Non-radial modes in classical Cepheids. What to look for in spectroscopy?

Recent photometric observations of first-overtone classical Cepheids and RR Lyrae stars have led to the discovery of additional frequencies showing a characteristic period ratio of 0.60-0.65 with the main pulsation mode. In a promising model proposed by Dziembowski (2016), these signals are suggested to be due to the excitation of non-radial modes with degrees 7, 8 and 9 (Cepheids) or 8 and 9 (RR Lyrae). Such modes usually have low amplitudes in photometric data. Spectroscopic time series offer an unexplored and promising way forward. We simulated time series of synthetic line profiles for a representative first-overtone classical Cepheid model and added a low-amplitude non-radial mode. We studied sets of spectra with dense sampling and without noise, so-called 'perfect' cases, as well as more realistic samplings and signal-to-noise levels. Besides the first-overtone mode and the non-radial mode, also the harmonics of both modes and combination signals were often detected, but a sufficiently high sampling and signal-to-noise ratio prove essential. The amplitudes of the non-radial mode and its harmonic depend on the azimuthal order $m$. The inclination is also an important factor determining the detectability of the non-radial mode and/or its harmonic. We compared the results obtained for the predicted high degrees with those for lower-degree modes. Finally, we studied the sampling requirements for detecting the non-radial mode. Our findings can be used to plan a spectroscopic observing campaign tailored to uncover the nature of these mysterious modes.