"Frozen-In" Ionization

[lazygun37]

If the characteristic flow time-scale in a wind -- t_dyn ~ R / v -- ever becomes (and stays) shorter than the ionization/recombination time-scale -- t_rec ~ 1/(ne*alpha) -- the ionization state of the flow becomes "frozen-in". In this case, the assumption of ionization equilibrium we make in each cell no longer holds. We should:

• check whether/when/how often this occurs in models we care about
• possibly implement a fix/correction fo rthis.

The simple approximimate fix that's been adopted by others in the past (e.g. Shlosman & Vitello, I believe), is to find the place where t_dyn = t_rec and assume standard ionization equlibrium for cells within this and adopt the ionization fraction of the "previous" cell (or, more exactly, of the previous part of the flow along a streamline) beyond this.

[jhmatthews]

Added a possible way to do this (very crudely using Case B recomb from Osterbrock and setting ne=nh): https://github.com/jhmatthews/python/tree/frozen-in

Using that branch, one can activate the mode using the -d flag (for advanced diags) and using the question @Diag.report_frozen_in_cells(yes,no). Without the mode activated, the code just reports to the user how many cells have tdyn < trec.

Initial investigations suggest this is a big problem in CV models.

[kslong]

@saultyevil @lazygun37 . Ed was asked about frozen-in ionization in the TDE models. We had already captured this here, and so we should try to close at the same time.

My view is that the cleanest way to answer this is to compare the cooling (or heating) timescale to the flow time over a characteristic distance.

Here is a Jupyter notebook that is my attempt to implement this (for a CV model).

Frozen.pdf

Here is a tarred up directory that contains the script
z.bug407_frozen.200328.tar.gz

[saultyevil]

@kslong I've compared your version and James' version for solving this problem for our default TDE model. They both look to be in good agreement - which is that they both highlight the same region where there is a bit of trouble.

In the image below, your method is on the left and James' is on the right. On the right, a value of 1 means that cell is frozen in.

[kslong]

Excellent, Ed. Thank you. Knox

[jhmatthews]

This should be added to a limitation section of the documentation, perhaps with some of Knox's plots/conclusions, and if it is straightforward we could merge my diagnostic from the https://github.com/jhmatthews/python/tree/frozen-in branch.

[kslong]

@lazygun37 Please make sure you include this is your list of limitations