Present-day multi-wavelength deep imaging surveys allow to characterise the outskirts of galaxies with unprecedented precision .
Taking advantage of this situation , we define a new physically motivated measurement of size for galaxies based on the expected location of the gas density threshold for star formation .
Employing both theoretical and observational arguments , we use the stellar mass density contour at 1 M _ { \odot } pc ^ { -2 } as a proxy for this density threshold for star formation .
This choice makes our size definition operative .
With this new size measure , the intrinsic scatter of the global stellar mass ( M _ { \star } ) - size relation ( explored over five orders of magnitude in stellar mass ) decreases to \sim 0.06 dex .
This value is 2.5 times smaller than the scatter measured using the effective radius ( \sim 0.15 dex ) and between 1.5 and 1.8 times smaller than those using other traditional size indicators such as R _ { 23.5 ,i } ( \sim 0.09 dex ) , the Holmberg radius R _ { H } ( \sim 0.09 dex ) and the half-mass radius R _ { e,M _ { \star } } ( \sim 0.11 dex ) .
Moreover , galaxies with 10 ^ { 7 } M _ { \odot } < M _ { \star } < 10 ^ { 11 } M _ { \odot } increase monotonically in size following a power-law with a slope very close to 1/3 , equivalent to an average stellar mass 3D density of \sim 4.5 \times 10 ^ { -3 } M _ { \odot } pc ^ { -3 } for galaxies within this mass range .
Galaxies with M _ { \star } > 10 ^ { 11 } M _ { \odot } show a different slope with stellar mass , which is suggestive of a larger gas density threshold for star formation at the epoch when their star formation peaks .