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 the1150-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 \pm 0.0003 M _ { \sun } .
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 M _ { \sun } .
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 .