Rate Of Period Change Research Articles

Orbital period modulation of the eclipsing binary system ER Vulpeculae: Real or not?

The reanalysis of the timing data of the binary system ER Vulpeculae revealed the superposition of a relatively slow increasing linear trend in the orbital period, having a relative period change rate of 2.73×10-8yr-1, and a low amplitude (≈3.5min) periodic modulation with a period of about 17.78yr. This periodicity is significantly shorter than that previously published, i.e., 30.6yr. We propose a methodology relying on Monte Carlo simulations which is intended to evaluate the detectability of the inferred signal. Both frequentist and Bayesian approaches have been considered. The actual amplitude of the orbital period modulation might be lower than that obtained via nonlinear least-squares modelling of the timing data, namely about 2.0min. Consequently, the amplitude of the underlying mechanism will be lower too. In the case of ER Vul, within the hypothesis of a third companion in the system, it could be a low mass star of about 113.8MJupiter, but also a brown dwarf of about 64.7MJupiter. Further theoretical and observational studies are needed in order to discriminate between this mechanism and the cyclic magnetic activity occurring in both component stars, as possible causes of the observed period variation.

CLASSICAL CEPHEIDS REQUIRE ENHANCED MASS LOSS

Measurements of rates of period change of Classical Cepheids probe stellar physics and evolution. Additionally, better understanding of Cepheid structure and evolution provides greater insight into their use as standard candles and tools for measuring the Hubble constant. Our recent study of the period change of the nearest Cepheid, Polaris, suggested that it is undergoing enhanced mass loss when compared to canonical stellar evolution model predictions. In this work, we expand the analysis to rates of period change measured for about 200 Galactic Cepheids and compare them to population synthesis models of Cepheids including convective core overshooting and enhanced mass loss. Rates of period change predicted from stellar evolution models without mass loss do not agree with observed rates whereas including enhanced mass loss yields predicted rates in better agreement with observations. This is the first evidence that enhanced mass loss as suggested previously for Polaris and delta Cephei must be a ubiquitous property of Classical Cepheids.

STELLAR PULSATIONS AND PERIOD CHANGES IN THE SX PHOENICIS STAR XX CYGNI

Time-series photometric observations were made for the SX Phoenicis star XX Cyg between 2007 and 2011 at the Xinglong Station of National Astronomical Observatories of China. With the light curves derived from the new observations, we do not detect any secondary maximum in the descending portion of the light curves of XX Cyg, as reported in some previous work. Frequency analysis of the light curves confirms a fundamental frequency f 0 = 7.4148 cycles day–1 and up to 19 harmonics, 11 of which are newly detected. However, no secondary mode of pulsation is detected from the light curves. The O–C diagram, produced from 46 newly determined times of maximum light combined with those derived from the literature, reveals a continuous period increase with the rate of (1/P)(dP/dt) = 1.19(13) × 10–8 yr-1. Theoretical rates of period change due to the stellar evolution were calculated with a modeling code. The result shows that the observed rate of period change is fully consistent with period change caused by evolutionary behavior predicted by standard theoretical models.

The rate of cooling of the pulsating white dwarf star G117−B15A: a new asteroseismological inference of the axion mass

We employ a state-of-the-art asteroseismological model of G117-B15A, the archetype of the H-rich atmosphere (DA) white dwarf pulsators (also known as DAV or ZZ Ceti variables), and use the most recently measured value of the rate of period change for the dominant mode of this pulsating star to derive a new constraint on the mass of axion, the still conjectural non-barionic particle considered as candidate for dark matter of the Universe. Assuming that G117-B15A is truly represented by our asteroseismological model, and in particular, that the period of the dominant mode is associated to a pulsation g-mode trapped in the H envelope, we find strong indications of the existence of extra cooling in this star, compatible with emission of axions of mass m_a \cos^2 \beta = 17.4^{+2.3}_{-2.7} meV.

THE PERIOD CHANGE OF THE CEPHEID POLARIS SUGGESTS ENHANCED MASS LOSS

Polaris is one of the most observed stars in the night sky, with recorded observations spanning more than 200 years. From these observations, one can study the real-time evolution of Polaris via the secular rate of change of the pulsation period. However, the measurements of the rate of period change do not agree with predictions from state-of-the-art stellar evolution models. We show that this may imply that Polaris is currently losing mass at a rate of $\dot{M} \approx 10^{-6} M_\odot$ yr$^{-1}$ based on the difference between modeled and observed rates of period change, consistent with pulsation-enhanced Cepheid mass loss. A relation between the rate of period change and mass loss has important implications for understanding stellar evolution and pulsation, and provides insight into the current Cepheid mass discrepancy.

Is there a mass discrepancy in the Cepheid binary OGLE-LMC-CEP0227?

Context. The Cepheid mass discrepancy, the difference between masses predicted from stellar evolution and stellar pulsation calculations, is a challenge for the understanding of stellar astrophysics. Recent models of the eclipsing binary Cepheid OGLE-LMC-CEP-0227 have suggested that the discrepancy may be resolved. Aims. We explore for what physical parameters do stellar evolution models agree with the measured properties of OGLE-LMC-CEP0227 and compare to canonical stellar evolution models assuming no convective core overshooting. Methods. We construct state-of-the-art stellar evolution models for varying mass, metallicity, and convective core overshooting and compare the stellar evolution predictions with the observed properties. Results. The observed mass, effective temperature, and radius of the two stars in the binary system are well fit by numerous combinations of physical parameters, suggesting a Cepheid mass discrepancy of 10-20% relative to canonical stellar evolution models. Conclusions. The properties of the observed binary Cepheid suggest that the Cepheid mass discrepancy is still a challenge and requires more specific observations, such as the rate of period change, to better constrain and understand the necessary physics for stellar evolution models to resolve the discrepancy.

Long-term photometric monitoring of RR Lyrae stars in Messier 3

The period-change behaviour of 134 RR Lyrae stars in the globular cluster Messier 3 (M3) is investigated on the ~120-year time base of the photometric observations. The mean period-change rates (\beta \approx 0.01 d Myr^-1) of the subsamples of variables exhibiting the most regular behaviour are in good agreement with theoretical expectations based on Horizontal-Branch stellar evolution models. However, a large fraction of variables show period changes that contradict the evolutionary expectations. Among the 134 stars studied, the period-change behaviour of only 54 variables is regular (constant or linearly changing), slight irregularities are superimposed on the regular variations in 23 cases and the remaining 57 stars display irregular period variations. The light curve of ~50 per cent of the RRab stars is not stable, i.e., these variables exhibit Blazhko modulation. The large fraction of variables with peculiar behaviour (showing light-curve modulation and/or irregular O-C variation) indicate that, probably, variables with regular period changes incompatible with their evolutionary stages also could display some kind of instability of the pulsation light curve and/or period, but the available observations have not disclosed it yet. The temporal appearence of the Blazhko effect in some stars, and the 70-90 years long regular changes preceded or followed by irregular, rapid changes of the pulsation period in some cases support this hypothesis. [...] Abstract truncated due to the limitations of astroph. See full abstract in the paper.

Fourier analysis of non-Blazhko ab-type RR Lyrae stars observed with the Kepler space telescope

Nineteen of the ~40 RR Lyr stars in the Kepler field have been identified as candidate non-Blazhko (or unmodulated) stars. In this paper we present the results of Fourier decomposition of the time-series photometry of these stars acquired during the first 417 days of operation (Q0-Q5) of the Kepler telescope. Fourier parameters based on ~18400 long-cadence observations per star (and ~150000 short-cadence observations for FN Lyr and for AW Dra) are derived. None of the stars shows the recently discovered `period-doubling' effect seen in Blazhko variables; however, KIC 7021124 has been found to pulsate simultaneously in the fundamental and second overtone modes with a period ratio P2/P0 ~ 0.59305 and is similar to the double-mode star V350 Lyr. Period change rates are derived from O-C diagrams spanning, in some cases, over 100 years; these are compared with high-precision periods derived from the Kepler data alone. Extant Fourier correlations by Kovacs, Jurcsik et al. (with minor transformations from the V to the Kp passband) have been used to derive underlying physical characteristics for all the stars. This procedure seems to be validated through comparisons of the Kepler variables with galactic and LMC RR Lyr stars. The most metal-poor star in the sample is NR Lyr, with [Fe/H]=-2.3 dex; and the four most metal-rich stars have [Fe/H] ranging from -0.6 to +0.1 dex. Pulsational luminosities and masses are found to be systematically smaller than L and mass values derived from stellar evolution models, and are favoured over the evolutionary values when periods are computed with the Warsaw linear hydrodynamics code. Finally, the Fourier parameters are compared with theoretical values derived using the Warsaw non-linear convective pulsation code.

The pulsations of PG 1351+489

PG 1351+489 is one of the 20 DBVs ― pulsating helium-atmosphere white dwarf stars ― known and has the simplest power spectrum for this class of star, making it a good candidate to study cooling rates. We report accurate period determinations for the main peak at 489.334 48 s and two other normal modes using data from the Whole Earth Telescope (WET) observations of 1995 and 2009. In 2009, we detected a new pulsation mode and the main pulsation mode exhibited substantial change in its amplitude compared to all previous observations. We were able to estimate the star's rotation period, of 8.9 h, and discuss a possible determination of the rate of period change of (2.0 ± 0.9) x 10 ―13 s s ―1 , the first such estimate for a DBV.

The evolutionary state of Miras with changing pulsation periods

Context: Miras are long-period variables thought to be in the asymptotic giant branch (AGB) phase of evolution. In about one percent of known Miras, the pulsation period is changing. It has been speculated that this changing period is the consequence of a recent thermal pulse in these stars. Aims: We aim to clarify the evolutionary state of these stars, and to determine in particular whether or not they are in the thermally-pulsing (TP-)AGB phase. Methods: One important piece of information that has been neglected so far when determining the evolutionary state is the presence of the radio-active s-process element technetium (Tc). We obtained high-resolution, high signal-to-noise-ratio optical spectra of a dozen prominent Mira variables with changing pulsation period to search for this indicator of TPs and dredge-up. We also use the spectra to measure lithium (Li) abundances. Furthermore, we establish the evolutionary states of our sample stars by means of their present-day periods and luminosities. Results: Among the twelve sample stars observed in this programme, five were found to show absorption lines of Tc. BH Cru is found to be a carbon-star, its period increase in the past decades possibly having stopped by now. We report a possible switch in the pulsation mode of T UMi from Mira-like to semi-regular variability in the past two years. R Nor, on the other hand, is probably a fairly massive AGB star, which could be true for all meandering Miras. Finally, we assign RU Vul to the metal-poor thick disk with properties very similar to the short-period, metal-poor Miras. Conclusions: We conclude that there is no clear correlation between period change class and Tc presence. The stars that are most likely to have experienced a recent TP are BH Cru and R Hya, although their rates of period change are quite different.

Long-term photometric monitoring of Messier 5 variables - I. Period changes of RR Lyrae stars

The period changes of 86 M5 RR Lyrae stars have been investigated on a one-hundred-year time base. The published observations have been supplemented by archival Asiago, Konkoly and Las Campanas photographic observations obtained between 1952 and 1993. About two thirds of the O-C diagrams could be fitted by a straight line or a parabola. 21 RR Lyrae stars have increasing, 18 decreasing and 16 constant period. The mean rates of period change of these variables are: <beta> = <\dot{P}> = -0.006\pm0.162 d Myr^{-1}, <alpha> = <P^{-1}\dot{P}> = -0.021 \pm0.308 Myr^{-1}. Ten RR Lyrae stars show fast period decrease with \dot{P} < - 0.10 d Myr^{-1}. At least some of these variables may be in the pre-zero-age horizontal-branch (ZAHB) evolutionary stage. The variables on the long-period sequence of the period-amplitude diagram are brighter than the other RR Lyrae stars of M5 and are in an advanced evolutionary stage moving off from the HB redward. More than one third of the M5 RR Lyrae stars investigated have irregular period change. The irregular period behaviour is relatively more frequent among the RRc (RR1) stars (50 per cent) than among the RRab (RR0) stars (34 per cent). A strict relationship has been found between the irregular period change and the Blazhko effect of M5 RRab stars. This fact indicates a common origin for these phenomena. It is remarkable that, if the RRab stars showing Blazhko effect are omitted from the sample, the mean rates of the period change have small positive values (<beta> = 0.012 \pm0.147 d Myr^{-1}, <alpha> = 0.013 \pm 0.279 Myr^{-1}), in excellent agreement with HB evolutionary model predictions.

PERIOD CHANGE SIMILARITIES AMONG THE RR LYRAE VARIABLES IN OOSTERHOFF I AND OOSTERHOFF II GLOBULAR SYSTEMS

We present period change rates (dP/dt) for 42 RR Lyrae variables in the globular cluster IC$\,$4499. Despite clear evidence of these period increases or decreases, the observed period change rates are an order of magnitude larger than predicted from theoretical models of this cluster. We find there is a preference for increasing periods, a phenomenon observed in most RR Lyrae stars in Milky Way globular clusters. The period-change rates as a function of position in the period-amplitude plane are used to examine possible evolutionary effects in OoI clusters, OoII clusters, field RR Lyrae stars and the mixed-population cluster $\omega$~ Centauri. It is found that there is no correlation between the period change rate and the typical definition of Oosterhoff groups. If the RR Lyrae period changes correspond with evolutionary effects, this would be in contrast to the hypothesis that RR Lyrae variables in OoII systems are evolved HB stars that spent their ZAHB phase on the blue side of the instability strip. This may suggest that age may not be the primary explanation for the Oosterhoff types.

A Strategy to Efficiently Extend the Change Rate of Period for Comb-Drive Micromechanical Pitch-Tunable Gratings

In this paper, we present a new design strategy with two major considerations to efficiently extend the change rate of period for comb-drive micromechanical pitch-tunable gratings. The proposed strategy is mainly based on the critical state when “side instability” happens. All the ideas were originated from our previous study to develop a silicon-on-glass (SOG)-based pitch-tunable grating with a large change rate of period, from which we found that once the comb structure was connected with the grating beams, the maximum displacement of movable fingers would be sharply decreased according to the experiments. Detailed discussions and analysis are thus performed to explain the finding. Finally, another grating sample based on the silicon-on-insulator (SOI) technology is developed to prove the new design strategy, and a change rate of period of 10.34% is ultimately achieved. The so-developed pitch-tunable grating will greatly expand the device's application domains.

Pulsation period changes as a tool to identify pre-zero age horizontal branch stars

One of the most dramatic events in the life of a low-mass star is the He flash, which takes place at the tip of the red giant branch (RGB) and is followed by a series of secondary flashes before the star settles into the zero-age horizontal branch (ZAHB). Yet, no stars have been positively identified in this key evolutionary phase, mainly for two reasons: first, this pre-ZAHB phase is very short compared to other major evolutionary phases in the life of a star; and second, these pre-ZAHB stars are expected to overlap the loci occupied by asymptotic giant branch (AGB), HB and RGB stars observed in the color-magnitude diagram (CMD). We investigate the possibility of detecting these stars through stellar pulsations, since some of them are expected to rapidly cross the Cepheid/RR Lyrae instability strip in their route from the RGB tip to the ZAHB, thus becoming pulsating stars along the way. As a consequence of their very high evolutionary speed, some of these stars may present anomalously large period change rates. We constructed an extensive grid of stellar models and produced pre-ZAHB Monte Carlo simulations appropriate for the case of the Galactic globular cluster M3 (NGC 5272), where a number of RR Lyrae stars with high period change rates are found. Our results suggest that some -- but certainly not all -- of the RR Lyrae stars in M3 with large period change rates are in fact pre-ZAHB pulsators.

Horizontal branch stars: the interplay between observations and theory, and insights into the formation of the Galaxy

We review and discuss horizontal branch (HB) stars in a broad astrophysical context, including both variable and non-variable stars. A reassessment of the Oosterhoff dichotomy is presented, which provides unprecedented detail regarding its origin and systematics. We show that the Oosterhoff dichotomy and the distribution of globular clusters in the HB morphology-metallicity plane both exclude, with high statistical significance, the possibility that the Galactic halo may have formed from the accretion of dwarf galaxies resembling present-day Milky Way satellites such as Fornax, Sagittarius, and the LMC—an argument which, due to its strong reliance on the ancient RR Lyrae stars, is essentially independent of the chemical evolution of these systems after the very earliest epochs in the Galaxy’s history. Convenient analytical fits to isochrones in the HB type–[Fe/H] plane are also provided. In this sense, a rediscussion of the second-parameter problem is also presented, focusing on the cases of NGC 288/NGC 362, M13/M3, the extreme outer-halo globular clusters with predominantly red HBs, and the metal-rich globular clusters NGC 6388 and NGC 6441. The recently revived possibility that the helium abundance may play an important role as a second parameter is also addressed, and possible constraints on this scenario discussed. We critically discuss the possibility that the observed properties of HB stars in NGC 6388 and NGC 6441 might be accounted for if these clusters possess a relatively minor population of helium-enriched stars. A technique is proposed to estimate the HB types of extragalactic globular clusters on the basis of integrated far-UV photometry. The importance of bright type II Cepheids as tracers of faint blue HB stars in distant systems is also emphasized. The relationship between the absolute V magnitude of the HB at the RR Lyrae level and metallicity, as obtained on the basis of trigonometric parallax measurements for the star RR Lyr, is also revisited. Taking into due account the evolutionary status of RR Lyr, the derived relation implies a true distance modulus to the LMC of (m–M)0=18.44±0.11. Techniques providing discrepant slopes and zero points for the MV(RRL)–[Fe/H] relation are briefly discussed. We provide a convenient analytical fit to theoretical model predictions for the period change rates of RR Lyrae stars in globular clusters, and compare the model results with the available data. Finally, the conductive opacities used in evolutionary calculations of low-mass stars are also investigated.

On the origin of white dwarfs with carbon-dominated atmospheres: the case of H1504+65

We explore different evolutionary scenarios to explain the helium deficiency observed in H1504+65, the most massive known PG1159 star. We concentrate mainly on the possibility that this star could be the result of mass loss shortly after the born-again and during the subsequent evolution through the [WCL] stage. This possibility is sustained by recent observational evidence of extensive mass-loss events in Sakurai's object and is in line with the recent finding that such mass losses give rise to PG1159 models with thin helium-rich envelopes and large rates of period change, as demanded by the pulsating star PG1159-035. We compute the post born again evolution of massive sequences by taking into account different mass-loss rate histories. Our results show that stationary winds during the post-born-again evolution fail to remove completely the helium-rich envelope so as to explain the helium deficiency observed in H1504+65. Stationary winds during the Sakurai and [WCL] stages only remove at most half of the envelope surviving the violent hydrogen burning during the born-again phase. In view of our results, the recently suggested evolutionary connection born-again stars --> H1504+65 --> white dwarfs with carbon-rich atmospheres is difficult to sustain unless the whole helium-rich envelope could be ejected by non-stationary mass-loss episodes during the Sakurai stage.

Assessing potential cluster Cepheids from a new distance and reddening parametrization and Two Micron All Sky Survey photometry

A framework is outlined to assess Cepheids as potential cluster members from readily available photometric observations. A relationship is derived to estimate colour excess and distance for individual Cepheids through a calibration involving recently published HST parallaxes and a cleaned sample of established cluster Cepheids. Photometric (V-J) colour is found to be a viable parameter for approximating a Cepheid's reddening. The non-universal nature of the slope of the Cepheid PL relation for BV photometry is confirmed. By comparison, the slopes of the VJ and VI relations seem relatively unaffected by metallicity. A new Galactic Cepheid confirmed here, GSC 03729-01127 (F6-G1 Ib), is sufficiently coincident with the coronal regions of Tombaugh 5 to warrant follow-up radial velocity measures to assess membership. CCD photometry and O--C diagrams are presented for GSC 03729-01127 and the suspected cluster Cepheids AB Cam and BD Cas. Fourier analysis of the photometry for BD Cas and recent estimates of its metallicity constrain it to be a Population I overtone pulsator rather than a Type II s-Cepheid. AB Cam and BD Cas are not physically associated with the spatially-adjacent open clusters Tombaugh 5 and King 13, respectively, the latter being much older (log t ~ 9) than believed previously. Rates of period change are determined for the three Cepheids from archival and published data. GSC 03729-01127 and AB Cam exhibit period increases, implying fifth and third crossings of the instability strip, respectively, while BD Cas exhibits a period decrease, indicating a second crossing, with possible superposed trends unrelated to binarity. More importantly, the observed rates of period change confirm theoretical predictions. The challenges and prospects for future work in this area of research are discussed.

The Pulsating White Dwarf Stars

ABSTRACTWe present a summary of what is currently known about the three distinct families of isolated pulsating white dwarfs. These are the GW Vir stars (He/C/O-atmosphere stars with Teff ≃ 120,000 K), the V777 Her stars (He-atmosphere, Teff ≃ 25,000 K), and the ZZ Ceti stars (H-atmosphere, Teff ≃ 12,000 K), all showing multiperiodic luminosity variations caused by low-order and low-degree g-mode instabilities. We also provide, in an , a very brief overview of the newly found evidence in favor of the existence of a fourth category of oscillating white dwarfs bearing strong similarities with these families of pulsators. We begin our survey with a short historical introduction, followed by a general discussion of pulsating white dwarfs as compact pulsators. We then discuss the class properties of these objects, including an updated census. We next focus on the instability domains for each family of pulsators in the log g - Teff diagram, and present their time-averaged properties in more detail. This is followed by a section on excitation physics, i.e., the causes of the pulsational instabilities, with emphasis on the common properties of the different types of pulsator. We then discuss the time-dependent properties of the pulsating white dwarfs featuring, among other things, a brief “picture tour” across the ZZ Ceti instability strip. We next review the methods used to infer or constrain the angular geometry of a pulsation mode in a white dwarf. These include multicolor photometry and time-resolved spectroscopy, the exploitation of the nonlinear features in the observed light curves, and rotational splitting. We also consider basic adiabatic asteroseismology starting with a discussion of the reaction of the period spectrum to variations of model parameters. We next review the various asteroseismological inferences that have so far been claimed for white dwarfs. We also discuss the potential of exploiting the rates of period change. We finally provide some concluding remarks, including a list with several suggestions for future progress in the field.

On the Enhancement of Mass Loss in Cepheids Due to Radial Pulsation

An analytical derivation is presented for computing mass-loss rates of Cepheids by using the method of Castor, Abbott, and Klein modified to include a term for momentum input from pulsation and shocks generated in the atmosphere. Using this derivation, mass-loss rates of Cepheids are determined as a function of stellar parameters. When applied to a set of known Cepheids, the calculated mass-loss rates range from 10−10 to 10−7 -->M☉ yr−1, larger than if the winds were driven by radiation alone. Infrared excesses based on the predicted mass-loss rates are compared to observations from optical interferometry and IRAS, and predictions are made for Spitzer observations. The mass-loss rates are consistent with the observations, within the uncertainties of each. The rate of period change of Cepheids is discussed and shown to relate to mass loss, albeit the dependence is very weak. There is also a correlation between the large mass-loss rates and the Cepheids with slowest absolute rate of period change due to evolution through the instability strip. The enhanced mass loss helps illuminate the issue of infrared excess and the mass discrepancy found in Cepheids.

Stellar evolution and variability in the pre-ZAHB phase

Context. One of the most dramatic events in the life of a low-mass star is the He flash, which takes place at the tip of the red giant branch and is followed by a series of secondary flashes before the star settles on the zero-age horizontal branch (ZAHB). Yet, no stars have ever been positively identified in this key phase in the life of a low-mass star (hereafter the “pre-ZAHB” phase). Aims. In this paper, we investigate the possibility that at least some pre-ZAHB stars may cross the instability strip, thus becoming variable stars whose properties might eventually lead to positive identifications. In particular, it has been suggested that some of the RR Lyrae stars with high period change rates ( u P) may in fact be pre-ZAHB stars. Here we present the first theoretical effort devoted to interpreting at least some of the high- u P stars as pre-ZAHB pulsators. Methods. We constructed an extensive grid of evolutionary tracks using the Garching Stellar Evolution Code (GARSTEC) for a chemical composition appropriate to the case of the globular cluster M 3 (NGC 5272), where a number of stars with high u P values are found. We follow each star’s pre-ZAHB evolution in detail, and compute the periods and period change rates for the stars lying inside the instability strip, also producing pre-ZAHB Monte Carlo simulations that are appropriate for the case of M 3. Results. Our results indicate that one should expect of order 1 pre-ZAHB star for every 60 or so bona fide HB stars in M 3. Among the pre-ZAHB stars, approximately 22% are expected to fall within the boundaries of the instability strip, presenting RR Lyrae-like pulsations. On average, these pre-ZAHB pulsators are expected to have longer periods than the bona fide HB pulsators, and 76% of them are predicted to show negative u P values. While the most likely u P value for the pre-ZAHB variables is ≈−0. 3d /Myr, more extreme u P values are also possible: 38% of the variables are predicted to have u P < −0. 8d /Myr. Conclusions. It appears likely, therefore, that some – but certainly not all – of the RR Lyrae stars in M 3 with high (absolute) u P values are in fact pre-ZAHB pulsators in disguise.