Magnitudes to flux conversion

Most public photometry tables report brightness of objects in terms of magnitudes as opposed to flux units (Jy or mJy). However, using software such as CIGALE and EAZY is made less ambiguous if fluxes are supplied. To enable this, we provide the function frb.surveys.catalog_utils.convert_mags_to_flux

The definition for magnitude errors arises from the following equation:

\[m\pm \delta m = ZP-2.5 \log_{10}(f\pm \delta f) \Rightarrow m = ZP-2.5 \log_{10}(f) \Rightarrow \delta m = 2.5 \log_{10}(1+\delta f/f)\]

While the math:delta m formula above is exact, most photometry software use a first order Taylor expansion in math:delta f/f assuming the error is typically small. i.e.

\[\delta m \approx \frac{2.5}{\log_{10}}(\delta f/f)\]

This will obviously break down when looking at really faint objects, barely at the threshold of detection above the noise floor. convert_mags_to_flux explicitly assumes the catalog mag errors are produced using this approximation. However, if you have reason to believe the exact formula was used, you can set exact_mag_err=True to get the correct flux error.