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 (35)

• Catastrophic disruptions revisited
• The Size Distribution of Trans-Neptunian Bodies
• Debris Disk Evolution Around A Stars
• Transience of hot dust around sun-like stars
• Spitzer IRS Spectroscopy of IRAS-Discovered Debris Disks
• Frequency of Debris Disks around Solar-Type Stars: First Results from a Spitzer/MIPS Survey
• Steady-state evolution of debris disks around A stars
• Properties of the Trans-Neptunian Belt: Statistics From the CFHT Survey
• Nearby debris disk systems with high fractional luminosity reconsidered
• Age dependence of the Vega Phenomenon: Theory
• Dust Dynamics, Surface Brightness Profiles, and Thermal Spectra of Debris Disks: The Case of AU Mic
• The Insignificance of P-R Drag in Detectable Extrasolar Planetesimal Belts
• 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
• Dusty Debris Around Solar-Type Stars: Temporal Disk Evolution
• Collisional processes and size distribution in spatially extended debris discs
• Shaping the Kuiper belt size spectrum by shattering large but strengthless bodies
• The Size Distribution of Kuiper Belt Objects
• Planets and IR Excesses: Preliminary Results from a Spitzer/MIPS Survey of Solar-Type Stars
• Formation and Evolution of Planetary Systems (FEPS): Primordial Warm Dust Evolution From 3-30 Myr around Sun-like Stars
• Dust Production from collisions in extrasolar planetary systems The inner Beta-Pictoris disc
• A Sub-Millimeter Search of Nearby Young Stars for Cold Dust: Discovery of Debris Disks around Two Low-Mass Stars
• A Spitzer Study of Dusty Disks in the Scorpius-Centaurus OB Association
• Formation and Evolution of Planetary Systems: Placing Our Solar System in Context with Spitzer
• Collisional dust avalanches in debris discs
• An 850 micron survey for dust around solar mass stars
• IRS Spectra of Solar-Type Stars: \break A Search for Asteroid Belt Analogs
• The Formation and Evolution of Planetary Systems: First Results from a Spitzer Legacy Science Program
• Spitzer 24 micron Survey of Debris Disks in the Pleiades
• Formation and Evolution of Planetary Systems: Cold Outer Disks Associated with Sun-like stars
• Search for Cold Debris Disks around M-dwarfs
• Spitzer Observations of G Dwarfs in the Pleiades: Circumstellar Debris Disks at 100 Myr Age
• An Unbiased Survey of 500 Nearby Stars for Debris Disks: A JCMT Legacy Program
• Mid-Infrared Spectra of Dust Debris Around Main-Sequence Stars
• First Fruits of the Spitzer Space Telescope: Galactic and Solar System Studies

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