Chemistry Along Accretion Streams in Protoplanetary Disks
Ellen M. Price
31 October 2019
Hi! My name is Ellen Price, and today I'll be
giving a brief overview of some of the work I've
done as part of my thesis here at Harvard.
Disk anatomy and processes
(inspired by Henning & Semenov 2013)
Protoplanetary disks are very complex systems of gas and dust that surround a young star. Disks have strong vertical and radial temperature gradients. The grain population can evolve with time. What I really want to draw your attention to, however, is the process of accretion, where most of the disk material spirals in towards the star and, eventually, falls onto the star. This is the process that I'll be focusing on in this talk, and I'll be assuming that other transport processes are negligible.
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
It's worth asking at this point why we should care about accretion in the first place. Intuitively, if material is spiraling in towards the star, then the composition of the material close to the star must be changing with time. Planets forming in the inner disk regions may experience a range of environments, then, as the disk evolves. Understanding the chemical evolution is important for understanding planet formation.
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!
We want to develop a method that is simple enough to be computationally tractable, but complex enough to tell us something interesting. The method I present here is largely local and relatively fast, particularly compared to a global simulation of disk chemistry.
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!
We start with the classical nonlinear diffusion equation for the surface density of an alpha-disk. Before I move on from this slide, I want to point out the function $\nu$, which encodes the viscosity, because...
Temperature is a circular problem!
Viscosity depends on temperature! We encounter a chicken-and-egg problem in trying to solve for the temperature because of the couplings between variables that I'm showing here.
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
To get around this problem, we use an iterative procedure that includes a Monte Carlo radiative transport code, RADMC-3d. We assume this temperature function and fit it over time and radius, eventually reaching convergence.
Methods: Solving for tracks
Once the surface density is known, the rest is relatively easy. We solve for the velocity of a small gas parcel as it spirals in and integrate to find the path it takes. I'm showing how various physical properties of the disk evolve along tracks in this figure. Finally, we solve the chemical evolution equations along the track.
Results: Accretion is important!
In our study, we found that accretion is very important! Here, I'm showing the enhancements and depletions of various chemical species, represented by the colored dots, compared to their abundances in a model without accretion. You can immediately see that we can achieve orders of magnitude enhancements in some species, particularly in hydrocarbons.
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
Cosmic rays play a huge role in this phenomenon. Cosmic-ray driven chemistry can happen rapidly in the outer disk because of the low surface density, and then the material migrates inward and is eventually found in the inner disk.
Takeaways
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!
Resume presentation
Chemistry Along Accretion Streams in Protoplanetary Disks
Ellen M. Price
31 October 2019
Hi! My name is Ellen Price, and today I'll be
giving a brief overview of some of the work I've
done as part of my thesis here at Harvard.
