Collisional parameters of planetesimal belts, precursor of debris disks, perturbed by a nearby giant planet

Abstract

Planetesimal belts are invoked to explain the prolonged existence of debris disks. Important parameters to model their collisional evolution and to compute the dust production rate are the intrinsic probability of collision $P_i$ and the mean impact velocity $U_c$. If a planet orbits close to the belt, the values of both these parameters are affected by its secular perturbations yielding a strong correlation between eccentricity $e$ and pericentre longitude $\varpi$. We adopt a new algorithm to compute both $P_i$ and $U_c$ in presence of various levels of secular correlation due to different ratios between proper and forced eccentricity. We tested this algorithm in a standard case with a Jupiter--sized planet orbiting inside a putative planetesimal belt finding that it is less collisionally active compared to a self--stirred belt because of the $e-\varpi$ coupling. The eccentricity of the planet is an important parameter in determining the amount of dust production since the erosion rate is 10 times faster when the planet eccentricity increases from 0.1 to 0.6. Also the initial conditions of the belt (either warm or cold) and its average inclination strongly affects $P_i$ and $U_c$ and then its long term collisional evolution in presence of the planet. We finally apply our method to the planetesimal belts supposedly refilling the dust disks around HD 38529 and $\epsilon$ Eridani. In the most collisionally active configurations, only a small fraction of bodies smaller than 100 km are expected to be fragmented over a time--span of 4 Gyr.

Accepted for publication on MNRAS

References in corpus (10)

• Optical Images of an Exosolar Planet 25 Light Years from Earth
• Transience of hot dust around sun-like stars
• Debris disks around Sun-like stars
• The Complete Census of 70-um-Bright Debris Disks within the FEPS (Formation and Evolution of Planetary Systems) Spitzer Legacy Survey of Sun-like Stars
• The Extrasolar Planet epsilon Eridani b - Orbit and Mass
• Relative velocities among accreting planetesimals in binary systems: the circumprimary case
• The dust, planetesimals and planets of HD 38529
• The unseen planets of double belt debris disk systems
• Searching for Planets in Holey Debris Disks with the Apodizing Phase Plate
• Extragalactic number counts at 100 um, free from cosmic variance