fit for the doublet ratio as a free parameter (with physical priors)

[moustakas]

The [OII] and [SII] doublet ratios depend on the electron density of the medium producing those lines, while the MgII doublet ratio can vary over a not-arbitrary range (for example, if one line is positive, the other line must be positive, too).

To integrate these physical priors into fastspecfit, consider using the ratio of these lines as one of the free parameters (with a sensible prior range) rather than either fixing the ratio or letting the individual line-amplitudes to be optimized independently.

Credit for this idea to Ben Weiner.

[moustakas]

I generated some figures to this notebook using pyneb to help establish the appropriate physical priors:
https://github.com/desihub/fastspecfit/blob/fuji-dev/doc/nb/nebular-lines.ipynb

[OII] 3726,29

For extreme (but not unphysical) ranges of electron temperature and density, this ratio varies between 0.66300 and 1.38312, with a typical value of 0.74107.

[SII] 6730,16

This ratio varies between 0.67794 and 1.19105, with a typical value of 0.74011.

(This notebook also shows, for completeness, that the [NII] 6584,48, [OIII] 5007/4959, and [OII] 7330,20 doublet ratios are independent of density and temperature, as expected from atomic physics. Yay!)

[moustakas]

Initial fitting results with this more physically flexible (and robust!) model can be seen in the screenshot below, which should be compared with the Everest version of the code:
https://data.desi.lbl.gov/desi/users/ioannis/fastspecfit/everest/tiles/cumulative/80613/fastspec-80613-cumulative-39633345008634465.png

Nothing crazy here and, in fact, I get an [SII] and [OII] doublet ratio of 0.76658603 and 0.73103347 (very close to the nominal values of 0.74), which correspond very closely to a nominal electron density of 100/cm3. Neat!

[moustakas]

BTW, the preceding fitting results were generated with

fastspec /global/cfs/cdirs/desi/spectro/redux/everest/tiles/cumulative/80613/20210324/redrock-4-80613-thru20210324.fits \
  -o fastspec.fits --targetids 39633345008634465 --specprod everest
fastspecfit-qa --fastspecfile ./fastspec.fits -o /global/homes/i/ioannis/desi-users/ioannis/tmp

Here's another example, an ELG at z=0.82, which is also quite well-behaved. (Here, the doublet ratio is 0.7071845, which is again very close to nominal electron density.)

fastspec /global/cfs/cdirs/desi/spectro/redux/everest/tiles/cumulative/80606/20201219/redrock-1-80606-thru20201219.fits \
  -o fastspec2.fits --targetids 39627658597767916 --specprod everest
fastspecfit-qa --fastspecfile ./fastspec2.fits -o /global/homes/i/ioannis/desi-users/ioannis/tmp

[moustakas]

Done in #55 and #69.