meeting 2025 04 17 n57 - JacobPilawa/TriaxSchwarzschild_wiki_5 GitHub Wiki

Following up on our quick meeting yesterday with some additional diagnostics and generally cleaning up the results so far. I've gotten the masked grid up to speed (after some Expanse scheduler issues), so I now have all the model points where yesterday I had been lacking a few.

Takeaways:

• I think the largest takeaway from these new diagnostics is related to the outermost bins in the masked case. We saw hints yesterday that masking these outer 4 bins seemed to push sigma quite high and wanted to look at this systemtically.
  • I've included 10 radial plots below from the 10 best models (in terms of NNLS chi2), and it does seem like masking these outer 4 bins results in the models inflating sigma/deflating h4 to a quite extreme degree. By masking these outer bins the chi2s are essentially 0 because of the large errors, but I do worry that the models are likely adding in a bunch of extra mass (either via increasing M/L or rho0) to fit the unmasked bins better, resulting in the outer most bins being so inflated in sigma (>300 km/s) and deflated in h4 (very negative near -0.1, well outside our fiducial error bar). This could potentially be why our new posteriors seemed to push the M/L and rho0 toward the boundary.
  • I think I'm more comfortable presenting results where this outer bin is misift rather than masked since I increasingly do believe the models are artificially adding a bunch of mass with the added freedom of not needing to fit this outermost bin. It's also encouraging that, when we include the outermost bins, the results from GPR + dynesty in which we include everything is in nice agremeent with the case where we don't count these outer 4 bins in the chi2 calculation.

I then grabbed the ten lowest chi2 (from the outer removed case) models and plotted their radial profiles, along with the corresponding model which has the outer 4 bins masked:

• I think this confirms broadly what we were seeing yesterday -- in the cases where we mask the outer 4 bins, the sigma profile in the outskirts gets inflated quite high to >300 km/s. This is quite different from the non-masked case, in which sigma is certianly misfit but not nearly as inflated.
• A similar trend is seen in h4, where the unmaksed cases seem to be within the errorbars of our data, whereas the masked cases push h4 to very negative values (near -0.1), well beyond our h4 errorbars.

Because the models seem to be pushing sigma/h4/h6 around so much, I'm less convinced now that we should be masking these outer bins. On one hand, it's a shame that the models are not able to fit this outer most point, but on the other hand, at least we know the models aren't putting an artificial amount of mass (either via M/L or rho0) in attempts to ignore this outermost bin while fitting the other bins much better.

• I think it's also encouraging that the case where we include all bins vs. exclude the outer 4 bins crudely are in good agremeent.

• Within the region where we have data (marked very roughly by vertical dashed lines), the anisotropies and orbit fractions are quite similar to one another. However outside this region, particularly at large radii, the two cases start to diverge with the "unmasked" models preferring the outermost anisotropy to be quite negative (in this outermost mass shell). We typically have not paid much attention to the inner/outermost anisotropy shells, so it's not entirely clear if we should be concerned about this, assuming we're moving forward with the "unmasked" case.

• One thing that is sort of interesting -- it seems like removing the outer 4 bins results in a preference for the high scalings, whereas including all the bins prefers the lower end of the scalings. I think this makes sense given the "masked" case seem to prefer higher masses in general, and thus these are preferentially better fit.

• In general there is really nice agreement between the "all bins" and "no outer 4" cases here. There's a bit of movement in rho0 and M/L which I think is to be expected since we're removing our outermost kinematic bin (likely most influenced by rho/the DM halo).
• With that said, all of the parameters are consistent within the 1 sigma confidence intervals of our fiducial case.

I quickly ran some tests on the "all bins" case with the 4200 models from the panels above. I ran GPR and dynesty for K = 40,60,80 and nu=0.5,1.5,2.5, and infinity which are the typical cases we've looked at in the past (though we've normally quoted the nu=1.5 case):

• Takeaways/Results: There appears to be essentially 0 dependence on nu and K for the ~4200 "all bins" models!

First, here's a vertical plot comparing the 1/2/3 sigma regions for the different K's and nu's:

• "All Bins" = All of the Grid C s=1.0 models while including all the bins
• "REMOVED Outer 4" = Same as "All Bins" but crudely removing the outer 4 bins
• "MASKED Outer 4" = Properly masking the outer 4 bins by inflating their errors

Results/Discussion:

• Interestingly, the "All Bins" case has generally decent looking contours for all parameters, but it seems like doing anything to the outer 4 bins for this Grid C s=1.0 set of models causes the parameters to move toward the edge.
  • I suspect this doesn't affect the "All Bins" case above which uses all ~4200 models because we have substantially better sampling of the space when expanding beyond the Grid C s=1.0 case alone. As a quick reminder, ~3200 of the 4200 models actually had scalings associated with them, in addition to simply searching over a broad range of parameters due to the additional grids.

Note these posteriors use K=60 (effectively all the models are included), and I've varied nu since lower nu has often been more "flexible" in our past testing.

• Interestingly, it actually seems like the nu=2.5 and nu=inf have slightly better resolved contours for the outer bins removed/masked cases. Using nu=2.5 or nu=infinity have generally result in "less flexible" GPR fits in the past, so it was a bit surprising to see these perform a bit better than their nu=0.5 or nu=1.5 counterparts.