The dark matter halo of the Milky Way is predicted to contain a very large number of smaller subhalos .
As a result of the dark matter annihilations taking place within such objects , the most nearby and massive subhalos could appear as point-like or spatially extended gamma-ray sources , without observable counterparts at other wavelengths .
In this paper , we use the results of the Aquarius simulation to predict the distribution of nearby subhalos , and compare this to the characteristics of the unidentified gamma-ray sources observed by the Fermi Gamma-Ray Space Telescope .
Focusing on the brightest high latitude sources , we use this comparison to derive limits on the dark matter annihilation cross section .
For dark matter particles lighter than \sim 200 GeV , the resulting limits are the strongest obtained to date , being modestly more stringent than those derived from observations of dwarf galaxies or the Galactic Center .
We also derive independent limits based on the lack of unidentified gamma-ray sources with discernible spatial extension , but these limits are a factor of \sim 2-10 weaker than those based on point-like subhalos .
Lastly , we note that four of the ten brightest high-latitude sources exhibit a similar spectral shape , consistent with 30-60 GeV dark matter particles annihilating to b \bar { b } with an annihilation cross section on the order of \sigma v \sim ( 5 - 10 ) \times 10 ^ { -27 } cm ^ { 3 } /s , or 8-10 GeV dark matter particles annihilating to \tau ^ { + } \tau ^ { - } with \sigma v \sim ( 2.0 - 2.5 ) \times 10 ^ { -27 } cm ^ { 3 } /s .