SciPy

darkhistory.physics

Physics functions as well as constants.

Throughout DarkHistory, we choose cm, s and eV as our system of units. Masses and temperatures are also given in eV. Particle Data Group central values [1] are used for constants, while cosmological parameters are set to the central values of the Planck 2018 baseline TT,TE,EE+lowE+lensing [2].

Fundamental Constants

Attributes

mp Proton mass in eV.
me Electron mass in eV.
mHe Helium nucleus mass in eV.
hbar hbar in eV s.
c Speed of light in cm s-1.
kB Boltzmann constant in eV K-1.
alpha Fine structure constant.
ele Electron charge in coulombs.
mass Masses of Standard Model particles.
thomson_xsec Thomson cross section in cm2.
stefboltz Stefan-Boltzmann constant in eV-3 cm-2 s-1.
ele_rad Classical electron radius in cm.
ele_compton Electron Compton wavelength in cm.

Cosmology

Attributes

h h parameter.
H0 Hubble parameter today in s-1.
omega_m Omega of all matter today.
omega_rad Omega of radiation today.
omega_lambda Omega of dark energy today.
omega_baryon Omega of baryons today.
omega_DM Omega of dark matter today.
rho_crit Critical density of the universe in eV cm-3.
rho_DM DM density in eV cm-3.
rho_baryon Baryon density in eV cm-3.
nB Baryon number density in eV cm-3.
nH Atomic hydrogen number density in cm-3.
nHe Atomic helium number density in cm-3.
nA Hydrogen and helium number density in cm-3.
chi Ratio of helium to hydrogen nuclei.
YHe Helium abundance by mass.

Functions

hubble(rs[, H0, omega_m, omega_rad, …]) Hubble parameter in s-1.
dtdz(rs[, H0, omega_m, omega_rad, omega_lambda]) dt/dz in s.
TCMB(rs) CMB temperature in eV.
CMB_N_density(T) CMB number density in cm-3.
CMB_eng_density(T) CMB energy density in eV cm-3.
CMB_spec(eng, temp) CMB spectrum in number of photons cm-3 eV-1.
Tm_std(rs) Baseline Tm value.
xHII_std(rs) Baseline nHII/nH value.
xHeII_std(rs) Baseline nHeII/nH value.
get_optical_depth(rs_vec, xe_vec) Computes the optical depth given an ionization history.
inj_rate(inj_type, rs[, mDM, sigmav, lifetime]) Dark matter annihilation/decay energy injection rate.
struct_boost_func([model, model_params]) Structure formation boost factor 1+B(z).

Atomic and Optical Physics

Attributes

rydberg Ionization potential of ground state hydrogen in eV.
lya_eng Lyman alpha transition energy in eV.
lya_freq Lyman alpha transition frequency in Hz.
width_2s1s_H Hydrogen 2s to 1s decay width in s-1.
bohr_rad Bohr radius in cm.
He_ion_eng Energy needed to singly ionize neutral He in eV.
He_exc_lambda HeI n=1 to n=2 excitation wavelength in cm.
He_exc_eng HeI n=1 to n=2 excitation energies in eV.
A_He_21p Einstein coefficient for 21p \(\to\) 1s decay in s-1.
A_He_23P1 Einstein coefficient for 23P1 \(\to\) 1s decay in s-1.
width_21s_1s_He Width of He 21s \(\to\) 1s decay in s-1.

Functions

alpha_recomb(T_m, species) Case-B recombination coefficient.
beta_ion(T_rad, species) Case-B photoionization coefficient.
peebles_C(xHII, rs) Hydrogen Peebles C coefficient.
C_He(xHII, xHeII, rs, species) Helium C coefficients.
xe_Saha(rs, species) Saha equilibrium ionization value for H and He.
d_xe_Saha_dz(rs, species) z-derivative of the Saha equilibrium ionization value.
photo_ion_rate(rs, eng, xH, xe[, atom]) Photoionization rate in cm-3 s-1.
photo_ion_xsec(eng, species) Photoionization cross section in cm2.
coll_exc_xsec(eng[, species]) e-e collisional excitation cross section in cm2.
coll_ion_sec_elec_spec(in_eng, eng[, species]) Secondary electron spectrum after collisional ionization.
coll_ion_xsec(eng[, species]) e-e collisional ionization cross section in cm2.
elec_heating_engloss_rate(eng, xe, rs) Electron energy loss rate of electrons due to Coulomb heating in eV s-1.

Footnotes

[1]
  1. Aghanim et al. [Planck Collaboration], “Planck 2018 results. VI. Cosmological parameters,” arXiv:1807.06209 [astro-ph.CO]
[2]Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 030001 (2018).