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\subsection{Observed Quiescent Fractions}
Figure~\ref{fig:quiescent_fraction} shows, for all observed satellite dwarf galaxies of the MW or M31, the fraction that are quiescent versus $\mstar$ \citep[see also][]{Phillips2014, SlaterBell2014}).
Blue circles show all satellites, while violet squares show those Based on our above definitions of
the MW ``satellite'' and
green triangles show those of M31.
The only star-forming/gas-rich ''quiescent'' dwarf galaxies, we group all satellites
are: LMC ($\mstar=1.5\times10^9\msun$) and SMC ($\mstar=4.6\times10^8\msun$) around in the
MW, LGS 3 ($\mstar=9.6\times10^5\msun$) and IC 10 ($\mstar=9\times10^7$) around M31.
At $\mstar<8\times10^7\msun$, 50 LG into 1-dex bins of
51 satellites are quiescent, $\mstar$ and
at $\mstar<9 \times10^5\msun$ \emph{all} are quiescent.
The error bars show 68\% uncertainty for a beta distribution \citep{Cameron2011} based on the observed counts.
In measuring compute the fraction of
satellites that which are
quiescent, we group them into 1-dex bins of $\mstar$. quiescent in each bin.
We do not attempt any correction for observational completeness as a function of $\mstar$, because we measure the \emph{relative fraction} that are quiescent in each
$\mstar$ bin, which
should be unbiased, is likely an unbiased metric, absent significant differential completeness as a function of recent star formation.
We consider the latter unlikely because star-forming galaxies are generally brighter, but the quiescent fraction is near unity across our range in $\mstar$.
However, we (We do take into account the maximum observed distance of
satellites dwarfs at each $\mstar$ bin when we compute the virial-infall times using the
simulations (see below). simulations, see below.)
Figure~\ref{fig:quiescent_fraction} shows the quiescent fraction for all satellite dwarf galaxies of the MW or M31 versus $\mstar$ \citep[see also][]{Phillips2014, SlaterBell2014}).
We show fractions for all such satellites (blue circles) as well as separately for those in the MW (violet squares) and M31 (green triangles).
The error bars show 68\% uncertainty for a beta distribution \citep{Cameron2011} based on the observed counts.
Of the NNN satellites, only 4 are star-forming/gas-rich: the LMC and SMC around the MW, LGS 3 and IC 10 around M31.
Moreover, at $\mstar<8\times10^7\msun$, 50 of 51 satellites are quiescent, and at $\mstar<9 \times10^5\msun$ \emph{all} NNN satellites are quiescent.
The error bars show 68\% uncertainty for a beta distribution \citep{Cameron2011} based on the observed counts.
These high quiescent fractions contrast strongly with the fact that essentially all isolated galaxies (that are not environmentally affected) are star-forming.