Source code for colibri.constants
import numpy as np
import math
[docs]def explanatory():
"""
This file contains a series of physical constants and conversion factors which are used in the other codes.
Also useful quantities not strictly related to cosmology are defined.
Conversion factors, distance
- ``km_to_cm``: 1 km in cm
- ``km_to_m``: 1 km in m
- ``pc_to_cm``: 1 pc in cm
- ``pc_to_m``: 1 pc in m
- ``pc_to_km``: 1 pc in km
- ``kpc_to_cm``: 1 kpc in cm
- ``kpc_to_m``: 1 kpc in m
- ``kpc_to_km``: 1 kpc in km
- ``Mpc_to_cm``: 1 Mpc in cm
- ``Mpc_to_m``: 1 Mpc in m
- ``Mpc_to_km``: 1 Mpc in km
Conversion factors, time
- ``yr_to_s``: 1 yr in s
- ``Myr_to_s``: 1 Myr in s
Conversion factors, energy
- ``eV``: electron-Volt in :math:`\mathrm{J}`
- ``keV``: kilo Electron-Volt in :math:`\mathrm{J}`
- ``MeV``: mega Electron-Volt in :math:`\mathrm{J}`
- ``GeV``: giga Electron-Volt in :math:`\mathrm{J}`
- ``TeV``: tera Electron-Volt in :math:`\mathrm{J}`
Proton & electron mass & charges
- ``mp``: proton mass in :math:`\mathrm{eV}`
- ``mp_g``: proton mass in :math:`\mathrm{g}`
- ``mp_J``: proton mass in :math:`\mathrm{J}`
- ``me``: eletron mass in :math:`\mathrm{eV^2}`
- ``me_g``: eletron mass in :math:`\mathrm{g}`
- ``me_J``: eletron mass in :math:`\mathrm{J}`
- ``q``: electron/proton charge in :math:`\mathrm{C}`
Neutrino properties
- ``Delta_m21_squared``: difference of squared masses in :math:`\mathrm{eV^2}`
- ``Delta_m32_squared_IH``: difference of squared masses in :math:`\mathrm{eV^2}`
- ``Delta_m32_squared_NH``: difference of squared masses in :math:`\mathrm{eV^2}`
- ``sin_theta_21_squared``: sine squared of mixing angle
- ``sin_theta_23_squared_IH``: sine squared of mixing angle, inverted hierarchy
- ``sin_theta_23_squared_NH``: sine squared of mixing angle, normal hierarchy
- ``sin_theta_13_squared``: sine squared of mixing angle
Constants of physics
- ``G``: Newton's gravitational constant in units of :math:`\mathrm{Mpc} \ M_\odot (\mathrm{km/s})^2`
- ``eps_0``: vacuum permittivity in :math:`\mathrm{F/m = C/V \ m}`
- ``mu_0``: magnetic permeability in :math:`\mathrm{H/m = T \ m^2/A = V \ s/A}`
- ``kB``: Boltzmann constant in :math:`\mathrm{eV/K}`
- ``c``: speed of light in :math:`\mathrm{km/s}`
- ``hP``: Planck constant in units of :math:`\mathrm{eV \ s}`
- ``sSB``: Stefan-Boltzmann constant in :math:`\mathrm{W \ m^{-2} \ K^{-4}}`
- ``N_A``: Avogadro constant in :math:`\mathrm{mol^{-1}}`
Derived constants
- ``e2``: electron/proton charge (squared!) in CGS units
- ``hPb``: reduced Planck constant (:math:`\\bar{h}`) in :math:`\mathrm{eV \ s}`
- ``hPJ``: Planck constant in :math:`\mathrm{J \ s}`
- ``hPJb``: reduced Planck constant (:math:`\\bar{h}`) in :math:`\mathrm{J \ s}`
- ``sSB_eV``: Stefan-Boltzmann constant in :math:`\mathrm{eV \ m^{-2} \ K^{-4}}`
- ``alpha_BB``: constant for blackbody energy density in :math:`\mathrm{J \ m^{-3} \ K^{-4}}`
- ``R``: perfect gas constant in :math:`\mathrm{J \ mol^{-1} \ K^{-1}}`
- ``alpha_EM``: fine structure constant
- ``lambda_e``: Compton wavelength for electron in :math:`\mathrm{m}`
- ``r_e``: electron classical radius in :math:`\mathrm{m}`
- ``sigma_T``: Thomson scattering cross section in :math:`\mathrm{m}^2`
- ``rhoch2``: critical density of the Universe :math:`h^2 \ M_\odot \ \mathrm{Mpc}^{-3}`
Planck units
- ``l_Pl``: Planck length in :math:`\mathrm{m}`
- ``t_Pl``: Planck time in :math:`\mathrm{s}`
- ``m_Pl``: Planck mass in :math:`\mathrm{g}`
- ``T_Pl``: Planck temperatur in :math:`\mathrm{K}`
- ``q_Pl``: Planck charge in :math:`\mathrm{C}`
Solar units
- ``Msun``: solar mass in :math:`\mathrm{g}`
- ``Rsun``: solar radius in :math:`\mathrm{cm}`
- ``Tsun``: solar surface temperature in :math:`\mathrm{K}`
- ``Lsun``: solar luminosity in :math:`\mathrm{erg \ s^{-1}}`
"""
return 0
#-------------------------------
# Conversion factors: distance
#-------------------------------
km_to_cm = 1e5 # 1 km in cm
km_to_m = 1e3 # 1 km in m
pc_to_cm = 3.085677581282e18 # 1 pc in cm
pc_to_m = 3.085677581282e16 # 1 pc in m
pc_to_km = 3.085667581282e13 # 1 pc in km
kpc_to_cm = 3.085677581282e21 # 1 kpc in cm
kpc_to_m = 3.085677581282e19 # 1 kpc in m
kpc_to_km = 3.085667581282e16 # 1 kpc in km
Mpc_to_cm = 3.085677581282e24 # 1 Mpc in cm
Mpc_to_m = 3.085677581282e22 # 1 Mpc in m
Mpc_to_km = 3.085667581282e19 # 1 Mpc in km
#-------------------------------
# Conversion factors: time
#-------------------------------
yr_to_s = 3.1536e7 # 1 yr in s
Myr_to_s = 3.1536e13 # 1 Myr in s
#-------------------------------
# Conversion factors: energy
#-------------------------------
eV = 1.60217663e-19 # Electron-Volt in J
keV = 10.**3.*eV # Kilo Electron-Volt in J
MeV = 10.**6.*eV # Mega Electron-Volt in J
GeV = 10.**9.*eV # Giga Electron-Volt in J
TeV = 10.**12.*eV # Tera Electron-Volt in J
#-------------------------------
# Proton & electron mass & charges
#-------------------------------
mp = 9.38e8 # Proton mass in eV
mp_g = 1.6726e-24 # Proton mass in g
mp_J = 0.938*GeV # Proton mass in J
me = 5.11e5 # Eletron mass in eV
me_g = 9.10938356e-28 # Eletron mass in g
me_J = 511.*keV # Eletron mass in J
q = 1.602176487e-19 # Electron/proton charge in C
#-------------------------------
# Neutrino properties
#-------------------------------
Delta_m21_squared = 7.53e-5 # Difference of squared masses [eV^2]
Delta_m32_squared_IH = -2.56e-3 # Difference of squared masses [eV^2
Delta_m32_squared_NH = 2.51e-3 # Difference of squared masses [eV^2]
sin_theta_21_squared = 0.307 # Sine squared of mixing angle
sin_theta_23_squared_IH = 0.592 # Sine squared of mixing angle, inverted hierarchy (S = 1.1)
sin_theta_23_squared_NH = 0.597 # Sine squared of mixing angle, normal hierarchy (S = 1.1)
sin_theta_13_squared = 2.12e-2 # Sine squared of mixing angle
#-------------------------------
# Constants of physics
#-------------------------------
G = 4.302180824e-9 # Newton's gravitational constant in units of [Mpc/M_sun (km/s)^2]
eps_0 = 8.85418781762e-12 # Vacuum permittivity in [F/m = C/V m]
mu_0 = 1.25663706144e-6 # Magnetic permeability in [H/m = T m^2/A = V s/A]
kB = 8.617342791e-5 # Boltzmann constant in [eV/K]
c = 2.99792458e5 # Speed of light in [km/s]
hP = 4.135667334e-15 # Planck constant in units of [eV s]
N_A = 6.022140857e23 # Avogadro constant [mol^-1]
#-------------------------------
# Derived constants
#-------------------------------
G_mks = 6.67428e-11 # Newton's gravitational constant in units of [m^3/kg/s^2]
sSB = 2*np.pi**5.*(kB*eV)**4/(15*(hP*eV)**3.*(c*km_to_m)**2.) # Stefan-Boltzmann constant [W/m^2 K^4]
e2 = q**2./(4.*np.pi*eps_0) # Electron/proton charge (squared!) in CGS units
hPb = hP/(2.*np.pi) # Reduced Planck constant in [eV s] ('h bar')
hPJ = hP*eV # Planck constant in [J s]
hPJb = hPb*eV # Reduced Planck constant in [J s] ('h bar')
sSB_eV = sSB/eV # Stefan-Boltzmann constant [eV/s m^2 K^4]
alpha_BB = 4.*sSB/(c*km_to_m) # Constant for blackbody energy density [J/m^3 K^4]
R = kB*eV*N_A # Perfect gas constant [J/mol K]
alpha_EM = e2/(hPJb*c*km_to_m) # Fine structure constant
lambda_e = hP*c*km_to_m/me # Compton wavelength for electron in [m]
r_e = alpha_EM*lambda_e/(2.*np.pi) # Electron classical radius in [m]
sigma_T = 8.*np.pi/3.*r_e**2. # Thomson scattering cross section in [m^2]
rhoch2 = (3.*100.**2.)/(8*np.pi*G) # Critical density of the Universe [h^2 Msun/Mpc^3]
rhoch2_mks = 1.8783472458e-31 # Critical density of the Universe [h^2 kg/m^3]
#-------------------------------
# Planck units
#-------------------------------
l_Pl = 1.616252e-35 # Planck length [m]
t_Pl = 5.39124e-44 # Planck time [s]
m_Pl = 2.17644e-5 # Planck mass [g]
T_Pl = 1.416785e32 # Planck temperature [K]
q_Pl = 1.87554587e-18 # Planck charge [C]
#-------------------------------
# Solar units
#-------------------------------
Msun = 1.989e33 # Solar mass [g]
Rsun = 6.957e10 # Solar radius [cm]
Tsun = 5772. # Solar surface temperature [K]
Lsun = 3.848e33 # Solar luminosity [erg/s]