Cross-entropy optimizer: a new tool to study precession in astrophysical jets

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 optimization. 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. With the aim of recovering these parameters, we applied the cross-entropy method to our precession model, varying exhaustively the quantities associated with 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 a 1 per cent level. Even for a non-precessing jet, our optimization method could point out successfully the lack of precession.

MODELING VERY LONG BASELINE INTERFEROMETRIC IMAGES WITH THE CROSS-ENTROPY GLOBAL OPTIMIZATION TECHNIQUE

We present a new technique for obtaining model fittings to very long baseline interferometric images of astrophysical jets. The method minimizes a performance function proportional to the sum of the squared difference between the model and observed images. The model image is constructed by summing N(s) elliptical Gaussian sources characterized by six parameters: two-dimensional peak position, peak intensity, eccentricity, amplitude, and orientation angle of the major axis. We present results for the fitting of two main benchmark jets: the first constructed from three individual Gaussian sources, the second formed by five Gaussian sources. Both jets were analyzed by our cross-entropy technique in finite and infinite signal-to-noise regimes, the background noise chosen to mimic that found in interferometric radio maps. Those images were constructed to simulate most of the conditions encountered in interferometric images of active galactic nuclei. We show that the cross-entropy technique is capable of recovering the parameters of the sources with a similar accuracy to that obtained from the very traditional Astronomical Image Processing System Package task IMFIT when the image is relatively simple (e. g., few components). For more complex interferometric maps, our method displays superior performance in recovering the parameters of the jet components. Our methodology is also able to show quantitatively the number of individual components present in an image. An additional application of the cross-entropy technique to a real image of a BL Lac object is shown and discussed. Our results indicate that our cross-entropy model-fitting technique must be used in situations involving the analysis of complex emission regions having more than three sources, even though it is substantially slower than current model-fitting tasks (at least 10,000 times slower for a single processor, depending on the number of sources to be optimized). As in the case of any model fitting performed in the image plane, caution is required in analyzing images constructed from a poorly sampled (u, v) plane.