HD 4539 ( alias PG 0044+097 or EPIC 220641886 ) 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 ( K 2 ) mission .
We use the K 2 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 HD 4539 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 HD 4539 has a rotation period longer than the K 2 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 HD 4539 , with amplitudes as low as a few ppm .
A large fraction of these modes can be identified and for \sim 29 % of them we obtain a unique and robust identification corresponding to l \leq 8 .
Our study includes also a new determination of the atmospheric parameters of the star .
From low-resolution spectroscopy we obtain T _ { \mathrm { eff } } =22,800 \pm 160 K , \log g =5.20 \pm 0.02 and log ( N ( He ) / N ( H ) ) =–2.34 \pm 0.05 .
By fitting the SED we obtain T _ { \mathrm { eff } } =23,470 ^ { +650 } _ { -210 } K , R _ { \star } =0.26 \pm 0.01 { \mathrm { R } } _ { \odot } and M _ { \star } =0.40 \pm 0.08 { \mathrm { M } } _ { \odot } .
Moreover , from 11 high-resolution spectra we see the radial velocity variations caused by the stellar pulsations , with amplitudes of \approx 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 \sim 300 days .