  Next-generation gravitational wave observatories are expected to use
cryogenically cooled, pendulum-suspended 200 kg test mass mirrors from a
crystalline material such as crystalline silicon. During operation of the
observatories, these mirrors undergo heating due to the absorption of laser
radiation of up to a watt. Low noise cooling techniques need to be developed.
Low-pressure helium exchange gas at 5 K might contribute to the challenging
task. Here, we report the measurement of the helium accommodation coefficient
$\alpha(11\,\mathrm{K}<T< 30\,\mathrm{K})$, which is the probability that a
helium atom thermalises with a surface at a given temperature, when reflected
from it. We find $\alpha(T) > 0.7$ for temperatures < 20 K, which increases the
cooling power compared to recently used assumptions. The idea of free molecular
flow helium gas cooling is thus supported and might find application in some
observatory concepts.
