tokens: 2 sequences, respectively. This results in all periodicities being identified with spacings similar to other Kepler -observed g-mode pulsators (Reed et al. 2011 ). Figure 4. Period spacing sequences indicated by the KS test. The solid blue (green) line indicates the l = 1 (2) period spacing sequence with the dashed line the overtone alias. Figure 5. Period transform of PG 1142 showing evenly spaced periods. Short blue (green) lines indicate the asymptotic l = 1 (2) sequence with full-length lines indicating those which match detected periodicities. The horizontal line indicates 4.35σ for reference. 3.2 Binary analysis PG 1142 has proven to be a very exciting target. The detection of fA and fB prompted follow-up spectroscopic observations (described in Section 2.1 ) to search for velocity variations, which were subsequently detected. Fitting the 24 RVs (in Table 1 ), and assuming a circular orbit, gives an orbital solution period of 0.541089 ± 0.000020 d (21.39 μHz), amplitude of 85 ± 2 km s −1 , and phase of BJD = 2457099.74105 ± 0.00204 (top panel of Fig. 6 ). The eccentricity was subsequently fitted at 0.079 ± 0.028, showing it is negligible for our calculations. Using the values of K = 85 ± 2 km s −1 and P = 0.541 d from spectroscopy, the sdB canonical mass M1=0.47 and assuming i = 90 o , we get the minimum values for M 2 of 0.26 M ⊙ and for the orbital separation a = a 1 + a 2 = 2.52 R ⊙ . Of course we know this is not the inclination as no eclipses are evident in the light curve. Figure 6. Velocity and photometric data folded over the orbital period. The K2 data have been phase-binned into 72 bins with 1σ error bars shown. We attempted several phase-folding and binning combinations of the photometry to improve the period and phase, however the thruster firings, at roughly every six hours, and pulsations decrease the accuracy, and so the RV data are better for constraining the period. Still, the photometry show evidence of two-component variations, occurring at similar levels, in agreement with the FT. From the phasing of the variations, we can deduce the sources. A reflection-effect companion in the binary would produce a reflection-effect maximum, which would occur during a Doppler boosting zero-point (halfway between maximum and minimum) or an ellipsoidal-effect minimum. A Doppler boosting maximum would occur during an ellipsoidal-variable maximum. Figs 7 and 8 show the results of two-component fits to the folded light curve (described below). The phasing indicates that the components are Doppler boosting and ellipsoidal variations. These two components indicate that PG 1142 is most likely an sdB+WD binary. Figure 7. Orbital elements removed from the light curve. Top panel shows original folded and binned light curve. Orbital fits are indicated by lines with green being the combined fit, blue the ellipsoidal deformation, and red the Doppler boosting. Middle panel shows the Doppler-corrected light curve (with ellipsoidal deformation
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