$t_{\rm L}(a1,a2) = \int_{a1}^{a2} \frac{da'}{a' H(a')}$

dz2dDc(z1, z2)[source]¶: Comoving distance between z1 and z2. Two calls to Dcz() are made and the results subtracted. z1 < z2 produces positive comoving distance.

$D_C(z1,z2) = d_{\rm H_0} \int_{z1}^{z2} \frac{dz'}{E(z')}$

dz2dtL(z1, z2)[source]¶: Lookback time between z1 and z2. The redshifts z1 and z2 are converted to scale factors and then da2dtL() is called. z1 < z2 produces positive lookback time.

$t_{\rm L}(z1,z2) = \int_{z1}^{z2} \frac{dz'}{(1+z') H(z')}$

eps_crita(a)[source]¶: Critical energy density at scale factor a, eps_crit(a)

$\epsilon_{c,a} = \epsilon_{c,0} \, E(a)^2$

eps_critz(z)[source]¶: Critical energy density at redshift z, eps_crit(z)

$\epsilon_{c,z} = \epsilon_{c,0} \, E(z)^2$

iEa(a)[source]¶: Reciprocal of Ea().

$E(a) = ( \Omega_R a^{-4} + \Omega_M a^{-3} + \Omega_{\Lambda} )^{-1/2}$

iEz(z)[source]¶: Reciprocal of Ez().

$E(z) = [ \Omega_R (1+z)^{4} + \Omega_M (1+z)^{3} + \Omega_{\Lambda} ]^{-1/2}$

nH_crita(a)[source]¶: Critical hydrogen number density at scale factor a, nH_crit(a)

$n_{\rm H,c,a} = n_{\rm H,c,0} \, E(a)^2$

nH_critz(z)[source]¶: Critical hydrogen number density at redshift z, nH_crit(z)

$n_{\rm H,c,z} = n_{\rm H,c,0} \, E(z)^2$

rho_crita(a)[source]¶: Critical mass density at scale factor a, rho_crit(a)

$\rho_{c,a} = \rho_{c,0} \, E(a)^2$

rho_critz(z)[source]¶: Critical mass density at redshift z, rho_crit(z)

$\rho_{c,z} = \rho_{c,0} \, E(z)^2$

tHa(a)[source]¶: Hubble time at scale factor a, tH(a)

$t_{\rm H(a)} = 1 / H(a)$

tHz(z)[source]¶: Hubble time at redshift z, tH(z)

$t_{\rm H(z)} = 1 / H(z)$

tL_at_Dc(Dc)[source]¶: Lookback time at a given comoving distance, tL(Dc). First finds a redshift z by inverting the function Dcz() using tabulated values. Second, calls tLz() to get a lookback time from z.

$z = {\rm Inverse}[ D_C(z) ] \\ t_L(z) = \int_0^z \frac{dz'}{(1+z') H(z')}$

tLa(a)[source]¶: Lookback from a = 1 to a, tL(a).

$t_{\rm L}(a) = \int_a^1 \frac{da'}{a' H(a')}$

tLz(z)[source]¶: Lookback from z = 0 to z, tL(z).

$t_{\rm L}(z) = \int_0^z \frac{dz'}{(1+z') H(z')}$

ta(a)[source]¶: Time since a=0 or age of the Universe, t(a).

$t(a) = \int_0^a \frac{da'}{a' H(a')}$

tz(z)[source]¶: Time since z=inf or age of the Universe t(z).

$t(z) = \int_z^\infty \frac{dz'}{(1+z') H(z')}$

z_at_Dc(Dc)[source]¶: Redshift at a given comoving distance, z(Dc). Inverts the function Dcz() by interpolating between tabulated values.

$z(D_C) = {\rm Inverse}[ D_C(z) ]$

z_at_tL(tL)[source]¶: Redshift at a given lookback time, z(tL). Inverts the function tLz() by interpolating between tabulated values.

$z(t_L) = {\rm Inverse}[ t_L(z) ]$

rabacus.cosmology.jeans module¶

A general Jeans scale module.

class rabacus.cosmology.jeans.Jeans(Yp=0.248, fg=0.154, gamma=1.6666666666666667)[source]¶

A Jeans scale class.

Provides access to Jeans scales functions. Default values for Yp and fg are taken from Planck Cosmological Parameters

Yp = 0.248 fg = Omega_b / Omega_m = 0.154

Args:

Kwargs:

Yp (float): helium mass fraction

fg (float): gas fraction

gamma (float): ratio of specific heats

L(nH, T, mu)[source]¶

Jeans length

Args:

nH (float): hydrogen number density

T (float): temperature

mu (float): mean molecular weight

NH(nH, T, mu)[source]¶

Jeans column density

Args:

nH (float): hydrogen number density

T (float): temperature

mu (float): mean molecular weight

cs(T, mu)[source]¶

Sound speed

Args:

T (float): temperature

mu (float): mean molecular weight

mu(xH2, xHe2, xHe3)[source]¶

Mean molecular weight, i.e. the mean mass of an ion in atomic mass units, as a function of ionization state.

Args:

xH2 (float): nHII / nH

xHe2 (float): nHeII / nHe

xHe3 (float): nHeIII / nHe

t_dyn(nH)[source]¶

Dynamical time

Args:

nH (float): number density of hydrogen

t_sc(L, T, mu)[source]¶

Sound crossing time.

Args:

L (float): length scale

T (float): temperature

mu (float): mean molecular weight

Module contents¶

A package for handling cosmological variables and calculations. The most fundamental being the Cosmology class.