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Weak S-type asteroids compared to C-type explain the observed size distribution of the main belt

Michael Vávra, Miroslav Brož

Abstract

The main belt, the region between the orbits of Mars and Jupiter, is home to more than 1 million asteroids. These asteroids form orbital groups, (i.e., asteroid families formed by collisions) and also spectral groups (taxonomies) with different chemical compositions, in particular carbonaceous (C-types) and silicate (S-types). In this paper, we extend the existing main-belt collisional model by finding the appropriate strength-versus-size dependence (also known as the scaling law) for these two groups. We used color indices and geometric albedos of 56 and 72 spectroscopically confirmed C- and S-types (control samples), along with statistical methods on 1 065 034 asteroids, to assign C-, S-, or other types. This allowed us to construct observed size-frequency distributions (SFDs) for several subpopulations constrained by either semimajor axis (inner, middle, outer) or taxonomy (C, S, other). Then we used a Monte Carlo collisional model to compute the long-term collisional evolution (4.5 billion years) and derive synthetic SFDs. Our best-fit scaling laws indicate that S-types must be weaker below approximately 0.2 km than C-types to explain the deficiency of asteroids in the inner part of the main belt near (and below) the observational limit. This may correspond to differences in chemical composition or material porosity. Future research will focus on the scaling laws of asteroids with rare or "extreme" taxonomies (e.g., V, M).

Weak S-type asteroids compared to C-type explain the observed size distribution of the main belt

Abstract

The main belt, the region between the orbits of Mars and Jupiter, is home to more than 1 million asteroids. These asteroids form orbital groups, (i.e., asteroid families formed by collisions) and also spectral groups (taxonomies) with different chemical compositions, in particular carbonaceous (C-types) and silicate (S-types). In this paper, we extend the existing main-belt collisional model by finding the appropriate strength-versus-size dependence (also known as the scaling law) for these two groups. We used color indices and geometric albedos of 56 and 72 spectroscopically confirmed C- and S-types (control samples), along with statistical methods on 1 065 034 asteroids, to assign C-, S-, or other types. This allowed us to construct observed size-frequency distributions (SFDs) for several subpopulations constrained by either semimajor axis (inner, middle, outer) or taxonomy (C, S, other). Then we used a Monte Carlo collisional model to compute the long-term collisional evolution (4.5 billion years) and derive synthetic SFDs. Our best-fit scaling laws indicate that S-types must be weaker below approximately 0.2 km than C-types to explain the deficiency of asteroids in the inner part of the main belt near (and below) the observational limit. This may correspond to differences in chemical composition or material porosity. Future research will focus on the scaling laws of asteroids with rare or "extreme" taxonomies (e.g., V, M).
Paper Structure (24 sections, 7 equations, 19 figures, 1 table)

This paper contains 24 sections, 7 equations, 19 figures, 1 table.

Table of Contents

  1. Introduction
  2. Identifying C- and S-types in catalogs
  3. Control sample of C- and S-types
  4. Algorithm for an assignment of C-types, S-types, and other types
  5. Observational incompleteness
  6. Distributions of sizes
  7. Collisional models with fixed rheology
  8. Scaling law
  9. Collisional probabilities and impact velocities
  10. Initial differential SFDs
  11. One main belt population
  12. Inner, middle, and outer parts
  13. C-types, S-types, and other types
  14. Problem with other types.
  15. Collisional models with variable rheology
  16. ...and 9 more sections

Figures (19)

  • Figure 1: Scatter plot of the C- (blue) and S-type (red) control samples in the $i-z$ vs. $a^*$ plane, along with their uncertainties $\sigma_{i-z}$ and $\sigma_{a^*}$.
  • Figure 2: Same as Fig. \ref{['a_star_i_z']}, but in the $pV$ vs. $a^*$ plane.
  • Figure 3: Scatter plot of eccentricity vs. semimajor axis (both proper or osculating) for all resulted $601\,213$ C-, $453\,998$ S-, and $9\,823$ other types across different parts of the MB (inner, middle, and outer) separated by vertical black lines. Above the plot are the relative numbers of each taxonomy (C-, S-, and other types) within the specific parts of the MB.
  • Figure 4: Observed SFD of the entire MB (green) and its individual parts: inner (red), middle (magenta), and outer (blue). We highlight the three largest asteroids in each region: inner -- (19) Fortuna, (7) Iris, and (4) Vesta (red points); middle -- (15) Eunomia, (2) Pallas, and (1) Ceres (magenta points); and outer -- (704) Interamnia, (52) Europa, and (10) Hygiea (blue points). The "star-shaped" points on each SFD mark the limit size ranges obtained in Sec. \ref{['obs_bias']}, below which the data are observationally incomplete for the entire MB (green), inner (red), middle (magenta), and outer (blue) parts. The observed SFDs differ significantly, even above $100\,{\rm km}$, where collisional evolution is negligible, implying different initial conditions.
  • Figure 5: Same as Fig. \ref{['SFD_whole_MB']}, but for C-types (blue), S-types (red), and other types (orange). We include: the five largest C-types -- (1) Ceres, (10) Hygiea, (52) Europa, (511) Davida, and (31) Euphrosyne (blue points); S-types -- (15) Eunomia, (7) Iris, (3) Juno, (532) Herculina, and (29) Amphitrite (red points); and other types (4) Vesta, (2) Pallas, (704) Interamnia, (65) Cybele, and (87) Sylvia (orange points).
  • ...and 14 more figures