Power Units Idea

[jdtsmith]

So Karl's idea of power-based model components is pretty brilliant for tying. Power itself is an awkward number though, unit wise. One of the only redeeming values of our crazy "meet-in-the-middle" mixed radio (f_nu) + optical (wavelength) units in the infrared is that the numbers are nice round values. E.g. 5 microns, a few mJy or MJy/sr, etc.

Integrating a Gaussian/Drude with those types of peak fluxes, and width of a few percent of its wavelength yields powers like f_nu*c/lam_0 with units [f_nu] * Hz. Since c/lam_0 is a large number of order 1e13, nice 1MJy/sr fluxes become ~1e13 MJy/sr Hz powers. This is ugly to look at, and isn't good for the fitter to deal wit (fitters prefer nice round numbers to avoid overflows and step-estimation mismatch).

Internally, to deal with this, I'm adopting the following: a scaled power density, PD=P lam_0/c where P is the "real" power.

Advantages of this re-scaling:

• It has implicit units the same as the spectrum itself (e.g. mJy, or MJy/sr or what have you).
• It doesn't require committing to any particular spectrum unit for display/calculation presentation, just re-using the existing ones.
• It has a nice physical interpretation: it's the amplitude at the peak a feature would have, if it that feature had a half-width at half-maximum equal to it's central wavelength (so pretty great for PAHs and other resolved features).

Disadvantages:

• Obviously requires people to be aware of what kind of unit they're dealing with, and convert back to real power units.
• Power ratios have implicit wavelength ratios in them.

Any thoughts? It's fine to keep this as a hidden convenience of the fitter; we certainly don't have to expose this in the Features table. But then again it might be an easier thing to deal with. As a final step we can convert to "real power" (which often involves multiplying by e.g. 1e-20 to get W/m^2/sr). Since eventually we have to actually deal with units, #28 and #53 are both relevant here.

[jdtsmith]

I just had the notion of people taking "power" in the model results Table at face-value, and blindly taking ratios and publishing them without realizing there is a factor of lam_1/lam_2 hiding in there. So, no... I'll stick with scaled_power for the internal units. I also think it may be useful to be able to specify either power or amplitude, and have PAHFIT just convert between them as appropriate.

I.e. amplitude is easy to "guess" staring at the spectrum, but power is more useful for ties.