PTF09dav is a peculiar subluminous type Ia supernova (SN) discovered by
the Palomar Transient Factory (PTF). Spectroscopically, it appears
superficially similar to the class of subluminous SN1991bg-like SNe, but
it has several unusual features which make it stand out from this
population. Its peak luminosity is fainter than any previously
discovered SN1991bg-like SN Ia (M_B -15.5), but without the unusually
red optical colors expected if the faint luminosity were due to
extinction. The photospheric optical spectra have very unusual strong
lines of Sc II and Mg I, with possible Sr II, together with stronger
than average Ti II and low velocities of ~6000 km/s. The host galaxy of
PTF09dav is ambiguous. The SN lies either on the extreme outskirts
(~41kpc) of a spiral galaxy, or in an very faint (M_R>-12.8) dwarf
galaxy, unlike other 1991bg-like SNe which are invariably associated
with massive, old stellar populations. PTF09dav is also an outlier on
the light-curve-width--luminosity and color--luminosity relations
derived for other sub-luminous SNe Ia. The inferred 56Ni mass is small
(0.019+/-0.003Msun), as is the estimated ejecta mass of 0.36Msun. Taken
together, these properties make PTF09dav a remarkable event. We discuss
various physical models that could explain PTF09dav. Helium shell
detonation or deflagration on the surface of a CO white-dwarf can
explain some of the features of PTF09dav, including the presence of Sc
and the low photospheric velocities, but the observed Si and Mg are not
predicted to be very abundant in these models. We conclude that no
single model is currently capable of explaining all of the observed
signatures of PTF09dav.