  We present a new derivation of the star formation history (SFH) of the dSph
galaxy Fornax in two central regions, characterised by unprecedented precision
and age resolution. It reveals that star formation has proceeded in sharp
bursts separated by periods of low-level or quiescent activity. The SFH was
derived through colour-magnitude diagram (CMD) fitting of two extremely deep
Hubble Space Telescope CMDs, sampling the centre and one core radius. The
attained age resolution allowed us to single out a major star formation episode
at early times, a second strong burst $4.6\pm0.4$ Gyr ago and recent
intermittent episodes $\sim2-0.2$ Gyr ago. Detailed testing with mock stellar
populations was used to estimate the duration of the main bursts and study the
occurrence of low-level star formation between them. The SFHs in both regions
show common features, with activity at the same epochs and similar
age-metallicity relationship. However, clear indications of a spatial gradient
were also found, with mean age increasing with radius and star formation
episodes being more prolonged in the centre. While some galaxy evolution models
predict bursty SFHs in dwarf galaxies and thus a secular origin of the observed
SFH cannot be excluded in Fornax, other evidence points to possible mergers or
interactions as the cause of its bursty SFH. In particular, we calculated the
Fornax orbit relative to the closest dwarfs and the Milky Way and observed a
correspondence between the main intermediate-age and young events and
peri-passages of Fornax around the Milky Way, possibly indicating
tidally-induced star formation.
