Radial Overtone Research Articles

Atomic diffusion and observations of pulsating A stars

Atomic diffusion – important in many contexts in stellar astrophysics and an important thread running through this meeting – is most spectacularly observable in the atmospheres of some A stars. The magnetic Ap stars and the non-magnetic Am stars show directly abundance anomalies caused by gravitational settling and radiative levitation. Over the last decade spectroscopic studies have begun to provide maps of abundance distributions in the magnetic Ap stars in three dimensions. Interestingly, high radial overtone p-mode pulsations in roAp stars have also given three-dimensional views of the stellar atmospheres with studies of rotational and line profile variations of pulsation amplitudes and phases. These detailed looks at the effects of microscopic atmospheric changes in the strongly non-LTE and magnetic upper atmospheric layers of Ap stars provide perhaps the most exciting challenge to atomic diffusion theory in terms of detailed explanation and prediction. Am stars were at one time thought not to pulsate because of gravitational settling of He from the He ii ionization zone that provides the κ-mechanism driving for δ Sct pulsations in A stars. In the last few years we have found with SuperWASP and Kepler observations that many Am stars do pulsate. More than half of all A stars pulsate at Kepler micromagnitude precision, yet there is a subset of A stars that truly do not pulsate at that level. Are these Am stars with the strongest signature of atomic diffusion? Is atomic diffusion the reason for the pulsational stability of these stars? The answers are not yet known.

The complex case of V445 Lyr observed with Kepler: two Blazhko modulations, a non-radial mode, possible triple mode RR Lyrae pulsation, and more

Rapid and strong changes in the Blazhko modulation of RR Lyrae stars, as they have recently been detected in high precision satellite data, have become a crucial topic in finding an explanation of the long-standing mystery of the Blazhko effect. We present here an analysis of the most extreme case detected so far, the RRab star V445 Lyr (KIC 6186029) which was observed with the Kepler space mission. V445 Lyr shows very strong cycle-to-cycle changes in its Blazhko modulation, which are caused both by a secondary long-term modulation period as well as irregular variations. In addition to the complex Blazhko modulation, V445 Lyr also shows a rich spectrum of additional peaks in the frequency range between the fundamental pulsation and the first harmonic. Among those peaks, the second radial overtone could be identified, which, combined with a metallicity estimate of [Fe/H]=-2.0 dex from spectroscopy, allowed to constrain the mass (0.55-0.65 M_sun) and luminosity (40-50 L_sun) of V445 Lyr through theoretical Petersen diagrams. A non-radial mode as well as possibly the first overtone are also excited. Furthermore, V445 Lyr shows signs of the period doubling phenomenon and a long term period change. A detailed Fourier analysis along with a study of the O-C variation of V445 Lyr is presented, and the origin of the additional peaks and possible causes of the changes in the Blazhko modulation are discussed. The results are then put into context with those of the only other star with a variable Blazhko effect for which a long enough set of high precision continuous satellite data has been published so far, the CoRoT star 105288363.

Does Kepler unveil the mystery of the Blazhko effect? First detection of period doubling in Kepler Blazhko RR Lyrae stars

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 nonlinear 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 (9th) 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 to solve this century-old enigma.

CoRoT light curves of RR Lyrae stars

The CoRoT (Convection, Rotation and planetary Transits) space mission provides a valuable opportunity to monitor stars with uninterrupted time sampling for up to 150 days at a time. The study of RR Lyrae stars, performed in the framework of the Additional Programmes belonging to the exoplanetary field, will particularly benefit from such dense, long-duration monitoring. The Blazhko effect in RR Lyrae stars is a long-standing, unsolved problem of stellar astrophysics. We used the CoRoT data of the new RR Lyrae variable CoRoT 101128793 (f0=2.119 c/d, P=0.4719296 d) to provide us with more detailed observational facts to understand the physical process behind the phenomenon. The CoRoT data were corrected for one jump and the long-term drift. We applied different period-finding techniques to the corrected timeseries to investigate amplitude and phase modulation. We detected 79 frequencies in the light curve of CoRoT 101128793. They have been identified as the main frequency f0, and its harmonics, two independent terms, the terms related to the Blazhko frequency, and several combination terms. A Blazhko frequency fB=0.056 c/d and a triplet structure around the fundamental radial mode and harmonics were detected, as well as a long-term variability of the Blazhko modulation. Indeed, the amplitude of the main oscillation is decreasing along the CoRoT survey. The Blazhko modulation is one of the smallest observed in RR Lyrae stars. Moreover, the additional modes f1=3.630 and f2=3.159 c/d are detected. Taking its ratio with the fundamental radial mode into account, the term f1 could be the identified as the second radial overtone. Detecting of these modes in horizontal branch stars is a new result obtained by CoRoT.

A new 2-D model of a thin annular disk using a modified assumption

The work describes an improved 2-D model for a thin annulus by using a modified assumption with regard to coupled vibration. With this approach, the impedance spectrum and displacements due to radial modes, both in radial and thickness direction of a thin ring, are obtained. Bending displacement is investigated by finite element analysis (FEA) and matches our model. The bending in the thickness direction is coupled to radial modes and shows several node circles in the high radial overtone frequency range. The model is validated by FEA with excellent agreement between the new theory and FEA results.

An asteroseismic study of the β Cephei star 12 Lacertae: multisite spectroscopic observations, mode identification and seismic modelling

We present the results of a spectroscopic multisite campaign for the β Cephei star 12 (DD) Lacertae. Our study is based on more than thousand high–resolution high S/N spectra gathered with eight different telescopes in a time span of 11 months. In addition, we make use of numerous archival spectroscopic measurements. We confirm 10 independent frequencies recently discovered from photometry, as well as harmonics and combination frequencies. In particular, the slowly pulsating B–stars (SPB)–like g–mode with frequency 0.3428 d−1 reported before is detected in our spectroscopy. We identify the four main modes as (ℓ1, m1) = (1, 1), (ℓ2, m2) = (0, 0), (ℓ3, m3) = (1, 0) and (ℓ4, m4) = (2, 1) for f1= 5.178 964 d−1, f2= 5.334 224 d−1, f3= 5.066 316 d−1 and f4= 5.490 133 d−1, respectively. Our seismic modelling shows that f2 is likely the radial first overtone and that the core overshooting parameter αov is lower than 0.4 local pressure scale heights.

Confirmation of simultaneous p and g mode excitation in HD 8801 and γ Peg from time-resolved multicolour photometry of six candidate ‘hybrid’ pulsators

We carried out a multi-colour time-series photometric study of six stars claimed as "hybrid" p and g mode pulsators in the literature. Gamma Peg was confirmed to show short-period oscillations of the Beta Cep type and simultaneous long-period pulsations typical of Slowly Pulsating B (SPB) stars. From the measured amplitude ratios in the Stromgren uvy passbands, the stronger of the two short period pulsation modes was identified as radial; the second is l=1. Three of the four SPB-type modes are most likely l=1 or 2. Comparison with theoretical model calculations suggests that Gamma Peg is either an 8.5 solar mass radial fundamental mode pulsator or a 9.6 solar mass first radial overtone pulsator. HD 8801 was corroborated as a "hybrid" Delta Sct Gamma Dor star; four pulsation modes of the Gamma Dor type were detected, and two modes of the Delta Sct type were confirmed. Two pulsational signals between the frequency domains of these two known classes of variables were confirmed and another was newly detected. These are either previously unknown types of pulsation, or do not originate from HD 8801. The O-type star HD 13745 showed small-amplitude slow variability on a time scale of 3.2 days. This object may be related to the suspected new type of supergiant SPB stars, but a rotational origin of its light variations cannot be ruled out at this point. 53 Psc is an SPB star for which two pulsation frequencies were determined and identified with low spherical degree. The behaviour of 53 Ari and Iota Her is consistent with non-variability during our observations, and we could not confirm light variations of the comparison star 34 Psc previously suspected. The use of signal-to-noise criteria in the analysis of data sets with strong aliasing is critically discussed.

The pulsating DA white dwarf star EC 14012−1446: results from four epochs of time-resolved photometry

The pulsating DA white dwarfs are the coolest degenerate stars that undergo self-driven oscillations. Understanding their interior structure will help us to understand the previous evolution of the star. To this end, we report the analysis of more than 200 h of time-resolved CCD photometry of the pulsating DA white dwarf star EC 14012-1446 acquired during four observing epochs in three different years, including a coordinated three-site campaign. A total of 19 independent frequencies in the star's light variations together with 148 combination signals up to fifth order could be detected. We are unable to obtain the period spacing of the normal modes and therefore a mass estimate of the star, but we infer a fairly short rotation period of 0.61 ±0.03 d, assuming the rotationally split modes are l =1. The pulsation modes of the star undergo amplitude and frequency variations, in the sense that modes with higher radial overtone show more pronounced variability and that amplitude changes are always accompanied by frequency variations. Most of the second-order combination frequencies detected have amplitudes that are a function of their parent mode amplitudes, but we found a few cases of possible resonantly excited modes. We point out the complications in the analysis and interpretation of data sets of pulsating white dwarfs that are affected by combination frequencies of the form f A +f B -f c intruding into the frequency range of the independent modes.

Multimode Pulsations of the λ Bootis Star 29 Cygni: The 1995 and 1996 Multisite Campaigns

In this paper we present the results of multisite photometric and spectroscopic campaigns, carried out during the years 1995 and 1996, to study the pulsations of a typical λ Bootis star, 29 Cyg. During the 1995 campaign we found well-defined multiperiodicity in 29 Cyg, which was studied in detail during a multilongitude campaign covering a 65 day time interval in 1996. The frequency analysis of the 1996 campaign's data easily revealed 11 excited low l degree modes with frequencies of oscillation ranging from 20.3 to 37.4 cycles day-1 and mean photometric amplitudes ranging from 10.65 to 0.96 mmag in the V filter. After removing the well-identified frequencies, the discrete Fourier transform of the residuals showed excess power in the 20-40 cycle day-1 domain, which indicates the probable existence of unresolved rich p-mode spectra with photometric V amplitudes below 0.5 mmag. We found a regular spacing of 2.41 cycles day-1 within the modes of 29 Cyg, which was interpreted as the spacing of consecutive even and odd l-values. The asteroseismic luminosity log L/L⊙ = 1.12, calculated from the frequency spacing, is in good agreement with the Hipparcos luminosity log L/L⊙ = 1.16 and with luminosities from photometric and spectroscopic calibrations. Using our multicolor photometry we tentatively identified the dominant f1 = 37.425 cycle day-1 mode as an l = 2, n = 5 mode, and made radial overtone identification for all frequencies. These ranged from n = 2 to 5. Analysis of the photometric data shows the long-term (years) and probable short-term (days) variability of amplitudes for all of these modes in 29 Cyg. Using our multicolor WBVR filter photometry, we found the wavelength dependence of the pulsation amplitudes for the five highest amplitude modes. Based on the Hα line radial velocity observations of 29 Cyg, we detected multiperiodic radial velocity variations with frequencies of 38.36 and 29.99 cycles day-1 and semiamplitudes of 1.0 and 0.8 km s-1, respectively. These frequencies coincide within the errors with the photometric frequencies of the two highest amplitude modes, 37.425 and 29.775 cycles day-1. For the highest amplitude l = 2, n = 5 mode (37.425 cycles day-1), the radial velocity-to-light amplitude ratio and velocity-to-light phase shift are equal to 2K(Hα)/ΔV = 94 km mag-1 s-1 and Φf1 = - V = +0.08 ± 0.01, respectively, and are in good agreement with values for δ Scuti stars. The rich multiperiodic spectrum makes 29 Cyg a promising target for future multisite campaigns.

The field high-amplitude SX Phoenicis variable BL Camelopardalis: results from a multisite photometric campaign

Context. BL Cam is an extreme metal-deficient field high-amplitude SX Phe-type variable where a very complex frequency spectrum is detected, with a number of independent nonradial modes excited, unusual among the high-amplitude pulsators in the Lower Classical Instability Strip. Aims. An extensive and detailed study has been carried out to investigate the pulsational content and properties of this object. Methods. The analysis is based on 283 h of CCD observations obtained in the Johnson V filter, during a long multisite photometric campaign carried out along the Northern autumn-winter of 2005–2006. Additionally, multicolour BI photometry was also collected to study the phase shifts and amplitude ratios, between light curves obtained in different filters, for modal discrimination of the main excited modes. Results. The detailed frequency analysis revealed a very rich and dense pulsational content consisting of 25 significant peaks, 22 of them corresponding to independent modes: one is the already known main periodicity f0 = 25.5765 cd −1 (∆V = 153 mmag) and the other 21 are excited modes showing very small amplitudes. Some additional periodicities are probably still remaining in the residuals. This represents the most complex spectrum ever detected in a high-amplitude pulsator of this type. The majority of the secondary modes suspected from earlier works are confirmed here and, additionally, a large number of new peaks are detected. The amplitude of the main periodicity f0 seems to be stable during decades, but the majority of the secondary modes show strong amplitude changes from one epoch to another. The suspected fundamental radial nature of the main periodicity of BL Cam is confirmed, while the secondary peak f1 = 25.2523 cd −1 is identified as a nonradial mixed mode g4 with � = 1. The radial double-mode nature, claimed by some authors for the main two frequencies of BL Cam, is not confirmed. Nevertheless, the frequency f6 = 32.6464 cd −1 could correspond to the first radial overtone.

Search for pulsation among suspected A-type binaries and the new multiperiodic δ Scuti star HD 217860

We have explored a sample of suspected A-type binaries in a systematic way, both spectroscopically and photometrically. Due to their location in the H-R diagram, indications of pulsation and/or chemical peculiarities among these suspected binary (or multiple) systems may be found. High-resolution spectroscopy obtained with the ELODIE and MUSICOS spectrographs was used in combination with a few nights of differential CCD photometry in order to search for pulsation(s). Of the 32 investigated targets, eight are spectroscopic binaries, one of which is a close binary also showing eclipses, and three have been identified as Delta Scuti pulsators with rapid line-profile variations. Among the latter stars, HD 217860 reveals interesting multiperiodic photometric and spectroscopic variations, with up to eight frequencies common to two large photometric data sets. We suggest that at least one radial overtone mode is excited among the two most dominant frequencies. We furthermore found evidence for a strong modulation of the amplitude(s) and/or the (radial) frequency content of this intriguing Delta Scuti star.

Determination of Exciton-Phonon Coupling Elements in Single-Walled Carbon Nanotubes by Raman Overtone Analysis

Raman excitation profiles are obtained and compared for carbon nanotube radial breathing mode (RBM) fundamental and overtone vibrations for 5 specific chiralities. Fitting of the Raman excitation data is performed using Raman transform theory. The Huang-Rhys factors obtained from the modeling are directly related to the magnitude of the RBM exciton-phonon coupling element, which is shown to be in a weak coupling limit. The values of exciton-phonon coupling strengths and the possible role of revealed non-Condon effects are in agreement with quantum-chemical modeling.

δ Ceti Is Not Monoperiodic: Seismic Modeling of a β Cephei Star fromMOSTSpace‐based Photometry

The β Cephei star δ Ceti was considered one of the few monoperiodic variables in its class. Despite (or perhaps because of) its apparently simple oscillation spectrum, it has been challenging and controversial to identify this star's pulsation mode and constrain its physical parameters seismically. Broadband time-resolved photometry of δ Ceti spanning 18.7 days with a duty cycle of about 65% obtained by the Microvariability and Oscillations of Stars (MOST) satellite—the first scientific observations ever obtained by MOST—reveals that the star is actually multiperiodic. Besides the well-known dominant frequency of f1 = 6.205886 day-1, we have discovered in the MOST data its first harmonic 2f1 and three other frequencies (f2 = 3.737, f3 = 3.673, and f4 = 0.318 day-1), all detected with a signal-to-noise ratio > 4. In retrospect, f2 was also present in archival spectral line-profile data but at lower S/N. We present seismic models whose modes match exactly the frequencies f1 and f2. Only one model falls within the common part of the error boxes of the star's observed surface gravity and effective temperature from photometry and spectroscopy. In this model, f1 is the radial (l = 0) first overtone, and f2 is the g2 (l = 2, m = 0) mode. This model has a mass of 10.2 ± 0.2 M☉ and an age of 17.9 ± 0.3 Myr, making δ Ceti an evolved β Cephei star. If f2 and f3 are rotationally split components of the same g2 mode, then the star's equatorial rotation velocity is either 27.6 km s-1 or half this value. Given its v sin i of about 1 km s-1, this implies that we are seeing δ Ceti nearly pole-on.

Pulsations of the Oe Star ζ Ophiuchi from MOST Satellite Photometry and Ground-based Spectroscopy

Twenty-four days of highly precise Microvariability and Oscillations of Stars (MOST) satellite photometry obtained in mid-2004 of the rapidly rotating O9.5 V star ζ Oph have yielded at least a dozen significant oscillation frequencies between 1 and 10 cycles day-1, clearly indicating its relationship to β Cephei variables. Eight periods were found in He I λ4922 and Hβ line profile variations (LPV) of which six coincide with those from the MOST photometry. This unique photometric and spectroscopic detection of radial and nonradial pulsations leads to a plausible model in which high l-modes are excited when their frequencies in the corotating frame are similar to those of low-order radial modes. We propose that the dominant photometric 4.6 hr period (f1) corresponds to a radial first overtone excited by the κ-mechanism associated with the Fe opacity bump. No unambiguous rotational period can be identified in either the light curve or the LPV.

Search for pulsating pre-main-sequence stars in NGC 6383

A search for pulsating pre-main-sequence (PMS) stars was performed in the young open cluster NGC 6383 using CCD time-series photometry in Johnson B and V filters. With an age of only ∼1.7 Myr all cluster members later than spectral type A0 have not reached the ZAMS yet, hence being ideal candidates for investigating PMS pulsation among A- and F-type stars. In total 286 stars have been analysed using classical Fourier techniques. From about a dozen stars within the boundaries of the classical instability strip, two stars were found to pulsate: NGC 6383 #170, with five frequencies simultaneously, and NGC 6383 #198, with a single frequency. In addition, NGC 6383 #152 is a suspected PMS variable star, but our data remain inconclusive. Linear, non-adiabatic models assuming PMS evolutionary phase and purely radial pulsation were calculated for the two new PMS pulsators. NGC 6383 #170 appears to pulsate radially in third and fifth overtones, while the other three frequencies seem to be of non-radial nature. NGC 6383 #198 pulsates monoperiodically, most probably in the third radial overtone. Magnitudes and B − V colours were available in the literature for only one third of all stars and we used them for calibrating the remaining. Ke yw ords: techniques: photometric ‐ stars: pre-main-sequence ‐ δ Scuti ‐ open clusters and associations: individual: NGC 6383.

Observations of Nonradial Pulsations in Radio Pulsars

We introduce a model for pulsars in which nonradial oscillations of high spherical degree (l) aligned to the magnetic axis of a spinning neutron star reproduce the morphological features of pulsar beams. In our model, rotation of the pulsar carries a pattern of pulsation nodes underneath our sight line, reproducing the longitude-stationary structure seen in average pulse profiles, while the associated timelike oscillations reproduce drifting subpulses?features that change their longitude between successive pulsar spins. We show that the presence of nodal lines can account for observed 180? phase jumps in drifting subpulses and their otherwise poor phase stability, even if the timelike oscillations are strictly periodic. Our model can also account for the mode changes and nulls observed in some pulsars as quasi-periodic changes between pulsation modes of different l or radial overtone n, analogous to pulsation mode changes observed in oscillating white dwarf stars. We discuss other definitive and testable requirements of our model and show that they are qualitatively supported by existing data. While reserving judgment until the completion of quantitative tests, we are inspired enough by the existing observational support for our model to speculate about the excitation mechanism of the nonradial pulsations, the physics we can learn from them, and their relationship to the period evolution of pulsars.

Peak finding at low signal-to-noise ratio: low- solar acoustic eigenmodes at n<= 9 from the analysis of BiSON data

We make use of 9 yr of full-disc helioseismic data - as collected by the ground-based Birmingham Solar-Oscillations Network (BiSON) - to search for low-frequency, low-angular-degree (low-l) acoustic modes. A range of tests are applied to the power spectrum of the observations that search for prominent mode-like structure: strong spikes, structure spanning several bins signifying the presence of width (from damping), and the occurrence of prominent multiplet structure at l greater than or equal to 1 arising principally from the solar rotation and made from several spikes separated suitably in frequency. For each test we present analytical expressions that allow the probability that the uncovered structure is part of the broad-band noise background to be assessed. These make use of the cumulative binomial (Bernoulli) distribution and serve to provide an objective measure of the significance of the detections. This work has to date uncovered nine significant detections of non-broad-band origin that we have identified as low-l modes with radial overtone numbers n less than or equal to 9.

The Clusters AgeS Experiment (CASE): RR Lyrae variables in the globular cluster NGC 6362

We present V- and B-band charge-coupled device (CCD) photometry of 35 RR Lyr stars in the Southern hemisphere globular cluster NGC 6362. Fourier decomposition of the light curves was used to estimate the basic properties of these variables. From the analysis of the RRc stars we obtain a mean mass M=0.531±0.014 M⊙, luminosity log L/L⊙=1.656±0.006, effective temperature Teff=7429±20 and helium abundance Y=0.292±0.002. The mean values of the absolute magnitude, metallicity (on Jurcsik's scale) and effective temperature for 14 RRab stars with ‘regular’ light curves are: MV=0.86±0.01,[Fe/H]=−0.93±0.04 and Teff=6555±25, respectively. From the B–V colours, periods and metallicities of the RRab stars we estimate the colour excess for NGC 6362 to be equal to E(B–V)=0.08±0.01. Using this value we derive the colours of the blue and red edges of the instability strip in NGC 6362 to be (B–V)BE0=0.17 and (B–V)RE0=0.43. From the relations between the Fourier coefficients of RRab and RRc stars and their absolute magnitudes we estimate the apparent distance modulus to NGC 6362 to be (m—M)V=14.46±0.10. From the mean value of log L/L⊙ of the RRc stars we obtain 14.59±0.03. The V-band light curves of three of the RRc stars exhibit changes in amplitude of over 0.1 mag on the time-scale of around one week. Near the radial first overtone frequency we find one or two peaks, which strongly suggests that these variables belong to the newly identified group of non-radial pulsating RR Lyr stars.

Depth of excitation and reversal of asymmetry of low- solar p modes: a complementary analysis of BiSON and VIRGO/SPM data

We use the solutions to a simple, one-dimensional wave equation – which is intended to describe the essential elements of the solar resonant acoustic cavity – as formalistic models to which to fit low-l modes in observational helioseismic power spectra. We have analysed data collected in velocity, by the ground-based Birmingham Solar-Oscillations Network (BiSON), and in intensity, by the full-disc VIRGO Sun photometers (SPM) on board the ESA/NASA SOHO satellite. Our analysis extracts, as a function of the modal radial overtone number n, direct estimates of: the location of the excitation source of the acoustic resonances; and the size of the component of the convective granulation that is correlated to the observations of the resonances, and is responsible for the reversal of asymmetry of the mode profiles when different observation techniques are applied (i.e. intensity or Doppler velocity measurements). This information is coded in the complicated forms of the observed, resonant profiles.

Mode switching in the nearby Mira-like variable R Doradus

We discuss visual observations spanning nearly 70 years of the nearby semiregular variable R Doradus. Using wavelet analysis, we show that the star switches back and forth between two pulsation modes having periods of 332 days and about 175 days, the latter with much smaller amplitude. Comparison with model calculations suggests that the two modes are the first and third radial overtone, with the physical diameter of the star making fundamental mode pulsation unlikely. The mode changes occur on a timescale of about 1000 d, which is too rapid be related to a change in the overall thermal structure of the star and may instead be related to weak chaos. The Hipparcos distance to R Dor is 62.4 +/- 2.8 pc which, taken with its dominant 332-day period, places it exactly on the period-luminosity relation of Miras in the Large Magellanic Cloud. Our results imply first overtone pulsation for all Miras which fall on the P-L relation. We argue that semiregular variables with long periods may largely be a subset of Miras and should be included in studies of Mira behaviour. The semiregulars may contain the immediate evolutionary Mira progenitors, or stars may alternate between periods of semiregular and Mira behaviour.