The first detection of the period doubling phenomenon is reported in the Kepler RR Lyrae stars RR Lyr, V808 Cyg and V355 Lyr. Interestingly, all these pulsating stars show Blazhko modulation. The period doubling manifests itself as alternating maxima and minima of the pulsational cycles in the light curve, as well as through the appearance of half‐integer frequencies located halfway between the main pulsation period and its harmonics in the frequency spectrum. The effect was found to be stronger during certain phases of the modulation cycle. We were able to reproduce the period‐doubling bifurcation in our non‐linear RR Lyrae models computed by the Florida–Budapest hydrocode. This enabled us to trace the origin of this instability in RR Lyrae stars to a resonance, namely a 9:2 resonance between the fundamental mode and a high‐order (ninth) radial overtone showing strange‐mode characteristics. We discuss the connection of this new type of variation to the mysterious Blazhko effect and argue that it may give us fresh insights into solving this century‐old enigma.
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 cannot 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 ∼ 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 ∼ 1/2f 2 and at ∼ 3/2f 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.
To maximize the number of planet detections, current microlensing follow-up observations are focusing on high-magnification events which have a higher chance of being perturbed by central caustics. In this paper, we investigate the properties of central caustics and the perturbations induced by them. We derive analytic expressions of the location, size, and shape of the central caustic as a function of the star-planet separation, $s$, and the planet/star mass ratio, $q$, under the planetary perturbative approximation and compare the results with those based on numerical computations. While it has been known that the size of the planetary caustic is \propto \sqrt{q}, we find from this work that the dependence of the size of the central caustic on $q$ is linear, i.e., \propto q, implying that the central caustic shrinks much more rapidly with the decrease of $q$ compared to the planetary caustic. The central-caustic size depends also on the star-planet separation. If the size of the caustic is defined as the separation between the two cusps on the star-planet axis (horizontal width), we find that the dependence of the central-caustic size on the separation is \propto (s+1/s). While the size of the central caustic depends both on $s$ and q, its shape defined as the vertical/horizontal width ratio, R_c, is solely dependent on the planetary separation and we derive an analytic relation between R_c and s. Due to the smaller size of the central caustic combined with much more rapid decrease of its size with the decrease of q, the effect of finite source size on the perturbation induced by the central caustic is much more severe than the effect on the perturbation induced by the planetary caustic. Abridged.Comment: 5 pages, 4 figures, ApJ accepte
Through time-series CCD photometry of the metal-poor globular cluster M53 we have discovered eight new SX Phoenicis-type stars (labeled '' SXP1 '' to '' SXP8 ''). All the new SX Phoenicis stars are located in the blue straggler star region of the color-magnitude diagram of M53. One of these stars (SXP2) is found to have very closely separated pulsation frequencies: f 1 /f 2 = 0.9595, where f 1 and f 2 are the primary and secondary frequencies, respectively. This may be due to excitation of nonradial modes. Six of these SX Phoenicis stars are considered to be pulsating in the fundamental mode. They show a tight linear correlation between the period and luminosity. We derive a period-luminosity relation for the fundamental mode for the period range of À1.36 < log P(days) < À1.15: hVi = À3.010(AE0.262) log P + 15.310(AE0.048) with an rms scatter of 0.038, corresponding to hM V i = À3.010 log P À 1.070 for an adopted distance modulus of (m À M) V = 16.38.
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