# Breaking an asteroid

Hi there! Asteroids, these small bodies in the Solar System, are fascinating by the diversity of their shapes. This is a consequence of their small sizes. Another consequence is their weakness, which itself helps to split some of them into different parts, sometimes creating binary objects, asteroids families… The study I present you today, Internal gravity, self-energy, and disruption of comets and asteroids, by Anthony R. Dobrovolskis and Donald G. Korycansky, proposes an accurate computation of the required energy to provoke this break-up, at any place of the asteroid, i.e. you are more efficient when you hit at a given location. This study has recently been accepted for publication in Icarus.

## Shapes of asteroids

Please allow me, in this context, to call asteroid a comet, a comet being a small body, i.e. like an asteroid, but with a cometary activity. The important thing is that the involved bodies are small enough.

Beyond a given size, i.e. a diameter of ~400 km, a planetary body is roughly spheroidal, i.e. it is an ellipsoid with it two equatorial axes almost equal and the polar one smaller, because of its rotation. For a tidally despun body, like the Moon, or a satellite of a giant planet, the shape is more triaxial, since the tidal (gravitational) action of the parent planet tends to elongate the equatorial plane. The same phenomenon affects Mercury.

However, for smaller bodies, the self-gravitation is not strong enough to make the body look more or less like a sphere. As a consequence, you can have almost any shape, some bodies are bilobate, some are contact binaries, i.e. two bodies which permanently touch together, some others are rubble piles, i.e. are weak aggregates of rocks, with many voids.

These configurations make these bodies likely to undergo or have undergone break-up. This can be quantified by the required energy to extract some material from the asteroid.

## The energies involved

For that, an energy budget must be performed. The relevant energies to consider are:

• The impact disruption energy: the minimum kinetic energy of an impactor, to shatter the asteroid and remove at least half of its mass,
• The shattering energy: the minimum energy needed to shatter the asteroid into many small pieces. It is part of the impact disruption energy. This energy is roughly proportional to the mass of the asteroid. It represents the cohesion between the adjacent pieces.
• The binding energy: this energy binds the pieces constituting the asteroid. In other words, once you have broken an asteroid (don’t try this at home!), you have to make sure the pieces will not re-aggregate… because of the binding energy. For that, you have to bring enough energy to disperse the fragments.
• The self-gravitational energy: due to the mutual gravitational interaction between the blocks constituting the asteroids. Bodies smaller than 1 km are strength-dominated, i.e. they exist thanks to the cohesion between the blocks, which is the shatter energy. However, larger bodies are gravity-dominated.
• The kinetic energy of rotation: the spin of these bodies tends to enlarge the equatorial section. In that sense, it assists the break-up process.

This study addresses bodies, which are far enough from the Sun. This is the reason why I do not mention its influences, i.e. the tides and the thermic effects, which could be relevant for Near-Earth Objects. In particular, the YORP effect is responsible for the fission of some of them. I do not mention the orbital kinetic energy of the asteroid either. Actually the orbital motion is part of the input energy brought by an impact, since the relative velocity of the impactor with respect to the target is relevant in this calculation.

I now focus on the two cases studied by the authors to illustrate their theory: the asteroid Kleopatra and the comet 67P/Churyumov-Gerasimenko.

## 2 peculiar cases: Kleopatra and Churyumov-Gerasimenko

216 Kleopatra is a Main-Belt asteroid. Adaptive optics observations have shown that is is constituted of two masses bound by material, giving a ham-bone shaped. As such, it can be considered as a contact binary. It is probably a rubble pile. Interestingly, observations have also shown that Kleopatra has 2 small satellites, Alexhelios and Cleoselene, which were discovered in 2008.

However, 67P Churyumov-Gerasimenko is a Jupiter-family comet, i.e. its aphelion is close to the orbit of Jupiter, while its perihelion is close to the one of the Earth. It has an orbital period of 6.45 years, and was the target of the Rosetta mission, which consisted of an orbiter and a lander, Philae. Rosetta orbited Churyumov-Gerasimenko between 2014 and 2016. The shape of this comet is sometimes described as rubber ducky, with two dominant masses, a torso and a head, bound together by some material, i.e. a neck.

216 Kleopatra 67P/Churyumov-Gerasimenko
Semimajor axis 2.794 AU 3.465 AU
Eccentricity 0.251 0.641
Inclination 13.11° 7.04°
Spin period 5.385 h 12.761 h
Mean radius 62 km 2.2 km
Magnitude 7.30 11.30
Discovery 1880 1969

The irregular shapes of these two bodies make them interesting targets for a study addressing the gravitation of any object. Let us see now how the authors addressed the problem.

## Numerical modeling

Several models exist in the literature to address the gravity field of planetary bodies. The first approximation is to consider them as spheres, then you can refine in seeing them as triaxial ellipsoids. For highly irregular bodies you can try to model them as cuboids, and then as polyhedrons. Another way is to see them as duplexes, this allows to consider the inhomogeneities dues to the two masses constituting bilobate objects. The existence of previous studies allow a validation of the model proposed by the authors.

And their model is a finite-element numerical modeling. The idea is to split the surface of the asteroid into small triangular planar facets, which should be very close to the actual surface. The model is all the more accurate with many small facets, but this has the drawback of a longer computation time. The facets delimit the volume over which the equations are integrated, these equations giving the local self-gravitational and the impact disruption energies. The authors also introduce the energy rebate, which is a residual energy, due to the fact that you can remove material without removing half of it. This means that the impact disruption energy, as it is defined in the literature, is probably a too strong condition to have extrusion of material.
The useful physical quantities, which are the gravitational potential, the attraction, and the surface slope, are propagated all along the body thanks to a numerical scheme, which accuracy is characterized by an order. This order quantifies the numerical approximation which is made at each integration step. A higher order is more accurate, but is computationally more expensive.

Once the code has been run on test cases, the authors applied it on Kleopatra and Churyumov-Gerasimenko, for which the shape is pretty well known. They used meshes of 4,094 and 5,786 faces, respectively.

## Results

The validation phase is successful. The authors show that with a 3rd order numerical scheme, they recover the results present in the literature for the test cases with an accuracy of ~0.1%, which is much better than the accuracy of the shape models for the real asteroids. Regarding Kleopatra and Churyumov-Gerasimenko, they get the gravity field at any location, showing in particular excesses of gravity at the two lobes.

Such a study is particularly interesting for further missions, which would determine the gravity field of asteroids, which would then be compared with the theoretical determination by this code. Other applications are envisaged, the authors mentioning asteroid mining.

## The study and its authors

And Merry Christmas!

# A quest for sources of meteor showers

Hi there! Today I will present you a study entitled Dynamical modeling validation of parent bodies associated with newly discovered CMN meteor showers, by D. Šegon, J. Vaubaillon, P. Gural, D. Vida, Ž. Andreić, K. Korlević & I. Skokić, which has recently been accepted for publication in Astronomy and Astrophysics. It addresses the following question: when you see meteors, where do they come from?

## The meteor showers

Imagine you have a comet, i.e. a small body, which wanders in the Solar System with a large eccentricity. This means that it orbits around the Sun, but with large variations of its distance with the Sun. The consequence is that it experiences large variations of temperature during its journey. In particular, when it reaches the perihelion, i.e. when its distance to the Sun is the smallest, the temperature is so hot that it outgasses. The result is the ejection of a cloud of small particles, which itself wanders in the Solar System, on its own orbit.

When the Earth meets it, then these particles are burnt in our atmosphere. This results in meteor showers. Such showers can be sporadic, or happen every year if the cloud is pretty static with respect to the orbit of the Earth. The body from which the particles originate is called the parent body. The study I present you today aims at identifying the parent body of some of these meteor showers.

## How to observe them

Understanding the meteor showers is an issue for the safety of the Earth environment, particularly our artificial satellites. Some meteors can even impact the surface of the Earth. This is why numerous observation programs exist, and for that amateurs are very helpful!

The first way to observe meteor showers is visually. When you know that meteor showers are likely to happen, you look at the sky and take note of the meteors you see: when you saw it, from where, where it came from, its magnitude (~its brightness), etc. The point from where the meteor seems to come is called the radiant. It is written as a set of two angles α and δ, i.e. right ascension and declination, which localize it on the celestial sphere.

For unpredicted showers, we can use cameras, which continually observe and record the sky. Then, algorithms of image processing can detect the meteor. Meteors can also be detected in the radio wavelengths.

## Dynamical modeling

If you want to simulate the orbit of a particle, you have to consider:

• the location of the parent body when the particle was ejected (initial position),
• the ejection velocity,
• the ejection time, likely when the parent body was close to its perihelion. The question how close? cannot be accurately answered,
• the gravitational action of the Sun and the planets of the Solar System,
• the non-gravitational forces, which might have a strong effect on such small bodies.

These non-gravitational forces, here the Poynting-Robertson drag, are due to the Solar radiation, which causes a loss of angular momentum of the particle during its orbital journey around the Sun. It is significant for particles smaller than the centimeter, which is often the case for such ejecta.

You cannot simulate the orbit of a specific particle that you would have identified before, just because they are too small to be observed as individuals. However, you can simulate a cloud, composed of a synthetic population of fictitious particles, with various sizes, ejection times, initial velocities… in such a way that your resulting cloud will have global properties which are close to the real cloud of ejecta. Then you can simulate the evolution of the cloud with time, and in particular determine the time, duration, direction, and intensity of a meteor shower.

Simulating such a cloud reveals interesting dynamical features. It presents an initial size, because of the variations in the ejection times of the particles. But it also widens with time, since the particles present different ejection velocities. This usually (but not always!) results in a kind of a tire which enshrouds the whole orbit of the parent body. Unfortunately, it can be observed only when the Earth crosses it. So, simulating the behavior of the cloud will tell you when the Earth crosses it, how long the crossing lasts, and the density of the cloud during the crossing.
It should be kept in mind that a cloud is composed of a hyue number of particles. For this reason, dedicated computation means are required.

## This study

This study aims at identifying the parent body of meteor showers, which were detected by the Croatian Meteor Network (CMN in the title). For that, the first step is to make sure that a shower is a shower.
The detected meteors should resemble enough, which can be measured with the D-criteria, that are a measurement of a distance, in a given space, between the orbits of two objects. Once a meteor shower is identified, the same D-criteria can be used to try to identify the parent body, from its orbit. The parent bodies are comets or asteroids, they are usually known enough for candidates to be determined. And once candidates are identified, then their outgassing is simulated, to predict the meteor showers associated. If a calculated meteor shower is close enough to an observed one, then it is considered that the parent body has been successfully identified. This last close enough is related to the time and duration of the showers, and the location of the radiants.

The authors analyzed 13 meteor showers, and successfully identified the parent body for 7 of them. Here is their list, the showers are identified under their IAU denominations:

• #549FAN – 49 Andromedids comes from the comet 2001 W2 Batters,
• #533 JXA – July ξ Arietids comes from the comet 1964 N1 Ikeya,
• #539 ACP – α Cepheids comes from the comet 255P Levy,
• #541 SSD – 66 Draconids comes from the asteroid 2001 XQ,
• #751 KCE – κ Cepheids comes from the asteroid 2009 SG18,
• #753 NED – November Draconids comes from the asteroid 2009 WN25,
• #754 POD – ψ Draconids comes from the asteroid 2008 GV.

For this last stream, the authors acknowledge that another candidate parent body has not been investigated: the asteroid 2015 FA118.

For the 6 other cases, either the identification of a parent body is speculated but not assessed enough, or just no candidate has been hinted, possibly because it is an asteroid or a comet which has not discovered yet, and / or because data are missing on the meteor shower.