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Period-colour and amplitude-colour relations in classical Cepheid variables - IV. The multiphase relations
The superb phase resolution and quality of the Optical GravitationalLensing Experiment (OGLE) data on the Large Magellanic Cloud (LMC) andSmall Magellanic Cloud (SMC) Cepheids, together with existing data onGalactic Cepheids, are combined to study the period-colour (PC) andamplitude-colour (AC) relations as a function of pulsation phase. Ourresults confirm earlier work that the LMC PC relation (at mean light) ismore consistent with two lines of differing slopes, separated at aperiod of 10 d. However, our multiphase PC relations reveal much newstructure which can potentially increase our understanding of Cepheidvariables. These multiphase PC relations provide insight into why theGalactic PC relation is linear but the LMC PC relation is non-linear.This is because the LMC PC relation is shallower for short (logP < 1)and steeper for long (logP > 1) period Cepheids than thecorresponding Galactic PC relation. Both of the short- and long-periodCepheids in all three galaxies exhibit the steepest and shallowestslopes at phases around 0.75-0.85, respectively. A consequence is thatthe PC relation at phase ~ 0.8 is highly non-linear. Further, theGalactic and LMC Cepheids with logP > 1 display a flat slope in thePC plane at phases close to the maximum light. When the LMCperiod-luminosity (PL) relation is studied as a function of phase, weconfirm that it changes with the PC relation. The LMC PL relation in Vand I band near the phase of 0.8 provides compelling evidence that thisrelation is also consistent with two lines of differing slopes joined ata period close to 10 d.
| The Distribution of the Elements in the Galactic Disk
This paper reports on the spectroscopic investigation of 54 Cepheids,deriving parameters and abundances. These Cepheids extend previoussamples by about 35% in number and increase the amount of the Galacticdisk coverage, especially in the direction of l~120deg. Wefind that there exists in the Galactic disk at that longitude and at asolar distance of about 3-4 kpc a region that has enhanced abundances,~+0.2, with respect to the local region. A simple linearfit to all Cepheid data now extant yields a gradientd[Fe/H]/dRG=-0.068+/-0.003 dex kpc-1. Afterconsideration of the spatial abundance inhomogeneities in the sample, weconclude that the best current estimate of the overall gradient isd[Fe/H]/dRG=-0.06 dex kpc-1.
| Sodium enrichment of the stellar atmospheres. II. Galactic Cepheids
The present paper is a continuation of our study of the sodium abundancein supergiant atmospheres (Andrievsky et al. 2002a). We present theresults on the NLTE abundance determination in Cepheids, and the derivedrelation between the sodium overabundance and their masses.
| New Period-Luminosity and Period-Color relations of classical Cepheids: I. Cepheids in the Galaxy
321 Galactic fundamental-mode Cepheids with good B, V, and (in mostcases) I photometry by Berdnikov et al. (\cite{Berdnikov:etal:00}) andwith homogenized color excesses E(B-V) based on Fernie et al.(\cite{Fernie:etal:95}) are used to determine their period-color (P-C)relation in the range 0.4~ 1.4). The latter effect is enhanced by asuggestive break of the P-L relation of LMC and SMC at log P = 1.0towards still shallower values as shown in a forthcoming paper.Table 1 is only available in electronic form at the CDS via anonymousftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/404/423
| The galactic abundance gradient from Cepheids. IV. New results for the outer disc
As a continuation of our previous work on the abundance gradient in theouter part of the galactic disc, this paper presents results on themetallicicty distribution over galactocentric distances up to 15 kpc.The outer disc is clearly separated from the middle part by theexistence of a step in the metallicity distribution at about 10 kpc.Taking the region of galactocentric distances from 10 kpc to 15 kpc, onecan derive an iron gradient -0.03 +/- 0.01 dex kpc-1 (25stars). The existence of a discontinuity can be caused by the effectivesuppression of mixing processes near the corotation circle where theradial component of the gas velocity should be very small.Based on spectra collected at the New Technology Telescope at ESO - LaSilla, Chile, under programme 68.D-0201(B).Table A.1 is only available in electronic form athttp://www.edpsciences.org
| Using Cepheids to determine the galactic abundance gradient. I. The solar neighbourhood
A number of studies of abundance gradients in the galactic disk havebeen performed in recent years. The results obtained are ratherdisparate: from no detectable gradient to a rather significant slope ofabout -0.1 dex kpc-1. The present study concerns theabundance gradient based on the spectroscopic analysis of a sample ofclassical Cepheids. These stars enable one to obtain reliable abundancesof a variety of chemical elements. Additionally, they have welldetermined distances which allow an accurate determination of abundancedistributions in the galactic disc. Using 236 high resolution spectra of77 galactic Cepheids, the radial elemental distribution in the galacticdisc between galactocentric distances in the range 6-11 kpc has beeninvestigated. Gradients for 25 chemical elements (from carbon togadolinium) are derived. The following results were obtained in thisstudy. Almost all investigated elements show rather flat abundancedistributions in the middle part of galactic disc. Typical values foriron-group elements lie within an interval from ~-0.02 to ~-0.04 dexkpc-1 (in particular, for iron we obtainedd[Fe/H]/dRG =-0.029 dex kpc-1). Similar gradientswere also obtained for O, Mg, Al, Si, and Ca. For sulphur we have founda steeper gradient (-0.05 dex kpc-1). For elements from Zr toGd we obtained (within the error bars) a near to zero gradient value.This result is reported for the first time. Those elements whoseabundance is not expected to be altered during the early stellarevolution (e.g. the iron-group elements) show at the solargalactocentric distance [El/H] values which are essentially solar.Therefore, there is no apparent reason to consider our Sun as ametal-rich star. The gradient values obtained in the present studyindicate that the radial abundance distribution within 6-11 kpc is quitehomogeneous, and this result favors a galactic model including a barstructure which may induce radial flows in the disc, and thus may beresponsible for abundance homogenization. Based on spectra collected atMcDonald - USA, SAORAS - Russia, KPNO - USA, CTIO - Chile, MSO -Australia, OHP - France. Full Table 1 is only available in electronicform at http://www.edpsciences.org Table A1 (Appendix) is only, andTable 2 also, available in electronic form at the CDS via anonymous ftpto cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/381/32
| Catalogue of Apparent Diameters and Absolute Radii of Stars (CADARS) - Third edition - Comments and statistics
The Catalogue, available at the Centre de Données Stellaires deStrasbourg, consists of 13 573 records concerning the results obtainedfrom different methods for 7778 stars, reported in the literature. Thefollowing data are listed for each star: identifications, apparentmagnitude, spectral type, apparent diameter in arcsec, absolute radiusin solar units, method of determination, reference, remarks. Commentsand statistics obtained from CADARS are given. The Catalogue isavailable in electronic form at the CDS via anonymous ftp tocdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcar?J/A+A/367/521
| The intermediate-band approach to the surface-brightness method for Cepheid radii and distance determination
The surface-brightness parameter Fν is calibrated in termsof the Strömgren intermediate-band colour b-y. The relationFν-(b-y)o valid for Cepheids is calibratedusing accurate near-infrared radii and distances for selected Cepheids.We have obtained uvby photometry for non-Cepheid giant and supergiantstars with known angular diameters and compared the slope and zero-pointof their Fν-(b-y)o relation with the Cepheidcalibration. We found that the two calibrations are significantlydifferent. The theoretical models lie in between the two calibrations.It is remarked that Fν-colour relations derived fromnon-Cepheids and involving blue colours (e.g. B-V or b-y) are notapplicable to Cepheids, while those involving redder colours (e.g. V-R,V-K or V-J) also produce good radii for Cepheids. Selected Cepheids ascalibrators lead to the accurate relationFν=3.898(+/-0.003)-0.378(+/-0.006)(b-y)o, whichallowed the calculation of radii and distances for a sample of 59Galactic Cepheids. The uncertainties in the zero-point and slope of theabove relation are similar to those obtained from near-infrared colours,and determine the accuracies in radii and distance calculations. Whileinfrared light and colour curves for Cepheids may be superior inprecision, the intermediate-band b-y colour allows the recovery of meanradii with an accuracy comparable to those obtained from the infraredsolutions. The derived distances are consistent within the uncertaintieswith those predicted by a widely accepted period-luminosityrelationship. Likewise, the resulting period-radius relation from theintermediate-band approach is in better agreement with infrared versionsthan with optical versions of this law. It is highlighted that theintermediate-band calibration of the surface-brightness method in thiswork is of comparable accuracy to the near-infrared calibrations. Thepresent results stress the virtues of uvby in determining the physicalparameters of supergiant stars of intermediate temperature.
| Galactic Cepheids. Catalogue of light-curve parameters and distances
We report a new version of the catalogue of distances and light-curveparameters for Galactic classical Cepheids. The catalogue listsamplitudes, magnitudes at maximum light, and intensity means for 455stars in BVRI filters of the Johnson system and (RI)_C filters of theCron-Cousins system. The distances are based on our new multicolour setof PL relations and on our Cepheid-based solution for interstellarextinction law parameters and are referred to an LMC distance modulus of18.25. The catalogue is only available in electronic form at the CDS viaanonymous ftp (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/Abstract.html
| The Vienna-KPNO search for Doppler-imaging candidate stars. I. A catalog of stellar-activity indicators for 1058 late-type Hipparcos stars
We present the results from a spectroscopic Ca ii H&K survey of 1058late-type stars selected from a color-limited subsample of the Hipparcoscatalog. Out of these 1058 stars, 371 stars were found to showsignificant H&K emission, most of them previously unknown; 23% withstrong emission, 36% with moderate emission, and 41% with weak emission.These spectra are used to determine absolute H&K emission-linefluxes, radial velocities, and equivalent widths of theluminosity-sensitive Sr ii line at 4077 Ä. Red-wavelengthspectroscopic and Strömgren y photometric follow-up observations ofthe 371 stars with H&K emission are used to additionally determinethe absolute Hα -core flux, the lithium abundance from the Li i6708 Å equivalent width, the rotational velocity vsin i, theradial velocity, and the light variations and its periodicity. Thelatter is interpreted as the stellar rotation period due to aninhomogeneous surface brightness distribution. 156 stars were found withphotometric periods between 0.29 and 64 days, 11 additional systemsshowed quasi-periodic variations possibly in excess of ~50 days. Further54 stars had variations but no unique period was found, and four starswere essentially constant. Altogether, 170 new variable stars werediscovered. Additionally, we found 17 new SB1 (plus 16 new candidates)and 19 new SB2 systems, as well as one definite and two possible new SB3systems. Finally, we present a list of 21 stars that we think are mostsuitable candidates for a detailed study with the Doppler-imagingtechnique. Tables A1--A3 are only available in electronic form at theCDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/Abstract.html
| Multi-colour PL-relations of Cepheids in the bt HIPPARCOS catalogue and the distance to the LMC
We analyse a sample of 236 Cepheids from the hipparcos catalog, usingthe method of ``reduced parallaxes'' in V, I, K and the reddening-free``Wesenheit-index''. We compare our sample to those considered by Feast& Catchpole (1997) and Lanoix et al. (1999), and argue that oursample is the most carefully selected one with respect to completeness,the flagging of overtone pulsators, and the removal of Cepheids that mayinfluence the analyses for various reasons (double-mode Cepheids,unreliable hipparcos solutions, possible contaminated photometry due tobinary companions). From numerical simulations, and confirmed by theobserved parallax distribution, we derive a (vertical) scale height ofCepheids of 70 pc, as expected for a population of 3-10 Msunstars. This has consequences for Malmquist- and Lutz-Kelker (Lutz &Kelker 1973, Oudmaijer et al. 1998) type corrections which are smallerfor a disk population than for a spherical population. The V and I datasuggest that the slope of the Galactic PL-relations may be shallowerthan that observed for LMC Cepheids, either for the whole period range,or that there is a break at short periods (near log P_0 ~ 0.7-0.8). Westress the importance of two systematic effects which influence thedistance to the LMC: the slopes of the Galactic PL-relations andmetallicity corrections. In order to assess the influence of thesevarious effects, we present 27 distance moduli (DM) to the LMC. Theseare based on three different colours (V,I,K), three different slopes(the slope observed for Cepheids in the LMC, a shallower slope predictedfrom one set of theoretical models, and a steeper slope as derived forGalactic Cepheids from the surface-brightness technique), and threedifferent metallicity corrections (no correction as predicted by one setof theoretical models, one implying larger DM as predicted by anotherset of theoretical models, and one implying shorter DM based onempirical evidence). We derive DM between 18.45 +/- 0.18 and 18.86 +/-0.12. The DM based on K are shorter than those based on V and I andrange from 18.45 +/- 0.18 to 18.62 +/- 0.19, but the DM in K could besystematically too low by about 0.1 magnitude because of a bias due tothe fact that NIR photometry is available only for a limited number ofstars. From the Wesenheit-index we derive a DM of 18.60 +/- 0.11,assuming the observed slope of LMC Cepheids and no metallicitycorrection, for want of more information. The DM to the LMC based on theparallax data can be summarised as follows. Based on the PL-relation inV and I, and the Wesenheit-index, the DM is 18.60 ± 0.11(± 0.08 slope)(^{+0.08}_{-0.15} ;metallicity), which is ourcurrent best estimate. Based on the PL-relation in K the DM is ;;;;18.52 +/- 0.18 (± 0.03 ;slope) (± 0.06 ;metallicity)(^{+0.10}_{-0} ;sampling ;bias). The random error is mostly due to thegiven accuracy of the hipparcos parallaxes and the number of Cepheids inthe respective samples. The terms between parentheses indicate thepossible systematic uncertainties due to the slope of the GalacticPL-relations, the metallicity corrections, and in the K-band, due to thelimited number of stars. Recent work by Sandage et al. (1999) indicatesthat the effect of metallicity towards shorter distances may be smallerin V and I than indicated here. From this, we point out the importanceof obtaining NIR photometry for more (closeby) Cepheids, as for themoment NIR photometry is only available for 27% of the total sample.This would eliminate the possible bias due to the limited number ofstars, and would reduce the random error estimate from 0.18 to about0.10 mag. Furthermore, the sensitivity of the DM to reddening,metallicity correction and slope are smallest in the K-band. Based ondata from the ESA HP astrometry satellite.
| Détermination des rayons de Céphéides. V. Vitesses radiales et dimensions de 22 Céphéides galactiques. Determination of the radii of Cepheids V. Radial velocities and dimensions of 22 galactic Cepheids
We present radial velocity data for 22 galactic Cepheid stars obtainedwith Coravel spectrometer. Continuous observation over several years hasenabled us to obtain 852 individual velocities covering all the phasesof the pulsation. The mean number of measurements per star is 39,ranging from 20 to 113. For each star radial velocity versus phasediagrams have been fitted by analytical relation, and the stellar radiusvariation has been derived by integration of this relation over thewhole period. Using recent ubv photometry of the literature and velocitycurves, we have calculated the radii of the stars using a method basedon the Baade-Wesselink concept. For these 22 Cepheids we give a linearlogarithmic period-radius relation with a range of 2,4 to 45 days. Lesobservations ont été effectuées àl'Observatoire de Haute-Provence (CNRS). Le tableau 1 est disponibleseulement sous forme électronique au CDS via ftp àcdsarc.u-strasbg.fr (130.79.128.5) ou viahttp://cdsweb.u-strasbg.fr/Abstract.html
| I- and JHK-band photometry of classical Cepheids in the HIPPARCOS catalog
By correlating the \cite[Fernie et al. (1995)]{F95} electronic databaseon Cepheids with the ``resolved variable catalog'' of the hipparcosmission and the simbad catalog one finds that there are 280 Cepheids inthe hipparcos catalog. By removing W Vir stars (Type ii Cepheids),double-mode Cepheids, Cepheids with an unreliable solution in thehipparcos catalog, and stars without photometry, it turns out that thereare 248 classical Cepheids left, of which 32 are classified asfirst-overtone pulsators. For these stars the literature was searchedfor I-band and near-infrared data. Intensity-mean I-band photometry onthe Cousins system is derived for 189 stars, and intensity-mean JHK dataon the Carter system is presented for 69 stars.
| Monitoring the Evolution of Cepheid Variables
Described here are preliminary results of a pilot project to monitorchanges in the ephemerides of northern hemisphere Cepheid's using anSBIG camera attached to the 0.4-m telescope of the campus obversatory atSaint Mary's University. Epochs of maximum light for fifteen Cepheid'shave been derived using published light curves for each variable astemplates, and the results are being used to update the O-C ephemeridesfor the program stars. Results for BB Her are presented here. Periodchanges for Cepheid variables are demonstrated to be an excellent meansof pinpointing their evolutionary status, as well as for investigatingother peculiarities of the class.
| UVBY beta Photometric Data and Fourier Coefficients for Galactic Population I and Population II Cepheids
Photometric data in the uvby beta system are presented for a sample of98 Population I Cepheids and seven W Virginis or Population II Cepheids.The importance of the Fourier decomposition technique in the study ofthe structure of pulsating stars is stressed. Mean values and Fourierdecomposition coefficients for the V, b - y, m1, and c1 variations arecalculated. Also, mean values of H beta are provided. New times ofmaximum V light are reported for the majority of the stars in thesample. Significant shifts of the light and color curves were found insome Cepheids; these are explained by their period variations. Thesestars are highlighted in the text.
| The shape and scale of Galactic rotation from Cepheid kinematics
A catalog of Cepheid variables is used to probe the kinematics of theGalactic disk. Radial velocities are measured for eight distant Cepheidstoward l = 300 deg; these new Cepheids provide a particularly goodconstraint on the distance to the Galactic center, R0. We model the diskwith both an axisymmetric rotation curve and one with a weak ellipticalcomponent, and find evidence for an ellipticity of 0.043 +/- 0.016 nearthe sun. Using these models, we derive R0 = 7.66 +/- 0.32 kpc andv(circ) = 237 +/- 12 km/s. The distance to the Galactic center agreeswell with recent determinations from the distribution of RR Lyraevariables and disfavors most models with large ellipticities at thesolar orbit.
| The HIPPARCOS Mission
Not Available
| Structural Properties of Pulsating Star Light Curves Through Fuzzy Divisive Hierarchical Clustering
Not Available
| Cepheid radii and the CORS method revisited.
We have refined the CORS method, introduced in 1980 for the computationof the cepheid radii, in order to extend its applicability to recent andextensive sets of observations. The refinement is based on thecomputation, from observational data only, of one of the terms of thesolving equation, previously based only on precise calibrations ofphotometric colors. A limited number of assumptions, generally acceptedin the literature, is used. New radii are computed for about 70cepheids, and the resulting P-R relation is discussed.
| Photometric Parameters for Short-Period Cepheids
Abstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1996AJ....111.1313E&db_key=AST
| Search for resonance effects in long period Cepheids.
Light curves of classical Cepheids with period longer than 8 days havebeen Fourier decomposed with the purpose of studying the characteristicsof high order Fourier parameters, and to detect possible effects ofresonances between pulsation modes other than the well known resonanceat P~10d. The possible effects of two expected resonances have beententatively identified: P_0_/P_1_=3/2 at P_0_~24 d and P_0_/P_3_=3 atP_0_~27d. The identification is not completely certain owing to the poornumber of Cepheids. The limitation could be overcome by observingaccurately other relatively faint Cepheids in our Galaxy, and severalCepheids in nearby galaxies.
| Rotation Curve of the System of Classical Cepheids and the Distance to the Galactic Center
Not Available
| A new approach to the surface brightness method for cepheid radii determination.
Abstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1994RMxAA..29..148R&db_key=AST
| Period-Radius and Period Luminosity Relations for the Classicla Cepheids. I.
The radii of 43 cepheids are computed by the method proposed by theauthor. A relation between the period and the radius for classicalcepheids is derived: log R = (11.9686 +/- 0.0216) + (0.7728 +/-0.197)*log P, where radius is in cm and period is in days.
| New radial velocities for classical cepheids. Local galactic rotation revisited
New centre-of-mass radial velocities are calculated for 107 classicalcepheids from CORAVEL observations. We generally determine thesevelocities from four to six measurements carefully spaced in phase, byfitting a "typical" radial velocity curve or the mirror image of thelight curve. A decomposition in Fourier series is used for stars withmore than 10 measurements. Distances are then computed through aperiod-luminosity-colour relation for 278 classical cepheids with knownradial velocity, and an axisymmetric galactic rotation model is appliedto the sample, using a generalised non-linear least square method withuncertainties on both the velocities and the distances. The bestresults, with a rotation curve modelled as a third order polynomial,are: Rsun_=8.09 +/-0.30 kpc, A=15.92 +/-0.34 km/s/kpc, 2ARsun_=257 +/-7 km/s, A2=d^2theta(R)/d R^2^=-3.38+/-0.38 km/s/kpc^2^, A3=d^3theta(R)/d R^3^=1.99 +/-0.62km/s/kpc^3^, u_0_=9.32 +/-0.80 km/s, v_0_=11.18 +/-0.65 km/s. The effectof modifying the distance scale of cepheids, the absorption coefficientor the fitting procedure algorithm are examined. It appears that theproduct 2 A Rsun_ is very robust towards these changes. Theextended sample of classical cepheids with known radial velocitypresented in this paper seems to imply a higher value for A thananterior studies. The radial velocity residuals show a systematic k-termof about 2 km/s. New evidence from cluster cepheids excludes anintrinsic cause for this shift, and a dynamical cause is proposed from acomparison with a N-body simulation of the Galaxy. The simulation showsthat a systematic bias of this magnitude is typical. The structure ofthe local residual velocity field is examined in some detail.
| The Cepheid Period-Luminosity Relation from Independent Distances of 100 Galactic Variables
Abstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1993ApJ...418..135G&db_key=AST
| The SVS Numbering Series Discontinued
Not Available
| Northern Cepheids: Period Update and Duplicity Effects
O-C diagrams have been continued for 64 northern Cepheids with theprimary aim of studying the effects of duplicity on the pulsationperiod. Because the light-time effect in the O-C diagrams of binaryCepheids has to be accompanied with properly phased variations in theγ-velocity, the radial velocity of the programme stars has beenstudied, as well. Light-time effect is suspected in the O-C diagram ofFM Aql, RW Cam, Y Lac and RS Ori, and confirmed for AW Per. One or morephase jumps are present or suspected in the O-C diagram of 19 northernCepheids (FF Aql, BY Cas, DD Cas, DL Cas, X Cyg, SU Cyg, SZ Cyg, DT Cyg,V532 Cyg, V924 Cyg, TX Del, DX Gem, X Lac, CV Mon, RS Ori, SV Per, SZTau, T Vul, X Vul). In addition to the Cepheids with known spectroscopicorbit, the spectroscopic binary nature based on the variability of theγ-velocity has been confirmed, revealed or suspected for themajority of the programme stars. The most probable new spectroscopicbinary Cepheids are: KL Aql, Eta Aql, SU Cas, V636 Cas, BZ Cyg, MW Cyg,V386 Cyg, W Gem, RZ Gem, AD Gem, RS Ori, SV Per, SW Tau, T Vul and UVul. A preliminary value of the orbital period is suggested for Eta Aql,SU Cas, RZ Gem, T Vul and U Vul.
| Color Excesses on a Uniform Scale for 328 Cepheids
Abstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1990ApJS...72..153F&db_key=AST
| The structure of the Cepheid instability strip
About 100 classical Cepheids having color excesses on a homogeneoussystem with standard errors of 0.02 or less mag are used with theFeast-Walker period-luminosity-color relation to study the distributionof such stars in the instability strip. It is found that mean (B-V)magis a better indicator of mean effective temperature than is mean B(i) -mean V(i)(i). The blue edge of the color-magnitude distribution isconsistent with the theoretical blue edge for Y = 0.28 and Z = 0.02.Although the highest amplitude stars are found near the center of theperiod-color array, high- and low-amplitude stars can intermingle, andboth kinds are to be found near the edges of the distribution. The sameis true on the C-M array. Finally, it is pointed out that the Cepheidsdo not populate the instability strip uniformly if the red edge is takento be parallel to the theoretical blue edge. Rather, the localinstability region runs as a parallelogram in the C-M array from thetheoretical blue edge upward and to the red.
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