1. Dynamical trapping (pile-up) of grains near the sublimation radius
Hot Dust around Main Sequence Stars? Observations, Theory and Future Prospects
May 20-22, California Institute of Technology, Pasadena, CA
Dynamical trapping
(pile-up) of grains
near the sublimation radius
Hiroshi Kobayashi (Nagoya Univ.)
Review:
Kobayashi et al. (2009) Icarus 201, 395
Kobayashi et al. (2011) EPS 63, 1067

2. Hot Debris Disks
Interferometric observations found excesses of near infrared emission, which indicate hot disks with T > 1000K (Ciardi et al. 2001; Absil et al. 2006, 2008, 2009; di Folco et al. 2007; Akeson et al. 2009; Defrère et al. 2011, 2012).

3. Sublimation Temperature
H: latent heat
μ: molecular weight
(Kobayashi+11)
The sublimation temperatures of silicates
are similar to those of hot debris disks.

4. Orbital Evolution with Sublimation
Stage I, a grain spirals in due to P-R drag.
Stage II, sublimation downsize the grain, resulting in stalling drift.
Balance between P-R drag and increase of radiation pressure.
Stage III, the grain is blown out.
(Kobayashi+09)

5. Pile-up Obsidian, Solar
Dust grains are produced in a planetesimal belt.
Dust drifts inward due to P-R drag.
Sublimation piles up grains.
The inner cavity is formed via sublimation of silicates for T > K.
ns(r) / ns(rout)
(Kobayashi+08,09)

6. Stellar Luminosity
Sublimation pile-up is more effective around luminous stars.
Sublimation distance increases with stellar luminosity.
Sublimation temperature is independent of stellar types. τ
(Kobayashi+09)

7. Temperature, Distance, & Pile-up
(Kobayashi+11)
We could analytically derive sublimation temperature, distance, and enhancement factor.

8. The enhancement factor depends on orbital eccentricity.
(Kobayashi+11)
The enhancement factor depends on orbital eccentricity.
An outer planetesimal belt results in pile-up, while little pile up for an inner dust source.

9. SED Vega w/o pile-up, olivine pyroxene w/ pile-up, olivine
The enhancement due to pile-up does not result in significant difference.
If we can arbitrarily chose the amount of drifting grains, sublimation cut-off may account for the SED of hot disks.
Pyroxene can better explain the SED of Vega.
w/ pile-up,
olivine
⚫︎◇ observation
(Absil+06)
Olivine: 1300K
Pyroxene: 1700K
(Kobayashi+11)

10. Amount of drifting grains
Sublimation is effective only when sufficient dust grains drift into the sublimation zone.
For Vega, τ ~ 4 x 10-4 with pyroxene.
However, the amount of grains are limited by collisions: tcol ~1/ τ Ω ~ tPR　(Wyatt 05).
For Vega, τ ~ 3 x 10-4 if dust source is located at ~0.5AU.
Collisional and orbital evolution with drag is necessary to determine τ accurately.

11. Summary
Refractory dust grains drift inward by P-R drag. They sublime in the vicinity of host stars.
Sublimation stalls P-R drift and piles up dust grains. Dust grains are eventually blown out.
Debris disks have cavities in the sublimation zone.
The cavity is important for SED but the pile-up is not.
We need mass and spatial evolution of grains including collisions, P-R drag, & sublimation.