SPH Opacity: Issue Discovery and Resolution
Last Updated: April 13, 2015Problem 1: We've always used the spatially varying opacity method to accelerate the winds in the SPH code developed by Stan and Atsuo where each wind has its own spatially varying opacity function (dependent on stellar and wind parameters) and areas of particle mixing use a density weighted average of the two opacities. As it turns out, this makes the opacity of a given region of space near a wind-wind boundary resolution dependent; the higher the resolution, the smaller the region where particles from both wind contribute to the density, so the smaller the transition region between the two opacities.
The most obvious manifestation of this was in Tom's eta Car sims of varying outer boundary since they have a wide range in resolutions. At periastron, the secondary wind is compressed into a small volume, and the lower res sims have primary particles contribute to the density -- and thus the opacity -- in the secondary wind cavity near the apex (out to about to 1.5a). High res sims, on the other hand, have enough particles that only secondary partcles contribute to the density in the majority of this region, so the opacity is not averaged. When the opacities of the two winds differ by more than two orders of magnitude, this makes a huge difference in the resulting dynamics. The strong primary radiation field accelerates the secondary wind much stronger in the high res sims due to this larger opacity, with the velocity of secondary material in the leading arm reaching speeds over 5000 km/s. This obviously creates lots of hot gas when it shocks. Such high velocity shocks never occurr in the lower res sims. This really messes up the CCE result when I embed the r=1.5a sim into the r=10a sim, and both those into the r=100a sim. The X-ray flux matches well for r=10a and r=100a, but adding in the r=1.5a makes the X-ray flux an order of magnitude too high around the Fe K line.
These two figures show the opacity values of the individual secondary wind particles as a function of distance from the center of mass (both in code units) in the R=10a (low res) sim on top and the R=1.5a (high res) sim on the bottom. Cleary the higher res sim has higher opacities. (To account for the differing number of particles in the sim, I'm only showing every 10th particle in the high res sim since the high res sim has 10 times the particles. The scales are also the same, so everything in the plots is directly comparable.)
These two figures show the resulting velocity structure in the orbital plane at periastron. The low res (R=10a sim) is on top, where the max velocity is about 3000 km/s in the central region, and the high res (R=1.5a sim) replaces the central region on the bottom plot, where the max velocity in the central region is just under 6000 km/s.
Solution 1: Assign each SPH particle an opacity based on its composition, not on its neighbors. If the particles are mixed, then the spatially averaged opacity will also be mixed, but each particle retains specific opacity. (Coding bonus: the contribution of the density from secondary particles no longer needs to be tracked.)
Now we have a choice for how the radiation field of one star interacts with its companions wind. Either the opacity can go with the wind, i.e. gi = ki Fi + ki Fj, or the opacity can go with the radiation field, i.e. gi = ki Fi + kj Fj. (Note: I'm ignoring the factor of c).
For eta Car, this make a big difference on the dynamics. k2 ~ 100 k1, so the 'wind scaling' means the secondary wind feels a large force from the primary radiation field since k2 F2 << k2 F1, while the 'radiation scaling' means the primary wind feels a large force from the secondary radiation field since k1 F1 << k2 F2. (By the same token, the 'wind scaling' means the primary wind feels a small force from the seconday radiation field, and the 'radiation scaling' means the secondary wind feels a small force from the primary radiation field.)
The following movies show this difference:
No contribution from companion: gi = ki Fi
opacity goes with wind: gi = ki Fi + ki Fj
opacity goes with radiation: gi = ki Fi + kj Fj
Problem 2 (and Solution 2?): The next thing is to get the companion's radiative force to follow the velocity gradient along the ray to the companion, just like in CAK theory. Currently all particles feel the influence of the companion regardless of their direction of travel, so the amount of radiative inhibition happening on material not moving directly towards or away from its companion is too large.
The following plot shows the relative velocity gradient of the primary wind (star located at {0, 0}, radius of 1) to the companion star (located at {-2, 5}). Only particles located at the surface on the opposite side from the companion should see the full radiative effect from the companion; everywhere else the radiative influence of the companion's radiation should be weighted by the amount shown in the plot. Note that the large volume of primary wind particles should experience <15% of what I'll dub the 'maximum radiative influence from the companion', i.e. when the velocity gradient isn't taken into account.
I can implement this 'velocity gradient correction' as a geometric argument where I assume the winds are being accelerated according to beta laws. It's not as ideal as taking the actual velocity gradient, but I think it will do better than what we've currently got since the companion's radiative influence is currently overestimated by a large extent throughout much of the simulation volume. Related to eta Car, this will be good since it will bring down the speed of the secondary wind in the shock cone around periastron in the 'wind scaling' method due to a mitigated primary radiative force on the secondary wind particles.
Problem 3 (and Solution 3?): Same as above, but for density.
eta Car -- does inhibition even exist?: As John Hillier pointed out in the Skype session where I first presented this issue (problem 1 and solution 1 only), it's not clear that the primary radiation will have any affect on the secondary's wind due to a large discrepancy in the stars' SEDs. The secondary wind is too ionized for the peak in the spectrum of the primary radiation to influence it, and vice-versa for the secondary. So the best sims might be the old no-inhibition sims.
Presumably there's a way to calculate this effect using the respective SEDs and ionization states from CMFGEN models, but for now I'll run no-inhibition models of eta Car as well.
The good news is this means that, with no inhibition in eta Car, the CCE result is back in business!
Home
My Bio
