[Paper Review] Discovery of Peculiar Double-Mode Pulsations and Period Doubling in KEPLER RRc Variables

P. Moskalik, R. Smolec+7 more|arXiv (Cornell University)|Aug 21, 2012

Stellar, planetary, and galactic studies1 references9 citations

TL;DR

This study analyzes Kepler Long Cadence photometry of four RRc stars and discovers unusual double-mode pulsations with a period ratio of ~0.63, accompanied by subharmonics at ~1/2f₂ and 3/2f₂, indicating period doubling. This marks the first detection of period doubling in RRc variables, establishing a new class of multiperiodic pulsators with nonradial modes, and extends the phenomenon to overtone RR Lyrae stars and Cepheids.

ABSTRACT

We analyzed the Long Cadence photometry of 4 first overtone RR Lyr-type stars (RRc stars) observed by the KEPLER telescope. All studied variables are multiperiodic. The strongest secondary peak appears for f_2/f_1 = 1.58-1.63, or P_2/P_1 = 0.61-0.63. In each star we detect at least one subharmonic of f_2, either at ~1/2 f_2 or at ~3/2 f_2. The presence of subharmonics is a characteristic signature of a period doubling.

Motivation & Objective

• To investigate multiperiodic pulsation behavior in first-overtone RRc stars observed by the Kepler space telescope.
• To determine whether period doubling—previously seen in RRab and BL Her stars—occurs in RRc variables.
• To identify the nature of secondary pulsation modes with unusual period ratios (~0.60–0.63) and their harmonic/subharmonic relationships.
• To explore the implications of these findings for pulsation theory, particularly the role of nonradial modes in RRc stars.

Proposed method

• Conducted frequency analysis using the standard consecutive prewhitening technique on Kepler Long Cadence (29.4 min) photometry from quarters Q0–Q2.
• Analyzed four RRc stars with a total observation baseline of 138 days, focusing on frequency spectra and combination tones.
• Identified dominant frequencies f₁ (~3.715 c/d) and f₂ (~5.879 c/d), with period ratio P₂/P₁ ≈ 0.6319.
• Detected subharmonics at ~1/2f₂ and ~3/2f₂, confirming period doubling via the presence of f₃ ≈ 2.937 c/d.
• Confirmed that all remaining signals were combination frequencies, not independent modes.
• Compared results with known cases in RRab stars, BL Her stars, and Cepheids to assess consistency and novelty.

Experimental results

Research questions

• RQ1 Do RRc stars exhibit period doubling similar to RRab and BL Her stars?
• RQ2 What is the origin and nature of the secondary pulsation mode with a period ratio of ~0.63 relative to the fundamental first overtone?
• RQ3 Are the detected subharmonics at ~1/2f₂ and ~3/2f₂ indicative of a nonlinear pulsation mechanism such as period doubling?
• RQ4 How do the observed period ratios and mode frequencies compare to theoretical expectations for radial and nonradial overtones?
• RQ5 Is the secondary mode f₂ consistent with a nonradial oscillation, given its frequency placement between the third and fourth radial overtones?

Key findings

• Four RRc stars in the Kepler field exhibit double-mode pulsations with a period ratio P₂/P₁ ≈ 0.6319, indicating a stable nonlinear pulsation state.
• The secondary frequency f₂ (~5.879 c/d) lies between the third and fourth radial overtones, implying it is a nonradial mode.
• Subharmonics at f₃ ≈ 2.937 c/d (~1/2f₂) and ~3/2f₂ are clearly detected, confirming period doubling as the underlying mechanism.
• The presence of combination frequencies in the Fourier spectrum confirms that the observed signals are not independent modes but harmonics and subharmonics of f₂.
• These findings extend period doubling to RRc variables, making them the third class of pulsators—alongside RRab and BL Her stars—where this phenomenon has been observed.
• The same period ratios (~0.60–0.63) are found in nine other RR Lyrae-type stars (including AQ Leo, Om Cen, and LMCRR), suggesting a common physical origin across different pulsation classes.