A new population of asteroids: the resonants 1:2 with Mars


www.fisica.edu.uy/~gallardo/marte12


VERSION EN ESPAŅOL AQUI



Dr. Tabare Gallardo
Departamento de Astronomia
Instituto de Fisica
Facultad de Ciencias
Universidad de la Republica
Montevideo, Uruguay
gallardo@fisica.edu.uy


Abstract

We describe here our recent discovery of a population of around 1500 asteroids gravitationally dominated by Mars. Those asteroids are captured in resonance with Mars, more precisely in the resonance 1:2. That means when asteroids complete a revolution around the Sun, Mars completes exactly 2 revolutions. This discovery breaks some paradigm (like the domination of Jupiter in the main belt of asteroids), generates new questions related to the formation and evolution of the Solar System (how was generated this population?) and probably give some answers to the origin of certain families of asteroids.






1) The distribution of asteroids in the Solar System

Every night hundreds of asteroids are discovered. After several observations (we are working on this at Observatorio Astronomico Los Molinos) over some years an orbit for each asteroid can be determined. The databases with the orbital parameters of the asteroids with confirmed orbits are of free access. One of them is ASTORB maintained by Ted Bowell from Lowell Observatory that at present (mid 2007) contains around 370000 asteroids.

Making a plot of the distribution of asteroids according to its mean distance to the Sun (or semimajor axis) we obtain the following figure:



distribution of asteroids




This distribution is the result of 4500 million years of evolution. At the beginning the population was more uniform and massive but mutual collisions, planetary perturbations and chaotic orbital evolution generated an erosion process. What we see today is the fraction of the population that survived to these erosion processes because have found a stable place in some stage of the orbital evolution.

It is possible to appreciate the "Kirkwood's gaps", places where there are a very small number of asteroids due to the existence of resonances with Jupiter that excites the orbits generating encounters and collisions between asteroids and planets Mars and Earth. Then, they cannot stay there for a long time because they are strongly perturbed. We also observe that exists concentrations at certain places: the Hildas at 3.97 AU, the Trojans at 5.2 AU and other smaller groups. These concentrations are due to "friendly" resonances that work as reservoirs of asteroids because they are very stable places. Resonances are located at places where the motion is at perfect synchrony with a planet, see below.




2) Resonances

Resonant motions only occur at very precisely positions in the Solar System because it is in these precise positions where the motion of the asteroid and planet are exactly synchronized. A little more far of the Sun or closer to the Sun the synchrony breaks up. In the following figure we reproduce the region of the main belt of asteroids including most important resonances in the region.




resonances




Here we indicate not only resonances with Jupiter but also with all the planets with different colors. Soft blue for resonances with Jupiter, violet with Saturn, red with Mars and green with Earth. Resonance 2:1J for example means that when the asteroid perform 2 revolutions around the Sun Jupiter has completed exactly 1. It is evident the destructive effect of the resonances 3:1, 5:2, 7:3 and 2:1 with Jupiter. We also indicate the "strength" associated with each resonance. Stronger resonances are represented with higher lines. A weak resonance should not produce any effect in the asteroidal motion but a strong one yes. It is not trivial to calculate the strength of the resonances. We have developed a method published in Icarus that was well recibed by readers. As a byproduct of this work we have found by first time a small number of asteroids in unusual resonances like 1:2 with Earth (3 asteroids) and 2:5 with Earth (6 asteroids). We also found 4 more asteroids in the resonance 1:2 with Venus that are added to the only one that was known there. That suggests that terrestrial planets could have some small orbital influence on the asteroids. Details of the method and some plots can be found here.




3) The excess of asteroids at 2.419 AU

We have realized that it seems to be a constructive effect in the resonance 1:2 with Mars because at that position there exists a peak, an excess, in the distribution of asteroids. Making a zoom in that region we can see it better:




resonance 1:2 with Mars




Exactly at resonance 1:2 with Mars there is an excess of asteroids. This excess is approximately of 400 asteroids if we compare with the number of asteroids in the background.

Would that concentration be due to a real effect of the resonance 1:2 with Mars?
Could this resonance operate as a protection mechanism against the natural erosion of the region of the asteroids?

We have proposed to answer those questions. We have chosen from the database ASTORB around 4000 asteroids near the peak and we have studied their orbital evolution 1 million years to the future. We can do this with programs like EVORB or Mercury which are of public domain. After some days of calculus the computer finished the numerical integration. And after analyzing the results we found that approximately 1500 asteroids are inside the resonance and dominated by it . Then we have confirmation that the resonance 1:2 with Mars operates as a reservoir against the natural erosion of the population of asteroids in the main belt. Maybe something similar to that happens to Hildas or Trojans.




The resonant population in the Solar System (applet java3D)




4) The distinction of being a resonant 1:2 with Mars

The fact that the motion of the asteroids is resonant 1:2 with Mars implies that the motion of the asteroids with respect to the rotating system Sun-Mars is very peculiar. In the following plot we see the motion in that system of an asteroid fictitious very near the resonance but out of it. We see the Sun (yellow dot), Mars (red dot) and in green it is plotted the trajectory as seen "from up", or as it could be seen by an astronaut located in the north of the plane of the solar system at several AUs from the Sun and rotating in such a way that Mars is always at his right.




asteroid outside of the resonance




With the flow of time the asteroid generates a trajectory that approaches dangerously to Mars.
Now we will see the case of 142 Polana, a real asteroid captured in the resonance:




asteroid inside the resonance




The synchrony with Mars is evident, the asteroid never approaches to Mars.
More or less all asteroids in resonance 1:2 have trajectories analog to this one.
In the following picture we see one of the asteroids that are more deep in the resonance, 2003 BO71:




asteroid 2003 BO71




....and now we see the same trajectory but with its spatial perspective:




asteroid 2003 BO71




The resonants 1:2 with Mars draw a kind of curl in the rotating system Sun-Mars. The resonant motion does not occur by chance, on the contrary it is an equilibrium state to where asteroids can evolve. The plots were generated with NEAPLOT.






ANIMATION OF ASTEROID 2003 BO71 (flash, 0.4MB)



java applet of asteroid 2003BO71



ANIMATION OF ALL RESONANT POPULATION (flash, 2.2MB)






5) Conclusions

We have found a new and numerous population of asteroids that like Hildas and Trojans are maintained under protection by a resonance, but surprisingly in this case with Mars. Some conclusions:
  • Not only Jupiter dominates the dynamics of asteroids but also Mars operates efficiently and in this case as a protector. By first time we found a low mass planet that generates a numerous dynamical family of asteroids.
  • The biggest asteroid in this population is 142 Polana with a diameter of 55 km. This could imply that some day this population will be called "the Polanas".
  • In a first examination the sizes of the resonant asteroids do not have any special characteristic. We cannot distinguish any special bias in the size distribution. On the other hand the orbital eccentricities of the resonant asteroids are clearly greater than the non resonant asteroids.




6) Open questions

The existence of a numerous population of asteroids in the resonance 1:2 with Mars opens a series of questions:
  • There exist other analogue populations in other resonances with low mass planets?
  • How was generated this population?
  • Is it there since the origin of the solar system or exists some mechanism that continuously replenishes the population?
  • Could it be formed by the capture in resonance of asteroids coming from other regions by means of non-gravitational effects like Yarkovsky effect? This is an effect that affect mostly the small asteroids.
  • Could it be formed by the capture in resonance due to a migration of Mars in it first steps of formation, in analogy as were captured the "plutinos" (Pluto is one of them, in the resonance 2:3N) and "twotinos" (resonance 1:2N) with Neptune?
The answer to these questions will generate new perspectives about the processes occurred in the inner solar system.








This discovery was possible thanks to the existence of programs of searching and following of asteroids from several observatories around the world and thanks to the elaboration and distribution of complete databases like ASTROB, MPCORB and AstDys.

This research was part of the Proyect CSIC (UdelaR) I+D "Dinamica Secular de Sistemas Planetarios y Cuerpos Menores", Facultad de Ciencias, that finished recently.