We use a long (300 ksec), continuous Suzaku X-ray observation of the active
nucleus in NGC1365 to investigate the structure of the circumnuclear BLR clouds
through their occultation of the X-ray source. The variations of the absorbing
column density and of the covering factor indicate that the clouds surrounding
the black hole are far from having a spherical geometry (as sometimes assumed),
instead they have a strongly elongated and cometary shape, with a dense head
(n=10^11 cm^-3) and an expanding, dissolving tail. We infer that the cometary
tails must be longer than a few times 10^13 cm and their opening angle must be
smaller than a few degrees. We suggest that the cometary shape may be a common
feature of BLR clouds in general, but which has been difficult to recognize
observationally so far. The cometary shape may originate from shocks and
hydrodynamical instabilities generated by the supersonic motion of the BLR
clouds into the intracloud medium. As a consequence of the mass loss into their
tail, we infer that the BLR clouds probably have a lifetime of only a few
months, implying that they must be continuously replenished. We also find a
large, puzzling discrepancy (two orders of magnitude) between the mass of the
BLR inferred from the properties of the absorbing clouds and the mass of the
BLR inferred from photoionization models; we discuss the possible solutions to
this discrepancy.Comment: Accepted for publication in A&A. 11 pages, 9 figure