# Variables Templates

## Physical Constants

 Symbol Definition Template_Name To insert the symbol associated with a given physical variable or constant into the text of any Wiki document, type ... {{ Math/Template_Name }} $c$ Speed of light;    Authoritative Value x0063 $G$ Newtonian gravitational constant;    Authoritative Value x0047 $h$ Planck constant;    Authoritative Value;    NOTE: $\hbar$ $\equiv$ $h$ /(2$\pi$ ) x0068 $k$ Boltzmann constant;    Authoritative Value x006B $N_{A}$ Avogadro constant;    Authoritative Value $m_{e}$ Electron mass;    Authoritative Value $m_{p}$ Proton mass;    Authoritative Value $m_{u}$ Atomic mass unit;    Authoritative Value;    NOTE: $m_{p}$ /$m_{u}$ = 1.007276 $\Re$ Gas constant = $k$ $N_{A}$ = 1.007276 $k$ /$m_{p}$ ;    Authoritative Value 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] $B_{\mathrm {F} }$ 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] $a_{\mathrm {rad} }$ 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]. $T_{e}$ Temperature associated with the rest-mass energy of the electron;    Context of Definition $T_{e}\equiv {\frac {m_{e}c^{2}}{k}}=5.9381\times 10^{9}~\mathrm {K}$ $e$ Charge on an electron;    Authoritative Value The cgs units (statcoulombs) are equivalent to $(\mathrm {g} ~\mathrm {cm} ^{3}~\mathrm {s} ^{-2})^{1/2}$ $\alpha _{\mathrm {fs} }$ Fine structure constant (dimensionless);    Authoritative Value $\alpha _{\mathrm {fs} }\equiv {\frac {e^{2}}{\hbar c}}={\frac {1}{137.0359997}}$ $\sigma _{T}$ Thompson cross-section;    Authoritative Value $\sigma _{T}\equiv {\frac {8\pi }{3}}{\biggl (}{\frac {\alpha _{\mathrm {fs} }\hbar }{m_{e}c}}{\biggr )}^{2}=0.6652458\times 10^{-24}~\mathrm {cm} ^{2}$ ## Variables

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

## Model Parameters

 Symbol Definition Template_Name To insert the symbol associated with a given physical variable or constant into the text of any Wiki document, type ... {{ Math/Template_Name }} $\gamma _{\mathrm {g} }$ Adiabatic Index (or Ratio of Specific Heats); dimensionless    Wikipedia Discussion ${\bar {\mu }}$ Mean molecular weight; dimensionless;    defined such that ${\bar {\mu }}$ = $\rho$ / ($m_{u}$ $n_{g}$ ). 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. x03BC $n$ Polytropic Index; dimensionless    Wikipedia Discussion x006E $K_{\mathrm {n} }$ Polytropic Constant; dimensions depend on choice of $n$ Wikipedia Discussion

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