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]_.

Module 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.
G	Newton's Gravitational Constant in cm3 g-1 s-2.
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.
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.
YHe	Helium abundance by mass.
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.
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

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.
C_He(xHII, xHeII, rs, species)	Helium C coefficients.
TCMB(rs)	CMB temperature in eV.
Tm_std(rs)	Baseline Tm value.
alpha_recomb(T_m, species)	Case-B recombination coefficient.
beta_ion(T_rad, species)	Case-B photoionization coefficient.
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.
d_xe_Saha_dz(rs, species)	z-derivative of the Saha equilibrium ionization value.
dtdz(rs[, H0, omega_m, omega_rad, omega_lambda])	dt/dz in s.
elec_heating_engloss_rate(eng, xe, rs[, nBscale])	Electron energy loss rate of electrons due to Coulomb heating in eV s-1.
f_std(mDM, rs[, inj_particle, inj_type, ...])	energy deposition fraction into channel c, f_c(z), as a function of dark matter mass and redshift.
get_optical_depth(rs_vec, xe_vec)	Computes the optical depth given an ionization history.
hubble(rs[, H0, omega_m, omega_rad, ...])	Hubble parameter in s-1.
inj_rate(inj_type, rs[, mDM, sigmav, lifetime])	Dark matter annihilation/decay energy injection rate.
peebles_C(xHII, rs)	Hydrogen Peebles C coefficient.
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.
struct_boost_func([model, model_params])	Structure formation boost factor 1+B(z).
xHII_std(rs)	Baseline nHII/nH value.
xHeII_std(rs)	Baseline nHeII/nH value.
xe_Saha(rs, species)	Saha equilibrium ionization value for H and He.