Nonradial oscillations in classical Cepheids: the problem revisited

We analyse the presence of nonradial oscillations in Cepheids, a problem which has not been theoretically revised since the work of Dziembowsky (1977) and Osaki (1977). Our analysis is motivated by a work of Moskalik et al. (2004) which reports the detec tion of low amplitude periodicities in a few Cepheids of the large Magellanic cloud. These newly discovered periodicities were interpreted as nonradial modes.} {Based on linear nonadiabatic stability analysis, our goal is to reanalyse the presence and stability of nonradial modes, taking into account improvement in the main input phys ics required for the modelling of Cepheids.} {We compare the results obtained from two different numerical methods used to solve the set of differential equations: a matrix method and the Ricatti method.} {We show the limitation of the matrix method to find low order p-modes ($l<6$), because of their dual character in evolved stars such as Cepheids. For higher order p-modes, we find an excellent agreement between the two methods.} {No nonradial instability is found below $l=5$, whereas many unstable nonradial modes exist for higher orders. We also find that nonradial modes remain unstable, even at hotter effective temperatures than the blue edge of the Cepheid instability strip, where no radial pulsations are expected.