In this study, we follow up our recent paper (Monteiro et al. 2020) and present a homogeneous sample of fundamental parameters of open clusters in our Galaxy, entirely based on Gaia DR2 data. We used published membership probability of the stars derived from Gaia DR2 data and applied our isochrone fitting code, updated as in Monteiro et al. ( 2020), to G_BP and G_RPGaia DR2 data for member stars. In doing this, we take into account the nominal errors in the data and derive distance, age, and extinction of each cluster. This work therefore provides parameters for 1743 open clusters and, as a by-product, a list of likely not physical or dubious open clusters is provided as well for future investigations. Furthermore, it was possible to estimate the mean radial velocity of 831 clusters (198 of which are new and unpublished so far), using stellar radial velocities from Gaia DR2 catalogue. By comparing the open cluster distances obtained from isochrone fitting with those obtained from a maximum likelihood estimate of individual member parallaxes, we found a systematic offset of (−0.05 ± 0.04) mas.

We present a catalog of mean proper motions and membership probabilities of individual stars for optically visible open clusters, which have been determined using data from the UCAC4 catalog in a homogeneous way. The mean proper motion of the cluster and the membership probabilities of the stars in the region of each cluster were determined by applying the statistical method in a modified fashion. In this study, we applied a global optimization procedure to fit the observed distribution of proper motions with two overlapping normal bivariate frequency functions, which also take the individual proper motion errors into account. For 724 clusters, this is the first determination of proper motion, and for the whole sample, we present results with a much larger number of identified astrometric member stars. Furthermore, it was possible to estimate the mean radial velocity of 364 clusters (102 unpublished so far) with the stellar membership using published radial velocity catalogs. These results provide an increase of 30% and 19% in the sample of open clusters with a determined mean absolute proper motion and mean radial velocity, respectively.

The main objective of this work is to determine the cluster members of 1876 open clusters, using positions and proper motions of the astrometric fourth United States Naval Observatory (USNO) CCD Astrograph Catalog (UCAC4). For this purpose, we apply three different methods, all based on a Bayesian approach, but with different formulations: a purely parametric method, another completely non-parametric algorithm and a third, recently developed by Sampedro & Alfaro, using both formulations at different steps of the whole process. The first and second statistical moments of the members’ phase-space subspace, obtained after applying the three methods, are compared for every cluster. Although, on average, the three methods yield similar results, there are also specific differences between them, as well as for some particular clusters. The comparison with other published catalogues shows good agreement. We have also estimated, for the first time, the mean proper motion for a sample of 18 clusters. The results are organized in a single catalogue formed by two main files, one with the most relevant information for each cluster, partially including that in UCAC4, and the other showing the individual membership probabilities for each star in the cluster area. The final catalogue, with an interface design that enables an easy interaction with the user, is available in electronic format at the Stellar Systems Group (SSG-IAA) web site (http://ssg.iaa.es/en/content/sampedro-cluster-catalog).

BL Lacertae is the prototype of the BL Lac class of active galactic nuclei, exhibiting intensive activity on parsec (pc) scales, such as intense core variability and multiple ejections of jet components. In particular, in previous works the existence of precession motions in the pc-scale jet of BL Lacertae has been suggested. In this work we revisit this issue, investigating temporal changes of the observed right ascension and declination offsets of the jet knots in terms of our relativistic jet-precession model. The seven free parameters of our precession model were optimized via a heuristic cross-entropy method, comparing the projected precession helix with the positions of the jet components on the plane of the sky and imposing constraints on their maximum and minimum superluminal velocities. Our optimized best model is compatible with a jet having a bulk velocity of 0.9824c, which is precessing with a period of about 12.1 yr in the observer's reference frame and changing its orientation in relation to the line of sight between 4° and 5°, approximately. Assuming that the jet precession has its origin in a supermassive binary black hole system, we show that the 2.3-yr periodic variation in the structural position angle of the very-long-baseline interferometry (VLBI) core of BL Lacertae reported by Stirling et al. is compatible with a nutation phenomenon if the secondary black hole has a mass higher than about six times that of the primary black hole.

In this work we revisit the issue of the rotation speed of the spiral arms and the location of the corotation radius of our Galaxy. This research was performed using homogeneous data set of young open clusters (age < 50 Myr) determined from Gaia DR2 data. The stellar astrometric membership were determined using proper motions and parallaxes, taking into account the full covariance matrix. The distance, age, reddening and metallicity of the clusters were determined by our non subjective multidimensional global optimization tool to fit theoretical isochrones to Gaia DR2 photometric data. The rotation speed of the arms is obtained from the relation between age and angular distance of the birthplace of the clusters to the present-day position of the arms. Using the clusters belonging to the Sagittarius-Carina, Local and Perseus arms, and adopting the Galactic parameters R₀ = 8.3 kpc and V₀ = 240 km s⁻¹, we determine a pattern speed of 28.2 ± 2.1 km s⁻¹ kpc⁻¹, with no difference between the arms. This implies that the corotation radius is R_c = 8.51 ± 0.64 kpc, close to the solar Galactic orbit (R_c/R₀ = 1.02 ± 0.07).