  HD4539 (alias PG0044+097 or EPIC220641886) is a bright (V=10.2) long-period
V1093 Her-type subdwarf B (sdB) pulsating star that was observed by the Kepler
spacecraft in its secondary (K2) mission. We use the K2 light curve (78.7 days)
to extract 169 pulsation frequencies, 124 with a robust detection. Most of
these frequencies are found in the low-frequency region typical of gravity
(g-)modes, but some higher frequencies corresponding to pressure (p-)modes are
also detected. Therefore HD4539 is a hybrid pulsator and both the deep and
surface layers of the star can potentially be probed through asteroseismology.
The lack of any frequency splitting in its amplitude spectrum suggests that
HD4539 has a rotation period longer than the K2 run and/or that it is seen
pole-on. From asymptotic period spacing we see many high-degree modes, up to
l=12, in the spectrum of HD4539, with amplitudes as low as a few ppm. A large
fraction of these modes can be identified and for ~29% of them we obtain a
unique and robust identification corresponding to l<=8. Our study includes also
a new determination of the atmospheric parameters of the star. From
low-resolution spectroscopy we obtain Teff=22,800+-160 K, logg=5.20+-0.02 and
log(N(He)/N(H))=-2.34+-0.05. By fitting the SED we obtain Teff=23,470+650-210
K, R_star=0.26+-0.01 Rsun and M_star=0.40+-0.08 Msun. Moreover, from 11
high-resolution spectra we see the radial velocity variations caused by the
stellar pulsations, with amplitudes of ~150~m/s for the main modes, and we can
exclude the presence of a companion with a minimum mass higher than a few
Jupiter masses for orbital periods below ~300 days.
