Joe,

I'm doing some basic test with PrismSpect of He-like f-i-r modeling.  This isn't just academic, as there are several different data sets that need some modeling for manuscripts I'm writing as well as (more time-critically) AAS posters (leaving on Sunday, Jan 9).  

I'm referring back also to an email you sent me on August 18, discussing (1) the lack of the 2nd IC line (^3P_2 > ^1S_0) in the atomic database ("must add by hand...Wang Ping is modifying ATBASE to include this line..."); and (2) a bug "resulting in a non-zero value being displayed when the line has no power/intensity."  

Without more specific information, this last bug you mention is, perhaps, a bit disturbing. 

You also sent along some figures (including calculations where you'd put the second IC line in by hand) which indicate, among other things, that the missing 2nd IC line does matter (i.e. it's power/transition probability is NOT included in the first line).  

OK, so there are some outstanding issues here, but even in the context of these issues, I've run a couple of tests, the results of which I wanted to share with you and get some input on. 

I'm doing these tests on silicon (I have a possibly interesting result on a PMS star showing Si XIII f/i ~ 1.5, which is a value intermediate between 0 and the low-density limit). 

At http://astro.swarthmore.edu/~cohen/projects/prismspect/f-i-r/
you'll find a zip archive containing the results of four different calculations (all using the same Prismspect workspace).  They all use Prismspect v2.3 and ATBASE 4.2.  They all use the same Si atm file (with only 86 levels of Li-, He-, and H-like having excited states).  Check the atm settings for He-like - I used the most detailed model possible for that ion only, including term splitting and fine structure.  Please let me know if you'd recommend something different. 

Without getting too much ahead of myself, here, I'll tell you that I'm planning on doing some comparisons where I vary the atomic model (choosing more highly excited states from both He-like and Li-like).  I'm hoping that the results will not change significantly.  In the past, I've noticed robustness issues (i.e. the calculation fails) depending on the choice of levels, but generally not much variation in the strengths of relevant lines.  

But OK, here's what I've done and found so far.  I'll describe the four runs you'll see in the zip archive and then give you some comments: 

All runs are non-LTE, steady-state, use the same atm file, have T=500 eV (most of the Si is He-like at this temperature, though I only checked the lower density case, but density shouldn't affect ionization balance much for a collisional plasma), 99.9% H and 0.1% Si. 

run1: zero width plasma, n_ion=1.e10 - calculation couldn't be completed (singular matrix error or somesuch error message).

run2: zero width plasma, n_ion=1.e11 - calculation completed, results looked sensible (see my general comments below, though).

run3: planar plasma, Delta(L)=1000 cm, n_ion=1.e11 - again, results look sensible (didn't note any deviations from the results in run 2, but they might not have been identical; the reason I did this run is described below - forbidden line not showing up in spectrum). 

run4: same as run3, but with five different values of log(n_ion)=11,12,13,14,15 - results look sensible (I was a little surprised that f/i didn't go to zero at even n_ion=1.e15, but the trend is right - see the figure Si_run4_f_to_i.jpg - just in the web directory, not in the zip archive). 

OK, the main thing I noticed that concerned me was that the forbidden line didn't show up at all in the model spectra.  Now, when I used the line intensities tool, and set the oscillator strength threshold very low, the forbidden line DID show up and its strength looked to be about right.  This is why I went to the planar plasma between runs 1 and 2, by the way, I thought there might be some optical depth criterion for the code deciding which lines to put in the output spectrum.  So, I guess, especially because of the bug you mentioned in your August 18 email, I'd like it if you'd verify that I can believe the results in the line intesities output, even if the forbidden line isn't showing up in the spectrum. 

I'd also like it if PrismSpect or the spectrum viewer tool could be modified or fixed so that this line is always included in the spectrum.  I understand that you don't want to plot every line with a tiny oscillator strength.  On the other hand (and especially since I'm doing some other calculations looking at density sensitive lines coming from metastable states), there may be other lines of interest having very low oscillator strengths.   What do you think? 

Since I'm getting to the point where I'd like to do some of these calculations for publication, I think it's important to include the 2nd I.C. line in the atomic models.  I've got datasets showing these He-like features in O, Ne, Mg, Si, and S.  What are the prospects for getting these transitions generally into ATBASE or, barring that, getting them put in by hand for the time being in these five ion stages? 

Finally, as I mentioned to you a while ago, I've been talking to this grad student of Steve Kahn's who's dissertation focuses (partly) on f/i ratios in O stars.  He's been using Blumenthal et al.'s 1972 paper to do the modeling.  They have an analytic formula for predicting f/i ratios (taking photoiexcitation into account too) that has only two parameters, the critical density and an anlagous parameter for photoexcitation, values of which are listed in the paper.  This grad student thinks that these values, though old, are pretty good, and that there's not really much need for custom models, whether they're HULLAC (which he certainly has access to) or PrismSpect/ATBASE.  I think it would be interesting to do a side-by-side comparison of PrismSpect/ATBASE and the Blumenthal et al. models.  Once we get the second IC lines in the relevant elements within ATBASE and verify that the results we're getting out of PrismSpect (given the atomic models, etc.) are sensible, I would be very glad to do such a comparison. 

So, to summarize - 

I'm asking you: 

1. Please verify my calculations (that the forbidden line doesn't show up in the spectra simply because of an osc. str. criterion or something, but that the values in the line intensities tool are reliable.  Also that the atomic model (atm file) I'm using is reasonable, plus some advice on zero-width vs. planar mode.  Reassure me that the bug causing zero-intensity lines to show up with finite intensities is no longer a problem in v2.3. 

2. Get the 2nd IC transition in there for the elements I mentioned. 

And I will: 

1. Do some systematic comparisons to help determine how big an atomic model is really needed. 

2. Do a systematic comparison with Blumenthal et al.'s analytic formula. 

3. Test the current models under the assumption of a non-zero radiation field (will also benchmark these against Blumenthal). 

Finally, in the next couple of weeks, my old student and I will get you our initial results on the iron L-shell comparisons with the Tokamak data. 

Thanks,
David
 
PS I know you're likely not working much during the holidays (Thanks for the Christmas card, by the way).  But please do let me know when you read this email, even if you won't have a chance to respond to all the particulars for a while.  Thanks.