TAC Meeting #2

Ellen M. Price

7 May 2020

Thesis outline

  • Protoplanetary disk chemical evolution
    • Effect of accretion in a viscously-evolving protoplanetary disk (published 2020)
    • Pebble drift with sublimation only
    • Pebble drift + full chemistry
  • Tidally distorted rocky planets
    • Constraining the composition of USP planets in the Kepler sample (published 2020)
    • Shapes of tidally-distorted transits and detectability
    • Analytic Roche theory for modified polytrope planets

Accretion paper


  • Iteratively compute the surface density that is consistent with RADMC temperature profile
    • This is important because the temperature determines viscosity, which determines the surface density of the gas and, by extension, the dust, which again feeds back into the temperature
  • Couple a chemistry solver to the interpolated physical properties of the gas and dust as they accrete


  • Found that accretion can increase the abundances of some species (like hydrocarbons) by orders of magnitude in the inner disk!
  • Cosmic ray chemistry also plays an important role, since cosmic-ray driven chemistry can produce intermediates that are then transported to the inner disk

Results: Enhancements and depletions

Temperature structure


  • Applies to midplane only — how does vertical mixing affect these results?
  • Gas and dust are well-coupled; can we relax that assumption?

Pebble drift paper

Lots of false starts!

  • Smoothed particle hydrodynamics is too noisy, and is very complex in cylindrical coordinates
  • Boundary conditions in two dimensions are non-trivial when we don't know the final solution a priori
  • Solving benchmarking problems is much easier than solving even a simple alpha-disk


  • Physical model from Birnstiel+2010:
    • One-dimensional disk surface density evolution equation
    • Analytic prescription for dust velocity as a function of gas velocity
  • Solve chemistry globally instead of locally with small water reaction network


  • Classic ssurface density evolution equation:

    $ \frac{\partial \Sigma}{\partial t} = \frac{3}{R} \frac{\partial}{\partial R} \left[R^{1/2} \frac{\partial}{\partial R} \left(\nu \Sigma R^{1/2}\right)\right] $

  • Dust surface density evolution equation:

    $ \frac{\partial \Sigma_d}{\partial t} + \frac{1}{R} \frac{\partial}{\partial R} \left[R \left(F_\mathrm{diff} + F_\mathrm{adv}\right)\right] = 0 $

Assumptions and caveats

  • The Lynden-Bell & Pringle equation assumes Keplerian gas, but the dust equation does not — slight inconsistency
  • Static temperature power law, which is not realistic
    • Could couple to RADMC
    • Could solve with flux-limited diffusion (this is likely more efficient, but more approximation)
    • Do we expect a large difference?

Possible direction: Cometary abundances

Using this model, could we explain certain “outlier” comets, such as 2I/Borisov, which have high CO-to-H2O ratios?

  • Need realistic temperature structure
  • Also may need stellar evolution to move the snowline

Preliminary results: Dust and gas

Preliminary results: Chemistry

Tidally-distorted planets paper


  • Used a relaxation method (originally proposed by Hachisu), modified to include a point-source star, to solve for planet properties in extreme gravitational fields
  • Showed that KOI-1843.03 is likely iron-enhanced to have survived at its position near or at the Roche limit


  • Given:
    • An equation of state for the core and mantle
    • Pressure at center and core-mantle boundary
    • Scaled separation from the star and axis ratio
  • Use an iterative relaxation method to find self-consistent solutions (to a specified tolerance) for the planet density at all mesh points
  • Planet properties cannot be specified in advance!

Results: Iron cores

Results: Polluted cores

Tidally-distorted transits paper


  • Using software I wrote, we have generated lots of planet shapes and their properties
  • Want to take those shapes and determine what their transits look like, then correlate with properties
  • Also want to explore the possibility of actually detecting distortion

Current progress

  • Machinery to raytrace transits is in place
  • More recently, added higher-quality RNG for photon generation
  • Outside software used: ISPC, TBB, Embree, OSPRay

Open questions

  • Can we constrain compositions from transit light curves?
  • Or is the effect washed out by limb darkening of the host star?
  • How do we correlate properties with transit shapes?

Future plans

Conferences and talks

  • Last summer: Invited speaker, PETSc users meeting
  • Upcoming:
    • Astrochemical Frontiers (virtual meeting, will submit abstract by May 18)
    • Heidelberg summer school on planet formation in protoplanetary disks (application due by June 1, but will university travel be allowed by August?)

Suggested timeline

  • End of summer 2020: First pebble drift paper
  • End of fall 2020: Tidally-distorted transits paper
  • End of spring 2021: Second pebble drift paper
  • Graduation in 2021

Career thoughts

  • Institute for Disease Modeling
  • Perimeter or Flatiron Institutes