Thanks for reaching out. The dered_flux_X and dered_mag_X columns were computed when we ingested the catalog, using the flux_X and mw_transmission_X columns as follows: (STILTS commands)
addcol -units mag -ucd phot.flux dered_flux_g "(float)(FLUX_G/MW_TRANSMISSION_G)";
addcol -units mag -ucd phot.mag dered_mag_g "(float)(22.5-2.5*log10(FLUX_G/MW_TRANSMISSION_G))";
Note however that the units for dered_flux_X are actually wrong in the catalog ('mag') but are nanomaggies instead.
Some more detailed information:
https://www.legacysurvey.org/dr9/catalogs/
https://www.sdss.org/dr12/algorithms/magnitudes/
Regarding your other question about the pre-crossmatched tables... We will add info to the Data Lab User Manual ( https://datalab.noirlab.edu/docs/manual/ ) but in the meantime a brief summary:
All our pre-crossmatched tables such as ls_dr9.x1p5__tractor__gaia_dr3__gaia_source have the same format for names and content. ln this example, the (left) ls_dr9.tractor table was x-matched with the (right) gaia_dr3.gaia_source table, using a default 1.5 arcsec radius. The pre-crossmatched tables only carry the single closest match for each row in the left table in the right table, and they don't keep rows for which no counterpart was found in the right table. The reverse pre-crossmatched table also always exists, i.e. in this case gaia_dr3.x1p5__gaia_source__ls_dr9__tractor. The columns in any pre-crossmatched table are:
id1,ra1,dec1,id2,ra2,dec2,distance
where 1 is the left table, 2 is the right table, and distance is in arcseconds. Note that the table schema browser shows them in a different order (alphabetically, for easier localization of columns):
https://datalab.noirlab.edu/query.php?name=ls_dr9.x1p5__tractor__gaia_dr3__gaia_source
Hope this is helpful,
Robert