Last week, I wrote a shock tracking method which focuses on individual shocks rather than the Lagrangian mass coordinate. It works like this: consider a snapshot of the wind velocity.
Instead of interpolating the velocity of a particle’s Lagrangian mass coordinate, we instead take each of the above shocks (theirs sizes marked in red), and convert the jumps to temperatures.
We use mass weighted binning, by adding the mass that flows through this shock in a single time-step to the correct bin. For example, we might start with bins like this:
We suddenly measure a single shock of temperature K, and it has velocity , density , and distance from the star . Then for a simulation time-step (in our case, 2.5 seconds), we would have a mass of
This is the mass flux from right before the shock hits. We add that mass to the appropriate bin.
Now, if we run this at every time-step, we can make a plot that looks like this. I do some summation so that the mass weighted histogram is reverse cumulative like .
This is the result of analysis on purely self-excited shocks (black) and limb darkening + base perturbations (red), featuring 100 linearly spaced temperature bins. I ran the group’s LDI simulation for 200 kiloseconds to let the solution relax, and then ran my analysis code for another 200 kiloseconds.
- This method doesn’t need interpolation or the Lagrangian mass coordinate. In my opinion, this makes it more robust.
- However, I’m unsure if this is a completely unbiased sample!
- The total shock rate is hard to extract from this method, unfortunately.
Finally, these results are not entirely off the mark when compared to the observations.
This plot is simply the box plots, with the limb-darkened and perturbed histogram superimposed. The only parameter I adjusted was the normalization , since I can’t calculate one from this method (yet! I have an idea…)