We present the analysis of four first overtone RR Lyrae stars observed with the Kepler space telescope , based on data obtained over nearly 2.5 yr. All four stars are found to be multiperiodic .
The strongest secondary mode with frequency f _ { 2 } has an amplitude of a few mmag , 20 - 45 times lower than the main radial mode with frequency f _ { 1 } .
The two oscillations have a period ratio of P _ { 2 } / P _ { 1 } = 0.612 - 0.632 that can not be reproduced by any two radial modes .
Thus , the secondary mode is nonradial .
Modes yielding similar period ratios have also recently been discovered in other variables of the RRc and RRd types .
These objects form a homogenous group and constitute a new class of multimode RR Lyrae pulsators , analogous to a similar class of multimode classical Cepheids in the Magellanic Clouds .
Because a secondary mode with P _ { 2 } / P _ { 1 } \sim 0.61 is found in almost every RRc and RRd star observed from space , this form of multiperiodicity must be common .
In all four Kepler RRc stars studied , we find subharmonics of f _ { 2 } at \sim 1 / 2 f _ { 2 } and at \sim 3 / 2 f _ { 2 } .
This is a signature of period doubling of the secondary oscillation , and is the first detection of period doubling in RRc stars .
The amplitudes and phases of f _ { 2 } and its subharmonics are variable on a timescale of 10 - 200 d. The dominant radial mode also shows variations on the same timescale , but with much smaller amplitude .
In three Kepler RRc stars we detect additional periodicities , with amplitudes below 1 mmag , that must correspond to nonradial g -modes .
Such modes never before have been observed in RR Lyrae variables .