The Link Between Planetary Systems, Dusty White Dwarfs, and Metal-Polluted White Dwarfs

The Link Between Planetary Systems, Dusty White Dwarfs, and Metal-Polluted White Dwarfs

Authors: John Debes, Kevin Walshe, and Christopher Stark

Purpose: To describe a model by which planetesimals around a white dwarf can be perturbed by the host star's evolution off the main sequence and form dusty debris disks around the white dwarf.


Motivation

• planetary systems are found in a wide range of environments
• there should be evidence of the existence of planetary systems around stars at all stages of their evolution
• it is important to understand how the planetary systems evolve in conjunction with the evolution of their host star
• since our sun will eventually become a white dwarf, we can study planetary systems around white dwarfs to see what the eventual outcome of our own solar system might be.

Finding "Dusty" White Dwarfs:

• Spitzer studies - look for the 10 micron silicate feature which is a telltale sign of small dust grains in orbit around the star (Jura et al. 2007)
• Optical ground based studies - look for the presence of metal absorption lines or gaseous emission lines against the otherwise smooth spectrum of the white dwarf (Melis et al. 2010)
• WISE studies have shown that 1% of WDs harbor infrared excesses suggestive of circumstellar dust
• However 20-25% of WDs have polluted atmospheres suggestive of recent planetesimal accretion

Characterizing "Dusty" White Dwarfs

• IR photometry --> dust must come from VERY close in to the WD (~few WD radii)
• dust at that distance couldn't have survived post-main-sequence evolution of the host star, so it must be evidence of tidally disrupted planetesimals coming from larger radial distances
• BUT not too far - planetesimals beyond the snow line should be icy, and would have been destroyed during post-main-sequence-evolution

Interior Mean Motion Perturbation Model

• Mean motion resonances are radial locations where gravitational perturbations from planets can excite planetesimals into high-eccentricity orbits, where they can undergo a close encounter with another planet and (a) be thrown into the host star, (b) be ejected from the system altogether, or (c) collide with the other planet
• One can define a width of the resonance trap in which a planetesimal can suffer this fate. This width grows as the star's mass goes down (or the planet's mass goes up).
• In our solar system, Jupiter is particularly good at tossing planetesimals caught in its 2:1 resonance into the Sun

A Story of Resonance Trapping

• as terrestrial planets form around a star, they leave behind a belt of unused planetesimal pieces
• some of these pieces will be in resonance gaps (in our solar system, "Kirkwood gaps") due to the gravitational influence of giant planets
• the giant planets will stir up these leftover planetesimals over the main sequence lifetime of the host star
• over time, the gaps will be cleared out as the planetesimals collide with one another and with other planets, get ejected from the system, or end up on star-crossing (fatal) trajectories
• As the star begins to evolve off the main sequence, it loses mass, and the resonance gaps grow
• planetesimals which were not originally in the gaps now find themselves excited to high eccentricities, since the giant planets now have more gravitational control over their motions (relative to the host star's now diminished gravitational control)
• due to close encounters with the host star (now evolved into a white dwarf), the planetesimals are  tidally destroyed, leaving a trail of dust in orbit around the white dwarf
• the dust particles in that trail collide with each other, which dissipates energy and allows the dust trail to settle into a more coherent disk 
• Eventually, the dust particles collide often enough that the remaining grains are small enough to be (mostly) accreted onto the WD

Numerical Simulations of this Model

• modelled the solar system's configuration, only following those asteroids large enough to survive the Sun's post main sequence evolution
• followed the behavior of the 2:1 resonance during mass loss phase
• 3 different sets of simulations:
• 10 run for 100 Myr
• 4 run for 200 Myr
• 3 run for 1 Gyr
• Destruction of a planetesimal via tidal disruption is modeled as a N-body simulation consisting of 5000 spherical particles

Results

• in the first 100 Myr, asteroid impacts occur every 10 Myr
• from 100-200 Myr, they occur every 71 Myr
• there is a peak in probability of tidal disruptions around 30 Myr, roughly consistent with observations
• tidal disruption ends in a tight stream of debris following closely the original orbit of the parent body 
• mass from collisions was not lost onto the surface of the WD immediately - pollution would follow a phase of viscous evolution of the small fragmented particles
• PROBLEM: how do the parameters of the simulation scale with the size of the planetary system?
• PROBLEM: how high are collisional velocities? too high could lead to evaporation before accretion onto the WD
• QUESTION: what happens to tidally disrupted material? 

Comparison with Observations

• Spitzer observed polluted WDs taken from Farihi et al. 2009, 2010
• ages determined from WD cooling time and an assumed age on the main sequence
• polluted WDs (non-disk systems) seem to have a bimodal distribution as a function of age
• non-disk systems seem to be on average older than disk hosting systems (when the total age of the system is used)

Conclusions:

• mechanism for producing dust around WDs:
• 1 Jupiter-sized planet
• asteroid belt (similar to that in the SS)
• IMMP mechanism for dust creation (see above)

Future

• observations of main-sequence stars dust in terrestrial planet formation zone (see Chen 2006, Lisse et al. 2009, Currie et al. 2011)
• how much dust to WD's start out with on the main sequence?