Chemistry Along Accretion Streams in Protoplanetary Disks

Ellen M. Price, Ilse Cleeves, and Karin Öberg

18 June 2020

Disk anatomy and processes

(inspired by Henning & Semenov 2013)

Why include accretion?

  • Accretion serves to change the local conditions of any given gas parcel
  • Planets form from the material available to them in the protoplanetary disk (gas and solids)
  • So a planet forming in an accreting disk is different from an analagous planet forming in a disk without accretion

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 globally, which is unnecessary under our assumptions
  • 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!
  • Solved with Crank-Nicolson timestepping, finite difference derivatives

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, parametric form for the temperature
  • Use RADMC-3d to generate “true” temperatures everywhere
  • Fit the function, update the surface density, and repeat until convergence

Methods: Solving for tracks

Methods: Evolving chemistry

  • Use a C++ implementation of a modified Fogel chemistry model
  • Approximately 600 species and 6000 reactions

Cautionary tale: Reaction order matters!

  • This is a purely numerical artifact that occurs because of finite floating point precision
  • When adding numbers of disparate orders of magnitude, the order in which they are added really matters
  • Experiment: What is the sum of $1$ and $10^{-9}$ added $10^9$ times in single precision?

Methods: How should we measure change?

  • Every track has a starting radius, which we set, and an ending radius, which we clip to 1 au or 1 Myr
  • We compare the composition of a moving parcel to its corresponding static counterparts at the initial and final radii of the track

Results: Changing fields

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!