Stellar systems in the direction of Pegasus I - I. Low surface
  brightness galaxies
  To enlarge the sample of known low-surface brightness (LSB) galaxies and to
try to provide clues about their nature, we report the detection of eight of
this type of objects ($\mu_{{eff}, g'} \simeq 27$ mag arcsec$^{-2}$) towards
the group of galaxies Pegasus I. They are located in the very center of Pegasus
I, close to the dominant elliptical galaxies NGC7619 and NGC7626. Assuming that
these galaxies are at the distance of Pegasus I, we have found that their sizes
are intermediate among similar objects reported in the literature. In
particular, we found that three of these galaxies can be classified as
ultra-diffuse galaxies and a fourth one displays a nucleus. The eight new LSB
galaxies show a significant color dispersion around the extrapolation towards
faint luminosities of the color-magnitude relation defined by typical
early-type galaxies. In addition, they display values of the S\'ersic index
below 1, in agreement with values obtained for LSB galaxies in other
environments. We also show that there seems to be a bias effect in the size
distributions of the detected LSBs in different environments, in the sense that
more distant groups/clusters lack small $r_{eff}$ objects, while large systems
are not found in the Local Group and nearby environments. While there may be an
actual shortage of large LSB galaxies in low-density environments like the
Local Group, the non-detection of small (and faint) systems at large distances
is clearly a selection effect. As an example, LSB galaxies with similar sizes
to those of the satellites of Andromeda in the Local Group, will be certainly
missed in a visual identification at the distance of Pegasus I.
