%0 Journal Article %T Asteroseismology of KIC 11754974: a high-amplitude SX Phe pulsator in a 343-day binary system %A S. J. Murphy %A A. Pigulski %A D. W. Kurtz %A J. C. Suarez %A G. Handler %A L. A. Balona %A B. Smalley %A K. Uytterhoeven %A R. Szabo %A A. O. Thygesen %A V. Elkin %A M. Breger %A A. Grigahcene %A J. A. Guzik %A J. M. Nemec %A J. Southworth %J Physics %D 2013 %I arXiv %R 10.1093/mnras/stt587 %X The candidate SX Phe star KIC 11754974 shows a remarkably high number of combination frequencies in the Fourier amplitude spectrum: 123 of the 166 frequencies in our multi-frequency fit are linear combinations of independent modes. Predictable patterns in frequency spacings are seen in the Fourier transform of the light curve. We present an analysis of 180 d of short-cadence Kepler photometry and of new spectroscopic data for this evolved, late A-type star. We infer from the 1150-d, long-cadence light curve, and in two different ways, that our target is the primary of a 343-d, non-eclipsing binary system. According to both methods, the mass function is similar, f(M)=0.0207 +/- 0.0003 Msun. The observed pulsations are modelled extensively, using separate, state-of-the-art, time-dependent convection (TDC) and rotating models. The models match the observed temperature and low metallicity, finding a mass of 1.50-1.56 Msun. The models suggest the whole star is metal-poor, and that the low metallicity is not just a surface abundance peculiarity. This is the best frequency analysis of an SX Phe star, and the only Kepler \delta\ Sct star to be modelled with both TDC and rotating models. %U http://arxiv.org/abs/1304.1543v2