Search for missing globular clusters associated with the Milky Way dwarf galaxies using Gaia DR2

We report the result of searching for globular clusters (GCs) around 56 Milky Way satellite dwarf galaxies within the distance of 450 kpc from the Galactic Center except for the Large and Small Magellanic Clouds and the Sagittarius dwarf. For each dwarf, we analyze the stellar distribution of sources in Gaia DR2, selected by magnitude, proper motion, and source morphology. Using the kernel density estimation of stellar number counts, we identify 61 possible GC candidates. Nine out of the 61 are known objects and only Fornax GC 1 -- 6 among them are associated with the dwarf galaxy whereas there is no strong evidence that the other 52 are GCs based on the analysis of existing imaging data. Using simulated GCs, we calculate the GC detection limit $M_{\rm V}^{\rm lim}$ that spans the range from $M_{\rm V}^{\rm lim} = -7$ for more distant dwarfs to $M_{\rm V}^{\rm lim} \sim 0$ for nearby systems. Assuming a Gaussian GC luminosity function, we compute that the completeness of the GC search is above 90 percent for most dwarf galaxies. We construct the 90 percent credible intervals/upper limits on the GC specific frequency $s$ of the MW dwarf galaxies: $12 < s < 47$ for the Fornax, $s < 20$ for the dwarfs with $-12 < M_{\rm V} < -10$, $s < 30$ for the dwarfs with $-10 < M_{\rm V} < -7$, and $s < 90$ for the dwarfs with $M_{\rm V} > -7$.