Appendix/VariablesTemplates

Variables Templates

Physical Constants

To insert the symbol associated with a given physical variable or constant into the text of any Wiki document, type ... {{ Math/Template_Name }}
Symbol	Definition	Template_Name	Unicode
$c$	Speed of light;    Authoritative Value	C_SpeedOfLight	x0063
$G$	Newtonian gravitational constant;    Authoritative Value	C_GravitationalConstant	x0047
$h$	Planck constant;    Authoritative Value;    NOTE: $\hbar$ $\equiv$ $h$/(2$\pi$)	C_PlanckConstant	x0068
$k$	Boltzmann constant;    Authoritative Value	C_BoltzmannConstant	x006B
$N_{A}$	Avogadro constant;    Authoritative Value	C_AvogadroConstant
$m_{e}$	Electron mass;    Authoritative Value	C_ElectronMass
$m_{p}$	Proton mass;    Authoritative Value	C_ProtonMass
$m_{u}$	Atomic mass unit;    Authoritative Value;    NOTE: $m_{p}$/$m_{u}$ = 1.007276	C_AtomicMassUnit
$\Re$	Gas constant = $k$$N_{A}$ = 1.007276 $k$/$m_{p}$;    Authoritative Value	C_GasConstant	x211C
$A_{\mathrm {F} }$	Characteristic Fermi pressure; $A_{\mathrm {F} }\equiv {\frac {\pi m_{e}^{4}c^{5}}{3h^{3}}}=6.00228\times 10^{22}~\mathrm {erg} ~\mathrm {cm} ^{-3}$ Reference (original): Chandraskehar, S. (1935) Reference (recent): See Appendix of Even & Tohline (2009) Reference (authoritative book): [C67]	C_FermiPressure
$B_{\mathrm {F} }$	Characteristic Fermi density; ${\frac {B_{\mathrm {F} }}{\mu _{e}}}\equiv {\frac {8\pi m_{p}}{3}}{\biggl (}{\frac {m_{e}c}{h}}{\biggr )}^{3}=9.81011\times 10^{5}~\mathrm {g} ~\mathrm {cm} ^{-3}$ Reference (original): Chandraskehar, S. (1935) Reference (recent): See Appendix of Even & Tohline (2009) Reference (authoritative book): [C67]	C_FermiDensity
$a_{\mathrm {rad} }$	Radiation [density] constant;    Authoritative Value $a_{\mathrm {rad} }\equiv {\frac {8\pi ^{5}}{15}}{\frac {k^{4}}{(hc)^{3}}}=7.56576\times 10^{-15}~\mathrm {erg} ~\mathrm {cm} ^{-3}~\mathrm {K} ^{-4}$ NOTE: $a_{\mathrm {rad} }=4\sigma _{\mathrm {SB} }/c$, where $\sigma _{\mathrm {SB} }$ is the Stefan-Boltzmann constant; see, for example, p. 428 of [HK94].	C_RadiationConstant
$T_{e}$	Temperature associated with the rest-mass energy of the electron;    Context of Definition $T_{e}\equiv {\frac {m_{e}c^{2}}{k}}=5.9381\times 10^{9}~\mathrm {K}$	C_ElectronTemperature
$e$	Charge on an electron;    Authoritative Value The cgs units (statcoulombs) are equivalent to $(\mathrm {g} ~\mathrm {cm} ^{3}~\mathrm {s} ^{-2})^{1/2}$	C_ElectronCharge
$\alpha _{\mathrm {fs} }$	Fine structure constant (dimensionless);    Authoritative Value $\alpha _{\mathrm {fs} }\equiv {\frac {e^{2}}{\hbar c}}={\frac {1}{137.0359997}}$	C_FineStructureConstant
$\sigma _{T}$	Thompson cross-section;    Authoritative Value $\sigma _{T}\equiv {\frac {8\pi }{3}}{\biggl (}{\frac {\alpha _{\mathrm {fs} }\hbar }{m_{e}c}}{\biggr )}^{2}=0.6652458\times 10^{-24}~\mathrm {cm} ^{2}$	C_ThompsonCrossSection

Variables

To insert the symbol associated with a given physical variable or constant into the text of any Wiki document, type ... {{ Math/Template_Name }}
Symbol	Definition	Template_Name	Unicode
$n_{g}$	Number density of gas particles;    units of "1/volume"	VAR_NumberDensity01	x004E
$\rho$	Mass density;    units of "mass/volume"	VAR_Density01	x03C1
$V$	Specific Volume = 1/$\rho$;    units of "volume/mass"	VAR_SpecificVolume01	x0056
$\Phi$	Newtonian gravitational potential;    units of "energy/mass" or "velocity-squared"	VAR_NewtonianPotential01	x03A6
$H$	Enthalpy;    units of "energy/mass" or "velocity-squared"	VAR_Enthalpy01	x0048
$P$	Pressure;    units of "force/area" or "energy/volume"	VAR_Pressure01	x0050
$\epsilon$	Specific internal energy;    units of "energy/mass" or "velocity-squared"	VAR_SpecificInternalEnergy01	x03B5
$s$	Specific entropy;	VAR_SpecificEntropy01	x0073
$t$	Time	VAR_Time01	x0074
$T$	Temperature;    units of "Kelvin"	VAR_Temperature01	x0054
${\vec {v}}$	Euclidean 3-space velocity vector;    units of "length/time"	VAR_VelocityVector01
${\vec {x}}$	Euclidean 3-space position vector	VAR_PositionVector01

Model Parameters

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Symbol	Definition	Template_Name	Unicode
$\gamma _{\mathrm {g} }$	Adiabatic Index (or Ratio of Specific Heats); dimensionless    Wikipedia Discussion	MP_AdiabaticIndex
${\bar {\mu }}$	Mean molecular weight; dimensionless;    defined such that ${\bar {\mu }}$ = $\rho$ / ($m_{u}$$n_{g}$).	MP_MeanMolecularWeight	x03BC
$\mu _{e}$	Molecular weight of electrons; dimensionless; defined such that $\mu _{e}$ = $\rho$ / ($m_{u}$ $N_{e}$), where $N_{e}$ is the number density of electrons.	MP_ElectronMolecularWeight	x03BC
$n$	Polytropic Index; dimensionless    Wikipedia Discussion	MP_PolytropicIndex	x006E
$K_{\mathrm {n} }$	Polytropic Constant; dimensions depend on choice of $n$    Wikipedia Discussion	MP_PolytropicConstant