Galaxies are generally found to follow a relation between their size and luminosity , such that luminous galaxies typically have large sizes .
The recent identification of a significant population of galaxies with large sizes but low luminosities ( “ ultra diffuse galaxies ” , or UDGs ) raises the question whether the inverse is also true , that is , whether large galaxies typically have high luminosities .
Here we address this question by studying a size -limited sample of galaxies in the Coma cluster .
We select red cluster galaxies with sizes r _ { \mathrm { eff } } > 2 \mathrm { kpc } down to M _ { g } \sim - 13 \mathrm { mag } in an area of 9 \mathrm { deg } ^ { 2 } , using carefully-filtered CFHT images .
The sample is complete to a central surface brightness of \mu _ { g, 0 } \approx 25.0 \mathrm { mag arcsec } ^ { -2 } and includes 90 % of Dragonfly-discovered UDGs brighter than this limit .
Unexpectedly , we find that red , large galaxies have a fairly uniform distribution in the size-luminosity plane : there is no peak at the absolute magnitude implied by the canonical size-luminosity relation .
The number of galaxies within \pm 0.5 magnitudes of the canonical peak ( M _ { g } = -19.69 for 2 < r _ { \mathrm { eff } } < 3 kpc ) is a factor of \sim 9 smaller than the number of fainter galaxies with -19 < M _ { g } < -13 .
Large , faint galaxies such as UDGs are far more common than large galaxies that are on the size-luminosity relation .
An implication is that , for large galaxies , size is not an indicator of halo mass .
Finally , we show that the structure of faint large galaxies is different from that of bright large galaxies : at fixed large size , the Sérsic index decreases with magnitude following the relation \log _ { 10 } n \approx - 0.067 M _ { g } -0.989 .