meeting 2025 04 07 n57 - JacobPilawa/TriaxSchwarzschild_wiki_5 GitHub Wiki
Context
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I've added s=(0.95, 0.98, 0.99, 1.01, 1.02, 1.05) scalings to our grid of 2200 models.
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Takeaways:
- The scalings have slightly improved the chi2 and coverage of the minimum, but as we expected the higher scale value models are almost entirely better fit than any of the small scale values, so I think we'll greatly benefit by running more models.
- The black hole seems to be closer to ~8 billion Msun, and the M/L likely closer to ~1.7 or so, though it seems our current grid however does capture the minimum in rho0 and the shapes.
- I think that the movement in the parameters is more or less what we would expect too. The new set of kinematics have systematically larger sigma in the GMOS data (with the Mitchell data being the same), so I would expect the black hole mass to increase while rho0 remains unaffected since this is likely most constrained by the outermost Mitchell data.
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Moving Forward:
- Given the 1d panels below (and the rough GPR and dynesty results), I think a grid of 1000 models over the following ranges would further improve our coverage:
- BH = [6e9, 10.5e9]
- ML = [1.5, 2.2]
- Rho0 = [2e9, 3.75e9]
- T = [0.15, 0.45]
- Tmaj = [0.6, 1.0]
- Tmin = [0, 0.15]
- Given the 1d panels below (and the rough GPR and dynesty results), I think a grid of 1000 models over the following ranges would further improve our coverage:
Diagnostics
- First, here are 1d panels colored by the scale factors/parameters/without coloring:
| No Color | Scales | BH | ML | Rho0 | T | Tmaj | Tmin |
|---|---|---|---|---|---|---|---|
| [images/250407/color_by_nothing.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250407/color_by_scale.png) | [images/250407/color_by_bh.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250407/color_by_ml.png) | [images/250407/color_by_rho0.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250407/color_by_T.png) | [images/250407/color_by_Tmaj.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250407/color_by_Tmin.png) |
- I also quickly ran the s=(1.02, 1.05) combined cases through GPR and dynesty (since these two set of scales were far and away the best fitting sets). While in our production plots we would likely want to only pick the best scaled models, I think this is fine for a rough estimate of where the minimum currently is. Here are the results for a few different K's:
| K=60 | K=80 | K=100 |
|---|---|---|
| [images/250407/test_grid_alpha_K60_nu1.5-1.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250407/test_grid_alpha_K80_nu1.5-1.png) | images/250407/test_grid_alpha_K100_nu1.5-1.png |
Email Follow Ups
- Just posting a few more plots following some exchanges over email:
- I've included a plot of the best scaled models only now (colored by scale factor, in which you can see that the high scale factors are curretly dominanting the fits).
- I also ran GPR + Dynesty on the Best Scaled Version only, since I had previously just combined by s=1.02 and s=1.05 grids without any cuts (I hadn't anticipated us moving right to rejection sampling).
- Lastly, I've got a proposed set of 1000 points built from rejection sampling the "best scales" case. The boundaries I am using for these rejection points are:
- BH = [6e9, 10.5e9]
- ML = [1.5, 2.2]
- Rho0 = [2.0e9,3.75e9]
- T = [0.15,0.45]
- Tmaj = [0.60,0.999]
- Tmin = [0.001,0.15]
Diagnositcs:
- First, here are the 1d panels for the best scaled set of models only. In this plot, blue: s=1.01, purple:s=1.02, black:s=1.03. The other scale factors have too poor of chi2 to be selected in the best scales.
| Best Scales Panels |
|---|
| images/250407/best_scales_colored_by_scale_factor.png |
- And here are the results from running these Best Scaled models through GPR and dynesty for a few different K and nu:
| K=60 | K=80 | K=100 | |
|---|---|---|---|
| nu=0.5 | [images/250407/best_scales_test_grid_alpha_K60_nu0.5-1.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250407/best_scales_test_grid_alpha_K80_nu0.5-1.png) | images/250407/best_scales_test_grid_alpha_K100_nu0.5-1.png | |
| nu=1.5 | [images/250407/best_scales_test_grid_alpha_K60_nu1.5-1.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250407/best_scales_test_grid_alpha_K80_nu1.5-1.png) | images/250407/best_scales_test_grid_alpha_K100_nu1.5-1.png |
- And lastly, I generated a set of 1000 model points using the K=80,nu=1.5 case above. This is what the distribution of models looks like:
| Proposed Model Points |
|---|
| images/250407/proposed_points.png |
