  The decay of the martian atmosphere - which is dominated by carbon dioxide -
is a component of the long-term environmental change on Mars from a climate
that once allowed rivers to flow to the cold and dry conditions of today. The
minimum size of craters serves as a proxy for palaeopressure of planetary
atmospheres, because thinner atmospheres permit smaller objects to reach the
surface at high velocities and form craters. The Aeolis Dorsa region near Gale
crater on Mars contains a high density of preserved ancient craters interbedded
with river deposits and thus can provide constraints on atmospheric density
around the time of fluvial activity. Here we use high-resolution orthophotos
and digital terrain models from the Mars Reconnaissance Orbiter to identify
ancient craters in Aeolis Dorsa that date to about 3.6 Gyr ago and compare
their size distribution with models of atmospheric filtering of impactors. We
obtain an upper limit of 0.9$\pm$0.1 bar, rising to 1.9$\pm$0.2 bar if rimmed
circular mesas - interpreted to be erosionally-resistant fills of floors of
impact craters - are excluded. We assume target properties appropriate for
desert alluvium: if sediment had rock-like rock-mass strength similar to
bedrock at the time of impact, the upper limit increases by a factor of up to
two. If Mars did not have a stable multibar atmosphere at the time that the
rivers were flowing - as suggested by our results - then the warm and wet
CO2/H2O greenhouse is ruled out, and long-term average temperatures were most
likely below freezing.
