Observations of ongoing HI accretion in nearby galaxies have only identified about 10% of the needed fuel to sustain star formation in these galaxies. Most of these observations have been conducted using interferometers and may have missed lower column density, diffuse, HI gas that may trace the missing 90% of gas. Such gas may represent the so-called cold flows predicted by current theories of galaxy formation to have never been heated above the virial temperature of the dark matter halo. As a first attempt to identify such cold flows around nearby galaxies and complete the census of HI down to N(HI)~10^18 cm^-2, I used the Robert C. Byrd Green Bank Telescope (GBT) to map the circumgalactic (r < 100-200 kpc) HI environment around NGC 2997 and NGC 6946. The resulting GBT observations cover a four square degree area around each galaxy with a 5-sigma detection limit of N(HI)~10^18 cm^-2 over a 20 km/s linewidth. This project complements absorption line studies, which are well-suited to the regime of lower N(HI). Around NGC 2997, the GBT HI data reveal an extended HI disk and all of its surrounding gas-rich satellite galaxies, but no filamentary features. Furthermore, the HI mass as measured with the GBT is only 7% higher than past interferometric measurements. After correcting for resolution differences, the HI extent of the galaxy is 23% larger at the N(HI)~1.2x10^18 cm^-2 level as measured by the GBT. On the other hand, the HI observations of NGC 6946 reveal a filamentary feature apparently connecting NGC 6946 with its nearest companions. This HI filament has N(HI)~10^18 cm^-2 and a FWHM of 55+-5 km/s and was invisible in past interferometer observations. The properties of this filament are broadly consistent with being a cold flow or debris from a past tidal interaction between NGC 6946 and its satellites.
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