Modelling dust distribution in the ejecta plume from nonspherical dust dynamics perspectives in support of the LICIACube and DART missions

Introduction

On September 30, 2022, NASA’s Double Asteroid Redirection Test (DART, [1]) mission will be the first space mission demonstrating the kinetic impactor method for planetary defense. DART will impact Didymos B (a 164±18 m secondary of asteroid (65803) Didymos [2]) with its mass of 650 kg and at a speed of 6.6 km/s. Such impact is expected to change the secondary orbital period by about 10 minutes. DART will carry as a piggyback the Light Italian Cubesat for Imaging of Asteroids (LICIACube, [3]) which will be released from DART ten days before the impact. LICIACube will provide evidence of the impact and will take multiple images of the target up to a distance of ~55 km from the target. The LICIACube narrow and wide angle cameras - LEIA (LICIACube Explorer Imaging for Asteroid) and LUKE (LICIACube Unit Key Explorer), respectively – will capture the post-impact processes coming from in situ events, such as the newly formed crater, the expanding ejecta and the dynamics of its plume.  In particular, the measurement of the motion of the slow (<5 m/s) ejecta in the plume will be feasible with LICIACube, thus allowing description of its structure and the evolution of the dust size and velocity distribution.  In this work, we study the motion of the plume evolution in terms of dust numerical simulations. To accomplish this, we modified the non-spherical dust model [4] and applied it to an asteroid impact scenario using analytical expressions to estimate the initial velocity and mass of ejecta.  As input we used the ejecta impact properties (ejecta mass, velocity, launch position distribution, orientation) constrained with iSALE numerical simulations [5]. We discuss the influence of the non-sphericity of the particles on the dynamical properties of the plume, such as the velocity and dust spatial distribution, and address the optical thickness not only in terms of particle size distribution but also as a function of particle shape and orientation.

Dust plume model

We use a 3D+t non-spherical dust model that solves the Euler dynamical and kinetic equations. Considering free-collisional dust regime we study the effects on the particle dynamics provided with different shapes, initial particle orientation and velocities as well as torque. Torque is computed from the law of variation of the angular momentum by using the Euler dynamic equations. The particles are assumed to be homogeneous, isothermal convex bodies, having the same physical properties of the target. The dust motion is governed by solar radiation pressure force, initial dynamical parameters (speed, orientation and torque) and gravity of the asteroid binary system. To compute the gravity we take into account that Didymos B is orbiting at distance of ~1.18 km the Didymos primary (780±80 m in size) [6].

As input we use the physical parameters obtained via numerically simulated impact into low-gravity and strength- dominated asteroid surface done with the iSALE numerical code [5]. A detailed description of the parameters set used in the impact modelling are reported in Table 1. As an example, in Fig.1, we show the iSALE simulation of the spatial distribution of tracer particles for 50 ms after the impact.

Table 1: Paremeters used for iSAle simulation. A detailed description can be found in [5].

Fig. 1: A snapshot of the formation of the crater resulting  from the iSALE modelling performed with parameters reported in Table 1. The colorbar represent the peak pressure of the ejecta tracer particles.

Non-spherical dust motion in the plume

We have studied the motion of non-spherical particles after the impact assuming various set of initial parameters coming from the iSALE simulations, such as particle mass, shape, initial orientation, launch position and computed velocity. The Didymos system physical parameters and particle temperature were taken from [7]. Here, in Fig. 2, we show the velocity and the distance from the surface where it has been reached for a prolate spheroid (aspect ratio = 2 [4]) with assumed density 2600 kg/m³. The particle mass is 7.45 x10^-2 kg, the initial velocity 0.94 m/s, the launch position is 11 m from the center of the crater and the initial tilt of the initial velocity vector away from local surface normal is 46 degrees. We plotted the results for two cases: 1) only the Didymos B gravity field is considered and 2) the gravity of the whole binary is used. Our results show that the particle dynamics is sensitive to parameters such as orientation and ejection velocity.  

Fig. 2: Velocity and distance at which it has been achieved for a prolate particle (aspect ratio a/b = 2). The complete set of parameters is given in the text. The solid line indicates the case when only gravity of Didymos B  was considered and the dashed line when the gravity of the whole binary was used (binary was approximated as a mass point).

This study of dust dynamics in expanding ejecta together with LICIACube plume evolution images can further constrain the momentum transfer efficiency estimation as well as the ejecta velocity and dust size distribution in the “far-field” expanding plume.

 

Acknowledgments

This research was supported by the Italian Space Agency (ASI) within the LICIACube project (ASI-INAF agreement AC n. 2019-31-HH.0).

 

References

 [1] Cheng A. F. et al. (2016) Planet. Space Sci., 121, 27-35. [2] de León, J. et al. (2010) Astron. Astrophys, 517, A23. [3] Dotto, E. et al., (submitted), Planet. Space Sci. [4] Ivanovski S. et al. (2017), Icarus 282, p. 333 - 350. [5] Raducan, S. D. et al. (2019), Icarus, 329, p. 282 - 295. [6] Michel, P. et al. (2016) Adv. Space Sci. 57, p. 2529 - 2547. [7] Yu Y. et al. (2017), Icarus 282, p.313 - 325