Three ways to solve the orbit of KIC 11 558 725: a 10-day beaming sdB+WD binary with a pulsating subdwarf

The recently discovered subdwarf B (sdB) pulsator KIC 11 558 725 is one of the 16 pulsating sdB stars detected in the Kepler field. It features a rich g-mode frequency spectrum, with a few low-amplitude p-modes at short periods. This makes it a promising target for a seismic study aiming to constrain the internal structure of this star, and of sdB stars ingeneral. We have obtained ground-based spectroscopic radial-velocity measurements of KIC 11 558 725 based on low-resolution spectra in the Balmer-line region, spanning the 2010 and 2011 observing seasons. From these data we have discovered that KIC 11 558 725 is a binary with period P = 10.05 d, and that the radial-velocity amplitude of the sdB star is 58 km s-1. Consequently the companion of the sdB star has a minimum mass of 0.63 M⊙, and is therefore most likely an unseen white dwarf. We analyse the near-continuous 2010–2011 Kepler light curve to reveal the orbital Doppler-beaming effect, giving rise to light variations at the 238 ppm level, which is consistent with the observed spectroscopic orbital radial-velocity amplitude of the subdwarf. We use the strongest 70 pulsation frequencies in the Kepler light curve of the subdwarf as clocks to derive a third consistent measurement of the orbital radial-velocity amplitude, from the orbital light-travel delay. The orbital radius asdBsini = 11.5 R⊙ gives rise to a light-travel time delay of 53.6 s, which causes aliasing and lowers the amplitudes of the shortest pulsation frequencies, unless the effect is corrected for. We use our high signal-to-noise average spectra to study the atmospheric parameters of the sdB star, deriving Teff = 27 910 K andlog g = 5.41 dex, and find that carbon, nitrogen and oxygen are underabundant relative to the solar mixture. Furthermore, we analyse the Kepler light curve for its pulsational content and extract more than 160 significant frequencies.We investigate the pulsation frequencies for expected period spacings and rotational splittings. We find period-spacing sequences of spherical-harmonic degrees ℓ = 1 and ℓ = 2, and we associate a large fraction of the g-modes in KIC 11 558 725 with these sequences. From frequency splittings we conclude that the subdwarf is rotating subsynchronously with respect to the orbit