Asteroid mass estimation with the robust adaptive Metropolis algorithm

Siltala, L.; Granvik, Mikael

doi:10.1051/0004-6361/201935608

Cited by 19 publications

(30 citation statements)

References 28 publications

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“…Combining our new volume estimates with the average of available mass estimates determined in Viikinkoski et al (2018) yields a density of 4.20 ± 0.60 g cm −3 for MPCD and 4.10 ± 0.61 g cm −3 for ADAM. We did not include the lower mass (1.5 × 10 19 kg) derived by Siltala & Granvik (2020) in the mass estimation as we consider this value to be an outlier. The physical characteristics of our new models compared to those of previous works are reported in Table 1.…”

Section: Bulk Densitymentioning

confidence: 99%

Asteroid (16) Psyche’s primordial shape: A possible Jacobi ellipsoid

Ferrais

Vernazza

Jordá

et al. 2020

A&A

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Context. Asteroid (16) Psyche is the largest M-type asteroid in the main belt and the target of the NASA Psyche mission. It is also the only asteroid of this size (D > 200 km) known to be metal rich. Although various hypotheses have been proposed to explain the rather unique physical properties of this asteroid, a perfect understanding of its formation and bulk composition is still missing. Aims. We aim to refine the shape and bulk density of (16) Psyche and to perform a thorough analysis of its shape to better constrain possible formation scenarios and the structure of its interior. Methods. We obtained disk-resolved VLT/SPHERE/ZIMPOL images acquired within our ESO large program (ID 199.C-0074), which complement similar data obtained in 2018. Both data sets offer a complete coverage of Psyche’s surface. These images were used to reconstruct the three-dimensional (3D) shape of Psyche with two independent shape modeling algorithms (MPCD and ADAM). A shape analysis was subsequently performed, including a comparison with equilibrium figures and the identification of mass deficit regions. Results. Our 3D shape along with existing mass estimates imply a density of 4.20 ± 0.60 g cm−3, which is so far the highest for a solar system object following the four telluric planets. Furthermore, the shape of Psyche presents small deviations from an ellipsoid, that is, prominently three large depressions along its equator. The flatness and density of Psyche are compatible with a formation at hydrostatic equilibrium as a Jacobi ellipsoid with a shorter rotation period of ∼3h. Later impacts may have slowed down Psyche’s rotation, which is currently ∼4.2 h, while also creating the imaged depressions. Conclusions. Our results open the possibility that Psyche acquired its primordial shape either after a giant impact while its interior was already frozen or while its interior was still molten owing to the decay of the short-lived radionuclide 26Al.

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Section: Bulk Densitymentioning

confidence: 99%

Asteroid (16) Psyche’s primordial shape: A possible Jacobi ellipsoid

Ferrais

Vernazza

Jordá

et al. 2020

A&A

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“…The only update to the algorithm presented in Siltala & Granvik (2020) is a slightly different acceptance criterion; where previously we computed the acceptance criterion with a single posterior probability density value based on the sum of the χ 2 values for all targets, we now consider the χ 2 values separately for each target and compute their product to obtain the final acceptance probability:…”

Section: Methodsmentioning

confidence: 99%

“…(1) where j represents each individual asteroid considered. Such an approach ensures that accepted proposals must fit each individual asteroid well as opposed to the criterion used by Siltala & Granvik (2020), which only required that the overall fit be acceptable. In addition, this means that each asteroid has the same weight in the acceptance criterion while with our previous approach the total χ 2 value and, by extension, acceptance criterion, is dominated by asteroids with more observations as such have a greater impact on the total value.…”

Section: Methodsmentioning

confidence: 99%

“…In addition, this means that each asteroid has the same weight in the acceptance criterion while with our previous approach the total χ 2 value and, by extension, acceptance criterion, is dominated by asteroids with more observations as such have a greater impact on the total value. We use a uniform prior of unity (see Siltala & Granvik 2020, and discussion therein).…”

Section: Methodsmentioning

confidence: 99%

“…In addition to Psyche itself we use the following 10 numbered test asteroids: (1052), ( 1082), ( 6442), ( 13206), ( 17799), ( 20837), ( 39054), ( 91495), ( 151878) and ( 211012). We have already previously studied four of these test asteroids, namely ( 17799), ( 20837), ( 91495), and ( 151878) (Siltala & Granvik 2020) whereas the other test asteroids have been identified and/or used by Fienga et al (2003); Baer & Chesley (2017); Galád & Gray (2002). Test asteroid ( 1054) is particularly noteworthy as it has six close encounters with Psyche during the observational timespan (Fienga et al 2003).…”

Section: Datamentioning

confidence: 99%

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New estimates of the mass and density of asteroid (16) Psyche

Siltala¹,

Granvik²

2024

Preprint

Self Cite

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Asteroid mass determination is performed by analyzing an asteroid's gravitational interaction with another object, such as a spacecraft, Mars, a companion in the case of binary asteroids, or a separate asteroid during a close encounter. During asteroid-asteroid close encounters, perturbations caused by the masses of larger asteroids can be detected in the post-encounter orbits of the smaller test asteroid involved in such an encounter. This can be described as an inverse problem where the aim is to fit six orbital elements for each asteroid and mass(es) for the perturbing asteroid(s), for a total of 13 parameters at minimum unless more asteroid-asteroid encounters are modeled simultaneously. To solve this inverse problem, which is traditionally done with least-squares methods, we have implemented a Markov-chain Monte Carlo (MCMC) based solution and recently (Siltala & Granvik 2020) reported, among others, significantly lower than expected masses and densities for the asteroid (16) Psyche in particular. Psyche is an interesting, and topical, object as it is the target of NASA's eponymous Psyche mission and is commonly thought to be of metallic or stony-iron composition, which our previous density estimates disagreed with. In our previous work our two separate mass estimates for Psyche were based on modeling encounters with two separate test asteroids in both cases. Since then we have further refined our mass estimate for Psyche by simultaneously using eight separate test asteroids for this object, significantly increasing the amount of observational data included on the model which, in turn, will narrow down the uncertainties of our results at the cost of additional model complexity. Here we report and discuss our latest results for the mass of Psyche based on this case and compute corresponding densities based on existing literature values for the volume. We obtain a mass of (0.972 &#177; 0.148) * 10^-11 solar masses for Psyche corresponding to a bulk density of (3.37 &#177; 0.58) g/cm&#179; which is higher than our previous results while remaining consistent with them considering the uncertainties involved. It still remains lower than other previous literature values. We compare our results to these previous literature values and briefly discuss possible physical implications of these results. In addition, due to previous interest from the scientific community, we have also computed mass estimates for Ceres and Vesta, both of which already have very precisely known masses from the Dawn mission. As such, our results for these two asteroids are not of direct scientific interest but they serve as an useful benchmark to verify that our algorithm provides realistic results as we have 'ground truth' values to compare our results to. We find that for both cases, our results are in line with those of Dawn.

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Ergonomic and Reliable Bayesian Inference with Adaptive Markov Chain Monte Carlo

Vihola¹

2020

Wiley StatsRef: Statistics Reference Online

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Adaptive Markov chain Monte Carlo (MCMC) methods provide an ergonomic way to perform Bayesian inference, imposing mild modeling constraints and requiring little user specification. The aim of this section is to provide a practical introduction to selected set of adaptive MCMC methods and to suggest guidelines for choosing appropriate methods for certain classes of models. We consider simple unimodal targets with random‐walk‐based methods, multimodal target distributions with parallel tempering, and Bayesian hidden Markov models using particle MCMC. The section is complemented by an easy‐to‐use open‐source implementation of the presented methods in Julia, with examples.

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Asteroid mass estimation with the robust adaptive Metropolis algorithm

Cited by 19 publications

References 28 publications

Asteroid (16) Psyche’s primordial shape: A possible Jacobi ellipsoid

Asteroid (16) Psyche’s primordial shape: A possible Jacobi ellipsoid

New estimates of the mass and density of asteroid (16) Psyche

Ergonomic and Reliable Bayesian Inference with Adaptive Markov Chain Monte Carlo

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