Hubble Deep Field Constraint on Baryonic Dark Matter

We use a new technique to search for faint red stars in the Hubble Deep Field (HDF) imaged by the Wide Field Camera (WFC2) on the {\it Hubble Space Telescope}. We construct a densely sampled stellar light profile from a set of undersampled images of bright stars in a low-latitude field. Comparison of this stellar light profile to densely sampled profiles of individual objects in the HDF constructed from multiple undersampled dithers allows us to distinguish unambiguously between stars and galaxies to $I=26.3$. We find no stars with $V-I>1.8$ in the outer 90% of the volume probed. This result places strong and general constraints on the $I$ band luminosity of the constituents of the Galactic dark halo: $$M_I>15.9+\frac{5}{3}\log \left(f\frac{0.5M_{\odot }}{M}\right)(V-I>1.8),$$ where $M$ is the mass of the objects and $f$ is their density as a fraction of the local halo density, taken to be ${\rho }_0=9\times {10}^{-3}{M}_{\odot }{\text{pc}}^{-3}$. If the halo is made of white dwarfs, this limit implies that these objects have $M_V\text{gsim}18.4$ and $V-I\text{gsim}2.5$. That is, they are $\text{gsim}2$ magnitudes fainter than the end of the disk white dwarf sequence. Faint red dwarfs account for $<1\mathrm{\%}$ of the Galactic dark halo for $M_I<14$, and $<6\mathrm{\%}$ for $M_I<15$ at the 95% confidence level. The density of inter-galactic Local Group stars is at least a factor 3000 smaller than the density of local Population II stars.