A method of immediate detection of objects with a near-zero apparent motion in series of CCD-frames

Abstract

The paper deals with a computational method for detection of the solar system minor bodies (SSOs), whose inter-frame shifts in series of CCD-frames during the observation are commensurate with the errors in measuring their positions. These objects have velocities of apparent motion between CCD-frames not exceeding three rms errors (3σ) of measurements of their positions. About 15% of objects have a near-zero apparent motion in CCD-frames, including the objects beyond the Jupiter's orbit as well as the asteroids heading straight to the Earth. The proposed method for detection of the object's near-zero apparent motion in series of CCD-frames is based on the Fisher f -criterion instead of using the traditional decision rules that are based on the maximum likelihood criterion. We analyzed the quality indicators of detection of the object's near-zero apparent motion applying statistical and in situ modeling techniques in terms of the conditional probability of the true detection of objects with a near-zero apparent motion. The efficiency of method being implemented as a plugin for the Collection Light Technology (CoLiTec) software for automated asteroids and comets detection has been demonstrated. Among the objects discovered with this plugin, there was the sungrazing comet C/2012 S1 (ISON). Within 26 min of the observation, the comet's image has been moved by three pixels in a series of four CCD-frames (the velocity of its apparent motion at the moment of discovery was equal to 0.8 pixels per CCD-frame; the image size on the frame was about five pixels). Next verification in observations of asteroids with a near-zero apparent motion conducted with small telescopes has confirmed an efficiency of the method even in bad conditions (strong backlight from the full Moon). So, we recommend applying the proposed method for series of observations with four or more frames.

Development and Improvements of Computational Methods Implemented to the Colitec Software

“…It has been used in about 700 000 observations, during which four comets C/2011 X1 (Elenin), P/2011 NO1 (Elenin), C/2012 S1 (ISON) and P/2013 V3 (Nevski) out of seven discovered in the CIS and the Baltic States over the past 20 years were identified using CoLiTec. In total, the CoLiTec software was used for discovery more than 1560 asteroids, including 5 NEO, 21 Trojan asteroids of Jupiter and 1 Centaur (see, also, Savanevych et al, 2012Savanevych et al, , 2018Khlamov et al, 2016Khlamov et al, , 2017Vavilova et al, 2012Vavilova et al, , 2017Vavilova, 2016).…”

“…Fisher F-criterion is used as significance criterion in this method. It allows detection of objects that have a shift between frames, which isn't exceeded the object's image size by 3 RMS (Savanevych et al, 2018). For example, at the time of discovery, the image size of the comet C 2012 S1 (ISON) was five pixels and it has been shifted by three pixels for the four frames (Khlamov et al, 2017).…”

New algorithm for astrometric reduction of the wide-field images

“… incomplete evidence for using the maximum likelihood criterion when some parameters are unknown [4,6];…”

On the “Solar System Small Bodies” Astroplate Project of the Ukrainian Virtual Observatory

“…The existing world databases of positional observations of the small bodies of the Solar System have a large number of photographic, modern CCD and satellite observations for these objects. Modern observations far exceed the previous ones in the accuracy of coordinates and number of positions, where new mathematical methods for the automated CCD images processing, positional frame-to-frame guidance and discovery of Solar system small bodies have a crucial role (see, for example, Savanevych et al, 2015;Savanevych et al, 2015;Savanevych et al, 2018).…”