The absolute magnitudes of Cepheids and the extragalacticdistance scale

It is pointed out that a Cepheid period–luminosity relation with a zero-point from Hipparcos trigonometrical parallaxes and a consistent reddening system zero-point implies that some recent estimates of H ₀ based on the Cepheid scale should be increased by ∼8 per cent. This result avoids using the distance to the Large Magellanic Cloud (LMC) as an intermediary point but is not significantly different from the result obtained by Feast & Catchpole via the LMC. A number of other issues are discussed, including metallicity effects on Cepheid distances and reddenings, and the age of metal-poor globular clusters.     

On the second-overtone stability among Small Magellanic Cloud Cepheids

We present a new set of Cepheid, full amplitude, non-linear, convective models which are pulsationally unstable in the second overtone (SO). Hydrodynamical models were constructed by adopting a chemical composition typical of Cepheids in the Small Magellanic Cloud (SMC) and for stellar masses ranging from 3.25 to 4 M_⊙. Predicted φ ₂₁ Fourier parameters agree, within current uncertainties, with empirical data for pure first- and second-overtone variables as well as for first-/second-overtone (FO/SO) double-mode Cepheids collected by Udalski et al. in the SMC. On the other hand, predicted I -band amplitudes are systematically larger than the observed ones in the short-period range, but attain values that are closer to the empirical ones for log  P _SO≥−0.12 and log  P _FO≥0.1 . We also find, in agreement with empirical evidence, that the region within which both second and first overtones attain a stable limit cycle widens when moving towards lower luminosities. Moreover, predicted P _SO/ P _FO and P _FO/ P _F period ratios agree quite well with empirical period ratios for FO/SO and fundamental/FO double-mode SMC Cepheids.
Interestingly enough, current models support the evidence that pure SO Cepheids and SO components in FO/SO Cepheids are good distance indicators. In fact, we find that the fit of the predicted period–luminosity–colour ( V , V – I ) relation to empirical SMC data supplies a distance modulus ( DM ) of 19.11±0.08 mag . The same outcome applies to pure FO Cepheids and FO components in FO/SO Cepheids, and indeed we find DM =19.16±0.19 mag . Current distance estimates do not account for, within current uncertainties on photometry and reddening, the so-called short distance scale.     

Further empirical evidence for the non-linearity of the period–luminosity relations as seen in the Large Magellanic Cloud Cepheids

Recent studies, using OGLE data for LMC Cepheids in the optical, strongly suggest that the period–luminosity (PL) relation for the Large Magellanic Cloud (LMC) Cepheids shows a break or non-linearity at a period of 10 d. In this paper we apply statistical tests, the chi-squared test and the F -test, to the Cepheid data from the MACHO project to test for a non-linearity of the V - and R -band PL relations at 10 d, and extend these tests to the near-infrared ( JHK -band) PL relations with 2MASS data. We correct the extinction for these data by applying an extinction map towards the LMC. The statistical test we use, the F -test, is able to take account of small numbers of data points and the nature of that data on either side of the period cut at 10 d. With our data, the results we obtained imply that the VRJH -band PL relations are non-linear around a period of 10 d, while the K -band PL relation is (marginally) consistent with a single-line regression. The choice of a period of 10 d, around which this non-linearity occurs, is consistent with the results obtained when this 'break' period is estimated from the data. We show that robust parametric (including least-squares, least absolute deviation, robust regression) and non-parametric regression methods, which restrict the influence of outliers, produce similar results. Long-period Cepheids are supplemented from the literature to increase our sample size. The photometry of these long-period Cepheids is compared with our data and no trend with period is found. Our main results remain unchanged when we supplement our data set with these long-period Cepheids. By examining our data at maximum light, we also suggest arguments as to why errors in reddening are unlikely to be responsible for our results. The non-linearity of the mean V -band PL relation as seen in both of the OGLE and the MACHO data, using different extinction maps, suggests that this non-linearity is real.     

Frequency analysis of Cepheids in the Large Magellanic Cloud: new types of classical Cepheid pulsators

We have performed a detailed systematic search for multiperiodicity in the Population I Cepheids of the Large Magellanic Cloud. In this process, we have identified for the first time several new types of Cepheid pulsational behaviour. We have found two triple-mode Cepheids pulsating simultaneously in the first three radial overtones. In 9 per cent of the first overtone (FO) Cepheids, we have detected weak but well-resolved secondary periodicities. They appear either very close to the primary pulsation frequency or at a much higher frequency with a characteristic period ratio of 0.60–0.64. In either case, the secondary periodicities must correspond to non-radial modes of oscillation. This result presents a major challenge to the theory of stellar pulsations, which predicts that such modes should not be excited in Cepheid variables. Non-radial modes have also been found in three of the fundamental first overtone (FU/FO) double-mode Cepheids, but no such oscillations have been detected in single-mode Cepheids pulsating in the FU mode.
In 19 per cent of double-mode Cepheids pulsating in the first two radial overtones (FO/SO type), we have detected a Blazhko-type periodic modulation of amplitudes and phases. Both modes are modulated with a common period, which is always longer than 700 d. Variations of the two amplitudes are anticorrelated, and maximum of one amplitude always coincides with minimum of the other. We have compared observations of modulated FO/SO Cepheids with predictions of theoretical models of the Blazhko effect, showing that the currently most popular models cannot account for properties of these stars. We propose that the Blazhko effect in FO/SO Cepheids can be explained by a non-stationary resonant interaction of one of the radial modes with another, perhaps non-radial, mode of oscillations.     

Two period-radius relations for classical Cepheids: Determining the pulsation mode and the distance scale

Based on our radial-velocity measurements and on published photometric observations, we calculated the radii of 64 classical Cepheids that were previously assumed to be fundamental-mode pulsators. Our detailed analysis of the period-radius diagram shows that the sample of Cepheids with pulsation periods shorter than 9 days probably contains a significant fraction (up to 30%) of stars pulsating in the first overtone. This fact leads to incorrect luminosity estimates for Cepheids and may be partly responsible for the discrepancy between the short and long distance scales.     

Some Magellanic Cloud topics

A review is given of a few of the aspects of Magellanic Cloud research which have been carried out by South African astronomers or by others using South African facilities.     

Optical Gravitational Lensing Experiment Cepheids Have Lower Amplitudes in the Small Magellanic Cloud than in the Large Magellanic Cloud

We selected Cepheids from the Optical Gravitational Lensing Experiment database for the Magellanic Clouds in the period range of 101.1相似文献   

Classical Cepheids and the Distances of HST Program Galaxies

The distances of HST program galaxies are revised using the PL-relations we have obtained previously along with a different method from that employed by Freedman et al. On the average, the resulting distances to these galaxies have higher internal accuracies than those obtained before by others. In addition, we have used no corrections for metallicity or for the incompleteness of the samples of classical cepheids in deriving these distances. Despite this, our distance moduli, with a dispersion of ±0^m.395, agree with those of Freedman et al. This indicates that these two effects have little or even no effect for the samples of classical cepheids in the HST program galaxies.     

Absolute Calibration of the PL-Relations for the Classical Cepheids Based on the HIPPARCOS Parallaxes and the Distances of the Magellanic Clouds

The zero points of the period-luminosity relations for the classical cepheids are calibrated based on the HIPPARCOS parallaxes of these stars. The calibrations are used to determine the distance moduli of the LMC and SMC: DM _LMC = 18^m.569 ± 0^m.117 and DM _SMC = 19^m.070 ± 0^m.119, respectively. It turns out that a calibration of the PL relations based on the distances of 25 FU classical cepheids in the galaxy by Gieren et al. yields a distance scale that is shorter by approximately 0^m.20 than the calibrations based on the HIPPARCOS parallaxes.     

Direct calibration of the Cepheid period–luminosity relation

After the first release of Hipparcos data, Feast & Catchpole gave a new value for the zero-point of the visual Cepheid period–luminosity relation, based on trigonometric parallaxes. Because of the large uncertainties on these parallaxes, the way in which individual measurements are weighted is of crucial importance. We therefore conclude that the choice of the best weighting system can be aided by a Monte Carlo simulation. On the basis of such a simulation, it is shown that (i) a cut ‐off in π or in σ _π π introduces a strong bias; (ii) the zero-point is more stable when only the brightest Cepheids are used; and (iii) the Feast & Catchpole weighting gives the best zero-point and the lowest dispersion. After correction, the adopted visual period–luminosity relation is 〈 M _V 〉=−2.77 log  P −1.44±0.05. Moreover, we extend this study to the photometric I band (Cousins) and obtain 〈 M _I 〉=−3.05 log  P −1.81±0.09.     

Period-Luminosity Relations for Classical Cepheids

BVIJHK period-luminosity relations for classical cepheids in the galaxy and magellanic clouds which pulsate in the fundamental mode are obtained on the basis of four samples. The period-luminosity relations for the BVI bands obtained here are more accurate than the analogous relations existing up to the present. Period-luminosity relations in terms of W functions are also obtained for these samples and have the same accuracy as the currently existing analogous relations.     

Period-Luminosity Relation for Classical Cepheids. Estimating the Intrinsic Scatter

Published photoelectric and CCD photometric data for fundamental-mode Cepheids in the Large Magellanic Cloud are analyzed. The inferred scatter of the observed period-luminosity relation decreases with increasing quality of the light curves used. The observed scatter of the period-luminosity relations in the V and IC bands is as low as 0m.11 and 0m.07, respectively, i.e., a factor of 1.5 smaller than the lowest published estimates. This, in particular, suggests that the intrinsic scatter might be lower than previously believed.     

The Large Magellanic Cloud and the distance scale

The Magellanic Clouds, especially the Large Magellanic Cloud, are places where multiple distance indicators can be compared with each other in a straight-forward manner at considerable precision. We here review the distances derived from Cepheids, Red Variables, RR Lyraes, Red Clump Stars and Eclipsing Binaries, and show that the results from these distance indicators generally agree to within their errors, and the distance modulus to the Large Magellanic Cloud appears to be defined to ±3% with a mean value (m−M)₀=18.48 mag, corresponding to 49.7 kpc. The utility of the Magellanic Clouds in constructing and testing the distance scale will remain as we move into the era of Gaia.     

Population I Cepheids and understanding star formation history of the Small Magellanic Cloud

In this paper, we study the age and spatial distributions of Cepheids in the Small Magellanic Cloud(SMC) as a function of their ages using data from the OGLE III photometric catalogue. A period- age relation derived for Classical Cepheids in the Large Magellanic Cloud(LMC) has been used to find the ages of Cepheids. The age distribution of the SMC Classical Cepheids is found to have a peak at log(Age) = 8.40 ± 0.10 which suggests that a major star formation event might have occurred in the SMC about 250 ± 50 Myr ago. It is believed that this star forming burst had been triggered by close interactions of the SMC with the LMC and/or the Milky Way. A comparison of the observed spatial distributions of the Cepheids and open star clusters has also been carried out to study the star formation scenario in the SMC.     

Confirmation of previous ground-based Cepheid P–L zero-points using Hipparcos trigonometric parallaxes

Comparisons show agreement at the 0.1-mag level between the calibration of the Cepheid period–luminosity (P–L) relation by Feast & Catchpole (FC) using the early release of Hipparcos data and four previous ground-based calibrations, three of which are either largely or totally independent of the distance to the Large Magellanic Cloud (LMC). Each of the comparisons has the sense that the FC calibration is brighter, but only at the level of ≲0.1 mag. In contrast, FC argue that their Hipparcos recalibration leads to a 0.2-mag revision in the distance to the LMC, and thereby to a 10 per cent decrease in the Hubble constant. We argue differently. The comparison of the Hipparcos recalibration with others should be made using only local Galactic Cepheids, not based on Cepheids in the LMC that require a set of precepts that are not germane to the direct Hipparcos recalibration. The comparison made here, using only Galactic Cepheids, gives a correction of ∼4 per cent or less to our value of H ₀ based on Type Ia supernovae, keeping all other factors and precepts the same.
  A second success of the Hipparcos mission is the calibration of the position of the main sequence in the Hertzsprung–Russell diagram as a function of metallicity using local subdwarfs. These data have been used by Reid and by Gratton et al. to obtain, similarly to FC, a brighter absolute magnitude of RR Lyrae stars by ∼0.3 mag from that often currently adopted. These new calibrations confirm the earlier brighter calibrations by Walker, by Sandage, and by Mazzitelli, D'Antona & Caloi, thereby reducing the ages of globular clusters by ∼30 per cent. This removes most of the cosmological time-scale problem if H ₀∼55 km s⁻¹ Mpc⁻¹. A similar conclusion, based on pulsation theory and MACHO data, has been reached by Alcock et al.     

Detached binaries in the Large Magellanic Cloud

Analysis of the radial-velocity and light curves of detached eclipsing binaries allows to derive stellar masses and radii and, in consequence, enables to find their distances. This method has been already applied to several LMC binaries, but in order to have the distance to the LMC determined with good accuracy, the study needs to be extended to a larger number of eclipsing systems. As a first step, we present results of the analysis of the photometry of over 80 detached binaries in the LMC selected from the OGLE-II catalog of 53,000 candidates for variables. If possible, we combine the OGLE-II data with the photometry from other projects (MACHO and EROS). As a result, we present the list of the brightest eclipsing binaries in the LMC suitable for distance determination.