Astronomy & Astrophysics manuscript no. viikinkoski_2017 c ESO 2018 October 14, 2018 Adaptive optics and lightcurve data of asteroids: twenty shape models and information content analysis M. Viikinkoski1, J. Hanuš2, M. Kaasalainen1, F. Marchis3, and J. Durechˇ 2 1 Department of Mathematics, Tampere University of Technology, PO Box 553, 33101 Tampere, Finland 2 Astronomical Institute, Faculty of Mathematics and Physics, Charles University, V Holešovickáchˇ 2, 18000 Prague, Czech Republic 3 SETI Institute, Carl Sagan Center, 189 Bernado Avenue, Mountain View CA 94043, USA Received x-x-2017 / Accepted x-x-2017 ABSTRACT We present shape models and volume estimates of twenty asteroids based on relative photometry and adaptive optics images. We discuss error estimation and the effects of myopic deconvolution on shape solutions. For further analysis of the information capacities of data sources, we also present and discuss ambiguity and uniqueness results for the reconstruction of nonconvex shapes from photometry. Key words. Instrumentation: adaptive optics – Methods: numerical, analytical – Minor planets, asteroids: general – Techniques: photometric 1. Introduction we construct shape models using both unprocessed and decon- voluted images, and compare their differences. In our previous paper (Hanuš et al. 2017b), we derived 3D shape This paper is organized as follows. In Sect. 2 we describe models for about 40 asteroids by combining disk-integrated the data reduction steps and outline the ADAM shape optimiza- photometry, adaptive optics (AO) images, and stellar occulta- 1 tion procedure. We discuss our results and comment on some tion timings by the All-Data Asteroid modelling (ADAM , Vi- of the individual asteroids in Sect. 3. We present a procedure ikinkoski et al. 2015a) procedure. Occultation chords are useful for uncertainty and information content estimation, in particular for the 3D shape construction and especially the size estimate noting that the post-processing of AO images, while useful for since they provide information on the silhouette of the asteroid the visual investigation of an image, is not necessarily needed or ˇ independently of the scattering law (Durech et al. 2011). even desirable in 3D asteroid modelling. In Sect. 4, we further There are several asteroids with resolved AO images ob- build on the information content analysis by revisiting the case tained by the Near InfraRed Camera (Nirc2) mounted on the of photometry only, with analytical results that are very scarce W.M. Keck II telescope and optical disk-integrated photometry for nonconvex shapes. We sum up our work in Sect. 5. that can be used for the 3D shape model determination, but lack- ing observed occultation timings. In this paper, we determine shape models and spin states for twenty such asteroids. Because the size estimates are based exclusively on the AO data of vary- 2. Methods ing quality, special attention must be paid when assessing their 2.1. Data reduction uncertainties. For instance, erroneous or badly resolved images may inflate the size of the shape model and hide details present All the adaptive optics images used in this paper, together with in other images. Since the obtaining of additional data is seldom the calibration data, were downloaded from the Keck Observa- an option, effects of bad quality data must be identified and mit- tory Archive (KOA). The AO images were acquired with the igated. Statistical resampling methods facilitate the detection of Near Infrared Camera (NIRC2) mounted at the W.M Keck II outlier images and the estimation of the uncertainties of recon- telescope. While the diffraction-limited angular resolution of the struction. telescope is 45 mas, the actual achievable detail varies with the arXiv:1708.05191v1 [astro-ph.EP] 17 Aug 2017 Another interesting topic is the effect of myopic deconvo- seeing conditions. lution on constructed shape models. Since the level of detail of Raw data were processed using the typical data reduction full shape models is necessarily lower than the apparent resolu- pipeline of dark frame and flat-field correction followed by the tion of AO images, it is natural to question the necessity of my- bad pixel removal. Finally, to obtain data with sufficient signal- opic deconvolution as a preprocessing step when data are used to-noise ratio, several short-exposure frames were shift-added for shape modelling. Furthermore, while deconvolution is useful together. for the visual inspection of individual images, processed images The compensation of atmospheric turbulence offered by the are potentially biased by prior assumptions and contaminated by AO instrument is only partial, and the point-spread function artifacts. To investigate the usefulness of myopic deconvolution, (PSF) is partially unknown. In order to mitigate the blurring ef- fect caused by the PSF, AO images are usually post-processed 1 https://github.com/matvii/ADAM with a myopic deconvolution algorithm. Article number, page 1 of 12 A&A proofs: manuscript no. viikinkoski_2017 Deconvolution is an ill-posed problem in the sense that high- the Fourier transform of the PSF corresponding to the AO image. frequency information is irrevocably lost during the imaging The offset (ox; oy) within the projection plane and and the scale process. To acquire an estimate of the original data, prior as- si are free parameters determined during the optimization. The 2 sumptions adapted to the structure of the observed object must term χlc is a square norm measuring the model fit (Kaasalainen be used. Typically, an L2−L1 regularization (e.g., total variation, & Torppa 2001) to the lightcurves. The last term corresponds see Starck & Murtagh 2006), which smooths out small gradients to regularization functions γi and their weights λi (Viikinkoski in the image and preserves large gradients, is preferred. et al. 2015a). In this paper, we apply the AIDA (Hom et al. 2007) deconvo- Shapes are represented by triangular meshes, where the ver- lution algorithm. The AIDA algorithm uses the Bayesian frame- tex locations are given by the parametrization. ADAM uses two work and iterative optimization to produce an estimate of the true different shape supports: octantoids (Kaasalainenp & Viikinkoski image and PSF, given the initial image and the partially known 2012), which utilize spherical harmonics, and 3-subdivision PSF obtained from the instrument. surfaces (Kobbelt 2000). In addition to the AO images (see Table A.1), we use the optical lightcurves available in the Database of Asteroid Mod- els from Inversion Techniques (DAMIT2, Durechˇ et al. 2010). 3. Results and discussion While recovering nonconvex features based on lightcurves alone is seldom possible, as we discuss below and in the correspond- We use a shape modelling approach similar to that in our pre- ing references, photometry is crucial for complementing the AO vious study (Hanuš et al. 2017b): For each asteroid, we choose data and stabilizing the shape optimization process. Moreover, initial weight terms in Eq. (1). Fixing the image data weight λAO, prior knowledge of the sidereal rotation period and the spin axis we decrease regularization weights λi and the lightcurve weight 2 orientation are useful inputs for the ADAM modelling. These are λLC until the image data fit χAO ceases to improve (Kaasalainen available in DAMIT as well. & Viikinkoski 2012). As the final step, the model fit to AO im- ages is assessed visually. This procedure is repeated for both de- convolved and raw AO images using two shape supports. The 2.2. Shape modelling usage of different shape representations allows us to separate the An intuitively direct approach to asteroid shape reconstruction effects of parametrization from the actual features supported by is contour matching (Carry et al. 2010; Kaasalainen 2011), in the data. If the available data constrain the shape sufficiently, which the asteroid boundary contour is extracted from the de- both octantoid and subdivision parametrizations should converge convolved image and compared with the corresponding plane- to similar shapes (Viikinkoski et al. 2015a). of-sky model boundary. This facilitates model fitting indepen- Given the shape models, we compute the volume-equivalent dently of the scattering law, but the contour identification in the diameter. To gauge the stability of the derived model, we use the AO images is problematic due to smearing and other imaging jackknife resampling method (Efron & Stein 1981). We produce artifacts. Besides, the boundary of a non-convex shape observed n additional shape models by leaving out one of the n available at high phase angles may break into disconnected contours. AO images. For asteroids with only one observation, the jack- In this paper we use the shape reconstruction algorithm knife method cannot obviously be used (28 Belona, 42 Isis, and ADAM (Viikinkoski et al. 2015a) that has been successfully ap- 250 Bettina). In these cases the uncertainty estimates are based plied to many asteroids (Viikinkoski et al. 2015b; Hanuš et al. on the variability observed with different shape supports. 2017a; Hanuš et al. 2017b; Marsset et al. 2017). The method In Table A.1, we have listed the mean pixel size in kilometers used in ADAM circumvents the boundary identification problem (adjusted to the asteroid distance), diameters of the reconstructed by minimizing the difference between the projected model and models based on both deconvolved and raw AO images, and the the image in the Fourier domain. In this way, contour extraction variability intervals obtained by resampling. The estimated spin is not required since the boundary is determined automatically parameters, together with their uncertainties, are listed in Ta- during the optimization, based on all the available data. More- ble 1. These uncertainty estimates result from combined varia- over, ADAM can use both deconvolved and unprocessed images, tions within all the shape supports. making the comparison between reconstructed models possible. It is apparent that the resampling method seems to detect po- ADAM facilitates the simultaneous use of various data tential outlier images (e.g. the fuzzy images of 121 Hermione), types with different weightings.