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.
In this paper we present an analysis of the physical and chemical conditions of the planetary nebula NGC 40 through spatially-resolved spectroscopic maps. We also introduce a new algorithm --2D_NEB-- based on the well-established IRAF nebular package
, which was developed to enable the use of the spectroscopic maps to easily estimate the astrophysical quantities of ionised nebulae. The 2D_NEB was benchmarked, and we clearly show that it works properly, since it compares nicely with the IRAF nebular software. Using this software, we derive the maps of several physical parameters of NGC 40. From these maps, we conclude that Te[NII] shows only a slight temperature variation from region to region, with its values constrained between ~8,000 K and ~9,500 K. Electron densities, on the other hand, have a much more prominent spatial variation, as Ne[SII] values vary from ~1,000 cm^(-3) to ~3,000 cm^(-3). Maps of the chemical abundances also show significant variations. From the big picture of our work, we strongly suggest that analysis with spatial resolution be mandatory for more complete study of the physical and chemical properties of planetary nebulae.
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.
