D. Cohen
memo: follow-up on MHD/MCWS slides for theta1 Ori C after meeting at Bartol on Fri., Dec. 25, 2007

With Marc's help (and some work from Asif and Steve St. Vincent – oh, and Rich too) I've put together some slides for members of the group to use when they want to show the good agreement between Asif's MHD simulations of theta1 Ori C and the phase-dependent Chandra observations of this star. These basically follow from Gagne et al. (2005), but are modified with the goal of providing simpler, more direct visual evidence. 

The original set of slides I put together is available here: 

http://astro.swarthmore.edu/~cohen/projects/magnetospheres/Cohen_Gagne_theta1OriC_MCWS_slides_v1.ppt

Note that they contain a lot of verbiage - explanatory slides, a couple of slides with background information; and also that some of the slides have notes associated with them (viewed in a window under the slide view). These notes include questions for group members, explanations for complicated graphics, and comments about how the material shown in a given slide might be elaborated on further. If you read these, and have a response, please let me know. 

I certainly don’t intend that anyone will show all these slides. Many are for background for group members. When you/we use them in a public setting, I envision group members using just a few of the slides, which they might modify somewhat. 

The presentation, with modest, mostly cosmetic, updates implemented after the meeting at Bartol last Friday, is here: 

http://astro.swarthmore.edu/~cohen/projects/magnetospheres/Cohen_Gagne_theta1OriC_MCWS_slides_v2.ppt

After meeting with the group, I developed a "wish list" of changes and additions to this set of slides. I've implemented a few trivial ones and plan on implementing more of them.  For completeness sake, I will list here all the suggestions and requests, whether acted on yet or not. Some of these are cosmetic, some involve taking the next few steps in the actual science. Some lie in between these two extremes. 

- Rich's animation on slide 5 - showing the magnetic field and rotation axes - could, perhaps, use more visual cues; especially to show that the rotation axis is inclined 45 degrees. Allard Jan suggested perhaps putting two lines on the star representing the magnetic and rotational equators. This could be worth trying. 

- Two figures (slides 9, 10) show a prediction of the occulted x-ray flux vs. viewing angle or phase. But I have to admit that I don't know exactly where these came from. The one on slide 9 was probably made >5 years ago by Stephanie Tonnesen, most likely from a single snapshot from an early MHD model of Asif's (probably isothermal - but then how was the x-ray emission level calculated? So maybe it was from an early sim with the full energy equation). The one on slide 10 is much more recent. It was made by some combination of Asif, Steve, and Marc. But it too (probably) comes from a single snapshot.   At the very least, we should remake this figure(s) generating a model of occulted X-ray flux in a way that we can document. Related science issues: (1) No one snapshot is truly representative; Steve and I and Asif had started work on "pseudo-3D" models, in which snapshots from a long 2-D simulation were put into different longitudinal slices. But detailed structure in given snapshots still dominated the emission variability. A more reasonable approach would seem to be some sort of averaging over time (in the context of the 2-D simulations). Asif, I think, should make it a high priority to do this, and other related things, connected to visualization (useful if he's going to write a paper on his beta Cep simulation, for example) and the analysis of the differential emission measure (see below; again, the issue is what's "representative" when we look at these simulations?). I recognize that Steve, with Asif’s help, sunk a lot of time into developing tools for visualization. But… realistically, it’s probably better and more efficient to start from scratch; especially since Rich has already developed a lot of the required expertise. (2) The overall normalization of the model prediction is fudged to agree with the data in both of these x-ray lightcurves. There's some uncertainty in how to relate x-ray emission measure to instrumental count rate (based on assumptions about the spectral energy distribution); but these can be pretty well constrained by the data. A bigger issue is that changing the mass-loss rate by a factor of 50% or so will change the overall X-ray emission level by, likely, a comparable amount. My personal opinion is that it's fair for us to force the out-of-eclipse normalization to match the data in these graphics. But we might want to explore the effects of varying the mass-loss rate in the MHD sims. Or at least document how well the overall emission measure agrees between the data and model. 

- Stan also suggested that we could make some theoretical x-ray emission curves over specific spectral ranges (and/or plot something like hardness ratio vs. phase). Spectral differences in these curves would be based, I would think, on a dependence between plasma temperature and location (like, hotter stuff should be at larger radii since shock heating will be stronger where the pre-shock wind velocity is higher, and therefore less occulted at high viewing angles). 

- We could include versions of Gagne et al. (2005) Fig. 4 (two panels) in the paper.  These show the phase-dependent magnetic field measurements, x-ray brightness, UV absorption excess, and H-alpha emission. This figure puts the simulations and x-ray data in context, and confirms the basic MCWS/rotationally-modulated scenario.  

- On slide 22 we show a DEM histogram from a snapshot of one of Asif's MHD simulations. There's a cosmetic issue - the axes on this graph and the observation-derived DEMs from Wojdowski & Schulz (2005) could be made more consistent with each other. (In any case, I will remake the W&S figure to make it clearer.) But there's a larger scientific issue, which is, how representative is the DEM histogram really? You can look at this histogram as a function of time in one of Asif's more recent 2D MHD simulations of theta1 Ori C, here: 

[Steve St. Vincent's webpage of diagnostic movies are at http://www.sccs.swarthmore.edu/users/07/sstvinc2/research/oldmovies.html - there are some movies of the DEM from Asif’s MHD simulation there; that web server’s been down for the last couple of days, though.]

Again, we should probably do some sort of averaging. And maybe exclude the early part of the simulation, while the magnetosphere is filling up and hasn't yet had a fall-back event. But in general, I think it's safe to say that the DEM histogram we have now is somewhat cherry-picked. 

- To what extent do the MHD simulations produce the right overall level of x-ray emission (in addition to the modulation of the relative amounts of emission)?  This is relevant to the DEM plots as well as the x-ray light curves. Again, this might go hand-in-hand with a scaling study of the assumed mass-loss rate. 

- f/i ratios (slides 12-20, but especially 20). I need to remake/remodel these, using three Gaussians (rather than Maurice's hewind routine, which assumes that the emission is from a beta-velocity law wind, and thus that the radial distribution of the f/i relative intensities also scales with the line profile shapes; for theta1 Ori C, the profile shapes (widths) should not be affected by the spatial distribution of the x-ray emitting plasma). I also will make similar figures for S XV and Si XIII. Plus, cosmetically, I should make the model line (red dashed line) even darker. 

- I’ve already fixed up the hard-to-see dark blue text, lines, and arrows in the f/i section.  Let me know if things still aren’t legible enough. 

- Line widths - no phase dependence (slide 26). I can try to put together a graphic showing how the lines in the data don't have widths that vary with phase (to go along with the admittedly complicated figure from Steve St. Vincent that shows how the MHD simulations don't predict much variation in line width with viewing angle; and again, these model predictions should really be taken from an average over the simulation output, not a single snapshot). Maybe we should remake those line profile and projected line-of-sight velocity map figures, in any case. 

- Stan suggested that we/Asif could find a better solution (than, e.g., slide 29) for showing the emission measure in conjunction with temperature information. There are also issues of 3-D visualization vs. 2-D slices. Can we overlay temperature color coding on top of emission measure grayscale? I could write lots about this... but maybe Rich and Asif should spend a little time brainstorming and then present some potential solutions to the group. (There's a related issue of showing the angle-/phase-dependence of a given MHD sim of a specific star that's got a non-zero obliquity - e.g. theta1 Ori C, but also beta Cep, tau Sco... - in other words, we want to be able to fully control the viewing angle of the simulation and have this change with simulation time. One way to think about what I’m talking about here is to look at Rich’s movie in slide 5 and imagine a visualization of an MHD simulation in place of Rich’s cartoon.)

- Also, Rich would really like to have a DEM for sigma Ori E (based on the data). Marc, you and I should put one (or more) together. I discussed issues of uniqueness, temperature continuity, and formal parameter uncertainties with Rich. I don't know how much effort we should put into this. But we should be able to produce a non-unique DEM that we feel OK about, and which Rich's RFHD models, for example, can be compared to. 

Finally, as we looked over these slides and discussed the simulations and the data, it became clear that, although the MHD simulations do a remarkable job of explaining the data, there are some important discrepancies that go beyond the level of detail and probably point to the existence of more complex physics, not well modeled (or not modeled at all) in the 2-D MHD simulations. I list a few of these here: 

- The X-ray eclipses (at edge-on viewing angles) are deeper than expected (either by analytic toy models or by the MHD simulations). This depth implies that the bulk of the hot plasma lies even closer to the star than what we're seeing in the simulations (or what we expect from the location of the Alfven radius or, alternately, the value of eta_*).   Could the plasma really lie closer to the star? Could the depth of the X-ray eclipses be influenced by attenuation by wind, disk, or "snake" material? 

- If we were to include revised model atmosphere fluxes (based on the downward revision of the O star temperature scale - e.g. Martins et al.), then the f/i diagnostics would also move the hot plasma closer in to the photosphere. 

- The shock temperatures achieved in the MHD simulations fall somewhat short of the 30 MK peak of the DEM derived from the Chandra data. This may not be a big deal. But if the shock-heated plasma actually is somewhat closer to the star, then the pre-shock velocity (and post-shock temperature) will likely be smaller. 

- The C IV (and general UV wind absorption) excess appears at edge-on viewing angles (phase ~ 0.5). This wasn't expected. In the generic Shore and Brown (1990, etc.) models, the fast, unconfined polar wind was supposed to give rise to this absorption excess. This was the assumption when the magnetic geometry was inferred for theta1 Ori C (e.g. Stahl 1996), before the actual detection of the field. However, with the Zeeman measurement of the field, it became clear that the UV excess does in fact occur at edge-on viewing angles. Asif's MHD simulations show that this is plausible, with mid-latitude wind flow directed toward the equator, but generally unconfined. However, his preliminary SEI modeling of UV absorption (Asif in the Potsdam proceedings) indicates that in the MHD simulations the excess absorption is seen at pole-on viewing angles. This would seem to be a major problem... 

- A related but more subtle issue is whether the evidence in Balmer and He lines of infall from the disk/torus at phase ~0.5 (Wade et al. 2006) is present in the MHD simulations. 

- The observed X-ray line widths are greater than those seen in the 2-D MHD simulations.  This may not be a big problem, however, as turbulence in the post-shock region and/or the influence of instability generated structure and shock heating on even the hardest X-ray emission lines could account for this extra line broadening. 

Have I forgotten anything in either of these lists?  Feedback is welcome.