Period-Luminosity Relation for Type II Cepheids
We have estimated magnitudes corrected to mean intensity for LMC type II Cepheids found in the OGLE-III survey. Period-luminosity relations (PLRs) are derived in as well as in a reddening-free parameter. The BL Her stars ( d) and the W Vir stars ( to 20 d) are co-linear in these PLRs. 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 of mag, uncorrected for any metallicity effects. We have now established the PLR of type II Cepheids as a distance indicator by confirming that (almost) the same PLR satisfies the distributions in the PL diagram of type II Cepheids in (at least) two different systems, i.e. the LMC and Galactic globular clusters, and by calibrating the zero point of the PLR. RV Tau stars in the LMC, as a group, are not co-linear with the shorter-period type II Cepheids in the infrared PLRs in marked contrast to such stars in globular clusters. We note differences in period distribution and infrared colors for RV Tau stars in the LMC, globular clusters and Galactic field. We also compare the PLR of type II Cepheids with that of classical Cepheids.
Keywords:Cepheid, Magellanic Clouds, distance
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Type II Cepheids (CephIIs) have periods in the same range as classical Cepheids but are lower-mass stars belonging to disk and halo populations. In 2006, we showed that CephIIs in globular clusters defined narrow period-luminosity relations (PLRs) in the near-infrared bands, Matsunaga-2006 . This suggests that these stars may be useful distance indicators for pop. II stellar systems. Pulsation parallaxes of Galactic CephIIs were used by Feast and collaborators to calibrate these cluster PLRs and to discuss the distances of the LMC and the Galactic Center Feast-2008 . Recently, the OGLE-III survey team catalogued 197 CephIIs in the LMC, confirming their clear PLR in visible Soszynski-2008 . In this contribution, we discuss near-IR observations of these CephIIs and their PLR. We also make a direct comparison between this PLR and that of classical Cepheids.
2 Sample and data analysis
We searched for near-IR counterparts of the LMC CephIIs Soszynski-2008 in the IRSF catalogue for the LMC Kato-2007 . This is a point-source catalogue in the bands obtained with the 1.4-m IRSF telescope and SIRIUS camera based at SAAO, Sutherland, South Africa. We found matches for 188 CephIIs with a tolerance of 0.5. Based on notes given by Soszynski-2008 , we omitted several stars, e.g. those blended with other stars and those showing eclipses, from the following discussion regarding the PLR. Since the OGLE-III catalogue Soszynski-2008 gives periods and dates of maximum in , we can derive the phases of the single observations. Assuming that the light curves in the near-IR bands are similar to those in , we obtained an estimate of the mean (phase-corrected) magnitude in each IR band. We confirmed the validity of this method by using the data for CephIIs which have two IRSF measurements observed within two neighboring frames (see Matsunaga-2009 for details).
3 Period-Luminosity relation
Fig. 1 plots the phase-corrected magnitudes against for the LMC CephIIs. It is evident that the RV Tau stars do not continue the linear PLRs to longer periods, so that they are not included in fitting the PLR. The slopes of the PLR do not differ significantly from those found by Matsunaga-2006 for CephIIs in globular clusters. The scatters around the linear solutions are compatible with those of the PLRs for the cluster variables.
There are two Galactic BL Her stars with known pulsation parallaxes: V553 Cen () and SW Tau () Feast-2008 . Using the data of tables 4 and 5 of Feast-2008 , we can calibrate the zero-points of the PLRs and hence estimate the modulus of the LMC, mag without any metallicity correction. This agrees well with those derived from classical Cepheids with trigonometrical parallaxes by vanLeeuwen-2007 and Benedict-2007 . These authors found from a PL() relation and from a PL() relation again without metallicity corrections.
In the course of our work we found an important implication for Pav. This star () has long been thought of as probably the nearest CephII and hence a prime candidate for fixing the distance scale for these objects. However, its pulsation parallax Feast-2008 leads to a distance modulus of mag placing it well above the PLRs in the optical and near-IR and in the region of the peculiar W Vir stars which was identified by S08. Further evidence that Pav belongs to the peculiar W Vir class is given by its color. Its intrinsic color, , is bluer than normal CephIIs of this period (W Vir stars) and similar to peculiar W Vir stars. This classification is supported by its light curve. In addition, Hipparcos astrometry suggests the existence of peculiar W Vir stars are binaries (see Feast-2008 ).
4 RV Tau variables
RV Tau stars in the LMC () do not lie on a linear extension of the PLRs defined by shorter-period CephIIs (Fig. 1). CephIIs in globular clusters in this period range, in contrast, are co-linear with the shorter-period stars in PL diagrams. In the color-color diagram (Fig. 2), the LMC stars with significant excesses lie at mag. Most of the others lie relatively close to the intrinsic line taken from Bessell-1988 . Galactic RV Tau stars from LloydEvans-1985 , triangles in Fig. 2, show a rather dispersed distribution; their colors range from 0.1 to 0.7 mag. While there may be some overlap between the three populations, in general they form distinctly different groupings. In Fig. 3, we plot period histograms for CephIIs in the LMC (top) and globular clusters (bottom). For days, the cluster variables seem simply the long-period tail of the distribution of W Vir stars whereas in the LMC there is a distinct population at these periods. RV Tau stars are apparently a heterogeneous group and further work is required to investigate this.
5 Comparison with the PLR of classical Cepheids
Since the OGLE-III project has discovered a sizable number of CephIIs and classical Cepheids, their PLRs can be compared directly based on a homogeneous dataset (the OGLE-III optical data and the IRSF near-IR data). We plot the PLRs of both classical Cepheids and CephIIs in Fig. 4. The data for the classical Cepheids come from Ita-2004 . It has long been known that the CephIIs are fainter than classical Cepheids of the same period. It has long been known that the CephIIs are fainter than classical Cepheids of the same period. Fig. 4 also illustrates their different PLR slopes. These slopes are related to the mass distributions of both groups of variables. For the classical Cepheids, mass increases with period while the masses of the CephIIs are almost constant with period Matsunaga-2006 . It is also interesting that there is a clear sequence of overtone pulsators for classical Cepheids which has not been seen for CephIIs.
We obtained PLRs in phase-corrected magnitudes for a combined set of BL Her and W Vir stars in the LMC. They have slopes consistent with those found previously in globular clusters. The zero-point of the PLR is also determined based on nearby CephIIs with pulsation parallaxes. These has led to the establishment of the PLR of CephIIs as a distance indicator, which will be a useful tool for investigating old stellar systems. Since observational information for CephIIs is gradually accumulated in a comprehensive way, e.g. Matsunaga-2006 and Soszynski-2008 , a theoretical effort to explain the recent observational results for CephIIs is highly desired.
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