Equidistant frequency triplets in pulsating stars: The Combination Mode Hypothesis

Multiplet structures are a common feature in pulsating stars, and can be the consequence of rotational splitting, mode interaction or sinusoidal amplitude variations. In this paper we examine the phenomenon of (nearly) equidistant triplets, which are unlikely to be caused by rotational splitting, in different types of pulsating stars: a Delta Scuti variable (1 Mon), an RR Lyrae variable (RR Lyr) and a short-period Cepheid (V743 Lyr). We examine the hypothesis that one of the modes forming the triplet results from a combination of the other two modes. The analyses were carried out on recent data sets by using multiple-frequency analyses and statistics with the package PERIOD04. In particular, the small departures from equidistance were calculated for the three selected stars. For the Delta Scuti variable 1 Mon, the departure from equidistance is only 0.000079 +- 0.000001 c/d (or 0.91 +- 0.01 nHz). For 1 Mon the Combination Mode Hypothesis with a mode excited by resonance is the most probable explanation. For the star RR Lyr, the hypothesis of resonance through a combination of modes should be considered. The results for the best-studied cepheid with a Blazhko period (V743 Lyr) are inconclusive because of an unfavorable period of 1.49d and insufficient data.Comment: 6 pages, 1 figure, accepted for publication in Astronomy and Astrophysic

Close frequency pairs in Delta Scuti stars

The majority of the well-studied Delta Scuti stars show frequency pairs in the power spectra with frequency separations less than 0.06 c/d(0.7 microHz) as well as amplitude variability. We examine the interpretation in terms of separate excited stellar pulsation modes,single modes with variable amplitudes, and observational problems. The variable-phase technique, which examines the phase jumps near the times of minimum amplitude of an assumed single frequency, is applied to the extensive data of the star BI CMi, which shows some of the most extreme behavior. The following results are found for the 5 features in the power spectrum which could be explained as single modes with variable amplitudes or as double modes: for three features it can be shown that these are indeed pairs of separate pulsation modes beating with each other: at times of minimum amplitude the phase jumps are observed and both the observed amplitude and phase variations can be predicted correctly by assuming two separate modes of nearly equal frequencies. Artifacts caused by observational error,insufficient frequency resolution or variable amplitudes can be ruled out. A fourth pair has a probable origin in two excited modes, while a 5th case is inconclusive due to long time scales of variability and small amplitudes.The existence of close frequencies need to be taken into account in planning the lengths of earth-based as well as space campaigns so that sufficient frequency resolution is obtained. Possible reasons for the existence of close frequencies in Delta Scuti stars are considered.They include the dense frequency spacing caused by the presence of mixed modes, rotational splitting as well as near-coincidence of the frequencies of modes with different l values (the so-called Small Spacing).Comment: 9 Pages, 5 Figures, Accepted by Astronomy and Astrophysics; alternative Download from ftp://ftp.deltascuti.net/pub/CloseFrequencies.pd

Amplitude variability and multiple frequencies in 44 Tau: 2000 - 2006

This study has three principal aims: (i) to increase the number of detected pulsation modes of 44 Tau, especially outside the previously known frequency ranges, (ii) to study the amplitude variability and its systematics, and (iii) to examine the combination frequencies. During the 2004/5 and 2005/6 observing seasons, high-precision photometry was obtained with the Vienna Automatic Photoelectric Telescope in Arizona during 52 nights. Together with previous campaigns, a data base from 2000 to 2006 was available for multifrequency analyses. Forty-nine pulsation frequencies are detected, of which 15 are independent pulsation modes and 34 combination frequencies or harmonics. The newly found gravity mode at 5.30 c/d extends the known frequency range of instability. Strong amplitude variability from year to year is found for the \ell = 1 modes, while the two radial modes have essentially constant amplitudes. Possible origins of the amplitude variability of the \ell = 1 modes, such as precession of the pulsation axis, beating and resonance effects are considered. The amplitudes of the combination frequencies, f_i + f_j, mirror the variations in the parent modes. The combination parameter, which relates the amplitudes of the combination frequencies to those of the parent modes, is found to be different for different parents.Comment: 10 pages, 8 figures, 4 tables, accepted for publication in A&

Pulsation of EE Cam

EE Cam is a previously little studied Delta Scuti pulsator with amplitudes between those of the HADS (High-Amplitude Delta Scuti stars) group and the average low-amplitude pulsators. Since the size of stellar rotation determines both which pulsation modes are selected by the star as well as their amplitudes, the star offers a great opportunity to examine the astrophysical connections. Extensive photometric measurements covering several months were carried out. 15 significant pulsation frequencies were extracted. The dominant mode at 4.934 cd$^{-1}$ was identified as a radial mode by examining the phase shifts at different wavelengths. Medium-dispersion spectra yielded a $v\sin i$ value of $40 \pm 3$ km s$^{-1}$. This shows that EE Cam belongs to the important transition region between the HADS and normal Delta Scuti stars.Comment: 13 pages, 3 figures, 3 table

Detection of high-degree prograde sectoral mode sequences in the A-star KIC 8054146?

This paper examines the 46 frequencies found in the Delta Sct star KIC 8054146 involving a frequency spacing of exactly 2.814 c/d (32.57 microHz), which is also a dominant low-frequency peak near or equal to the rotational frequency. These 46 frequencies range up to 146 c/d. Three years of Kepler data reveal distinct sequences of these equidistantly spaced frequencies, including the basic sequence and side lobes associated with other dominant modes (i.e., small amplitude modulations). The amplitudes of the basic sequence show a high-low pattern. The basic sequence follows the equation fm = 2.8519 + m * 2.81421 c/d with m ranging from 25 to 35. The zero-point offset and the lack of low-order harmonics eliminate an interpretation in terms of a Fourier series of a non-sinusoidal light curve. The exactness of the spacing eliminates high-order asymptotic pulsation. The frequency pattern is not compatible with simple hypotheses involving single or multiple spots, even with differential rotation. The basic high-frequency sequence is interpreted in terms of prograde sectoral modes. These can be marginally unstable, while their corresponding low-degree counterparts are stable due to stronger damping. The measured projected rotation velocity (300 km/s) indicates that the star rotates with app. 70% of the Keplerian break-up velocity. This suggests a near equator-on view. We qualitatively examine the visibility of prograde sectoral high-degree g-modes in integrated photometric light in such a geometrical configuration and find that prograde sectoral modes can reproduce the frequencies and the odd-even amplitude pattern of the high-frequency sequence