%\begin{table} \begin{center} \begin{small} \begin{tabular}{p{0.32\textwidth} p{0.42\textwidth} p{0.26\textwidth}} variable & name & units (cgs) \\[.5em] %--------------------------------------------------------------------------------------------------- \hline \\ $I_\nu (\x, \mathbf{n}, t)$ & specific intensity & $[I_\nu] = \frac{\text{erg}}{\text{cm}^2 \text{ rad Hz s}}$ \\[.5em] $u_\nu (\x, \mathbf{n}, t) = \frac{I_\nu}{c}$ & radiation energy density & $[u_\nu] = \frac{\text{erg}}{\text{cm}^3 \text{ rad Hz}}$ \\[.5em] $E_\nu (\x, t) = \int_{4 \pi} \frac{I_\nu}{c} \de \Omega$ & total energy density & $[E_\nu] = \frac{\text{erg}}{\text{cm}^3 \text{ Hz}}$ \\[.5em] $N_\nu (\x, t) = E_\nu / h$ & photon number density & $[N_\nu] = \frac{1}{\text{cm}^3 \text{ Hz}}$ \\[.5em] $E_{rad} (\x, t) = \int_{0}^{\infty} E_\nu \de \nu$ & total integrated energy density & $[E_{rad}] = \frac{\text{erg}}{\text{cm}^3}$ \\[.5em] $N_{rad} (\x, t) = E_{rad} / h$ & integrated photon number density & $[N_{rad}] = \frac{1}{\text{cm}^3}$ \\[.5em] % $J_\nu (\x, t) = \int_{4 \pi} I_\nu \frac{\de \Omega}{4 \pi} % = \frac{c}{4 \pi} E_\nu$ & % mean radiation specific intensity & % $[J_\nu] = \frac{\text{erg}}{\text{cm}^2 \text{ Hz s}}$ % \\[.5em] $\mathbf{F}_\nu(\x, t) = \int_{4 \pi} I_\nu \mathbf{n} \de \Omega$ & radiation flux & $[\mathbf{F}_\nu] = \frac{\text{erg}}{\text{cm}^2 \text{ s Hz}}$ \\[.5em] $\mathbf{P}_\nu (\x, t) = \frac{\F_\nu}{c^2}$ & radiation momentum density & $[\mathbf{P}_\nu] = \frac{\text{erg}}{ \text{cm}^4 \text{ s}^{-1} \text{ Hz}}$ \\[.5em] $\mathds{P}_\nu (\x, t) = \int_{4 \pi} \frac{I_\nu}{c} \mathbf{n} \otimes \mathbf{n} \de \Omega$ & radiation pressure tensor & $[\mathds{P}_\nu ] = \frac{\text{erg}}{\text{cm}^3 \text{ Hz}}$ \\ %--------------------------------------------------------------------------------------------------- \hline\\ $\eta_\nu(\x, t)$ & source function (of $I_\nu$)& $[ \eta_\nu ] = \frac{\text{erg}}{\text{cm}^3 \text{ rad Hz s}}$ \\[.5em] $n(\x, t)$ & number density & $[ n ] = \text{cm}^{-3}$ \\[.5em] $\mathcal{J}_\nu(T)$ & (specific intensity of a) spectrum & $[\mathcal{J}_\nu (T)] = \frac{\text{erg}}{\text{cm}^2 \text{ rad Hz s}}$ \\[.5em] $\Gamma_{\nu, j}$ & photoionization rate of species $j$ & $[\Gamma] = \text{s}^{-1}$ \\[.5em] $\mathcal{H}_{\nu,j}$ & (photo)heating rate of species $j$ & $[\mathcal{H}_{\nu,j}] = \frac{\text{erg}}{s\ cm}^{3}$ \\[.5em] $\alpha_\nu = \frac{1}{\lambda_\nu} = \rho \kappa_\nu = n \sigma_\nu$ & absorption coefficient & $[\alpha_\nu] = \text{cm}^{-1}$ \\[.5em] % $\alpha_E = \frac{\int_0^\infty \alpha_\nu E_\nu \de \nu}{\int_0^\infty E_\nu \de \nu}$ & % energy mean of abs. coeff. & % $[\alpha_E] = \text{cm}^{-1}$ % \\[.5em] % $\alpha_F = \frac{\int_0^\infty \alpha_\nu F_\nu \de \nu}{\int_0^\infty F_\nu \de \nu}$ & % flux mean of abs. coeff. & % $[\alpha_F] = \text{cm}^{-1}$ % \\[.5em] % $j_\nu $ & % emission coefficient & % $[j_\nu] = \frac{\text{erg}}{\text{cm}^3 \text{rad Hz s}}$ % \\[.5em] $\lambda_\nu $ & mean free path & $[\lambda_\nu] = \text{cm}$ \\[.5em] $\kappa_\nu $ & opacity & $[\kappa_\nu] = \frac{\text{cm}^2}{\text{g}}$ \\[.5em] $\tau_\nu(s) = \int_0^s \alpha_\nu(x) \de x$ & optical depth & $[\tau_\nu] = 1$ \\[.5em] $\sigma_{j\nu}$ & interacton cross section (of species $j$)& $[\sigma_{j\nu}] = \text{cm}^2$ \\[.5em] $\sigma_{ij}^N = \int_{\nu_{i}} N_\nu \ \sigma_{j\nu} \de \nu / \int_{\nu_i} N_\nu \de \nu$ & number weighted average cross section & $[\sigma_{ij}^N] = \text{cm}^2$ \\[.5em] $\sigma_{ij}^E = \int_{\nu i} E_\nu \ \sigma_{j\nu} \de \nu / \int_{\nu i} E_\nu \de \nu$ & energy weighted average cross section & $[\sigma_{ij}^E] = \text{cm}^2$ % \end{tabular} \end{small} \end{center} %\caption{Common quantities appearing in the context of radiative transfer, and their units.} %\label{tab:rt-variables} %\end{table}