The Philae lander of the Rosetta mission, aimed at the in situ investigation of comet 67P/C-G, was deployed to the surface of the comet nucleus on 12 Nov 2014 at 2.99 AU heliocentric distance. The Dust Impact Monitor (DIM) as part of the Surface Electric Sounding and Acoustic Monitoring Experiment (SESAME) on the lander employed piezoelectric detectors to detect the submillimetre- and millimetre-sized dust and ice particles emitted from the nucleus. We determine the upper limit of the ambient flux of particles in the measurement range of DIM based on the measurements performed with the instrument during Philaes descent to its nominal landing site Agilkia at distances of about 22 km, 18 km, and 5 km from the nucleus barycentre and at the final landing site Abydos. The geometric factor of the DIM sensor is calculated assuming an isotropic ambient flux of the submillimetre- and millimetre-sized particles. For the measurement intervals when no particles were detected the maximum true impact rate was calculated by assuming Poisson distribution of the impacts, and it was given as the detection limit at a 95% confidence level. Based on measurements performed with DIM, the upper limit of the flux of particles in the measurement range of the instrument was of the order of $10^{-8}-10^{-7}m^{-2}s^{-1}sr^{-1}$ during descent and $1.6cdot10^{-9}m^{-2}s^{-1}sr^{-1}$ at Abydos on 13 and 14 Nov 2014. Considering particle speeds below escape velocity, the upper limit for the volume density of particles in the measurement range of DIM was constrained to $10^{-11}m^{-3}-10^{-12}m^{-3}$. Results of the calculations performed with the GIPSI tool on the expected particle fluxes during the descent of Philae were compatible with the non-detection of compact particles by the DIM instrument.
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