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 T Monocerotis: collected maximum times and a new ephemerisThe period of this classical cepheid is variable. I give 209 reportedtimes of maximum light and a revised ephemeris. Angular diameter amplitudes of bright Cepheids.Expected mean angular diameters and amplitudes of angular diametervariations are estimated for all monoperiodic Classical Cepheidsbrighter than < V > = 8.0 mag. The catalog is intended to helpselecting best Cepheid targets for interferometric observations. Contact Binaries with Additional Components. I. The Extant DataWe have attempted to establish observational evidence for the presenceof distant companions that may have acquired and/or absorbed angularmomentum during the evolution of multiple systems, thus facilitating orenabling the formation of contact binaries. In this preliminaryinvestigation we use several techniques (some of themdistance-independent) and mostly disregard the detection biases ofindividual techniques in an attempt to establish a lower limit to thefrequency of triple systems. While the whole sample of 151 contactbinary stars brighter than Vmax=10 mag gives a firm lowerlimit of 42%+/-5%, the corresponding number for the much better observednorthern-sky subsample is 59%+/-8%. These estimates indicate that mostcontact binary stars exist in multiple systems. Elemental Abundance Ratios in Stars of the Outer Galactic Disk. III. CepheidsWe present metallicities, [Fe/H], and elemental abundance ratios,[X/Fe], for a sample of 24 Cepheids in the outer Galactic disk based onhigh-resolution echelle spectra. The sample members have galactocentricdistances covering 12 kpc<=RGC<=17.2 kpc, making themthe most distant Galactic Cepheids upon which detailed abundanceanalyses have been performed. We find subsolar ratios of [Fe/H] andoverabundances of [α/Fe], [La/Fe], and [Eu/Fe] in the programstars. All abundance ratios exhibit a dispersion that exceeds themeasurement uncertainties. As seen in our previous studies of old openclusters and field giants, enhanced ratios of [α/Fe] and [Eu/Fe]reveal that recent star formation has taken place in the outer disk withType II supernovae preferentially contributing ejecta to theinterstellar medium and with Type Ia supernovae playing only a minorrole. The enhancements for La suggest that asymptotic giant branch starshave contributed to the chemical evolution of the outer Galactic disk.Some of the young Cepheids are more metal-poor than the older openclusters and field stars at comparable galactocentric distances. Thisdemonstrates that the outer disk is not the end result of the isolatedevolution of an ensemble of gas and stars. We showed previously that theolder open clusters and field stars reached a basement metallicity atabout 10-11 kpc. The younger Cepheids reach the same metallicity but atlarger galactocentric distances, roughly 14 kpc. This suggests that theGalactic disk has been growing with time, as predicted from numericalsimulations. The outer disk Cepheids appear to exhibit a bimodaldistribution for [Fe/H] and [α/Fe]. Most of the Cepheids continuethe trends with galactocentric distance exhibited by S. M. Andrievsky'slarger Cepheid sample, and we refer to these stars as the GalacticCepheids.'' A minority of the Cepheids show considerably lower [Fe/H]and higher [α/Fe], and we refer to these stars as the MergerCepheids.'' One signature of a merger event would be compositiondifferences between the Galactic and Merger Cepheids. The Cepheidssatisfy this requirement, and we speculate that the distinctcompositions suggest that the Merger Cepheids may have formed under theinfluence of significant merger or accretion events. The short lifetimesof the Cepheids reveal that the merger event may be ongoing, with theMonoceros Ring and Canis Major galaxy being possible merger candidates.This paper makes use of observations obtained at the National OpticalAstronomy Observatory, which is operated by the Association ofUniversities for Research in Astronomy (AURA), Inc., under contract fromthe National Science Foundation. We also employ data products from theTwo Micron All Sky Survey, which is a joint project of the University ofMassachusetts and the Infrared Processing and Analysis Center,California Institute of Technology, funded by the National Aeronauticsand Space Administration and the National Science Foundation. Extended envelopes around Galactic Cepheids. I. ℓ Carinae from near and mid-infrared interferometry with the VLTIWe present the results of long-baseline interferometric observations ofthe bright southern Cepheid ℓ Carinae in the infrared N (8-13 μm)and K (2.0-2.4 μm) bands, using the MIDI and VINCI instruments of theVLT Interferometer. We resolve in the N band a large circumstellarenvelope (CSE) that we model with a Gaussian of 3 Rstar(≈500 Rȯ ≈ 2-3 AU) half width at half maximum. Thesignature of this envelope is also detected in our K band data as adeviation from a single limb darkened disk visibility function. Thesuperimposition of a Gaussian CSE on the limb darkened disk model of theCepheid star results in a significantly better fit of our VINCI data.The extracted CSE parameters in the K band are a half width at halfmaximum of 2 Rstar, comparable to the N band model, and atotal brightness of 4% of the stellar photosphere. A possibility is thatthis CSE is linked to the relatively large mass loss rate of ℓ Car.Though its physical nature cannot be determined from our data, wediscuss an analogy with the molecular envelopes of RV Tauri, redsupergiants and Miras. Galactic Cepheids. I. Elemental Abundances and Their Implementation for Stellar and Galactic EvolutionWe have added data for 16 distant Cepheids observed with the echellespectrograph of the Apache Point 3.5 m telescope to improve thecorrelations of abundance parameters with pulsation period and distancefrom the Galactic center (RG ). While we see no importanttrends with pulsation period, some important ratios are closely relatedto the evolution of stars through the instability strip. The mostinteresting is the N/C ratio, which is predicted to be enhanced by afactor of 4 when an evolving supergiant cools to Teff=4000 Kand the outer convection zone reaches the depth at which CN processinghas converted C to N. We find a Gaussian distribution around a value of[N/C]=0.6, just as predicted. The ratio of about 30:1 mixed to unmixedstars can be taken as the ratio of evolutionary time spent on the blueloop to the time spent on the first crossing through the instabilitystrip. According to stellar models, the main mixing event takes placewhen Teff drops below 4000 K, which is outside the red edgeof the instability strip; i.e., after stars have crossed the instabilitystrip for the first time. We have confirmed previously knowncorrelations of [Fe/H] with RG. We find that [Fe/H] shows agradient of -0.06 Kpc-1. The only other significant gradientis that of [Eu/Fe], which increases with RG, thereby showingan increasing ratio of SN II/SN Ia in the outer Galaxy. Mean JHK Magnitudes of Fundamental-Mode Cepheids from Single-Epoch ObservationsWe present an empirical method for converting single-point near-infraredJ, H, and K measurements of fundamental-mode Cepheids to meanmagnitudes, using complete light curves in V or I bands. The algorithmis based on the template light curves in the near-infrared bandpasses.The mean uncertainty of the method is estimated to about 0.03 mag, whichis smaller than the uncertainties obtained in other approaches to theproblem in the literature. A spectroscopic study of bright southern Cepheids - a high-resolution view of Cepheid atmospheresWe present high-resolution spectroscopic observations andspecies-by-species radial velocities of a number of southern Cepheids.The stars (BP Cir, V350 Sgr, AX Cir, V636 Sco, W Sgr, S Mus, β Dor,TT Aql, Y Oph, YZ Car, SW Vel, X Pup, T Mon and l Car) were observed aspart of a long-term programme at Mt John University Observatory. Radialvelocities were determined with the line bisector technique, and have aprecision of ~300 ms-1. Velocity differences as large as 30kms-1 were found for Hα and CaII when referenced to themetallic line velocity curves, but more subtle variations (of 1-2kms-1) were also detected in many other species. Pulsationalphase anticorrelations are found between lines of SiII and BaII,confirming the propagation time delay between line-forming layersproducing these two species. We find that the amplitude and phasedifferences between the various species increase with period. Zur Beobachtung und Auswertung von Cepheiden-Lichtkurven.Not Available 130 Jahre T Monocerotis.Not Available Welchen Lichtwechsel kann ein Beobachter bei Cepheiden erwarten?Not Available Infrared Surface Brightness Distances to Cepheids: A Comparison of Bayesian and Linear-Bisector CalculationsWe have compared the results of Bayesian statistical calculations andlinear-bisector calculations for obtaining Cepheid distances and radiiby the infrared surface brightness method. We analyzed a set of 38Cepheids using a Bayesian Markov Chain Monte Carlo method that had beenrecently studied with a linear-bisector method. The distances obtainedby the two techniques agree to 1.5%+/-0.6%, with the Bayesian distancesbeing larger. The radii agree to 1.1%+/-0.7%, with the Bayesiandeterminations again being larger. We interpret this result asdemonstrating that the two methods yield the same distances and radii.This implies that the short distance to the Large Magellanic Cloud foundin recent linear-bisector studies of Cepheids is not caused bydeficiencies in the mathematical treatment. However, the computeduncertainties in distance and radius for our data set are larger in theBayesian calculation by factors of 1.4-6.7. We give reasons to favor theBayesian computations of the uncertainties. The larger uncertainties canhave a significant impact on interpretation of Cepheid distances andradii obtained from the infrared surface brightness method. Pulsation and Evolutionary Masses of Classical Cepheids. I. Milky Way VariablesWe investigate a selected sample of Galactic classical Cepheids withavailable distance and reddening estimates in the framework of thetheoretical scenario provided by pulsation models, computed with metalabundance Z=0.02, helium content in the range of Y=0.25-0.31, andvarious choices of the stellar mass and luminosity. After transformingthe bolometric light curve of the fundamental models into BVRIJKmagnitudes, we derived analytical relations connecting the pulsationperiod with the stellar mass, the mean (intensity averaged) absolutemagnitude, and the color of the pulsators. These relations are usedtogether with the Cepheid observed absolute magnitudes in order todetermine the pulsation'' mass, Mp, of each individualvariable. The comparison with the evolutionary'' masses,Me,can, given by canonical (no convective core overshooting,no mass loss) models of central He-burning stellar structures revealsthat the Mp/Me,can ratio is correlated with theCepheid period, ranging from ~0.8 at logP=0.5 to ~1 at logP=1.5. Wediscuss the effects of different input physics and/or assumptions on theevolutionary computations, as well as of uncertainties in the adoptedCepheid metal content, distance, and reddening. Eventually, we find thatthe pulsational results can be interpreted in terms of mass loss duringor before the Cepheid phase, whose amount increases as the Cepheidoriginal mass decreases. It vanishes around 13 Msolar andincreases up to ~20% at 4 Msolar. Direct Distances to Cepheids in the Large Magellanic Cloud: Evidence for a Universal Slope of the Period-Luminosity Relation up to Solar AbundanceWe have applied the infrared surface brightness (ISB) technique toderive distances to 13 Cepheid variables in the LMC that span a periodrange from 3 to 42 days. From the absolute magnitudes of the variablescalculated from these distances, we find that the LMC Cepheids definetight period-luminosity (PL) relations in the V, I, W, J, and K bandsthat agree exceedingly well with the corresponding Galactic PL relationsderived from the same technique and are significantly steeper than theLMC PL relations in these bands observed by the OGLE-II Project in V, I,and W and by Persson and coworkers in J and K. We find that the LMCCepheid distance moduli we derive, after correcting them for the tilt ofthe LMC bar, depend significantly on the period of the stars, in thesense that the shortest period Cepheids have distance moduli near 18.3,whereas the longest period Cepheids are found to lie near 18.6. Sincesuch a period dependence of the tilt-corrected LMC distance modulishould not exist, there must be a systematic, period-dependent error inthe ISB technique not discovered in previous work. We identify as themost likely culprit the p-factor, which is used to convert the observedCepheid radial velocities into their pulsational velocities. Bydemanding (1) a zero slope on the distance modulus versus period diagramand (2) a zero mean difference between the ISB and ZAMS fitting distancemoduli of a sample of well-established Galactic cluster Cepheids, wefind that p=1.58(+/-0.02)-0.15(+/-0.05)logP, with the p-factor dependingmore strongly on Cepheid period (and thus luminosity) than indicated bypast theoretical calculations. When we recalculate the distances of theLMC Cepheids with the revised p-factor law suggested by our data, we notonly obtain consistent distance moduli for all stars but also decreasethe slopes in the various LMC PL relations (and particularly in thereddening-independent K and W bands) to values that are consistent withthe values observed by OGLE-II and Persson and coworkers. From our 13Cepheids, we determine the LMC distance modulus to be 18.56+/-0.04 mag,with an additional estimated systematic uncertainty of ~0.1 mag. Usingthe same corrected p-factor law to redetermine the distances of theGalactic Cepheids, the new Galactic PL relations are also foundconsistent with the observed optical and near-infrared PL relations inthe LMC. Our main conclusion from the ISB analysis of the LMC Cepheidsample is that, within current uncertainties, there seems to be nosignificant difference between the slopes of the PL relations in theMilky Way and LMC. With literature data on more metal-poor systems, itseems now possible to conclude that the slope of the Cepheid PL relationis independent of metallicity in the broad range in [Fe/H] from -1.0 dexto solar abundance, within a small uncertainty. The new evidence fromthe first ISB analysis of a sizable sample of LMC Cepheids suggests thatthe previous, steeper Galactic PL relations obtained from this techniquewere caused by an underestimation of the period dependence in themodel-based p-factor law used in the previous work. We emphasize,however, that our current results must be substantiated by newtheoretical models capable of explaining the steeper period dependenceof the p-factor law, and we will also need data on more LMC fieldCepheids to rule out remaining concerns about the validity of ourcurrent interpretation. Phase-dependent Variation of the Fundamental Parameters of Cepheids. II. Periods Longer than 10 DaysWe present the results of a detailed multiphase spectroscopic analysisof 14 classical Cepheids with pulsation periods longer than 10 days. Foreach star, we have derived phased values of effective temperature,surface gravity, microturbulent velocity, and elemental abundances. Weshow that the elemental abundance results for these Cepheids areconsistent for all pulsational phases. Mean Angular Diameters and Angular Diameter Amplitudes of Bright CepheidsWe predict mean angular diameters and amplitudes of angular diametervariations for all monoperiodic PopulationI Cepheids brighter than=8.0 mag. The catalog is intended to aid selecting mostpromising Cepheid targets for future interferometric observations. CHARM2: An updated Catalog of High Angular Resolution MeasurementsWe present an update of the Catalog of High Angular ResolutionMeasurements (CHARM, Richichi & Percheron \cite{CHARM}, A&A,386, 492), which includes results available until July 2004. CHARM2 is acompilation of direct measurements by high angular resolution methods,as well as indirect estimates of stellar diameters. Its main goal is toprovide a reference list of sources which can be used for calibrationand verification observations with long-baseline optical and near-IRinterferometers. Single and binary stars are included, as are complexobjects from circumstellar shells to extragalactic sources. The presentupdate provides an increase of almost a factor of two over the previousedition. Additionally, it includes several corrections and improvements,as well as a cross-check with the valuable public release observationsof the ESO Very Large Telescope Interferometer (VLTI). A total of 8231entries for 3238 unique sources are now present in CHARM2. Thisrepresents an increase of a factor of 3.4 and 2.0, respectively, overthe contents of the previous version of CHARM.The catalog is only available in electronic form at the CDS viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/431/773 The influence of chemical composition on the properties of Cepheid stars. I. Period-Luminosity relation vs. iron abundanceWe have assessed the influence of the stellar iron content on theCepheid Period-Luminosity (PL) relation by relating the V band residualsfrom the Freedman et al. (\cite{fre01}) PL relation to [Fe/H] for 37Galactic and Magellanic Clouds Cepheids. The iron abundances weremeasured from FEROS and UVES high-resolution and high-signal to noiseoptical spectra. Our data indicate that the stars become fainter asmetallicity increases, until a plateau or turnover point is reached atabout solar metallicity. Our data are incompatible with both nodependence of the PL relation on iron abundance, and with the linearlydecreasing behavior often found in the literature (e.g. Kennicutt et al.\cite{ken98}; Sakai et al. \cite{sak04}). On the other hand, non-lineartheoretical models of Fiorentino et al. (\cite{fio02}) provide a fairlygood description of the data.Based on observations made with ESO Telescopes at La Silla and ParanalObservatories under proposal ID 66.D-0571.Table \ref{tab:log} is only available in electronic form athttp://www.edpsciences.org The orbits of southern binary CepheidsHigh-resolution spectroscopic observations have been made of a number ofsouthern Cepheids. The stars studied were part of a long-term programmeto observe southern variable stars and to complete a data base of radialvelocities over a long time interval. The radial velocities have aprecision of ~300 m s-1, allowing the detection of velocitydifferences of ~1 km s-1 with confidence. Our new dataprovide a consistent set of data against which other sources of data canbe compared.Masses were determined for two systems, the 9-d Cepheid S Mus (6.2 +/-0.2 Msolar) and the 5-d Cepheid V350 Sgr (6.0 +/- 0.9Msolar). For another seven Cepheids (Y Car, YZ Car, AX Cir,BP Cir, V636 Sco, W Sgr and T Mon), new or improved orbital solutionswere found.New results presented here include the first orbital solution for AXCir, a completely revised orbital solution for YZ Car, which establishedits eccentricity and orbital motion, and a new pulsation period (2.39819 d) for BP Cir. The pulsational mass determinations provide furtherconfirmation of the convergence of mass determinations between dynamicaland evolutionary methods. Period-luminosity relations for Galactic Cepheid variables with independent distance measurementsIn this paper, we derive the period-luminosity (PL) relation forGalactic Cepheids with recent independent distance measurements fromopen cluster, Barnes-Evans surface brightness, interferometry and HubbleSpace Telescope astrometry techniques. Our PL relation confirms theresults from recent works, which showed that the Galactic Cepheidsfollow a different PL relation to their Large Magellanic Cloud (LMC)counterparts. Our results also show that the slope of the Galactic PLrelation is inconsistent with the LMC slope with more than 95 per centconfidence level. We apply this Galactic PL relation to find thedistance to NGC 4258. Our result of μo= 29.49 +/- 0.06 mag(random error) agrees at the ~1.4σ level with the geometricaldistance of μgeo= 29.28 +/- 0.15 mag from water masermeasurements. A new Period-Radius relation for Galactic Classical CepheidsWe discuss a new Period-Radius (PR) relation for Galactic ClassicalCepheids, obtained by means of a new version of the CORS method whichhas been modified in order to be run with the Strömgren photometricsystem. The major change consists in the calibration of the SurfaceBrightness as a function of the two reddening free'' colourindexes [c1] and [m1], by means of the model atmospheres by Castelli etal. (1997). In this contribution we first briefly discuss somenumerical experiments performed on the basis of synthetic Cepheid lightcurves to test the accuracy of the method, and then report thePeriod-Radius relation for Classical Cepheids obtained by applying thethe new method to a sample of Galactic Cepheids. Beobachtungsergebnisse Bundesdeutsche Arbeitsgemeinschaft fur Veranderlichen Serne e.V.Not Available Improvement of the CORS method for Cepheids radii determination based on Strömgren photometryIn this paper we present a modified version of the CORS method based ona new calibration of the Surface Brightness function in theStrömgren photometric system. The method has been tested by meansof synthetic light and radial velocity curves derived from nonlinearpulsation models. Detailed simulations have been performed to take intoaccount the quality of real observed curves as well as possible shiftsbetween photometric and radial velocity data. The method has been thenapplied to a sample of Galactic Cepheids with Strömgren photometryand radial velocity data to derive the radii and a new PR relation. As aresult we find log R = (1.19 ± 0.09) + (0.74 ± 0.11) logP (rms = 0.07). The comparison between our result and previous estimatesin the literature is satisfactory. Better results are expected from theadoption of improved model atmosphere grids. The metallicity dependence of the Cepheid PL-relationA sample of 37 Galactic, 10 LMC and 6 SMC cepheids is compiled for whichindividual metallicity estimates exist and BVIK photometry in almost allcases. The Galactic cepheids all have an individual distance estimateavailable. For the MC objects different sources of photometry arecombined to obtain improved periods and mean magnitudes. Amulti-parameter Period-Luminosity relation is fitted to the data whichalso solves for the distance to the LMC and SMC. When all three galaxiesare considered, without metallicity effect, a significant quadratic termin log P is found, as previously observed and also predicted in sometheoretical calculations. For the present sample it is empiricallydetermined that for log P < 1.65 linear PL-relations may be adopted,but this restricts the sample to only 4 LMC and 1 SMC cepheid.Considering the Galactic sample a metallicity effect is found in thezero point in the VIWK PL-relation (-0.6 ± 0.4 or -0.8 ±0.3 mag/dex depending on the in- or exclusion of one object), in thesense that metal-rich cepheids are brighter. The small significance ismostly due to the fact that the Galactic sample spans a narrowmetallicity range. The error is to a significant part due to the errorin the metallicity determinations and not to the error in the fit.Including the 5 MC cepheids broadens the observed metallicity range anda metallity effect of about -0.27 ± 0.08 mag/dex in the zeropoint is found in VIWK, in agreement with some previous empiricalestimates, but now derived using direct metallicity determinations forthe cepheids themselves. The effect of metallicity on the Cepheid Period-Luminosity relation from a Baade-Wesselink analysis of Cepheids in the Galaxy and in the Small Magellanic CloudWe have applied the near-IR Barnes-Evans realization of theBaade-Wesselink method as calibrated by Fouqué & Gieren(\cite{FG97}) to five metal-poor Cepheids with periods between 13 and 17days in the Small Magellanic Cloud as well as to a sample of 34 GalacticCepheids to determine the effect of metallicity on the period-luminosity(P-L) relation. For ten of the Galactic Cepheids we present new accurateand well sampled radial-velocity curves. The Baade-Wesselink analysisprovides accurate individual distances and luminosities for the Cepheidsin the two samples, allowing us to constrain directly, in a purelydifferential way, the metallicity effect on the Cepheid P-L relation.For the Galactic Cepheids we provide a new set of P-L relations whichhave zero-points in excellent agreement with astrometric andinterferometric determinations. These relations can be used directly forthe determination of distances to solar-metallicity samples of Cepheidsin distant galaxies, circumventing any corrections for metallicityeffects on the zero-point and slope of the P-L relation. We findevidence for both such metallicity effects in our data. Comparing ourtwo samples of Cepheids at a mean period of about 15 days, we find aweak effect of metallicity on the luminosity similar to that adopted bythe HST Key Project on the Extragalactic Distance Scale. The effect issmaller for the V band, where we find Δ MV/Δ[Fe/H] = -0.21±0.19, and larger for the Wesenheit index W, wherewe find Δ MW/Δ [Fe/H] = -0.29±0.19. Forthe I and K bands we find Δ MI/Δ [Fe/H] =-0.23± 0.19 and Δ MK/Δ [Fe/H] =-0.21± 0.19, respectively. The error estimates are 1 σstatistical errors. It seems now well established that metal-poorCepheids with periods longer than about 10 days are intrinsicallyfainter in all these bands than their metal-rich counterparts ofidentical period. Correcting the LMC distance estimate of Fouquéet al. (\cite{FSG03}) for this metallicity effect leads to a revised LMCdistance modulus of (m-M)_0 = 18.48± 0.07, which is also inexcellent agreement with the value of (m-M)_0 = 18.50± 0.10adopted by the Key Project. From our SMC Cepheid distances we determinethe SMC distance to be 18.88±0.13 magirrespective of metallicity.Some of the observations reported here were obtained with the MultipleMirror Telescope, operated jointly by the Smithsonian Institution andthe University of Arizona.Tables A.2-A.11 are only available in electronic form at the CDS viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/415/531 Consistent distances from Baade-Wesselink analyses of Cepheids and RR LyraesBy using the same algorithm in the Baade-Wesselink analyses of GalacticRR Lyrae and Cepheid variables, it is shown that, within 0.03-mag1σ statistical error, they yield the same distance modulus for theLarge Magellanic Cloud. By fixing the zero-point of thecolour-temperature calibration to those of the current infrared fluxmethods and using updated period-luminosity-colour relations, we get anaverage value of 18.55 for the true distance modulus of the LMC. Cepheid Variables in the AAVSO International DatabaseThere are 205,500 visual observations for 148 Cepheids as well as 182photoelectric observations for 7 Cepheids in the AAVSO InternationalDatabase. These data were reduced with Hertzprung's method and 2,010times of maximum brightness were obtained. O-C diagrams for 21well-observed Cepheids are presented and results obtained are comparedwith existing data. Beobachtungsegebnisse Bundesdeutsche Arbeitsgemainschaft fur Veranderliche Sterne e.V.Not Available A Bayesian Analysis of the Cepheid Distance ScaleWe develop and describe a Bayesian statistical analysis to solve thesurface brightness equations for Cepheid distances and stellarproperties. Our analysis provides a mathematically rigorous andobjective solution to the problem, including immunity from Lutz-Kelkerbias. We discuss the choice of priors, show the construction of thelikelihood distribution, and give sampling algorithms in a Markov chainMonte Carlo approach for efficiently and completely sampling theposterior probability distribution. Our analysis averages over theprobabilities associated with several models rather than attempting topick the best model'' from several possible models. Using a sample of13 Cepheids we demonstrate the method. We discuss diagnostics of theanalysis and the effects of the astrophysical choices going into themodel. We show that we can objectively model the order of Fourierpolynomial fits to the light and velocity data. By comparison withtheoretical models of Bono et al. we find that EU Tau and SZ Tau areovertone pulsators, most likely without convective overshoot. Theperiod-radius and period-luminosity relations we obtain are shown to becompatible with those in the recent literature. Specifically, we findlog()=(0.693+/-0.037)[log(P)-1.2]+(2.042+/-0.047) andv>=-(2.690+/-0.169)[log(P)-1.2]-(4.699+/-0.216). Interstellar Extinction and the Intrinsic Colors of Classical Cepheids in the Galaxy, the LMC, and the SMCNew methods are applied to samples of classical cepheids in the galaxy,the Large Magellanic Cloud, and the Small Magellanic Cloud to determinethe interstellar extinction law for the classical cepheids, R B:R V:RI:R J:R H:R K= 4.190:3.190:1.884:0.851:0.501:0.303, the color excessesfor classical cepheids in the galaxy,E(B-V)=-0.382-0.168logP+0.766(V-I), and the color excesses for classicalcepheids in the LMC and SMC, E(B-V)=-0.374-0.166logP+0.766(V-I). Thedependence of the intrinsic color (B-V)0 on the metallicity of classicalcepheids is discussed. The intrinsic color (V-I)0 is found to beabsolutely independent of the metallicity of classical cepheids. A highprecision formula is obtained for calculating the intrinsic colors ofclassical cepheids in the galaxy:(-)0=0.365(±0.011)+0.328(±0.012)logP.
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