Optical integral-field spectroscopy was used to investigate the planetary nebula NGC 3242. We analysed the main morphological components of this source, including its knots, but not the halo. In addition to revealing the properties ofthe physical and
chemical nature of this nebula, we also provided reliable spatially resolved constraints that can be used for future photoionisation modelling of the nebula. The latter is ultimately necessary to obtain a fully self-consistent 3D picture of the physical and chemical properties of the object. The observations were obtained with the VIMOS instrument attached to VLT-UT3. Maps and values for specific morphological zones for the detected emission-lines were obtained and analysed with routines developed by the authors to derive physical and chemical conditions of the ionised gas in a 2D fashion. We obtained spatially resolved maps and mean values of the electron densities, temperatures, and chemical abundances, for specific morphological structures in NGC 3242. These results show the pixel-to-pixel variations of the the small- and large-scale structures of the source. These diagnostic maps provide information free from the biases introduced by traditional single long-slit observations. In general, our results are consistent with a uniform abundance distribution for the object, whether we look at abundance maps or integrated fluxes from specified morphological structures. The results indicate that special care should be taken with the calibration of the data and that only data with extremely good signal-to-noise ratio and spectral coverage should be used to ensure the detection of possible spatial variations.
Continuing our series of papers on the 3-D structure and accurate distances of Planetary Nebulae (PNe), we present here the results obtained for the planetary nebula NGC,40. Using data from different sources and wavelengths, we construct 3-D photoion
ization models and derive the physical quantitities of the ionizing source and nebular gas. The procedure, discussed in detail in the previous papers, consists of the use of 3-D photoionization codes constrained by observational data to derive the three-dimensional nebular structure, physical and chemical characteristics and ionizing star parameters of the objects by simultaneously fitting the integrated line intensities, the density map, the temperature map, and the observed morphologies in different emission lines. For this particular case we combined hydrodynamical simulations with the photoionization scheme in order to obtain self-consistent distributions of density and velocity of the nebular material. Combining the velocity field with the emission line cubes we also obtained the synthetic position-velocity plots that are compared to the observations. Finally, using theoretical evolutionary tracks of intermediate and low mass stars, we derive the mass and age of the central star of NGC,40 as $(0.567 pm 0.06)$M$_{odot}$ and $(5810 pm 600)$yrs, respectively. The distance obtained from the fitting procedure was $(1150 pm 120)$pc.
In the last decades we witnessed an increase in studies of open clusters of the Galaxy, especially because of the good determination for a wide range of values of parameters such as age, distance, reddening, and proper motion. The reliable determinat
ion of the parameters strongly depends on the photometry available and especially on the U filter, which is used to obtain the color excess E(B-V) through the color-color diagram (U-B) by (B-V) by fitting a zero age main-sequence. Owing to the difficulty of performing photometry in the U band, many authors have tried to obtain E(B-V) without the filter. But because of the near linearity of the color-color diagrams that use the other bands, combined with the fact that most fitting procedures are highly subjective (many done by eye) the reliability of those results has always been questioned. Our group has recently developed, a tool that performs isochrone fitting in open-cluster photometric data with a global optimization algorithm, which removes the need to visually perform the fits and thus removes most of the related subjectivity. Here we apply our method to a set of synthetic clusters and two observed open clusters (Trumpler 1 and Melotte 105) using only photometry for the BVRI bands. Our results show that, considering the cluster structural variance caused only by photometric and Poisson sampling errors, our method is able to recover the synthetic cluster parameters with errors of less than 10% for a wide range of ages, distances, and reddening, which clearly demonstrates its potential. The results obtained for Trumpler 1 and Melotte 105 also agree well with previous literature values.
We present a new technique to fit color-magnitude diagrams of open clusters based on the Cross-Entropy global optimization algorithm. The method uses theoretical isochrones available in the literature and maximizes a weighted likelihood function base
d on distances measured in the color-magnitude space. The weights are obtained through a non parametric technique that takes into account the star distance to the observed center of the cluster, observed magnitude uncertainties, the stellar density profile of the cluster among others. The parameters determined simultaneously are distance, reddening, age and metallicity. The method takes binary fraction into account and uses a Monte-Carlo approach to obtain uncertainties on the determined parameters for the cluster by running the fitting algorithm many times with a re-sampled data set through a bootstrapping procedure. We present results for 9 well studied open clusters, based on 15 distinct data sets, and show that the results are consistent with previous studies. The method is shown to be reliable and free of the subjectivity of most previous visual isochrone fitting techniques.
Evidence of jet precession in many galactic and extragalactic sources has been reported in the literature. Much of this evidence is based on studies of the kinematics of the jet knots, which depends on the correct identification of the components to
determine their respective proper motions and position angles on the plane of the sky. Identification problems related to fitting procedures, as well as observations poorly sampled in time, may influence the follow up of the components in time, which consequently might contribute to a misinterpretation of the data. In order to deal with these limitations, we introduce a very powerful statistical tool to analyse jet precession: the cross-entropy method for continuous multi-extremal optimisation. Only based on the raw data of the jet components (right ascension and declination offsets from the core), the cross-entropy method searches for the precession model parameters that better represent the data. In this work we present a large number of tests to validate this technique, using synthetic precessing jets built from a given set of precession parameters. Aiming to recover these parameters, we applied the cross-entropy method to our precession model, varying exhaustively the quantities associated to the method. Our results have shown that even in the most challenging tests, the cross-entropy method was able to find the correct parameters within 1%-level. Even for a non-precessing jet, our optimization method could point out successfully the lack of precession.
