Heat diffusion equation and thermophysical modelling of asteroids

• Thesis title in Czech: Rovnice vedení tepla a termofyzikální modelování planetek
• Thesis title in English: Heat diffusion equation and thermophysical modelling of asteroids
• Key words: asteroidy, planetky, rovnice vedení tepla, inverze světelných křivek
• English key words: asteroids, small bodies of the Solar System, Heat Conduction Equation, Light curve inversion
• Academic year of topic announcement: 2012/2013
• Thesis type: diploma thesis
• Thesis language: angličtina
• Department: Astronomical Institute of Charles University (32-AUUK)
• Supervisor: doc. Mgr. Josef Ďurech, Ph.D.
• Author: hidden - assigned and confirmed by the Study Dept.
• Date of registration: 15.10.2012
• Date of assignment: 24.10.2012
• Confirmed by Study dept. on: 19.12.2012
• Date and time of defence: 22.05.2014 00:00
• Date of electronic submission: 11.04.2014
• Date of submission of printed version: 11.04.2014
• Date of proceeded defence: 22.05.2014
• Opponents: RNDr. David Čapek, Ph.D.

Guidelines

A new method that combines asteroid photometry in visible light with thermal infrared (IR) radiometry and derives physical models of asteroids has been recently developed (Durech et al. 2012). The new general method uses the same representation as the standard lightcurve inversion but includes both data types at once and optimizes all relevant physical parameters. This way, the full physical model (shape, size, spin vector, scattering properties of the surface, surface roughness, thermal inertia) is created. The thermal emission is computed by solving 1D heat diffusion on the surface.

The aim of this work is to further develop this method focusing on the heat diffusion problem. Because the problem is computationally demanding, it is necessary to optimize the algorithm that solves the heat diffusion equation (HDE) and make it faster. Different resolutions and methods for the HDE solution have to be tested with respect to the efficiency and accuracy of the computation. As a result of this testing, an optimum algorithm should be developed given the accuracy of input thermal IR data. The trade-off between the accuracy and the speed should be discussed.

Another part of the work will deal with the problem of stability and uniqueness of the solution of the inverse problem. The uncertainty and reliability of the physical parameters and their correlations will be discussed. The physical model of some selected asteroids will be derived and the results (namely the size of the models - the basic physical parameter) compared with results obtained by other methods.

References

M. Kaasalainen, J. Torppa, and K. Muinonen (2001): Optimization methods for asteroid lightcurve inversion. II. The complete inverse problem. Icarus 153, 37
Müller et al. (2011): Thermo-physical properties of 162173 (1999 JU3), a potential flyby and rendezvous target for interplanetary missions, Astronomy and Astrophysics 525, A145
Delbo, M.; Tanga, P. (2009): Thermal inertia of main belt asteroids smaller than 100 km from IRAS data, Planetary and Space Science 57, Issue 2, 259
Lagerros, J. S. V. (1996): Thermal physics of asteroids. I. Effects of shape, heat conduction and beaming, Astronomy and Astrophysics 310, 1011
Lagerros, J. S. V. (1998): Thermal physics of asteroids. IV. Thermal infrared beaming, Astronomy and Astrophysics 332, 1123
Durech, J.; Delbo, M.; Carry, B. (2012): Asteroid Models Derived from Thermal Infrared Data and Optical Lightcurves, Asteroids, Comets, Meteors 2012, Proceedings of the conference held May 16-20, 2012 in Niigata, Japan. LPI Contribution No. 1667

Preliminary scope of work

Tepelné vlastnosti planetek, jejich velikost a odrazivost byly tradičně odvozovány za použití jednoduchých modelů předpokládajících, že planetka je kulatá. Novější přístup kombinuje tvary planetek odvozené z fotometrie s infračervenými daty a odvozuje termofyzikální parametry. Naše nová metoda používá stejnou reprezentaci modelu jako standardní inverze světelných křivek, ale používá oba typy dat najednou a optimalizuje všechny relevantní fyzikální parametry. Tímto způsobem je v blízké budoucnosti možné odvodit fyzikální modely tisíců planetek.

Preliminary scope of work in English

Traditionally, thermal properties of asteroids, their size, and reflectivity were derived using simple models assuming that the asteroid is spherical. More recently, the convex shapes of asteroids from lightcurve inversion were combined with thermal IR to derive the thermophysical parameters. Our new general method uses the same representation as the standard lightcurve inversion but includes both data types at once and optimizes all relevant physical parameters. This way, the full physical models of thousands of asteroid can be derived in the near future.