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The recently discovered subdwarf B (sdB) pulsator KIC11558725 features a richg-mode frequency spectrum, with a few low-amplitude p-modes at short periods,and is a promising target for a seismic study aiming to constrain the internalstructure of this star, and of sdB stars in general.  We have obtained ground-based spectroscopic Balmer-line radial-velocitymeasurements of KIC11558725, spanning the 2010 and 2011 observing seasons. Fromthese data we have discovered that KIC11558725 is a binary with period P=10.05d, and that the radial-velocity amplitude of the sdB star is 58 km/s.Consequently the companion of the sdB star has a minimum mass of 0.63 M\odot,and is therefore most likely an unseen white dwarf.  We analyse the near-continuous 2010-2011 Kepler light curve to reveal orbitalDoppler-beaming light variations at the 238 ppm level, which is consistent withthe observed spectroscopic orbital radial-velocity amplitude of the subdwarf.We use the strongest 70 pulsation frequencies in the Kepler light curve of thesubdwarf as clocks to derive a third consistent measurement of the orbitalradial-velocity amplitude, from the orbital light-travel delay.  We use our high signal-to-noise average spectra to study the atmosphericparameters of the sdB star, deriving Teff = 27 910K and log g = 5.41 dex, andfind that carbon, nitrogen and oxygen are underabundant relative to the solarmixture.  Furthermore, we extract more than 160 significant frequencies from the Keplerlight curve. We investigate the pulsation frequencies for expected periodspacings and rotational splittings. We find period-spacing sequences ofspherical-harmonic degrees \ell=1 and \ell=2, and we associate a large fractionof the g-modes in KIC11558725 with these sequences. From frequency splittingswe conclude that the subdwarf is rotating subsynchronously with respect to theorbit.

Three ways to solve the orbit of KIC11558725: a 10 day beaming sdB+WD binary with a pulsating subdwarf