Period–colour and amplitude–colour relations in classical Cepheid variables – IV. The multiphase relations

The superb phase resolution and quality of the Optical Gravitational Lensing Experiment (OGLE) data on the Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC) Cepheids, together with existing data on Galactic Cepheids, are combined to study the period–colour (PC) and amplitude–colour (AC) relations as a function of pulsation phase. Our results confirm earlier work that the LMC PC relation (at mean light) is more consistent with two lines of differing slopes, separated at a period of 10 d. However, our multiphase PC relations reveal much new structure which can potentially increase our understanding of Cepheid variables. These multiphase PC relations provide insight into why the Galactic PC relation is linear but the LMC PC relation is non-linear. This is because the LMC PC relation is shallower for short  (log  P < 1)  and steeper for long  (log  P > 1)  period Cepheids than the corresponding Galactic PC relation. Both of the short- and long-period Cepheids in all three galaxies exhibit the steepest and shallowest slopes at phases around 0.75–0.85, respectively. A consequence is that the PC relation at phase ∼ 0.8 is highly non-linear. Further, the Galactic and LMC Cepheids with  log  P > 1  display a flat slope in the PC plane at phases close to the maximum light. When the LMC period–luminosity (PL) relation is studied as a function of phase, we confirm that it changes with the PC relation. The LMC PL relation in V and I band near the phase of 0.8 provides compelling evidence that this relation is also consistent with two lines of differing slopes joined at a period close to 10 d.     

Period–colour and amplitude–colour relations in classical Cepheid variables – III. The Large Magellanic Cloud Cepheid models

Period–colour (PC) and amplitude–colour (AC) relations are studied for the Large Magellanic Cloud (LMC) Cepheids under the theoretical framework of the hydrogen ionization front (HIF)–photosphere interaction. LMC models are constructed with pulsation codes that include turbulent convection, and the properties of these models are studied at maximum, mean and minimum light. As with Galactic models, at maximum light the photosphere is located next to the HIF for the LMC models. However, very different behaviour is found at minimum light. The long-period  ( P > 10 d)  LMC models imply that the photosphere is disengaged from the HIF at minimum light, similar to the Galactic models, but there are some indications that the photosphere is located near the HIF for the short-period  ( P < 10 d)  LMC models. We also use the updated LMC data to derive empirical PC and AC relations at these phases. Our numerical models are broadly consistent with our theory and the observed data, though we discuss some caveats in the paper. We apply the idea of the HIF–photosphere interaction to explain recent suggestions that the LMC period–luminosity (PL) and PC relations are non-linear with a break at a period close to 10 d. Our empirical LMC PC and PL relations are also found to be non-linear with the F -test. Our explanation relies on the properties of the Saha ionization equation, the HIF–photosphere interaction and the way this interaction changes with the phase of pulsation and metallicity to produce the observed changes in the LMC PC and PL relations.     

Period–luminosity relations for type II Cepheids and their application

JHK _s magnitudes corrected to mean intensity are estimated for Large Magellanic Cloud (LMC) type II Cepheids in the OGLE-III survey the third phase of the Optical Gravitational Lensing Experiment (OGLE). Period–luminosity (PL) relations are derived in JHK _s as well as in a reddening-free VI parameter. Within the uncertainties, the BL Her stars  ( P < 4 d)  and the W Vir stars (   P = 4  to 20 d) are colinear in these PL relations. The slopes of the infrared relations agree with those found previously for type II Cepheids in globular clusters within the uncertainties. Using the pulsation parallaxes of V553 Cen and SW Tau, the data lead to an LMC modulus uncorrected for any metallicity effects of  18.46 ± 0.10  mag. The type II Cepheids in the second-parameter globular cluster, NGC 6441, show a PL( VI ) relation of the same slope as that in the LMC, and this leads to a cluster distance modulus of  15.46 ± 0.11  mag, confirming the hypothesis that the RR Lyrae variables in this cluster are overluminous for their metallicity. It is suggested that the Galactic variable κ Pavonis is a member of the peculiar W Vir class found by the OGLE-III group in the LMC. Low-resolution spectra of OGLE-III type II Cepheids with   P > 20  d (RV Tau stars) show that a high proportion have TiO bands; only one has been found showing C₂. The LMC RV Tau stars, as a group, are not colinear with the shorter period type II Cepheids in the infrared PL relations in marked contrast to such stars in globular clusters. Other differences between LMC, globular cluster and Galactic field type II Cepheids are noted in period distribution and infrared colours.     

The linearity of the Wesenheit function for the Large Magellanic Cloud Cepheids

There is strong evidence that the period–luminosity (PL) relation for the Large Magellanic Cloud (LMC) Cepheids shows a break at a period around 10 d. Because the LMC PL relation is extensively used in distance scale studies, the non-linearity of the LMC PL relation may affect the results based on this LMC calibrated relation. In this paper we show that this problem can be remedied by using the Wesenheit function in obtaining Cepheid distances. This is because the Wesenheit function is linear, although recent data suggest that the PL and the period–colour (PC) relations that make up the Wesenheit function are not. We test the linearity of the Wesenheit function and find strong evidence that the LMC Wesenheit function is indeed linear. This is because the non-linearity of the PL and PC relations cancel out when the Wesenheit function is constructed. We discuss this result in the context of distance scale applications. We also compare the distance moduli obtained from  μ₀=μ _V − R (μ _V −μ _I )  (equivalent to Wesenheit functions) constructed with the linear and the broken LMC PL relations, and we find that the typical difference in distance moduli is  ∼ ±0.03 mag  . Hence, the broken LMC PL relation does not seriously affect current distance scale applications. We also discuss the random error calculated with equation  μ₀=μ _V − R (μ _V −μ _I )  , and show that there is a correlation term that exists from the calculation of the random error. The calculated random error will be larger if this correlation term is ignored.     

On the metallicity dependence of classical Cepheid light amplitudes

Classical Cepheids remain a cornerstone of the cosmic distance scale, and thus characterizing the dependence of their light amplitude on metallicity is important. Period-amplitude diagrams constructed for longer-period classical Cepheids in IC 1613, NGC 3109, SMC, NGC 6822, LMC, and the Milky Way imply that very metal-poor Cepheids typically exhibit smaller V-band amplitudes than their metal-rich counterparts. The results provide an alternate interpretation relative to arguments for a null and converse metallicity dependence. The empirical results can be employed to check predictions from theoretical models, to approximate mean abundances for target populations hosting numerous long-period Cepheids, and to facilitate the identification of potentially blended or peculiar objects.     

The period–luminosity relation for type II Cepheids in globular clusters

We report the result of our near-infrared observations ( JHK _s) for type II Cepheids (including possible RV Tau stars) in galactic globular clusters. We detected variations of 46 variables in 26 clusters (10 new discoveries in seven clusters) and present their light curves. Their periods range from 1.2 d to over 80 d. They show a well-defined period–luminosity relation at each wavelength. Two type II Cepheids in NGC 6441 also obey the relation if we assume the horizontal branch stars in NGC 6441 are as bright as those in metal-poor globular clusters in spite of the high metallicity of the cluster. This result supports the high luminosity which has been suggested for the RR Lyr variables in this cluster. The period–luminosity relation can be reproduced using the pulsation equation     assuming that all the stars have the same mass. Cluster RR Lyr variables were found to lie on an extrapolation of the period–luminosity relation. These results provide important constraints on the parameters of the variable stars.
Using Two Micron All-Sky Survey (2MASS) data, we show that the type II Cepheids in the Large Magellanic Cloud (LMC) fit our period–luminosity relation within the expected scatter at the shorter periods. However, at long periods (   P > 40  d, i.e. in the RV Tau star range) the LMC field variables are brighter by about one magnitude than those of similar periods in galactic globular clusters. The long-period cluster stars also differ from both these LMC stars and galactic field RV Tau stars in a colour–colour diagram. The reasons for these differences are discussed.     

Period–colour and amplitude–colour relations in classical Cepheid variables – V. The Small Magellanic Cloud Cepheid models

Period–colour (PC) and amplitude–colour (AC) relations at maximum, mean and minimum light are constructed from a large grid of full amplitude hydrodynamic models of Cepheids with a composition appropriate for the Small Magellanic Cloud (SMC). We compare these theoretical relations with those from observations. The theoretical relations are, in general, in good agreement with their observational counterparts, though there exist some discrepancy for short period  (log [ P ] < 1)  Cepheids. We outline a physical mechanism which can, in principle, be one factor to explain the observed PC/AC relations for the long and short period Cepheids in the Galaxy, Large Magellanic Cloud (LMC) and SMC. Our explanation relies on the hydrogen ionization front (HIF)–photosphere interaction and the way this interaction changes with pulsation period, pulsation phase and metallicity. Since the PC relation is connected with the period–luminosity (PL) relation, it is postulated that such a mechanism can also explain the observed properties of the PL relation in these three galaxies.     

Construction of the Database for Pulsating Variable Stars

A database for pulsating variable stars is constructed to favor the study of variable stars in China. The database includes about 230,000 variable stars in the Galactic bulge, LMC and SMC observed in an about 10 yr period by the MACHO(MAssive Compact Halo Objects) and OGLE(Optical Gravitational Lensing Experiment) projects. The software used for the construction is LAMP, i.e., Linux+Apache+MySQL+PHP. A web page is provided for searching the photometric data and light curves in the database through the right ascension and declination of an object. Because of the flexibility of this database, more up-to-date data of variable stars can be incorporated into the database conveniently.     

Period–luminosity relations for red supergiant variables – I.The calibration

We present CCD photometry of red supergiant long-period variables (LPVs) in the Per OB1 association, the Large Magellanic Cloud (LMC) and M33. The photometry was obtained in the Kron–Cousins R and I bandpasses and in a narrow bandpass ( λ ₀=8250 Å, FWHM=300 Å) chosen to avoid TiO bands in the spectral energy distribution of the LPVs. Because the strength of the TiO bands varies greatly with temperature, which varies with the phase of an LPV, avoiding TiO reduces the amplitude of the photometric variations seen in LPVs. The result is a lower dispersion and a well defined period–luminosity (PL) relation.
For the LMC sample we find an rms dispersion of 0.27 mag in the narrow-band PL relation and slightly larger dispersions for the LPVs in Per OB1 and M33. This dispersion is comparable to that of the Cepheid PL relation at similar wavelengths. Adopting a distance modulus of 18.5±0.1 mag for the LMC, we obtain distance moduli of 11.68±0.15 mag for Per OB1 and 24.85±0.13 mag for M33. These distances agree well with those based on main sequence fitting for Per OB1 and the Cepheid distance for M33. Since LPVs are ∼ 5 times more common than Cepheids and have a well defined PL relation, LPVs provide a promising method for estimating Galactic and extra galactic distances.     

Ultra long period Cepheids: a primary standard candle out to the Hubble flow

The cosmological distance ladder crucially depends on classical Cepheids (with P=3–80 days), which are primary distance indicators up to 33 Mpc. Within this volume, very few SNe Ia have been calibrated through classical Cepheids, with uncertainty related to the non-linearity and the metallicity dependence of their period–luminosity (PL) relation. Although a general consensus on these effects is still not achieved, classical Cepheids remain the most used primary distance indicators. A possible extension of these standard candles to further distances would be important. In this context, a very promising new tool is represented by the ultra-long period (ULP) Cepheids (P≳80 days), recently identified in star-forming galaxies. Only a small number of ULP Cepheids have been discovered so far. Here we present and analyse the properties of an updated sample of 37 ULP Cepheids observed in galaxies within a very large metallicity range of 12+log(O/H) from ∼7.2 to 9.2 dex. We find that their location in the colour-magnitude (V−I,V) diagram as well as their Wesenheit (V−I) index-period (WP) relation suggests that they are the counterparts at high luminosity of the shorter-period (P≲80 days) classical Cepheids. However, a complete pulsation and evolutionary theoretical scenario is needed to properly interpret the true nature of these objects. We do not confirm the flattening in the studied WP relation suggested by Bird et al. (Astrophys. J. 695:874, 2009). Using the whole sample, we find that ULP Cepheids lie around a WP relation similar to that of the LMC, although with a large spread (∼ 0.4 mag).     

The PL calibration for Milky Way Cepheids and its implications for the distance scale

The rationale behind recent calibrations of the Cepheid PL relation using the Wesenheit formulation is reviewed and reanalyzed, and it is shown that recent conclusions regarding a possible change in slope of the PL relation for short-period and long-period Cepheids are tied to a pathological distribution of HST calibrators within the instability strip. A recalibration of the period-luminosity relation is obtained using Galactic Cepheids in open clusters and groups, the resulting relationship, described by log L/L _⊙=2.415(±0.035)+1.148(±0.044)log P, exhibiting only the moderate scatter expected from color spread within the instability strip. The relationship is confirmed by Cepheids with HST parallaxes, although without the need for Lutz-Kelker corrections, and in general by Cepheids with revised Hipparcos parallaxes, albeit with concerns about the cited precisions of the latter. A Wesenheit formulation of W _V =−2.259(±0.083)−4.185(±0.103)log P for Galactic Cepheids is tested successfully using Cepheids in the inner regions of the galaxy NGC 4258, confirming the independent geometrical distance established for the galaxy from OH masers. Differences between the extinction properties of interstellar and extragalactic dust may yet play an important role in the further calibration of the Cepheid PL relation and its application to the extragalactic distance scale.     

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   

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.     

脉动变星数据库的建立

为了方便国内学者对脉动变星进行研究,建立了一个数据库,目前包含了时间长达10 yr左右的巡天项目MAssive Compact Halo Objects(大质量致密银晕天体,MACHO)和Optical Gravitational Lensing Experiment(光学引力透镜实验,OGLE)发现的脉动变星,一共容纳了来自银河系核球与大小麦哲伦云中的共近23万颗变星.采用的软件是LAMP,即Linux+Apache+MySQL+PHP.数据库的使用通过网页的简单搜索界面实现,搜索参数主要是天体的赤经、赤纬和半径.鉴于本数据库的灵活性,将来很方便加入其他的变星数据.     

Cepheid parallaxes and the Hubble constant

Revised Hipparcos parallaxes for classical Cepheids are analysed together with 10 Hubble Space Telescope ( HST )-based parallaxes. In a reddening-free V , I relation we find that the coefficient of log  P is the same within the uncertainties in our Galaxy as in the Large Magellanic Cloud (LMC), contrary to some previous suggestions. Cepheids in the inner region of NGC 4258 with near solar metallicities confirm this result. We obtain a zero-point for the reddening-free relation and apply it to the Cepheids in galaxies used by Sandage et al. to calibrate the absolute magnitudes of Type Ia supernova (SNIa) and to derive the Hubble constant. We revise their result for H ₀ from 62 to 70 ± 5 km s⁻¹ Mpc⁻¹. The Freedman et al. value is revised from 72 to 76 ± 8 km s⁻¹ Mpc⁻¹. These results are insensitive to Cepheid metallicity corrections. The Cepheids in the inner region of NGC 4258 yield a modulus of 29.22 ± 0.03 (int.) compared with a maser-based modulus of 29.29 ± 0.15. Distance moduli for the LMC, uncorrected for any metallicity effects, are 18.52 ± 0.03 from a reddening-free relation in V , I ; 18.47 ± 0.03 from a period–luminosity relation at K ; 18.45 ± 0.04 from a period–luminosity–colour relation in J , K . Adopting a metallicity correction in V , I from Macri et al. leads to a true LMC modulus of 18.39 ± 0.05.     

Calibrating the Cepheid Period-Luminosity relation from the near-infrared surface brightness technique

We have applied the near-infrared surface-brightness method to 111 Cepheids in the Milky Way and in the Large and the Small Magellanic Clouds determining distances and luminosities for the individual stars. We find that the K-band Period-Luminosity (PL-)relations for Milky Way and Large Magellanic Cloud Cepheids are almost identical, whereas the zero point of the Wesenheit relation depends significantly on metallicity, metal poor Cepheids being fainter.     

Circularization in B-type eclipsing binaries in both Magellanic Clouds

By making use of detached eclipsing binaries with B-type components discovered by the OGLE and MACHO teams in the SMC and in the LMC, we give the value of the fractional radius above which circularization occurs. This critical radius is around 0.24–0.26, regardless of the mass, surface gravity or metallicity, and is consistent with that found by Giuricin et al. [A&A 134 (1984) 365] for galactic binaries. These empirical facts are shown to be consistent with Zahn's [A&A 41 (1975) 329] theory of tidal dissipation. As a by-product of this study, we provide approximate stellar parameters of the average component of 148 binaries in the SMC and of up to 353 binaries (some of which might be non-detached) in the LMC, under the assumption of equal components.     

Searching for periodicities in the MACHO light curve of LMC X-2

Using the exceptional long-term monitoring capabilities of the MACHO project, we present here the optical history of LMC X-2 for a continuous 6-yr period. These data were used to investigate the previously claimed periodicities for this source of 8.15 h and 12.54 d: we find upper limits of 0.10 mag and 0.09 mag, respectively.     

Study by MOA of extrasolar planets in gravitational microlensing events of high magnification

A search for extrasolar planets was carried out in three gravitational microlensing events of high magnification, MACHO  98–BLG–35  , MACHO  99–LMC–2  and OGLE  00–BUL–12  . Photometry was derived from observational images by the MOA and OGLE groups using an image subtraction technique. For MACHO  98–BLG–35  , additional photometry derived from the MPS and PLANET groups was included. Planetary modelling of the three events was carried out in a supercluster computing environment. The estimated probability for explaining the data on MACHO  98–BLG–35  without a planet is <1 per cent. The best planetary model has a planet of mass ∼(0.4–1.5)× M _Earth at a projected radius of either ∼1.5 or ∼2.3 au. We show how multiplanet models can be applied to the data. We calculate exclusion regions for the three events and find that Jupiter-mass planets can be excluded with projected radii from as wide as about 30 au to as close as around 0.5 au for MACHO  98–BLG–35  and OGLE  00–BUL–12  . For MACHO  99–LMC–2  , the exclusion region extends out to around 10 au and constitutes the first limit placed on a planetary companion to an extragalactic star. We derive a particularly high peak magnification of ∼160 for OGLE  00–BUL–12  . We discuss the detectability of planets with masses as low as Mercury in this and similar events.     

Be star candidates in the Large Magellanic Cloud: the catalogue and comparison with the Small Magellanic Cloud sample

We present a catalogue with coordinates and photometric data of 2446 Be star candidates in the Large Magellanic Cloud (LMC), based on a search of the OGLE II data base. The I -band light curves of these stars show outbursts in 24 per cent of the sample (Type-1 stars), high and low states in 10 per cent, periodic variations in 6 per cent (Type-3 stars), and stochastic variations in 60 per cent of the cases. We report on the result of the statistical study of light curves of Type-1 and Type-3 stars in the LMC, and the comparison with the previously reported results of the Small Magellanic Cloud (SMC) sample. We find a statistically significant difference between amplitude, duration and asymmetry distributions of outbursts in both galaxies. Outbursts of SMC Type-1 stars are usually brighter, longer and with a slower decline. We find a bimodal distribution of periods of Type-3 stars in both galaxies, probably related to the recently discovered double periodic blue variables. We find also period and amplitude distributions of Type-3 LMC stars statistically different from those of the SMC stars. Our findings above suggest that the mechanisms causing the observed photometric variability of Type-1 and Type-3 stars could depend on metallicity. Moreover, they suggest that the outbursts are not primarily caused by stellar winds.