Units of (modified) Blackbody amplitude

[drvdputt]

Currently, tau is used as the strength of the blackbody (stellar continuum) and modified Blackbody (dust continuum) components, and the equation for evaluating the blackbody looks like this

            amplitude
            * 3.97289e13
            / x**3
            / (np.exp(1.4387752e4 / x / temperature) - 1.0)

where the fitted amplitude is reported as tau in the Features table.

In general, the fact the we often have to deal with the tails of the blackbody profile, makes them hard to use. In my experience, the typical order of magnitude of the resulting tau values can be very different, scaling strongly with the temperature of the blackbody. I feel like this causes numerical issues sometimes; very often, the minimizer will use only two components, while all the rest of the tau values are set to 0.

We could think of an alternate parameterization / normalization for these components. A few ideas:

• Amplitude at the peak wavelength. This becomes a problem however when the peak is far "off screen", and only the tail of the blackbody is seen
• Amplitude at a fixed wavelength, say 20 or 30 microns. Would be ok for most dust components, since at most dusty temperatures, the blackbody profile will have a reasonable contribution there. This will not work for the stellar component however.
• Total power: we could introduce something like "PowerBlackbody". Again, this might be problematic for components that peak far outside the wavelength range. But at least it would allow us to set reasonable and perhaps physically motivated upper limits.