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] |
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[2] | Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 030001 (2018). |