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

## 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 }} ${\displaystyle n_{g}}$ Number density of gas particles;    units of "1/volume" x004E ${\displaystyle \rho }$ Mass density;    units of "mass/volume" x03C1 ${\displaystyle V}$ Specific Volume = 1/${\displaystyle \rho }$;    units of "volume/mass" x0056 ${\displaystyle \Phi }$ Newtonian gravitational potential;    units of "energy/mass" or "velocity-squared" x03A6 ${\displaystyle H}$ Enthalpy;    units of "energy/mass" or "velocity-squared" x0048 ${\displaystyle P}$ Pressure;    units of "force/area" or "energy/volume" x0050 ${\displaystyle \epsilon }$ Specific internal energy;    units of "energy/mass" or "velocity-squared" x03B5 ${\displaystyle s}$ Specific entropy; x0073 ${\displaystyle t}$ Time x0074 ${\displaystyle T}$ Temperature;    units of "Kelvin" x0054 ${\displaystyle {\vec {v}}}$ Euclidean 3-space velocity vector;    units of "length/time" ${\displaystyle {\vec {x}}}$ 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 }} ${\displaystyle \gamma _{\mathrm {g} }}$ Adiabatic Index (or Ratio of Specific Heats); dimensionless    Wikipedia Discussion ${\displaystyle {\bar {\mu }}}$ Mean molecular weight; dimensionless;    defined such that ${\displaystyle {\bar {\mu }}}$ = ${\displaystyle \rho }$ / (${\displaystyle m_{u}}$${\displaystyle n_{g}}$). x03BC ${\displaystyle \mu _{e}}$ Molecular weight of electrons; dimensionless; defined such that ${\displaystyle \mu _{e}}$ = ${\displaystyle \rho }$ / (${\displaystyle m_{u}}$ ${\displaystyle N_{e}}$), where ${\displaystyle N_{e}}$ is the number density of electrons. x03BC ${\displaystyle n}$ Polytropic Index; dimensionless    Wikipedia Discussion x006E ${\displaystyle K_{\mathrm {n} }}$ Polytropic Constant; dimensions depend on choice of ${\displaystyle n}$    Wikipedia Discussion

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