meeting 2024 12 08 n315 - JacobPilawa/TriaxSchwarzschild_wiki_5 GitHub Wiki

Context

  • I ran a quick grid using MGE B3 over the weekend to explore the parameter inference with different MGEs.

    • I started by fixing rho0/T/Tmaj/Tmin to the best fitting values in the paper, and sampled 100 models (Latin hypercube style) over BH and ML. These were chosen in the last meeting to roughly encompass our current fit + a bit in the direction of the fit preferred from Boizelle+21. The net result was sampling over BH = [2.0, 3.4], and ML = [2.4, 2.8].
    • The results look really great! I'm not sure if we need to explore any further. The chi2 values are very similar to the chi2s from MGE A, and the shape of the landscapes are quite consistent between the two.
    • I tried to run GPR + dynesty on the 100 models I ran (to be taken with a grain of salt), and the best-fitting parameters are ~consistent within 1 sigma of our current best fit.
      • In the paper, we currently quote BH = 3.2+/-0.2e9, ML = 2.62+/-0.04 as our parameters, and the 100 models below favor BH = 3.0e9, ML = 2.57 or so. Again, I hesistate to take the exact values as serious numbers but we're broadly consistent with what we've been finding.

  • If we wanted, it's extremely cheap to add scalings to this if the results are still too fuzzy. Given I think we'd only have to explore higher scale values if we did, but I'm personally comfortable at the current level of our results.

Plots and Results

  • First, here's the 1d panels showing chi2 vs. BH and ML, as well as a 2d scatter plot showing the models colored by their chi2 value. Note that I've included our best fit model as the red star. The "trough" is broadly consisten where our best fitting model currently is in both 1d panels and the 2d scatter.
1d Panels 2D Scatter
  • And here's two really quick tests with GPR and dynesty. Note that I'm including all 100 models in this GPR run which effectively means a K = 100. I've included both nu = 0.5 and nu = 1.5 though they're very similar.
Nu=0.5 Nu=1.5

Additional Information

  • I figured out the "bump" we were seeing in the MGE SB and rho plots and admittedly it was a very silly mistake on my end. The upshot is that the bump had no impact on our models and was purely a plotting issue, so none of our conclusions will have changed up to this point. Here's a bit of a breakdown of the bug:

    • The first time we were looking at the MGEs is on this page adn you can in fact still see the bug here. If you check the tables for each of the MGE components, you'll notice that the 4th component of MGE A and B on that page have the same amplitude, but different sigma and different q's. The value that is listed in those tables is in fact the correct amplitude for MGE A Component #4, but I must have accidentally not updated that specific component's amplitude in the MGE.
    • Many of the subsequent plots referenced these tables/files when construction my MGE plots for rho/enclosed mass/surface brightness, and this incorrect component amplitude is giving rise to the "bump" we see in the surface brightness.
    • THE KEY POINT: A week ago when we ran the MGE B2 test models, I had actually gone back and recomputed the MGE components by hand before feeding things into the models. In this iteration I entered the corrected MGE component, so the model was actually seeing the correct information. Only when I was generating plots from the old data files did we notice the bump.

  • First, here's some corrected plots with the MGE B2 component replaced. Note that these are the files directly going into the TriOS MGE:

Plot Ratio A/B2 Ratio A/B3
  • I've also plotted a the MGEs with and without the PSF convolution simply for us to get a sense of how things move around. I've included some (scraped) data from Jonelle's paper for a better comparison to the Fig1/Fig4 in the paper:
Zoomed Out Zoomed in to Central Region
  • As a sanity check that there are no other typos, here are tables of the MGEs straight from the TriOS models that were run last week. These values match the values in Jonelle's paper:
MGE B1
log10(I) sigma q PA
3.798 0.58 0.871 0
3.895 1.237 0.786 0
3.485 2.347 0.704 0
3.483 4.132 0.722 0
3.017 8.191 0.664 0
2.844 13.25 0.748 0
2.085 26.51 0.763 0
2.155 30.9 0.689 0
1.839 61.95 0.81 0
0.939 192.6 0.98 0
MGE B2
log10(I) sigma q PA
3.924 0.178 0.764 0
3.896 0.617 0.716 0
3.899 1.292 0.777 0
3.459 2.414 0.706 0
3.474 4.159 0.722 0
3.014 8.211 0.663 0
2.844 13.26 0.748 0
2.071 26.5 0.765 0
2.164 30.83 0.689 0
1.839 61.95 0.81 0
0.939 192.6 0.98 0
MGE B3
log10(I) sigma q PA
4.407 0.119 0.787 0
3.912 0.644 0.681 0
3.891 1.294 0.781 0
3.457 2.409 0.705 0
3.476 4.152 0.722 0
3.015 8.206 0.663 0
2.844 13.26 0.748 0
2.073 26.49 0.763 0
2.164 30.84 0.69 0
1.839 61.95 0.81 0
0.939 192.6 0.98 0
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