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test this
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brryan committed Jan 8, 2025
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@@ -11,20 +11,21 @@ singularity-opac provides a uniform API for all opacity models. The following fu
(here, $\sigma$ is the frequency- and angle-dependent cross section in units of ${\rm cm}^2$):
| Function | Expression | Description | Units |
| --------------------- | ---------- | --------------------- | ------- |
| AbsorptionCoefficient | $n \sigma$ | Absorption coefficient | `cm^{-1}` |
| AngleAveragedAbsorptionCoefficient | `\frac{1}{4 \pi}\int n \sigma d\Omega` | Absorption coefficient averaged over solid angle | `cm^{-1}` |
| EmissivityPerNuOmega | `j_{\nu} = \frac{dE}{d^3x dt d\Omega d\nu}` | Frequency- and angle-dependent emissivity | `erg cm^{-3} s^{-1} Sr^{-1} Hz^{-1}` |
| EmissivityPerNu | `\int j_{\nu} d\Omega` | Frequency-dependent emissivity | `erg cm^{-3} s^{-1} Hz^{-1}` |
| Emissivity | `\int j_{\nu} d\nu d\Omega` | Total emissivity | `erg cm^{-3} s^{-1}` |
| NumberEmissivity | `\int \frac{1}{h \nu} j_{\nu} d\Omega d\nu` | Total number emissivity | `cm^{-3} s^{-1}` |
| ThermalDistributionOfTNu | `B_{\nu} = \frac{dE}{dA dt d\Omega d\nu}` | Specific intensity of thermal distribution | `erg cm^{-2} s^{-1} Sr^{-1} Hz^{-1}` |
| DThermalDistributionOfTNuDT | `dB_{\nu}/dT` | Temperature derivative of specific intensity of thermal distribution | `erg cm^{-2} s^{-1} Sr^{-1} Hz^{-1} K^{-1}` |
| ThermalDistributionOfT | `B = \int B_{\nu} d\Omega d\nu` | Frequency- and angle-integrated intensity of thermal distribution | `erg cm^{-2} s^{-1}` |
| ThermalNumberDistributionOfT | `B = \int \frac{1}{h \nu} B_{\nu} d\Omega d\nu` | Frequency- and angle-integrated intensity of thermal distribution | `erg cm^{-2} s^{-1}` |
| AbsorptionCoefficient | $n \sigma$ | Absorption coefficient | $cm^{-1}$ |
| AngleAveragedAbsorptionCoefficient | $\frac{1}{4 \pi}\int n \sigma d\Omega$ | Absorption coefficient averaged over solid angle | ${\rm cm}^{-1}$ |
| EmissivityPerNuOmega | $j_{\nu} = \frac{dE}{d^3x dt d\Omega d\nu}$ | Frequency- and angle-dependent emissivity | ${\rm erg~cm}^{-3} {\rm s}^{-1} {\rm Sr}^{-1} {\rm Hz}^{-1}$ |
| EmissivityPerNu | $\int j_{\nu} d\Omega$ | Frequency-dependent emissivity | ${\rm erg~cm}^{-3} {\rm s}^{-1} {\rm Hz}^{-1}$ |
| Emissivity | $\int j_{\nu} d\nu d\Omega$ | Total emissivity | ${\rm erg~cm}^{-3} {\rm s}^{-1}$ |
| NumberEmissivity | $\int \frac{1}{h \nu} j_{\nu} d\Omega d\nu$ | Total number emissivity | ${\rm cm}^{-3} {\rm s}^{-1}$ |
| ThermalDistributionOfTNu | $B_{\nu} = \frac{dE}{dA dt d\Omega d\nu}$ | Specific intensity of thermal distribution | ${\rm erg~cm}^{-2} {\rm s}^{-1} {\rm Sr}^{-1} {\rm Hz}^{-1}$ |
| DThermalDistributionOfTNuDT | $dB_{\nu}/dT$ | Temperature derivative of specific intensity of thermal distribution | ${\rm erg~cm}^{-2} {\rm s}^{-1} {\rm Sr}^{-1} {\rm Hz}^{-1} {\rm K}^{-1}$ |
| ThermalDistributionOfT | $B = \int B_{\nu} d\Omega d\nu$ | Frequency- and angle-integrated intensity of thermal distribution | ${\rm erg~cm}^{-2} {\rm s}^{-1}$ |
| ThermalNumberDistributionOfT | $B = \int \frac{1}{h \nu} B_{\nu} d\Omega d\nu$ | Frequency- and angle-integrated intensity of thermal distribution | ${\rm erg~cm}^{-2} {\rm s}^{-1}$ |

Note that the thermal radiation energy density `u = 1/c ThermalDistributionOfT` and the thermal radiation number density `n = 1/c ThermalNumberDistributionOfT`.

Internally singularity-opac always uses CGS units, as in the above table. However, arbitrary units are supported through the units modifier.
Internally singularity-opac always uses CGS units, as in the above table. However, arbitrary units are supported through the units modifier, which accepts
function argument inputs in the arbitrary unit system, and returns the result from the function in those same arbitrary units.

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