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TThe Period-Luminosity (PL) relation for Cepheid variable stars in the Large Magellanic Cloud (LMC) is crucial for distance measurements in astronomy. This study analyzes the impact of using the median rather than the mean on the PL relation's slope and zero point. It also examines the persistence of the break at approximately 10 days and addresses specification issues in the PL relation model. Using $VI$-band median and mean magnitudes from the OGLE-IV survey, corrected for extinction, we fit the PL relation employing robust $MM$-regression, which features a high breakdown point and robust standard errors. Statistical tests and residual analysis are conducted to identify and correct model deficiencies. Our findings indicate a significant change in the PL relation for Cepheids with periods of 10 days or longer, regardless of whether median or mean magnitudes are used. A bias in the zero point and slope estimators is observed when using median magnitudes instead of mean magnitudes, especially in the $V$-band. By identifying and correcting regression issues and considering the period break, our estimators for slope and zero point are more accurate for distance calculations. Comparative analysis of the models for each band quantifies the bias introduced by using median magnitudes, highlighting the importance of considering the Cepheids' period for accurate location measure results, similar to those obtained using mean magnitudes.

We revisit the subject of Be star candidates towards the Magellanic Clouds, previously studied by the authors using SPM4 proper motions. We obtain GAIA DR2 parallaxes and proper motions for 2357 and 994 LMC and SMC Be candidates, respectively. Parallaxes and proper motions vs. color V-I easily reveal the presence of the redder galactic contaminant foreground, as concluded in our previous work, but this time we do find a few red Be stars candidates consistent with being true Magellanic objects. A membership assessment to each Magellanic Cloud is done for each Be candidate, based on the distribution of their parallaxes and proper motions. From a compilation of published catalogues of spectroscopically confirmed Be stars, we found that 40 (LMC) and 64 (SMC) of these Be candidates, are in fact Be stars. Near infrared IRSF JHKs magnitudes were obtained for about 70% the Be stars candidates with GAIA DR2 astrometric data. Mid-infrared SAGE IRAC 3.6, 4.5, 5.8 and 8.0 $\mu$m magnitudes were obtained for about 85% as well. 6 LMC and 7 SMC confirmed Be stars show optical, near- or mid-infrared colours redder than what has been typically measured for Classical Be stars. Several of the Be candidates follow those redder-than-expected colours distributions suggesting the existence of more red Magellanic Be stars., Comment: Slight change in title, two new more authors, 15 pages, 12 figures, accepted by MNRAS

We present a proper motion investigation of a sample of Be star candidates towards the Magellanic Clouds, which has resulted in the identification of separate populations, in the Galactic foreground and in the Magellanic background. Be stars are broadly speaking B-type stars that have shown emission lines in their spectra. In this work, we studied a sample of 2446 and 1019 Be star candidates towards the LMC and SMC respectively, taken from the literature and proposed as possible Be stars due to their variability behaviour in the OGLE-II I band. JHKs magnitudes from the IRSF catalog and proper motions from the SPM4 catalog, were obtained for 1188 and 619 LMC and SMC Be stars candidates, respectively. Color-color and vector-point diagrams were used to identify different populations among the Be star candidates. In the LMC sample, two populations with distinctive infrared colours and kinematics were found, the bluer sample is consistent with being in the LMC and the redder one with belonging to the Milky Way disk. This settles the nature of the redder sample which had been described in previous publications as a possible unknown subclass of stars among the Be candidates in the LMC. In the SMC sample, a similar but less evident result was obtained, since this apparent unknown subclass was not seen in this galaxy. We confirm that in the selection of Be stars by their variability, although generally successful, there is a higher risk of contamination by Milky Way objects towards redder B$-$V and V$-$I colors., Comment: 8 pages, 7 figures

The universality and linearity of the Leavitt law are hypotheses commonly adopted in studies of galaxy distances using Cepheid variables as standard candles. In order to test these hypotheses, we obtain slopes of the Leavitt law using linear regressions of fundamental-mode Cepheids observed by the Optical Gravitational Lensing Experiment project in the Magellanic Clouds. We find that the slopes in $VI$-bands and in the Wesenheit index behave exponentially, indicating non-linearity. We also find that the slopes obtained using long-period Cepheids can be considered as universal in the $VI$-bands, but not in the Wesenheit index., Comment: 8 pages, 3 figures. Accepted for publication in MNRAS