Study of Photometric Phase Curve: Assuming a Cellinoid Ellipsoid Shape of Asteroid (106) Dione
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RAA 2017 Vol. X No. XX, 000–000 R c 2017 National Astronomical Observatories, CAS and IOP Publishing Ltd. esearch in Astronomy and http://www.raa-journal.org http://iopscience.iop.org/raa Astrophysics Study of photometric phase curve: assuming a Cellinoid ellipsoid shape of asteroid (106) Dione Yi-Bo Wang1,2,3, Xiao-Bin Wang1,3,4, Donald P. Pray5 and Ao Wang1,2,3 1 Yunnan Observatories, Chinese Academy of Sciences, Kunming 650216, China; [email protected], [email protected] 2 University of Chinese Academy of Sciences, Beijing 100049, China 3 Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences, Kunming 650216, China 4 Center for Astronomical Mega-Science, Chinese Academy of Sciences, Beijing 100012, China 5 Sugarloaf Mountain Observatory, South Deerfield, MA 01373, USA Received 2017 May 9; accepted 2017 May 31 Abstract We carried out the new photometric observations of asteroid (106) Dione at three apparitions (2004, 2012 and 2015) to understand its basic physical properties. Based on a new brightness model, the new photometric observational data and the published data of (106) Dione were analyzed to characterize the morphology of Dione’s photometric phase curve. In this brightness model, Cellinoid ellipsoid shape and three-parameter (H, G1, G2) magnitude phase function system were involved. Such a model can not only solve the phase function system parameters of (106) Dione by considering an asymmetric shape of asteroid, but also can be applied to more asteroids, especially for those asteroids without enough photometric data to solve the convex shape. Using a Markov Chain Monte Carlo (MCMC) method, +0.03 +0.077 Dione’s absolute magnitude H =7.66−0.03 mag, and phase function parameters G1 =0.682−0.077 and +0.042 G2 = 0.081−0.042 were obtained. Simultaneously, a Dione’s simplistic shape, orientation of pole and rotation period were also determined. Key words: asteroids: general: photometric phase curve — asteroids: individual: (106) Dione — tech- niques: photometric; MCMC method 1 INTRODUCTION Mishchenko 1999, 2013; Belskaya & Shevchenko 2000; Muinonen et al. 2002; Oszkiewicz et al. 2012). Asteroids are thought to be the remnants of the planetes- In 1985, a semi-empirical H − G magnitude system imals related to the progenitor bodies which formed ter- (Bowell et al. 1989) was adopted as the standard magni- restrial planets and cores of giant planets. They can pro- tude system by International Astronomical Union (IAU), vide us the important clues to pristine composition of the where H and G are the absolute magnitude of an aster- solar nebula (Michel et al. 2015). oid and the slope factor, respectively. The H − G sys- Photometric phase curve, as one of the crucial phys- tem reflecting Lumme-Bowell reflectance law (Lumme ical properties of an asteroid, presents the observational & Bowell 1981), has been used to study the behavior brightness variations at the different solar phase angles of the photometric phase curve of asteroid for many (hereafter phase angle). It can also provide us the im- years. However, it cannot accurately fit the photomet- portant information on the nature of surface of an aster- ric phase curves of low-albedo and high-albedo aster- oid, such as porosity, asymmetry factor and roughness oids (Belskaya & Shevchenko 2000). Therefore, a three- (Hapke 1984, 1986, 2002; Muinonen 1994; Dlugach & parameter (H, G1, G2) magnitude phase function system 2 Y.-B. Wang, X.-B. Wang, D. P. Pray and A. Wang (Muinonen et al. 2010) was adopted as the new standard orientation of pole and shape are not obtained. In order to magnitude system in the 28th General Assembly of IAU. accurately determine the phase function system parame- This new system improves the fitting results of photomet- ters, spin parameters and Cellinoid shape of Dione, new ric phase curves for all taxonomical asteroids (Muinonen observations at three apparitions (2004, 2012 and 2015) et al. 2010; Oszkiewicz et al. 2012; Penttil¨aet al. 2016; were carried out with the 1.0-m telescope at Yunnan Shevchenko et al. 2016). The parameters G1 and G2, Observatories (IAU Observatory Code 286). to some extent, can also be used to infer the surface- Section 2 contains the observation and data reduc- material information of small objects of the solar system, tion of asteroid (106) Dione. In Section 3, we introduce especially for those distant small objects. the new brightness model and the Markov Chain Monte In order to study the photometric phase curve of the Carlo (MCMC) method. The application result of this asteroid, observational data derived in a large range of model for (106) Dione is presented in Section 4 and the phase angles are needed. However, the sufficient data are discussion is contained in Section 5. Finally, in the last difficult to obtain with the ground-based instruments in section we conclude this work. a single apparition, due to the weather condition and the observation time constraint. For the observational data 2 OBSERVATION AND DATA REDUCTION obtained during different apparitions, due to the effect of non-spherical shape of asteroid, the phase function sys- To understand the basic physical properties of (106) tem parameters will be changed with the geometries of Dione, we carried out the photometric observations with observations varying. the 1-m telescope of Yunnan Observatories in 2004, 2012 A brightness model has been used to estimate the and 2015. The photometric observational data of (106) phase function system parameters of (107) Camilla Dione in 2004 were gathered by the 1k×1k pixel PI by considering a tri-axial ellipsoid shape and the 1024TKB CCD camera with a field of view (FOV) of 6.5′ × 6.5′; the data in 2012 and 2015 were obtained by (H, G1, G2) magnitudephase function system in our pre- the 2k×2kpixel Andor DW436 CCD camera with a FOV vious work (Wang et al. 2016). However, this simple tri- ′ ′ axial ellipsoid cannot be applied appropriately to those of 7.3 × 7.3 . asteroids with the irregular shape. All the scientific images were reduced using the In this paper, we develop a new brightness model Image Reduction and Analysis Facility (IRAF) software. which can more accurately estimate the magnitude-phase Following the standard reduction process, bias and flat relation, rotation period, orientation of pole and shape of effects were corrected on the scientific images. The cos- an asteroid. In detail, we consider an asymmetric shape mic rays hinting occasionally in these images were iden- model — Cellinoid ellipsoid (Cellino et al. 1989; Lu tified by a criterion of four times of the standard devia- et al. 2014) consisting of adjacent eight octants of el- tion of sky background and then were removed. Utilizing the APPHOT task, the instrumental magnitudes of refer- lipsoid with different semi-axes (a1,a2,b1,b2,c1,c2) in this new brightness model, which allows for a better fit ence stars and target asteroid are measured by an optimal to asteroid with irregular shape. In addition, the three- aperture. Before the analysis of photometric phase curve, the parameter (H, G1, G2) magnitude phase function system is also used. instrumental magnitudes of asteroid needed to be con- We applied the new brightness model to analyze the verted into the standard photometry system (e.g. the photometric data of a main-belt asteroid (106) Dione. Landolt standard photometry system). The procedure of At present, for asteroid (106) Dione, its photometric ob- magnitude calibration contains two steps: (1) To ob- tain the transformation relation between the instrument servational data had been obtained by several groups ′ (Harris et al. 1992; Pray 2005). Harris et al. (1992) magnitude mobs and the magnitude r of the Carlsberg and Pray (2005) obtained the different rotation periods Meridian Catalogue (CMC 15) system (Mui˜nos & Evans (15 hours vs. 16.26 hours). In addition, Harris et al. 2014) by the reference stars in the observed images, (1992) firstly estimated the absolute magnitude of Dione ′ mobs = k(J − K)+ r + m0, (1) H = 7.41 mag by assuming a slope factor G = 0.09. Later, Shevchenko & Tedesco (2006) obtained its abso- where, the examined parameter k and m0 are solved by lute magnitude H = 7.66 mag by the occultation data. the linear least square method. J- and K-bands mag- However, until now, the detailed information on Dione’s nitudes are derived from 2MASS catalogue. Then, the Study of photometric phase curve: asteroid (106) Dione. 3 Table 1 Information on the New Photometric Observations of Asteroid (106) Dione Date r ∆ α filter Note (UT) (AU) (AU) (◦) 2004/11/03.8 2.684 1.830 13.1 I 1.0-m YNAO 2004/11/04.8 2.685 1.824 12.7 V,I 1.0-m YNAO 2004/11/06.9 2.687 1.810 12.0 I 1.0-m YNAO 2004/11/07.8 2.688 1.804 11.6 I 1.0-m YNAO 2004/11/08.9 2.689 1.798 11.3 I 1.0-m YNAO 2004/12/01.8 2.714 1.730 1.8 I 1.0-m YNAO 2004/12/03.8 2.716 1.731 1.0 V,I 1.0-m YNAO 2012/03/13.7 3.578 2.591 2.1 R 1.0-m YNAO 2012/03/14.7 3.579 2.590 1.9 R 1.0-m YNAO 2012/03/15.8 3.580 2.590 1.8 R 1.0-m YNAO 2012/03/17.8 3.582 2.590 1.6 R 1.0-m YNAO 2015/11/15.6 2.651 1.694 6.8 C 1.0-m YNAO 2015/11/16.6 2.651 1.698 7.2 C 1.0-m YNAO -0.25 -0.25 2004-11-08 (1.0-m) 2004-11-03 (1.0-m) -0.20 -0.20 2004-11-04 (1.0-m) 2004-12-01 (1.0-m) 2004-11-06 (1.0-m) 2004-12-03 (1.0-m) -0.15 -0.15 2004-11-07 (1.0-m) -0.10 -0.10 -0.05 -0.05 0.00 0.00 0.05 0.05 2004-12-04 (Pray 2005) 0.10 0.10 2004-12-18 (Pray 2005) RelativeMagnitude RelativeMagnitude 1981-09-20 (Harris et al.