meeting 2025 03 05 n315 - JacobPilawa/TriaxSchwarzschild_wiki_5 GitHub Wiki

Context

  • I ran the reminimization on Grids D + E Base models with the updated kinematics. As a quick reminder, these new kinematics were made by:

    • Taking the (bias = 0.2 + Full Barth Stars) results, and replaced the three strange bins with the (bias = 0.2 + 13 Barth Stars) results.
    • I then point symmetrized the kinematics, and then masked the outer 4 Mitchell and overlapping Mitchell bin.
    • Added dummies out to h12 (the proper way, where I replace the errors AFTER symmetrization).

  • The full results are below, but I am very happy with the outcome. Despite the kinematics being quite different, the actual parameters do not move around much. In fact, the only parameter which appreciably moves is T which shifts from T=0.97 to the now T=0.9 or so. Thankfully, our coverage of T with Grids D and E seemed adequate enough to capture this.

    • Additionally, the chi2 is GREATLY improved, going from ~2900 down to ~1560, MUCH more in line with what we've seen for other galaxies. The new reduced chi2 would be ~1560/(244x8 + 55x6) = 0.68.
    • I also processed the two sets of chi2s with GPR + Dynesty with the same settings and things are in very nice agreement at this stage given that we're only using base models without any scaling involved.
      • In fact, the cornerplots below have identical BH masses within our rounding!

  • I think that our agreement between the grids + coverage on our updated minima are sufficient enough that we can simply add scalings from Grids D and E using our new kinematics. I think something like +/- 3% in the masses should be sufficient to start with, and we can always add more scalings in (or other, previous grids) if we think we need to. After adding the scalings we'll just run through the same "select-best-scalings" approach as before.

Plots + Diagnostics

  • First, here's the 1d NNLS chi2 vs. parameters (with the same y-scale) for the Base Grid D + E models for both the old kinematics (left) and new kinematics (right). The most significant difference is in T which had a minimum near T=0.97 in the old kinematics, which has now moved closer to T=0.9 or so.
1d Panels
images/250305/chi2_profiles.png
  • And I quickly ran the points above through GPR and dynesty just to get a sense of their current agreement (without any scaling and using these already quite zoomed in grids). I chose K = 100 and nu = 1.5 which is currently what we use in the paper.
Old Kinematics (Above) New Kinematics (Above)
[images/250305/test_old_grids_grid_alpha_K100_nu1.5-1.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250305/test_new_grids_grid_alpha_K100_nu1.5-1.png)
  • And here's a direct one-to-one of the two NNLS chi2s (colored by different parameters). I think these trends make sense, where the parameter that seems to explain most of the difference in chi2 is T. The low T points have preferentially lower chi2 for the new kineamtics.
BH ML Rho0 T Tmaj Tmin
[images/250305/One_to_one_comparison_0.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250305/One_to_one_comparison_1.png) [images/250305/One_to_one_comparison_2.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250305/One_to_one_comparison_3.png) [images/250305/One_to_one_comparison_4.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250305/One_to_one_comparison_5.png)

Current Best Fitting Kinematics

  • I also wanted to quickly check how the radial profiles looked for the new best fitting model. I've left the inner 5 bins in this plot (they're excluded from the Chi2s above, however) just to get a sense of the improvement. I still think things are a bit weird in the center/they're slightly underpredicted so I think we should still mask them, but they're definitely marginally better looking than before:
Radial Moments
images/250305/moments_new_grid-1.png

Follow Ups from Email

  • I've got a few updates that Chung-Pei had asked for over email relating to both the new kinematics and our switch from nMC=10 to nMC=100.

    • As a quick reminder, in the tests below, the nMC=100 and nMC=10 kinematics are both produced using the incorrect template library (and additionally both have bias =0.0). We found that the uncertainties in the nMC=100 case were on average a bit larger (1.5 times or so) than the nMC=10 case.

  • When using the nMC=100 kinematics:

    • Our previous best fit model's chi2 drops from ~2905 to ~1699 indicating that our tiny uncertainties were likely driving the chi2 to be so large. Given that we found only a slight change in the parameters with new templates in the test at the top of the page, it seems like the uncertainties have been the driving factor of the weirdness we're seeing in the models.

  • When comparing the new kinematic errors (correted Barth library) to the old kinematic errors (incorrect library), it looks like my original sigma and h5 are on the lower side of the relative size of the errors, whereas the other moments all seem to be larger for the new set of kinematics. I think this is broadly consistent with what we've seen in the past. For example, h6 seems to have the largest increase in error, but it also had the largest chi2 so its contribution gets significantly "dampened" with the new uncertainties/kinematics.

Plots
  • First, here's a comparison of the old heatmaps (old best fitting model) to the new heatmaps (new best fitting model from Grid D + E). The original best fittting NNLS chi2 is 2905 compared to ~1561 using the new, correct template kinematics.
Old Heatmap New Heatmap
Full [images/250226/gmos_nnls.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250305/gmos_nnls.png)
Summed Over Bins [images/250226/gmos_nnls_moments.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250305/gmos_nnls_moments.png)
  • And here's a heatmap showing a ratio of the uncertainties on a bin-by-bin and moment-by-moment basis. The ratio plotted here is (new)/(old), so it seems like the new h2 and h5 uncertainties are a bit smaller than what we had in the past, whereas everything else seems to be inflated relative to our fiducial case. This seems to go in the right direction (e.g., h6 is able to be much better fit due to their relatively larger errors).
Error Ratio
images/250305/gmos_error_ratio.png
  • I also reminimized our old best fitting model with the nMC=100 kinematics to try to isolate why our chi2 has improved so subtantially. Replacing the moments and unceratinties with those coming from the nMC=100 case leads to a huge decrease in our chi2 as well, down from ~2905 to ~1699. This seems to indicate that the uncertainties being on the smaller end have been driving much of the weirdness in our chi2. Here's the original heatmap compared to the new heatmap broken out by bins and moments:
Old Heatmap (nMC=10) New Heatmap (nMC=100)
Full [images/250305/nmc10_heatmap.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250305/nmc100_heatmap.png)
Summed over bins [images/250305/gmos_nmc10_moments.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250305/gmos_nmc100_moments.png)
  • And here are the radial kinematics for the best nMC=10 vs. nMC=100 model:
nMC=10 nMC=100
[images/250305/nmc10_moments_best-1.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250305/nmc100_moments_best-1.png)