Mayall II = G1 is one of the most luminous globular clusters ( GCs ) known in M31 .
New deep , high-resolution observations with the Advanced Camera for Surveys on the Hubble Space Telescope are used to provide accurate photometric data to the smallest radii yet .
In particular , we present the precise variation of ellipticity and position angle , and of surface brightness for the core of the object .
Based on these accurate photometric data , we redetermine the structural parameters of G1 by fitting a single-mass isotropic King model .
We derive a core radius , r _ { c } = 0.21 \pm 0.01 \arcsec~ { } ( = 0.78 \pm 0.04 ~ { } pc ) , a tidal radius , r _ { t } = 21.8 \pm 1.1 \arcsec~ { } ( = 80.7 \pm 3.9 ~ { } pc ) , and a concentration index c = \log ( r _ { t } / r _ { c } ) = 2.01 \pm 0.02 .
The central surface brightness is 13.510 mag arcsec ^ { -2 } .
We also calculate the half-light radius , at r _ { h } = 1.73 \pm 0.07 \arcsec ( = 6.5 \pm 0.3 ~ { } pc ) .
The results show that , within 10 core radii , a King model fits the surface brightness distribution well .
We find that this object falls in the same region of the M _ { V } vs . \log R _ { h } diagram as \omega Centauri , M54 and NGC 2419 in the Milky Way .
All three of these objects have been claimed to be the stripped cores of now defunct dwarf galaxies .
We discuss in detail whether GCs , stripped cores of dwarf spheroidals and normal dwarf galaxies form a continuous distribution in the M _ { V } versus \log R _ { h } plane , or if GCs and dwarf spheroidals constitute distinct classes of objects ; we present arguments in favour of this latter view .