The Dragonfly Nearby Galaxies Survey. III. The Luminosity Function of
  the M101 Group
  We obtained follow-up HST observations of the seven low surface brightness
galaxies discovered with the Dragonfly Telephoto Array in the field of the
massive spiral galaxy M101. Out of the seven galaxies, only three were resolved
into stars and are potentially associated with the M101 group at $D=7\text{
Mpc}$. Based on HST ACS photometry in the broad F606W and F814W filters, we use
a maximum likelihood algorithm to locate the Tip of the Red Giant Branch (TRGB)
in galaxy color-magnitude diagrams. Distances are $6.38^{+0.35}_{-0.35},
6.87^{+0.21}_{-0.30}$ and $6.52^{+0.25}_{-0.27} \text{ Mpc}$ and we confirm
that they are members of the M101 group. Combining the three confirmed low
luminosity satellites with previous results for brighter group members, we find
the M101 galaxy group to be a sparsely populated galaxy group consisting of
seven group members, down to $M_V = -9.2 \text{ mag}$. We compare the M101
cumulative luminosity function to that of the Milky Way and M31. We find that
they are remarkably similar; In fact, the cumulative luminosity function of the
M101 group gets even flatter for fainter magnitudes, and we show that the M101
group might exhibit the two known small-scale flaws in the
$\Lambda\textrm{CDM}$ model, namely `the missing satellite' problem and the
`too big to fail' problem. Kinematic measurements of M101$'$s satellite
galaxies are required to determine whether the `too big to fail' problem does
in fact exist in the M101 group.
