arXiv subjects

Mikko Kaasalainen

Publications and source records attributed to Mikko Kaasalainen.

At least 19 recordsLinked to original sources

arXiv2020

Asteroid models from generalised projections: Essential facts for asteroid modellers and geometric inverse problem solvers

We present a review of the problem of asteroid shape and spin reconstruction from generalised projections; i.e., from lightcurves, disk-resolved images, occultation silhouettes, radar range-Doppler data, and interferometry. The aim of this text is to summarize all important mathematical facts and proofs related to this inverse problem, to describe their implications to observers and modellers, and to provide the reader with all relevant references.

astro-ph.EP↗

arXiv2020

Basis functions and uniqueness in orbit-averaged population analysis of asteroids

Time-resolved photometry of asteroids can be used for shape and spin reconstruction. If the number of measurements per asteroid is not sufficient to create a model, the whole data set can be used to reconstruct the distribution of shape elongations and pole latitudes in the population. This is done by reconstructing amplitudes of lightcurves that are estimated from dispersion of points observed at (assumed) constant aspect angle. Here, we formulate orbit-averaged approach where the observable is the orbit-averaged dispersion of brightness.

astro-ph.EP↗

arXiv2018

Far-Field Inversion for the Deep Interior Scanning CubeSat

This study aims at advancing mathematical and computational techniques for reconstructing the interior structure of a near earth asteroid (NEA) via Computed Radar Tomography (CRT). We introduce a far-field model for full-wave CRT and validate it numerically for sparse and limited-angle data and an orbiting distance of about 5 km. As a potential future application of the proposed method, we consider the Deep Interior Scanning CUbeSat (DISCUS) concept in which two small spacecraft carrying a bistatic radar localize internal macropores inside a rubble pile asteroid.

astro-ph.IM↗

arXiv2017

LEADER: fast estimates of asteroid shape elongation and spin latitude distributions from scarce photometry

Many asteroid databases with lightcurve brightness measurements (e.g. WISE, Pan-STARRS1) contain enormous amounts of data for asteroid shape and spin modelling. While lightcurve inversion is not plausible for individual targets with scarce data, it is possible for large populations with thousands of asteroids, where the distributions of the shape and spin characteristics of the populations are obtainable. We aim to introduce a software implementation of a method that computes the joint shape elongation p and spin latitude beta distributions for a population, with the brightness observations given in an asteroid database. Other main goals are to include a method for performing validity checks of the algorithm, and a tool for a statistical comparison of populations. The LEADER software package read the brightness measurement data for a user-defined subpopulation from a given database. The observations were used to compute estimates of the brightness variations of the population members. A cumulative distribution function (CDF) was constructed of these estimates. A superposition of known analytical basis functions yielded this CDF as a function of the (shape, spin) distribution. The joint distribution can be reconstructed by solving a linear constrained inverse problem. To test the validity of the method, the algorithm can be run with synthetic asteroid models, where the shape and spin characteristics are known, and by using the geometries taken from the examined database. LEADER is a fast and robust software package for solving shape and spin distributions for large populations. There are major differences in the quality and coverage of measurements depending on the database used, so synthetic simulations are always necessary before a database can be reliably used. We show examples of differences in the results when switching to another database.

astro-ph.EP↗

arXiv2017

Adaptive optics and lightcurve data of asteroids: twenty shape models and information content analysis

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.

astro-ph.EP↗

arXiv2017

Volumes and bulk densities of forty asteroids from ADAM shape modeling

Disk-integrated photometric data of asteroids do not contain accurate information on shape details or size scale. Additional data such as disk-resolved images or stellar occultation measurements further constrain asteroid shapes and allow size estimates. We aim to use all available disk-resolved images of about forty asteroids obtained by the Near-InfraRed Camera (Nirc2) mounted on the W.M. Keck II telescope together with the disk-integrated photometry and stellar occultation measurements to determine their volumes. We can then use the volume, in combination with the known mass, to derive the bulk density. We download and process all asteroid disk-resolved images obtained by the Nirc2 that are available in the Keck Observatory Archive (KOA). We combine optical disk-integrated data and stellar occultation profiles with the disk-resolved images and use the All-Data Asteroid Modeling (ADAM) algorithm for the shape and size modeling. Our approach provides constraints on the expected uncertainty in the volume and size as well. We present shape models and volume for 41 asteroids. For 35 asteroids, the knowledge of their mass estimates from the literature allowed us to derive their bulk densities. We clearly see a trend of lower bulk densities for primitive objects (C-complex) than for S-complex asteroids. The range of densities in the X-complex is large, suggesting various compositions. Moreover, we identified a few objects with rather peculiar bulk densities, which is likely a hint of their poor mass estimates. Asteroid masses determined from the Gaia astrometric observations should further refine most of the density estimates.

astro-ph.EP↗

arXiv2016

Shape model of asteroid (130) Elektra from optical photometry and disk-resolved images from VLT/SPHERE and Nirc2/Keck

Asteroid (130) Elektra belongs to one of the six known triple asteroids in the main belt, so its mass has been reliably determined. We aim to use all available disk-resolved images of (130) Elektra obtained by the SPHERE instrument at VLT and by the Nirc2 of the Keck telescope together with the disk-integrated photometry to determine its shape model and its size. The volume can be then used in combination with the known mass to derive the bulk density of the primary. We apply the All-Data Asteroid Modeling (ADAM) algorithm to the optical disk-integrated data, 2 disk-resolved images obtained by the SPHERE instrument and 13 disk-resolved images from the Nirc2 of the Keck telescope, and derive the shape model and size of Elektra. We present the shape model, volume-equivalent diameter (199$\pm$7 km) and bulk density (1.60$\pm$0.13 g cm$^{-3}$) of the C-type asteroid Elektra.

astro-ph.EP↗

arXiv2016

Distribution of spin-axes longitudes and shape elongations of main-belt asteroids

Context: Large all-sky surveys provide us with a lot of photometric data that are sparse in time (typically few measurements per night) and can be potentially used for the determination of shapes and rotational states of asteroids. The method which is generally used to derive these parameters is the lightcurve inversion. However, for most asteroids their sparse data are not accurate enough to derive a unique model and the lightcurve inversion method is thus not very efficient. Aims: To fully utilize photometry sparse in time, we developed a new simplified model and applied it on the data from the Lowell photometric database. Our aim was to derive spin axis orientations and shape elongations of asteroids and to reconstruct distributions of these parameters for selected subpopulations to find if there are some differences. Methods: We model asteroids as geometrically scattering triaxial ellipsoids. Observed values of mean brightness and the dispersion of brightness are compared with computed values obtained from the parameters of the model -- ecliptical longitude $λ$ and latitude $β$ of the pole and the ratios $a/b$, $b/c$ of axes of the ellipsoid. These parameters are optimized to get the best agreement with the observation. Results: We found that the distribution of $λ$ for main-belt asteroids is not uniform (in agreement with findings of Bowell et al., 2014, M&PS, 49, 95) and is dependent on the inclination of orbit. Surprisingly, the non-uniformity of $λ$ distribution is larger for asteroids residing on low-inclination orbits. We also studied distributions of $a/b$ for several groups of asteroids and found that small asteroids ($D<25\,$km) are on average more elongated than large ones.

astro-ph.EP↗

arXiv2016

Electromagnetic 3D subsurface imaging with source sparsity for a synthetic object

This paper concerns electromagnetic 3D subsurface imaging in connection with sparsity of signal sources. We explored an imaging approach that can be implemented in situations that allow obtaining a large amount of data over a surface or a set of orbits but at the same time require sparsity of the signal sources. Characteristic to such a tomography scenario is that it necessitates the inversion technique to be genuinely three-dimensional: For example, slicing is not possible due to the low number of sources. Here, we primarily focused on astrophysical subsurface exploration purposes. As an example target of our numerical experiments we used a synthetic small planetary object containing three inclusions, e.g. voids, of the size of the wavelength. A tetrahedral arrangement of source positions was used, it being the simplest symmetric point configuration in 3D. Our results suggest that somewhat reliable inversion results can be produced within the present a priori assumptions, if the data can be recorded at a specific resolution. This is valuable early-stage knowledge especially for design of future planetary missions in which the payload needs to be minimized, and potentially also for the development of other lightweight subsurface inspection systems.

astro-ph.IM↗

arXiv2016

Orbiter-to-orbiter tomography: a potential approach for small planetary objects

The goal of this paper is to advance mathematical and computational methodology for orbiter-to-orbiter radio tomography of small planetary objects. In this study, an advanced full waveform forward model is coupled with a total variation based inversion technique. We use a satellite formation model in which a single unit receives a signal that is transmitted by one or more transponder satellites. Numerical results for a 2D domain are presented.

astro-ph.IM↗

arXiv2016

Shape and spin distributions of large object populations from random projection areas

We model the shape and spin characteristics of an object population when there are not enough data to model its single members. The data are random projection areas of the members. We construct a mapping $f(x)\rightarrow C(y)$, $x\in\mathbb{R}^2$, $y\in\mathbb{R}$, where $f(x)$ is the distribution function of the shape elongation and spin vector obliquity, and $C(y)$ is the cumulative distribution function of an observable $y$ describing the variation of the observed projection areas of one member, and show that the mapping is invertible. Using the projected area of an ellipsoid as our model, we obtain analytical basis functions for a function series of $C(y)$ and prove uniqueness and stability properties of the inverse problem. Even though the model error is considerably larger than the measurement noise for realistic cases of arbitrary shapes (such as asteroids), the main characteristics of $f(x)$ (such as the locations of peaks) are robustly recovered from the data.

physics.data-an↗

arXiv2015

ADAM: a general method for using various data types in asteroid reconstruction

We introduce ADAM, the All-Data Asteroid Modelling algorithm. ADAM is simple and universal since it handles all disk-resolved data types (adaptive optics or other images, interferometry, and range-Doppler radar data) in a uniform manner via the 2D Fourier transform, enabling fast convergence in model optimization. The resolved data can be combined with disk-integrated data (photometry). In the reconstruction process, the difference between each data type is only a few code lines defining the particular generalized projection from 3D onto a 2D image plane. Occultation timings can be included as sparse silhouettes, and thermal infrared data are efficiently handled with an approximate algorithm that is sufficient in practice due to the dominance of the high-contrast (boundary) pixels over the low-contrast (interior) ones. This is of particular importance to the raw ALMA data that can be directly handled by ADAM without having to construct the standard image. We study the reliability of the inversion by using the independent shape supports of function series and control-point surfaces. When other data are lacking, one can carry out fast nonconvex lightcurve-only inversion, but any shape models resulting from it should only be taken as illustrative global-scale ones.

astro-ph.EP↗

arXiv2014

Sparse source travel-time tomography of a laboratory target: accuracy and robustness of anomaly detection

This study concerned conebeam travel-time tomography. The focus was on a sparse distribution of signal sources that can be necessary in a challenging in situ environment such as in asteroid tomography. The goal was to approximate the minimum number of source positions needed for robust detection of refractive anomalies, e.g., voids within an asteroid or a casting defects in concrete. Experimental ultrasonic data were recorded utilizing as a target a 150 mm plastic cast cube containing three stones with diameter between 22 and 41 mm. A signal frequency of 55 kHz (35 mm wavelength) was used. Source counts from one to six were tested for different placements. Based on our statistical inversion approach and analysis of the results, three or four sources were found to lead to reliable inversion. The source configurations investigated were also ranked according to their performance. Our results can be used, for example, in the planning of planetary missions as well as in material testing.

astro-ph.IM↗

arXiv2014

Near-integrability as a numerical tool in solar system dynamics

We present a simple choice of integration variables that can be used to exploit the near-integrable character of problems in celestial mechanics. The approach is based on the well-known principle of variation of parameters: instead of orbital elements, we use the phase-space coordinates the object would have at a given point in its (Keplerian) orbit if the perturbing forces were removed. This formulation is suitable for almost any numerical integrator; thus, multistep schemes are easy to build, stepsize can be adjusted, and dissipative forces are allowed. Compared with traditional non-symplectic N-body integrators, the approach often offers increase in speed or accuracy if perturbations are small.

astro-ph.EP↗

arXiv2014

Poincaré inverse problem and torus construction in phase space

The phase space of an integrable Hamiltonian system is foliated by invariant tori. For an arbitrary Hamiltonian H such a foliation may not exist, but we can artificially construct one through a parameterised family of surfaces, with the intention of finding, in some sense, the closest integrable approximation to H. This is the Poincaré inverse problem (PIP). In this paper, we review the available methods of solving the PIP and present a new iterative approach which works well for the often problematic thin orbits.

math-ph↗

arXiv2014

Canonical methods of constructing invariant tori by phase-space sampling

Invariant tori in phase space can be constructed via a nonperturbative canonical transformation applied to a known integrable Hamiltonian H. Hitherto, this process has been carried through with H corresponding to the isochrone potential and the harmonic oscillator. In this paper, we expand the applicability regime of the torus construction method by demonstrating that H can be based on a Stäckel potential, the most general known form of an integrable potential. Also, we present a simple scheme, based on phase space sampling, for recovering the angle variables on the constructed torus. Numerical examples involving axisymmetric galactic potentials are given.

math-ph↗

arXiv2014

Gravitational scattering by giant planets

We seek to characterize giant-planet systems by their gravitational scattering properties. We do this to a given system by integrating it numerically along with a large number of hypothetical small bodies that are initially in eccentric habitable zone (HZ)-crossing orbits. Our analysis produces a single number, the escape rate, which represents the rate at which the small-body flux is perturbed away by the giant planets into orbits that no longer pose a threat to terrestrial planets inside the HZ. Obtaining the escape rate this way is similar to computing the largest Liapunov exponent as the exponential rate of divergence of two nearby orbits. For a terrestrial planet inside the HZ, the escape rate value quantifies the "protective" effect that the studied giant-planet system offers. Therefore, escape rates could provide information on whether certain giant-planet configurations produce a more desirable environment for life than the others. We present some computed escape rates on selected planetary systems, focusing on effects of varying the masses and semi-major axes of the giant planets. In the case of our Solar System we find rather surprisingly that Jupiter, in its current orbit, may provide a minimal amount of protection to the Earth.

astro-ph.EP↗

arXiv2012

Optimal computation of brightness integrals parametrized on the unit sphere

We compare various approaches to find the most efficient method for the practical computation of the lightcurves (integrated brightnesses) of irregularly shaped bodies such as asteroids at arbitrary viewing and illumination geometries. For convex models, this reduces to the problem of the numerical computation of an integral over a simply defined part of the unit sphere. We introduce a fast method, based on Lebedev quadratures, which is optimal for both lightcurve simulation and inversion in the sense that it is the simplest and fastest widely applicable procedure for accuracy levels corresponding to typical data noise. The method requires no tessellation of the surface into a polyhedral approximation. At the accuracy level of 0.01 mag, it is up to an order of magnitude faster than polyhedral sums that are usually applied to this problem, and even faster at higher accuracies. This approach can also be used in other similar cases that can be modelled on the unit sphere. The method is easily implemented in lightcurve inversion by a simple alteration of the standard algorithm/software.

astro-ph.EP↗