Observed H i accretion around nearby galaxies can only account for a fraction of the gas supply needed to sustain the currently observed star formation rates .
It is possible that additional accretion happens in the form of low column density cold flows , as predicted by numerical simulations of galaxy formation .
To contrain the presence and properties of such flows , we present deep H i observations obtained with the NRAO Green Bank Telescope of an area measuring 4 ^ { \circ } \times 4 ^ { \circ } around NGC 2403 .
These observations , with a 5 \sigma detection limit of 2.4 \cdot 10 ^ { 18 } cm ^ { -2 } over a 20 km s ^ { -1 } linewidth , reveal the presence of a low-column density , extended cloud outside the main H i disk , about 17 ^ { \prime } ( \sim 16 kpc or \sim 2 R _ { 25 } ) to the NW of the center of the galaxy .
The total H i mass of the cloud is 6.3 \cdot 10 ^ { 6 } M _ { \odot } , or 0.15 percent of the total H i mass of NGC 2403 .
The cloud is associated with an 8-kpc anomalous-velocity H i filament in the inner disk , previously observed in deep VLA observations by Fraternali et al .
( 2001 , 2002 ) .
We discuss several scenarios for the origin of the cloud , and conclude that it is either accreting from the intergalactic medium , or is the result of a minor interaction with a neigbouring dwarf galaxy .