Subject: Re: f line fluxes From: David Cohen Date: Mon, 19 Nov 2007 12:58:05 -0500 To: Skinner Steve CC: "Gagne, Marc" , "David H. Cohen" Steve, Regarding the f- lines, these He-like complexes generally, and the constraints the f/i ratios provide: - I had a lot of trouble fitting the Mg XI complex with three Gaussians plus a continuum. This surprised me a bit, because the r and i lines aren't that weak and the lines are narrow enough that blending isn't really a problem. I tied the widths of all three Gaussians together but allowed their common width to be a free parameter. Typically I'd find some relatively reasonable looking fit, but then in the process of putting confidence limits on the fit parameters, the steppar or error routines in XSPEC would find a new minimum of the fit statistic in model parameter space. In general, the improved fit would have a weaker forbidden line (perhaps this is consistent with your findings, in that a finite forbidden flux is found from the fitting, but the result doesn't really hold up). I ultimately have to conclude that there's no evidence for a finite forbidden flux. Here's a figure showing one of my "best fits" to the whole complex: http://astro.swarthmore.edu/~cohen/projects/sigOri/mgxi_test.png Formally, it's not a good fit. - And that's my second main point: no matter what I do, I can't get a fit to this complex that's formally good (absent f line; finite f line; fixed line widths, free line widths; higher continuum... nothing works). Looking at these data, I think that possible causes of this inability to achieve a good fit regardless of the model details might be caused by the weird shape of the resonance line and (more importantly) the "fuzz" redward of the intercombination line; I don't think this is true continuum, because when I fit the continuum on the blue and red sides of the whole complex (9.0 to 9.1 A and 9.4 to 9.5 A) it's much, much weaker than what we see in this part of the spectrum. Could this relatively featureless flux from 9.25 to 9.35 be perhaps several weak satellite lines? I don't know. I don't think it's iron lines - there's really nothing significant in APED or in higher S/N datasets (I like to use tau Sco's MEG spectrum as a guide to what weak lines might be present in the Chandra spectrum of other hot stars). - In any case, I took the following approach to deciding how much forbidden line flux is there in the data: I fit a Gaussian at 9.3143 A on top of a weak power-law continuum (6.e-6; determined from fitting the two regions to the blue and red of the whole complex). I kept the width of the Gaussian fixed, as well as its central wavelength and the strength of the continuum. So, the normalization was the only free parameter. I tried two different fits, one with a relatively narrow line (sigma = 6 mA) and one with a broader line (sigma = 10 mA). In both cases, the best-fit normalization is zero. So I then asked - how big can the normalization be and still provide a good fit? I translate this as: "how big can the normalization be and give a C statistic value that's only 1.0 bigger than the best-fit model's C statistic?" The answer is: 1.7e-7 for the Gaussian with a 10mA width and 1.5e-7 for the Gaussian with a 6 mA Here's a figure showing the 68% upper limit model for the 6mA Gaussian: http://astro.swarthmore.edu/~cohen/projects/sigOri/mgxi_f_only_6ma_upperlimit.png I frankly don't know if I believe this, either. I think it's too low. I think that this fit is being affected by all those bins with one or two counts. The fit is formally not good. But still... what else can we do? However, again, looking at these data and the model in this figure, don't you feel like the model normalization could be several times bigger and still plausibly fit the data? In any case, the intercombination line flux is something like 3e-6 (from your revised table, and also from the independent modeling that I've done). Even if we're generous with the forbidden line and give it a normalization of 6e-7, f/i is still something like 0.2 or less. - Now, to the modeling. Using a solar abundance TLUSTY atmosphere model (32500, 4.0), and the formalism in Blumenthal, Drake, and Tucker (1972) and Leutenegger et al. (2006), taking an average of the photospheric fluxes at the wavelengths of the two ^3S - ^3P_1,2 transitions (which are at 997.5 and 1034.3 A for Mg IX) - actually, averaging these fluxes over ~3 A blueward of these wavelengths to account for the Doppler shift in the wind (see Leutenegger et al.), and evaluating the quantity phi_*, I find an analytic expression for the ratio, R \equiv f/i of R(r) = 2.7/(1 + 177W(r)) where W is the dilution factor. This model of the f/i ratio as a function of height above the photosphere (radius in terms of Rstar, really) is plotted here: http://astro.swarthmore.edu/~cohen/projects/sigOri/sOriA_mgxi_model.png The blue line represents the f/i ratio in your table (0.33) and the drop down to the x-axis then gives you the radius of formation of this complex. The green cross-hatched region represents the upper and lower limits of f/i based on the confidence limits listed in your revised table (essentially 0. to 1.02). However, if we say that f/i < 0.2, actually, then that constrains the location of the plasma emitting this Mg XI complex to < 2.0 Rstar. * In terms of the data analysis, at this point I'd like to leave it up to you to determine what the reasonable upper limit is in the f-line flux and thus on f/i. I can remake this figure showing the model and the implied observational constraints once you/we settle on what we think the data are saying. - Interestingly, we can compare the Mg XI complex in sigma Ori A to that in beta Cru (B0.5 III - with Teff ~ 27000). Here's the same complex in the beta Cru spectrum: http://astro.swarthmore.edu/~cohen/projects/betacru/mgxi_best_fit.png You can see that the forbidden line is a bit stronger in that star, which is no surprise since the star is a bit cooler and so the UV flux around 1000 A is weaker and, all other things being equal, the forbidden line will be slightly less affected by the UV flux in this star. Note that the factor 177 in the analytic expression for the strength of the Mg XI f/i ratio in sigma Ori, which I quote above, is 126 in the same expression for beta Cru (because the emergent photospheric flux is that much weaker in beta Cru). Anyway.... let me know if you'd like a more detailed explanation of the modeling (or of my fitting of the upper limits on the f line); if you'd like me to remake the figure showing the modeling results and the associated constraints on the radius of formation of this complex; if you'd like me to further document my attempts to fit these data; or if you'd like me to do something similar for any of the other f/i ratios (Si is almost certainly too weak; and Ne is too uninteresting - e.g. no real constraints on the radius of formation). David Skinner Steve wrote: > > David: > > We may end up changing the fluxes of the > Mg XI and Ne IX 'f' lines in the Table to > upper limits. I dont see anything that > looks like a convincing f line detection > in either case. > > What's your take? Should we quote these as > detections or upper limits? > > Steve > > > > > ******************************************************* > * * > * Steve Skinner * > * * > * Center for Astrophysics and Space Astronomy (CASA) * > * 389 UCB * > * University of Colorado * > * Boulder, CO 80309-0389 USA * > * * > * Tel. 303-492-4202 * > * Fax. 303-492-4052 * > * E-mail skinners@casa.colorado.edu * > * Web: http://casa.colorado.edu/~skinners/ss.html * > * * > *******************************************************