Constants¶
Physical, mathematical and astrophysical constants available in the Galacticus source (defined via <constant> directives). Constants whose value is provided by the GNU Scientific Library note the GSL symbol rather than a literal value.
Astrophysical constants¶
arcminutesToDegrees=1.0d0/60.0e0[\(^\circ/^\prime\)]Conversion factor from arcminutes to degrees.
Defined.
arcsecondsToDegrees=1.0d0/3600.0e0[\(^\circ/^{\prime\prime}\)]Conversion factor from arcseconds to degrees.
Defined.
degreesToRadians=2.0d0*Pi/360.0e0[\(\mathrm{rad}/^\circ\)]Conversion factor from degrees to radians.
Defined.
gigayear=giga*year(\(\mathrm{Gyr}\)) [s]Gigayear—\(10^9\) years.
Derived.; more
heliumByMassPrimordial=0.2486e+00(\(\mathrm{Y}_\mathrm{p}\))Primordial helium fraction by mass. (Theoretical expectation based on WMAP results.)
cite{cyburt_update_2008}
heliumByMassSolar=0.2740e0(\(\mathrm{Y}_\odot\))Solar helium fraction by mass.
heliumToHydrogenAbundancePrimordial=(heliumByMassPrimordial/atomicMassHelium)/(hydrogenByMassPrimordial/atomicMassHydrogen)(\(\mathrm{He/H}_\mathrm{p}\))Primordial helium to hydrogen ratio by number.
Derived.
heliumToHydrogenAbundanceSolar=(heliumByMassSolar/atomicMassHelium)/(hydrogenByMassSolar/atomicMassHydrogen)(\(\mathrm{He/H}_\odot\))Solar helium to hydrogen ratio by number.
Derived.
hoursToDegrees=360.0d0/24.0e0[\(^\circ/^{\prime}\)]Conversion factor from hours to degrees.
Defined.
hoursToRadians=2.0d0*Pi/24.0e0[\(\mathrm{rad}/^{\prime}\)]Conversion factor from hours to radians.
Defined.
hydrogenByMassPrimordial=0.7514e+00(\(\mathrm{X}_\mathrm{p}\))Primordial hydrogen fraction by mass.
cite{cyburt_update_2008}
hydrogenByMassSolar=0.7070e0(\(\mathrm{X}_\odot\))Solar hydrogen fraction by mass.
kiloParsec=kilo*parsec(\(\mathrm{kpc}\)) [m]Kiloparsec—\(10^3\) parsecs.
Derived.; more
lithiumToHydrogenAbundancePrimordial=5.2400e-10(\(\mathrm{Z}_\mathrm{Li,p}\))Primordial lithium fraction by mass.
cite{cyburt_update_2008}
luminositySolar=3.845e26(\(\mathrm{L}_\odot\)) [W]Solar luminosity.
luminosityZeroPointAB=(10.0d0**(-offsetAB/2.5d0))*4.0d0*Pi*((10.0d0*parsec*hecto)**2)*ergs[W/Hz]The luminosity zero point offset in the AB magnitude system, found by computing the flux of a zeroth magnitude source at 10pc.
cite{oke_secondary_1983}; more
massSolar(\(\mathrm{M}_\odot\)) [kg]Solar mass.
value from GSL
GSL_CONST_MKSA_SOLAR_MASS; Gnu Scientific LibrarymeanAtomicMassPrimordial=1.0d0/(2.0d0*hydrogenByMassPrimordial/atomicMassHydrogen+3.0d0*heliumByMassPrimordial/atomicMassHelium)(\(\mu_\mathrm{p}\))Primordial mean atomic mass.
Derived.
megaParsec=mega*parsec(\(\mathrm{Mpc}\)) [m]Megaparsec—\(10^6\) parsecs.
Derived.; more
metallicityPrimordial=lithiumToHydrogenAbundancePrimordial*atomicMassLithium7/atomicMassHydrogen(\(\mathrm{Z}_\mathrm{p}\))Primordial metallicity.
Derived.
metallicitySolar=0.0188e0(\(\mathrm{Z}_\odot\))Solar metal fraction by mass.
minutesToDegrees=360.0d0/24.0d0/60.0e0[\(^\circ/^{\prime\prime}\)]Conversion factor from minutes to degrees.
Defined.
MpcPerKmPerSToGyr=megaParsec/kilo/gigaYear[Mpc/km s\(^{-1}\)/Gyr]The conversion from Mpc/(km s\(^{-1})\) to Gyr.
Derived.
offsetAB=48.57e0The zero point offset in the AB magnitude system: \(m = -2.5\log_{10}(F_\nu/\mathrm{[ergs/s/cm}^2\mathrm{/Hz]})-48.57\). This zero point is chosen such that AB and Vega magnitude systems agree in the V-band. The original definition of the AB system zero point used a value of \(48.60\) (Oke and Gunn, 1983) to achieve this. However, more recent measurements give Vega a magnitude of \(+0.03\) in the Vega magnitude system, which is why the AB magnitude zero point is now also shifted by \(0.03\) relative to the original definition.
cite{oke_secondary_1983}; more
opticalDepthToMagnitudes=2.5d0/log(10.0d0)The conversion factor between magnitudes of extinction and optical depth.
Derived.
parsec(\(\mathrm{pc}\)) [m]Parsec—the distance at which 1 AU subtends an angle of one arcsecond.
value from GSL
GSL_CONST_MKSA_PARSEC; Gnu Scientific Library; moreradiusSolar=6.95508e8(\(\mathrm{R}_\odot\)) [m]Solar radius.
secondsToDegrees=360.0d0/24.0d0/3600.0e0[\(^\circ/^{\prime\prime}\)]Conversion factor from seconds to degrees.
Defined.
Atomic physics constants¶
atomicMassHelium=4.0026032545e0(\(A_{^4\mathrm{He}}\)) [amu]Atomic mass of the \(^4\)He isotope of helium.
atomicMassHydrogen=1.0078250322e0(\(A_{^1\mathrm{H}}\)) [amu]Atomic mass of the \(^1\)H isotope of hydrogen.
atomicMassLithium7=7.01600344e0(\(A_{^7\mathrm{Li}}\)) [amu]Atomic mass of the \(^7\)Li isotope of lithium.
atomicMassUnit(\(\mathrm{u}\)) [kg]The unified atomic mass unit.
value from GSL
GSL_CONST_MKSA_UNIFIED_ATOMIC_MASS; Gnu Scientific LibrarylymanSeriesLimitWavelengthHydrogen_atomic=+plancksConstant*speedLight/rydberg*metersToAngstroms/(+1.0d0-electronMass/massHydrogenAtom)(\(R^{-1}_\mathrm{H}\)) [\(\AA\)]Hydrogen Lyman series limit wavelength including correction for finite mass of the atom.
Derived.; more
massHeliumAtom=atomicMassHelium*atomicMassUnit(\(m_\mathrm{He}\)) [kg]Mass of the \(^4\)He isotope of helium.
Derived
massHydrogenAtom=atomicMassHydrogen*atomicMassUnit(\(m_\mathrm{H}\)) [kg]Mass of the \(^1\)H isotope of hydrogen.
Derived
rydberg(\(\mathrm{Ry}\)) [J]Rydberg—the ionization energy of hydrogen in its ground state.
value from GSL
GSL_CONST_MKSA_RYDBERG; Gnu Scientific Library
GNU Scientific Library constants¶
CBLAS_DiagEnumeration of whether a CBLAS triangular matrix has unit diagonal or not.
value from GSL
CBLAS_DIAG; Gnu Scientific LibraryCBLAS_TransposeEnumeration of CBLAS transpose options.
value from GSL
CBLAS_TRANSPOSE; Gnu Scientific LibraryCBLAS_UpLoEnumeration of CBLAS matrix upper/lower options.
value from GSL
CBLAS_UPLO; Gnu Scientific LibraryGSL_ContinueError code for iteration has not converged.
value from GSL
GSL_CONTINUE; Gnu Scientific LibraryGSL_EBadFuncError code for problem with user-supplied function.
value from GSL
GSL_EBADFUNC; Gnu Scientific LibraryGSL_EBadTolError code for user-specified invalid tolerance.
value from GSL
GSL_EBADTOL; Gnu Scientific LibraryGSL_EDomError code for input domain error, e.g sqrt(-1).
value from GSL
GSL_EDOM; Gnu Scientific LibraryGSL_EMaxIterError code for exceeding the maximum number of iterations.
value from GSL
GSL_EMAXITER; Gnu Scientific LibraryGSL_ENoProgError code for iteration not making progress towards solution.
value from GSL
GSL_ENOPROG; Gnu Scientific LibraryGSL_ERangeError code for output range error, e.g. exp(1e100).
value from GSL
GSL_ERANGE; Gnu Scientific LibraryGSL_ERoundError code for failure because of roundoff error.
value from GSL
GSL_EROUND; Gnu Scientific LibraryGSL_ESingError code for apparent singularity detected.
value from GSL
GSL_ESING; Gnu Scientific LibraryGSL_ETolError code for failure to reach the specified tolerance.
value from GSL
GSL_ETOL; Gnu Scientific LibraryGSL_EUndrFlwError code for underflow.
value from GSL
GSL_EUNDRFLW; Gnu Scientific LibraryGSL_EZeroDivError code for attempt to divide by zero.
value from GSL
GSL_EZERODIV; Gnu Scientific LibraryGSL_FailureError code for generic failure.
value from GSL
GSL_FAILURE; Gnu Scientific LibraryGSL_Integ_Gauss15Indicator for 15-point Gauss-Kronrod integration rule.
value from GSL
GSL_INTEG_GAUSS15; GSLGSL_Integ_Gauss21Indicator for 21-point Gauss-Kronrod integration rule.
value from GSL
GSL_INTEG_GAUSS21; GSLGSL_Integ_Gauss31Indicator for 31-point Gauss-Kronrod integration rule.
value from GSL
GSL_INTEG_GAUSS31; GSLGSL_Integ_Gauss41Indicator for 41-point Gauss-Kronrod integration rule.
value from GSL
GSL_INTEG_GAUSS41; GSLGSL_Integ_Gauss51Indicator for 51-point Gauss-Kronrod integration rule.
value from GSL
GSL_INTEG_GAUSS51; GSLGSL_Integ_Gauss61Indicator for 61-point Gauss-Kronrod integration rule.
value from GSL
GSL_INTEG_GAUSS61; GSLGSL_Prec_ApproxSpecifies GSL approximate-precision mode.
value from GSL
GSL_PREC_APPROX; Gnu Scientific LibraryGSL_Prec_DoubleSpecifies GSL double-precision mode.
value from GSL
GSL_PREC_DOUBLE; Gnu Scientific LibraryGSL_Prec_SingleSpecifies GSL single-precision mode.
value from GSL
GSL_PREC_SINGLE; Gnu Scientific LibraryGSL_SuccessError code for success.
value from GSL
GSL_SUCCESS; Gnu Scientific Library
Kernel constants¶
Kernel_EACCESError code for permission denied.
Kernel_ELOOPError code for loop exists in symbolic links.
Kernel_EMLINKError code for too many links.
Kernel_ENAMETOOLONGError code for name too long.
Kernel_ENOENTError code for non-existent directory.
Kernel_ENOSPCError code for no space on file system.
Kernel_ENOTDIRError code for not a directory.
Kernel_EROFSError code for read only file system.
Mathematical constants¶
catalan=0.91596559417721901505460351493238411077e0(\(G\))Catalan’s constant.
e(\(\mathrm{e}\))Euler’s number—the base of natural logarithms.
value from GSL
M_E; Gnu Scientific Library; moreeulersConstant(\(\gamma\))Euler’s constant.
value from GSL
M_EULER; Gnu Scientific Library; moreln10(\(\log 10\))The natural logarithm of 10.
value from GSL
M_LN10; Gnu Scientific Libraryln2(\(\log 2\))The natural logarithm of 2.
value from GSL
M_LN2; Gnu Scientific LibraryPi(\(\pi\))The ratio of a circle’s perimeter to its diameter.
value from GSL
M_PI; Gnu Scientific Library; morePiQuadPrecision=3.141592653589793238462643383279502884197(\(\pi\))The ratio of a circle’s perimeter to its diameter (to quadruple precision).
riemannZeta3=1.20205690315959428539973816151144999076e0(\(\zeta(3)\))Riemann zeta function evaluated at \(s=3\).
Physical constants¶
boltzmannsConstant(\(\mathrm{k}\)) [J/K]Boltzmann’s constant.
value from GSL
GSL_CONST_MKSA_BOLTZMANN; Gnu Scientific LibraryelectronCharge(\(\mathrm{e}\)) [C]The charge of the electron.
value from GSL
GSL_CONST_MKSA_ELECTRON_CHARGE; Gnu Scientific LibraryelectronMass(\(\mathrm{m}_\mathrm{e}\)) [kg]The mass of an electron.
value from GSL
GSL_CONST_MKSA_MASS_ELECTRON; Gnu Scientific LibraryelectronRadius=1.0d0/(4.0d0*Pi*permittivityFreeSpace)*electronCharge**2/(electronMass*speedLight**2)(\(r_\mathrm{e}\)) [m]The classical electron radius.
Definition.; more
fineStructure(\(\alpha\))The electromagnetic fine structure constant.
value from GSL
GSL_CONST_NUM_FINE_STRUCTURE; Gnu Scientific LibrarygravitationalConstant(\(\mathrm{G}\)) [N m\(^2\) kg\(^{-2}\)]The gravitational constant.
value from GSL
GSL_CONST_MKSA_GRAVITATIONAL_CONSTANT; Gnu Scientific LibrarygravitationalConstant_internal=gravitationalConstant*massSolar/(kilo**2)/megaParsec[km\(^2\)s\(^{-2}\)Mpc/\(\mathrm{M}_\odot\)]Newton’s gravitational constant in Galacticus’ \(\mathrm{M}_\odot\), Mpc, km/s unit system.
Derived.
permittivityFreeSpace(\(\epsilon_0\)) [m/s]The permittivity of free space.
value from GSL
GSL_CONST_MKSA_VACUUM_PERMITTIVITY; Gnu Scientific LibraryplancksConstant(\(\mathrm{h}\)) [J s]Planck’s constant.
value from GSL
GSL_CONST_MKSA_PLANCKS_CONSTANT_H; Gnu Scientific LibraryradiationConstant=4.0d0*stefanBoltzmannConstant/speedLight(\(a\)) [J/m\(^3\)/K\(^4\)]The radiation density constant.
Definition.; more
speedLight(\(\mathrm{c}\)) [m/s]The speed of light in vacuum.
value from GSL
GSL_CONST_MKSA_SPEED_OF_LIGHT; Gnu Scientific Library; morestefanBoltzmannConstant(\(\sigma\)) [J/s/m\(^2\)/K\(^4\)]The Stefan-Boltzmann constant.
value from GSL
GSL_CONST_MKSA_STEFAN_BOLTZMANN_CONSTANT; Gnu Scientific LibrarythomsonCrossSection(\(\sigma_\mathrm{T}\)) [m/s]The Thompson cross-section.
value from GSL
GSL_CONST_MKSA_THOMSON_CROSS_SECTION; Gnu Scientific Library
SI prefixes¶
atto=1.0e-18(\(\mathrm{a}\))SI prefix.
centi=1.0e-02(\(\mathrm{c}\))SI prefix.
deca=1.0e+01(\(\mathrm{da}\))SI prefix.
deci=1.0e-01(\(\mathrm{d}\))SI prefix.
exa=1.0e+18(\(\mathrm{E}\))SI prefix.
femto=1.0e-15(\(\mathrm{f}\))SI prefix.
giga=1.0e+09(\(\mathrm{G}\))SI prefix.
hecto=1.0e+02(\(\mathrm{h}\))SI prefix.
kilo=1.0e+03(\(\mathrm{k}\))SI prefix.
mega=1.0e+06(\(\mathrm{M}\))SI prefix.
micro=1.0e-06(\(\mu\))SI prefix.
milli=1.0e-03(\(\mathrm{m}\))SI prefix.
nano=1.0e-09(\(\mathrm{n}\))SI prefix.
peta=1.0e+15(\(\mathrm{P}\))SI prefix.
pico=1.0e-12(\(\mathrm{p}\))SI prefix.
quecto=1.0e-30(\(\mathrm{q}\))SI prefix.
quetta=1.0e+30(\(\mathrm{Q}\))SI prefix.
ronna=1.0e+27(\(\mathrm{R}\))SI prefix.
ronto=1.0e-27(\(\mathrm{r}\))SI prefix.
tera=1.0e+12(\(\mathrm{T}\))SI prefix.
yocto=1.0e-24(\(\mathrm{y}\))SI prefix.
yotta=1.0e+24(\(\mathrm{Y}\))SI prefix.
zepto=1.0e-21(\(\mathrm{z}\))SI prefix.
zetta=1.0e+21(\(\mathrm{Z}\))SI prefix.
Units¶
arcminutesToDegrees=1.0d0/60.0e0[\(^\circ/^\prime\)]Conversion factor from arcminutes to degrees.
Defined.
arcsecond=Pi/180.0d0/60.0d0/60.0e0(\(^{\prime\prime}\)) [rad]Arcsecond—unit of angle.
Derived; more
arcsecondsToDegrees=1.0d0/3600.0e0[\(^\circ/^{\prime\prime}\)]Conversion factor from arcseconds to degrees.
Defined.
atomicMassUnit(\(\mathrm{u}\)) [kg]The unified atomic mass unit.
value from GSL
GSL_CONST_MKSA_UNIFIED_ATOMIC_MASS; Gnu Scientific Librarybarn=1.0e-28(\(\mathrm{b}\)) [m\(^2\)]Unit of area used for nuclear cross-sections.
degree=Pi/180.0e0(\(^\circ\)) [rad]Degree—unit of angle.
Derived; more
degreesToRadians=2.0d0*Pi/360.0e0[\(\mathrm{rad}/^\circ\)]Conversion factor from degrees to radians.
Defined.
electronVolt(\(\mathrm{eV}\)) [J]Electron-volt—the energy of an electron accelerated through a 1 volt electric field.
value from GSL
GSL_CONST_MKSA_ELECTRON_VOLT; Gnu Scientific Libraryergs=1.0e-7(\(\mathrm{ergs}\)) [J]Unit of energy in the CGS system.
cite{jackson_classical_1999}; more
gigayear=giga*year(\(\mathrm{Gyr}\)) [s]Gigayear—\(10^9\) years.
Derived.; more
gravitationalConstant_internal=gravitationalConstant*massSolar/(kilo**2)/megaParsec[km\(^2\)s\(^{-2}\)Mpc/\(\mathrm{M}_\odot\)]Newton’s gravitational constant in Galacticus’ \(\mathrm{M}_\odot\), Mpc, km/s unit system.
Derived.
hoursToDegrees=360.0d0/24.0e0[\(^\circ/^{\prime}\)]Conversion factor from hours to degrees.
Defined.
hoursToRadians=2.0d0*Pi/24.0e0[\(\mathrm{rad}/^{\prime}\)]Conversion factor from hours to radians.
Defined.
kiloParsec=kilo*parsec(\(\mathrm{kpc}\)) [m]Kiloparsec—\(10^3\) parsecs.
Derived.; more
megaParsec=mega*parsec(\(\mathrm{Mpc}\)) [m]Megaparsec—\(10^6\) parsecs.
Derived.; more
metersToAngstroms=1.0e10(\(\text{\AA}/\mathrm{m}\)) [AA/m]Number of Angstroms per meter.
Defined.
micronsToAngstroms=1.0e4(\(\text{\AA}/\mu\mathrm{m}\)) [Å/\(\mu\)m]Number of Angstroms per micron.
Defined.
minutesToDegrees=360.0d0/24.0d0/60.0e0[\(^\circ/^{\prime\prime}\)]Conversion factor from minutes to degrees.
Defined.
MpcPerKmPerSToGyr=megaParsec/kilo/gigaYear[Mpc/km s\(^{-1}\)/Gyr]The conversion from Mpc/(km s\(^{-1})\) to Gyr.
Derived.
parsec(\(\mathrm{pc}\)) [m]Parsec—the distance at which 1 AU subtends an angle of one arcsecond.
value from GSL
GSL_CONST_MKSA_PARSEC; Gnu Scientific Library; morerydberg(\(\mathrm{Ry}\)) [J]Rydberg—the ionization energy of hydrogen in its ground state.
value from GSL
GSL_CONST_MKSA_RYDBERG; Gnu Scientific LibrarysecondsToDegrees=360.0d0/24.0d0/3600.0e0[\(^\circ/^{\prime\prime}\)]Conversion factor from seconds to degrees.
Defined.
year=3.15581497635456e7(\(\mathrm{yr}\)) [s]Sidereal year.