Long-Term Collisional Evolution of Debris Disks

Abstract

We simulated the long-term collisional depletion of debris disks around solar-type (G2V) stars with our code. The numerical results were supplemented by, and interpreted through, a new analytic model. A few general scaling rules for the disk evolution are suggested. The timescale of the collisional evolution is inversely proportional to the initial disk mass and scales with radial distance as r^4.3 and with eccentricities of planetesimals as e^-2.3. Further, we show that at actual ages of debris disks between 10 Myr and 10 Gyr, the decay of the dust mass and the total disk mass follow different laws. The reason is that the collisional lifetime of planetesimals is size-dependent. At any moment, there exists a transitional size, which separates larger objects that still have the ``primordial'' size distribution set in the growth phase from small objects whose size distribution is already set by disruptive collisions. The dust mass and its decay rate evolve as that transition affects objects of ever-larger sizes. Under standard assumptions, the dust mass, fractional luminosity, and thermal fluxes all decrease as t^xi with xi = -0.3...-0.4. Specific decay laws of the total disk mass and the dust mass, including the value of xi, largely depend on a few model parameters, such as the critical fragmentation energy as a function of size, the primordial size distribution of largest planetesimals, as well as the characteristic eccentricity and inclination of their orbits. With standard material prescriptions and a distribution of disk masses and extents, a synthetic population of disks generated with our analytic model agrees quite well with the observed Spitzer/MIPS statistics of 24 and 70 micron fluxes and colors versus age.

16 pages, 15 figures, accepted for publication in ApJ (23 Oct 2007), abstract shortened; v2: typos corrected (forgotten "-" in "e^-2.3"), two references updated; v3: slight revision to section 5.1 and Figure 14; scheduled publication date: Feb 10, 2008

References in corpus (12)

• Debris Disk Evolution Around A Stars
• Transience of hot dust around sun-like stars
• Spitzer IRS Spectroscopy of IRAS-Discovered Debris Disks
• Nearby debris disk systems with high fractional luminosity reconsidered
• New Debris Disks Around Nearby Main Sequence Stars: Impact on The Direct Detection of Planets
• Steady-State Size Distributions for Collisional Populations: Analytical Solution with Size-Dependent Strength
• Collisional processes and size distribution in spatially extended debris discs
• Collisional dust avalanches in debris discs
• IRS Spectra of Solar-Type Stars: \break A Search for Asteroid Belt Analogs
• Spitzer 24 micron Survey of Debris Disks in the Pleiades
• Search for Cold Debris Disks around M-dwarfs
• An Unbiased Survey of 500 Nearby Stars for Debris Disks: A JCMT Legacy Program

Cited by in corpus (38)

• Variations on Debris Disks: Icy Planet Formation at 30-150 AU for 1-3 Solar Mass Main Sequence 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
• Resolved Debris Discs Around A Stars in the Herschel DEBRIS Survey
• The History of the Solar System's Debris Disc: Observable Properties of the Kuiper Belt
• Disk Radii and Grain Sizes in Herschel-Resolved Debris Disks
• Outer edges of debris discs: how sharp is sharp?
• ALMA observations of the $\eta$ Corvi debris disc: inward scattering of CO-rich exocomets by a chain of 3-30 M${}_{\oplus }$ planets?
• A near-infrared interferometric survey of debris-disc stars. IV. An unbiased sample of 92 southern stars observed in H-band with VLTI/PIONIER
• Planetesimal driven migration as an explanation for observations of high levels of warm, exozodiacal dust
• Solution to the debris disc mass problem: planetesimals are born small?
• Stirring in massive, young debris discs from spatially resolved Herschel images
• Collisional and Thermal Emission Models of Debris Disks: Towards Planetesimal Population Properties
• Long-wavelength observations of debris discs around sun-like stars
• Resolved debris disk emission around eta Tel: a young Solar System or ongoing planet formation?
• Planet populations inferred from debris discs: insights from 178 debris systems in the ISPY, LEECH and LIStEN planet-hunting surveys
• Population synthesis of exocometary gas around A stars
• Inner mean-motion resonances with eccentric planets: A possible origin for exozodiacal dust clouds
• Debris Disc Constraints on Planetesimal Formation
• A $75\%$ Occurrence Rate of Debris Discs around F stars in the $\beta$ Pic Moving Group
• Does warm debris dust stem from asteroid belts?
• Constraining planetesimal stirring: how sharp are debris disc edges?
• Stellar Winds and Dust Avalanches in the AU Mic Debris Disk
• Debris disc formation induced by planetary growth
• Dust size and spatial distributions in debris discs: predictions for exozodiacal dust dragged in from an exo-Kuiper belt
• Dust Populations in the Iconic Vega Planetary System Resolved by ALMA
• No significant correlation between radial velocity planet presence and debris disc properties
• Dynamical Simulations of the Planetary System HD69830
• Collisional modelling of the debris disc around HIP 17439
• Extrasolar Kuiper Belts
• Oort cloud asteroids: Collisional evolution, the Nice Model, and the Grand Tack
• Multiwavelength Vertical Structure in the AU Mic Debris Disk: Characterizing the Collisional Cascade
• Rapid Formation of Exoplanetesimals Revealed by White Dwarfs
• On the steady state collisional evolution of debris disks around M dwarfs
• Dust Spreading in Debris Discs: Do Small Grains Cling on to Their Birth Environment?
• The big sibling of AU Mic: a cold dust-rich debris disk around CP-72 2713 in the $\beta$ Pic moving group
• A multi-wavelength study of the debris disc around 49 Cet
• Twisted debris: how differential secular perturbations shape debris disks
• An ALMA 1.3 millimeter Search for Debris Disks around Solar-type Stars in the Pleiades