Chemistry Along Accretion Streams in Protoplanetary Disks

Ellen M. Price

31 October 2019

Disk anatomy and processes

(inspired by Henning & Semenov 2013)

Why do we care?

  • Planets form from the material available to them in the protoplanetary disk (gas and solids)
  • If accretion significantly changes the composition of that material, then simulations should take that into account

Why this method?

  • Want something simple enough to be tractable, but complex enough to tell us something interesting
  • Other models may try to solve everything at once or exclude accretion
  • The method I will present is local and fast!

Methods: Surface density solve

$$ \frac{\partial \Sigma}{\partial t} - \frac{3}{R} \frac{\partial}{\partial R} \left[R^{1/2} \frac{\partial}{\partial R} \left(\nu \Sigma R^{1/2}\right)\right] = 0 $$

  • Nonlinear diffusion equation for $\Sigma = \int \rho~\mathrm{d} z$, from Lynden-Bell & Pringle
  • Need two boundary conditions!

Temperature is a circular problem!

Methods: Temperature solve

$$T = T_0 \left(e^{-\psi \tau} + \omega\right) e^{\beta_0 \log x + \beta_1 \log^2 x}$$

  • Assume this flexible form and use RADMC-3d to generate “true” temperatures everywhere
  • Fit the function, update the surface density, and repeat until convergence

Methods: Solving for tracks

Results: Accretion is important!

Why does this happen?

  • Chemistry is (usually) fastest at high temperatures and high densities
  • Cosmic ray flux is highest at low surface densities, so CR-driven chemistry can happen far out in the disk and then the products travel inwards


  • Accretion changes the compositions along streams of material in the disk, potentially changing the compositions of planets that form there
  • Signs of accretion (like enhanced hydrocarbons) might be observable with JWST if vertical mixing is strong and lofts midplane material into the upper disk layers
  • Stay tuned for Part 2!