Observational Study Of Photometric Phase Curves Of Asteroids

The studies of asteroids opening a window,make us seeing segment of a whole fascinating world.Asteroids are thought to be leftover planetesimals that had formed both the terrestrial planets and the cores of the giant planets, which contain much information on the solar nebula during the stage of planetary formation. This information can help us understand the original composition and the condition in the initial stage of the solar system. Meanwhile, asteroids can provide us the information on how life started on Earth. In addition, Near-Earth-Asteroids,as the potential "killers",pose a risk of human civilization. Undoubtedly, a series of studies of basic physical properties such as size, shape, rotation period, interior structure and material characterizations on the surface are the foundations to comprehend the asteroids for the scien-tists, the important pre-condition on whether the exploiters can successfully exploit the mineral resources, and the necessary security to defend the asteroids hitting the Earth. So to say, the studies on the fundamental physical properties of asteroids are one of the most important mat-ters.Photometric phase curve, describing the relation of the brightness variations of asteroids with the solar phase angles changing, embodies the concrete characterizations (such as rough-ness, porosity, asymmetry factor etc.) of material on the asteroidal surface. Therefore, photo-metric phase curve can provide us the clues to the physical properties of asteroid regolith ma-terial. In the current studies of asteroid photometric phase curve, being an implicit assumption,namely assuming the spherical shape of asteroid, it is aim to ignore the effect of non-spherical shape of the reality asteroid in the brightness model. In order to effectively fit the photometric phase curve and obtaining the accurate phase function parameters, the phase angles distributing a large range are needed during the observations. In addition, in order to retain the spherical assumption, the short observational duration should be satisfied. However, for the majority of main-belt asteroids, due to these factors on the weather condition, facility operation and appari-tion duration in the practical observations, it is difficult to obtain the enough observational data which must distribute in a large range of phase angle. In order to estimate the phenomenon that the brightness non-linearly enhances with the phase angle decreasing, namely opposition effect,the observational data obtained in a small phase angle must be involved, but these observations(? ? 2°) cannot be carried out in each apparition. These reasons metioned above restrict the development of studies of asteroid photometric phase curve. Comparing with more than five thousand asteroids who have been observed at more than three apparitions, at present, the pho-tometric phase curves of about one hundred asteroids have only been analyzed. Resulting in this condition so many observational data not to be used to study the asteroid photometric phase curve, the main reason is that the unreasonable sphere-assumption of asteroid shape has been used in current analysis method. In fact, for the majority of asteroids, their shapes are irregu-lar. Therefore, changing the observational views causes the intersection angle varying between the direction of pole and the direction of observer's sight (namely aspect angle), which finally results in the cross section area change of the irregular shape of an asteroid for the photometric data derived from different apparitions. Thus, the brightness in the photometric phase curve not only varies with the phase angle changing, but it can also be influenced obviously by the aspect angle changing. Therefore, the accurate analysis consequence of phase curve cannot be estimated.In order to solve this problem, the effect of change of aspect angles must be considered,when the variation of asteroid's brightness is studied with the phase angle changing. Based on the three-parameter H - G1 - G2 magnitude phase function system, firstly, we use a typical tri-axial ellipsoid model as the approximate of the shape of an asteroid, and then propose a photometric phase curve brightness model that considers an effect of non-spherical shape of an asteroid. This model can be used to these asteroids whose light curves show the character-izations of the similar sine or cosine. Using this model and collecting the photometric data,we analyzed the photometric phase curve of asteroid (87) Sylvia, and well obtained its result.Meanwhile, we carried out the new observations of asteroid (107) Camilla in March 2015 at 1-m telescope of Yunnan Observatories, and obtained its phase function parameters by com-bining the data derived from other researchers with ours. However, for the more asteroids, they have more complex geometrical shapes than the tri-axial ellipsoid; thus, one more irregular shape model should be needed to describe the reality shape of an asteroid. Here, we adopted the Cellinoid ellipsoid model — an asymmetrical enclosing ellipsoid that consists of eight co-herent ocents of ellipsoid. Therefore, we developed a new brightness model that considered the effect of asymmetrical shape of an asteroid. This model has many advantages such as a simple mathematical formalism and less free parameters and can be used effectively to fit the topogra-phy of photometric phase curves of the different type asteroids by combining the data derived from the different apparitions. Meanwhile, the determination of rotation period, orientation of pole and shape can be obtained by this model. Using this new brightness model and the collect-ed photometric data derived from different apparitions, I have analyzed the photometric phase curves of asteroid (17) Thetis, (22) Kalliope, (29) Amphitrite, (44) Nysa and (511) Davida and better obtained these results. Furthermore, to obtain the accurate information of the physical properties of asteroid (106) Dione, we carried out more observations at 1-m telescope of Yun-nan Observatories in three apparitions 2004, 2012 and 2015. By employing a Markov chain monte carlo (MCMC) method and combining the other published observational data with ours,we studied the photometric phase curve of (106) Dione, estimated its more accurate rotation period and firstly determined the orientation of pole and shape. It is expected that broadly using this model in the future can enlarge number of the sample of photometric phase curve, and then provides us the more research candidates to study the physical properties of asteroid regolith material.