  V407 Vul (= RXJ1914.4+2457) shows pulsations in X-ray flux on a period of 9.5
minutes, which have been ascribed to accretion onto a magnetic white dwarf,
with the X-ray pulses seen as the accreting pole moves into and out of view.
The X-ray flux drops to zero between pulses, and no other periods are seen,
suggesting that V407 Vul is a type of system known as a ``polar'' in which the
white dwarf has a strong enough field to lock to the orbit of its companion. If
so, then V407 Vul has the shortest orbital period known for any binary star.
However, unlike other polars, V407 Vul shows neither polarization nor line
emission. In this paper we propose that V407 Vul is the first example of a new
type of X-ray emitting binary in which the mass transfer stream directly hits a
non-magnetic white dwarf as a result of the very compact orbit. Our model
naturally explains the X-ray and optical pulsations, as well as the absence of
polarization and line emission. We show that direct impact will occur for
plausible masses of the accreting star and its companion, e.g. M1 ~ 0.5, M2 ~
0.1 Msun. In our model V407 Vul retains its status as the binary star with the
shortest known orbital period, and is therefore a strong source of
low-frequency gravitational waves. V407 Vul is representative of an early phase
of the evolution of the AM CVn class of binary stars and will evolve into the
normal disc-accretion phase on a timescale of 10^6 to 10^7 yr. The existence of
V407 Vul supports the double-degenerate route for the formation of AM CVn
stars.
