Master thesis defense by Ísól Lilja Róbertsdóttir

Modeling the Spectral Index of Protoplanetary Disks: Effect of Dust Evolution and Substructure

Abstract

Protoplanetary disks around young stars form with tens to hundreds of Earth masses of pebble-sized solids that are the building blocks of planet formation. Dust evolution models argue for size-limited pebbles through fragmentation and a depletion of the dust mass reservoir due to radial drift. Interestingly, the millimeter spectral index of protoplanetary disks provides a direct probe of dust grain sizes, yet observed values are systematically lower than what current dust evolution models predict. In this work, the chemcomp 1D disk evolution code is used to simulate the time evolution of gas and dust in protoplanetary disks, with grain- size-dependent opacities computed from the DSHARP-OPAC package.

The millimeter spectral index alpha(1−3 mm) is calculated from the simulated fluxes and compared to observed values in Taurus, Ophiuchus, Lupus, and Orion. We find that smooth disk models overpredict the spectral index, rising above alpha(1−3 mm) ~3 within 1–2 Myr and failing to reproduce the low values observed in most disks. Increasing the fragmentation velocity or fixing the grain size to millimeter or centimeter values lowers the spectral in-dex initially, but large grains drift efficiently and deplete the disk too quickly to remain consistent with observations of dust over disk lifetimes of several Myr. However, during planet formation, gas giant planets carve gaps and outer-edge pressure bumps are formed.

A single planet-induced gap reduces the spectral index for large grain sizes, but is insufficient to reproduce the low spectral indices and high fluxes seen in observed disks, even for massive planets of 100Mearth. We also explored the effect of three Gaussian pressure bumps combined with large fragmentation velocities (vfrag = 10 m/s) which slows the temporal evolution of the spectral index significantly and keeps αlpha(1−3 mm) within the observed range of 2–3 over several Myr. When a range of initial disk sizes is considered, this combination covers much of the observed scatter in the observed flux–spectral index parameter space.

No model reproduces alpha(1−3 mm) < 2, suggesting that additional physical effects are needed, or observational errors accounted for, to explain the lowest observed values. The model predicts a Mie resonance feature in the radial spectral index profile that is not observed in real disks, suggesting that porous grain opacities may be needed in future models. Additionally, the midplane dust-to-gas ratio at pressure bump locations exceeds the threshold for the streaming instability, indicating that planetesimal formation could represent an important missing process in the current framework.

Vejledere

Anders Johansen, Michiel Lambrechts, and Jes Jørgensen

Censor

Hans Kjeldsen, AU