The Asteroid Challenge for LSST
Karri Muinonen1,2
1Department of Physics, University of Helsinki, Finland 2Finnish Geodetic Institute, Masala, Finland
LSST@Europe: The Path to Science Cambridge, U.K., September 9-12, 2013 Introduction
• From orbits via rotation periods, pole orientations, and shapes to surface composition • Plane of scattering, solar phase angle • Markov chain Monte Carlo methods (MCMC) • Challenges for phase curves, lightcurves, and astrometry • Near-Earth-object impact hazard: collision probabilities Introduction
Photometric phase curves
Muinonen et al., in Asteroids III, 123, 2002 (obs. ref. therein; lightcurve mean or peak brightness) Lowell Observatory Photometric database • Lowell observatory photometric database (Bowell et al., MAPS, in press; Oszkiewicz et al., JQSRT 112, 1919, 2011; Oszkiewicz et al., Icarus 219, 283, 2012) • Altogether over 70 million photometric points for over 400,000 asteroids, typically hundreds of points for each asteroid • All Minor Planet Center photometry calibrated at Lowell Observatory but still of low accuracy
Polarimetric phase curves
Muinonen et al., in Asteroids III, 123, 2002 (obs. ref. therein)
Phase curve inversion challenge
• Linear least-squares modeling for 6 x 106 objects and (6 x 106) x 800 = 4.8 x 109 observations after a 10-year LSST survey: feasible! • Nonlinear treatment for each object using a coherent-backscattering radiative-transfer model: challenge! • Polarimetric observations: an open question Photometric lightcurves
• Lightcurves observed for asteroids at different apparitions • Rotation period, pole orientation, and shape from convex lightcurve inversion • Equivalence of photometric lightcurves and phase curves Asteroid (171) Ophelia Virtual-Observation MCMC • Generate virtual observations by adding random errors to each observation • Compute a virtual least-squares solution with the virtual observations • Repeat to obtain another virtual least-squares solution • In the parameter phase space, compute the difference vector between the two virtual solutions • Generate the MCMC proposal parameters by adding the difference vector to the current parameters
• For more details, see Muinonen et al., PSS, 2012 (random-walk Metropolis-Hastings with a symmetric proposal) • Lommel-Seeliger ellipsoid model with analytical disk-integrated brightness (unpublished) Gaussian-Sphere Asteroid
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Systematic period scan, 69 observations sparsely distributed over 5 years of Gaia survey Gaussian-Sphere Asteroid Gaussian-Sphere Asteroid Lightcurve inversion challenge
• Data-processing after 10-year LSST survey • Single-core computing times (2013) – Virtual-observation MCMC with ellipsoids: (6 x 106) x 5 h = 3 x 107 h = 1.25 x 106 d ≈ 3.4 x 103 a – Virtual-observation MCMC with convex models: (6 x 106) x 100 h = 6 x 108 h = 2.5 x 107 d ≈ 6.8 x 104 a Orbital inversion • Orbits from two or more astrometric observations • Markov-chain Monte Carlo ranging (MCMC ranging, Oszkiewicz et al., MAPS, 2009; cf. Virtanen et al., Icarus 2001, and Muinonen et al., CMDA, 2001) • OpenOrb open source software (Granvik et al., MAPS, 2009) • Virtual-observation MCMC (Muinonen et al., PSS, 2012) • Incorporation of statistical methods into the Gaia/ DPAC data-processing pipeline
Example: 1998 OX4 • Discovery appari on only: 21 observa ons spanning 9.1 days in July-August 1998 • Single outlier observa on omi ed • Standard devia ons for R.A. and Dec.: 0.57 arcsec and 0.34 arcsec • See Virtanen et al. (Icarus, 2001) and Muinonen et al. (CMDA, 2001) • 30,000 sample elements using MCMC ranging and virtual-observa on MCMC in 1 min 50 s and 30 min 32 s, respec vely (with acceptance rates of 1.0% and 0.082%)
Orbital inversion challenge • Daily data processing in a 10-year LSST survey • Single-core computing times (2013) – Idealistic total in 10 years with MCMC orbital ranging: (6 x 106) x 0.1 h = 6 x 105 h = 2.5 x 10 4 d ≈ 68.4 a – MCMC orbital ranging on the first night: (400 x 6 x 106)/(10 x 365.25) x 0.1 h ≈ 6.57 x 105 h ≈ 2.74 x 103 d ≈ 7.50 a – First night, worst-case scenario with real objects: 400 x 2.74 x 103 d ≈ 1.10 x 106 d ≈ 3000 a Solar System inversion challenge • Gaia, number of nonlinear unknowns N – ellipsoidal model asteroids: (3 x 105) x (6 + 1 + 4 + 2) = 3.9 x 106 – convex model asteroids: (3 x 105) x (6 + 1 + 4 + 100) = 3.3 x 107 • LSST, number of nonlinear unknowns N – ellipsoidal model asteroids: (6 x 106) x (6 + 1 + 4 + 2) = 7.8 x 107 – convex model asteroids: (6 x 106) x (6 + 1 + 4 + 1000) = 6.1 x 109 • N x N covariance matrices! Conclusions • Solar System science to be ramped up with an extremely large, homogeneous LSST data set of astrometry and photometry • Computational challenge vs. sophistigation of models • NEOs vs. space debris, impact hazard • Illposedness of inverse problems for outer Solar System • Solution of the full nonlinear Solar System inverse problem: dream for Gaia and LSST Twin System!
Survey strategies …
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