An October 15, 2020 pre-print comes up with a theoretically rather than observationally motivated way to measure the size of a galaxy that reduces the scatter in certain measurements from ± 15% at one standard deviation (0.06 dex) from ± 45% at one standard deviation (0.18 dex).
This suggests that the some of the scatter in the "radial acceleration relation" is due to an imperfect definition of radius and tends to make the relation even tighter.
As used in the abstract of that paper, a dex is an order of magnitude (i.e. factor of 10), So 10dex equals the scatter in terms of a ratio value, which times 100 equal a percentage variation.
A dex is completely equivalent to a “bel” or “decade” which occasionally come up in engineering and physics. The bel is much more widely known with its deci- prefix as the “decibel.” A decibel is therefore equal to 0.1 dex.
Using the dex terminology is one way to make big margins of error (which are common in astronomy) look smaller, and also is helpful when you are discussing power law functions where logarithmic error relationships make more sense that quoting scatter in absolute terms that don't adjust the upper limit and lower limit relative to each other for scale.
A historical perspective on the concept of galaxy size
A brief narrative on how the effective radius and isophotal diameters were accepted as galaxy size measures is presented. Evidence suggests that these parameters were defined only based on observational premises, independent of any astrophysical theories. An alternative, new physically motivated size definition based on the expected gas density threshold required for star formation in galaxies is discussed. The intrinsic scatter of the size-stellar mass relation using the new size measure is 0.06 dex, three times smaller than that of the relation with the effective radius as size. The new physically motivated size measure can be adopted in upcoming deep, wide imaging surveys.
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