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 ... {{ User:Tohline/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: $\hslash$ $\equiv$ $h$/(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
$\mathrm{\Re }$	Gas constant = $k$$N_A$ = 1.007276 $k$/$m_p$;    Authoritative Value	C_GasConstant	x211C
$A_{\mathrm{F}}$	Characteristic Fermi pressure; $A_{\mathrm{F}}\equiv \frac{\pi m_e^4{c}^5}{3h^3}=6.00228\times 10^{22}\mathrm{e}\mathrm{r}\mathrm{g}{\mathrm{c}\mathrm{m}}^{-3}$ 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; $\frac{B_{\mathrm{F}}}{{\mu }_e}\equiv \frac{8\pi m_p}{3}(\frac{m_{e}c}{h}{)}^3=9.81011\times 10^5\mathrm{g}{\mathrm{c}\mathrm{m}}^{-3}$ Reference (original): Chandraskehar, S. (1935) Reference (recent): See Appendix of Even & Tohline (2009) Reference (authoritative book): [C67]	C_FermiDensity
$a_{\mathrm{r}\mathrm{a}\mathrm{d}}$	Radiation [density] constant;    Authoritative Value $a_{\mathrm{r}\mathrm{a}\mathrm{d}}\equiv \frac{8{\pi }^5}{15}\frac{k^4}{(hc{)}^3}=7.56576\times 10^{-15}\mathrm{e}\mathrm{r}\mathrm{g}{\mathrm{c}\mathrm{m}}^{-3}{\mathrm{K}}^{-4}$ NOTE: $a_{\mathrm{r}\mathrm{a}\mathrm{d}}=4{\sigma }_{\mathrm{S}\mathrm{B}}/c$, where ${\sigma }_{\mathrm{S}\mathrm{B}}$ 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 $(\mathrm{g}{\mathrm{c}\mathrm{m}}^3{\mathrm{s}}^{-2}{)}^{1/2}$	C_ElectronCharge
${\alpha }_{\mathrm{f}\mathrm{s}}$	Fine structure constant (dimensionless);    Authoritative Value ${\alpha }_{\mathrm{f}\mathrm{s}}\equiv \frac{e^2}{\hslash c}=\frac{1}{137.0359997}$	C_FineStructureConstant
${\sigma }_T$	Thompson cross-section;    Authoritative Value ${\sigma }_T\equiv \frac{8\pi }{3}(\frac{{\alpha }_{\mathrm{f}\mathrm{s}}\hslash }{m_{e}c}{)}^2=0.6652458\times 10^{-24}{\mathrm{c}\mathrm{m}}^2$	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
$\mathrm{\Phi }$	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
$ϵ$	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
$\overrightarrow{v}$	Euclidean 3-space velocity vector;    units of "length/time"	VAR_VelocityVector01
$\overrightarrow{x}$	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
$\overline{\mu }$	Mean molecular weight; dimensionless;    defined such that $\overline{\mu }$ = $\rho$ / ($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