meeting 2023 08 01 n57 - JacobPilawa/TriaxSchwarzschild_wiki_5 GitHub Wiki

Summary of N57 Status

General Information & High-Level

  • Some general information on N57:

    • D = 66.9 ± 2.9 (Jensen+2021) – this is 10 Mpc different from the previous distance measurement of 76.3 Mpc
    • GMOS PA: +41.0 E of N, Mitchell PA: +41.1;
    • GMOS PSF: Using Avg. weighted FWHM = 0.81"; Mitchell PSF: 0.5 (from N1453+N2693)
    • 215 GMOS bins, 41 Mitchell bins
    • Also had done some preliminary sersic fits to determine R_core; could be interesting to revisit

  • First, here's a quick summary of our past cubes/models:

Cube Name Date Summary
Cube A1 Feb 3, 2022 6d hypercube, with gNFW profile. A bit undersampled, seemed to miss minimum.
Cube A2 Feb 10, 2022 Submitted 1000 more models to cover higher black hole and higher halo region. Points chosen to have ~uniform density in the space.
Cube A1A2 Scaled Feb 22, 2022 Scalings. Scaled the 13 models above to 13 different scales between 0.9 and 1.1, giving ~26,000 models total.
Cube B March 1, 2022 Rejection sampled cube incorrectly built from 26,000 scaled models. ~1000 rejection sampled models. The error was in applying the "scale" to the models. Also scaled these models.
Cube B Prime March 15, 2022 Corrected the scaling issue from Cube B and ran ~1000 more models. Also scaled these models.
Cube C March 21, 2022 Rejection cube of 1000 models built from Cube A1A2 + Cube B Prime.
Lipka Tests March-April 2022 729 models at fixed masses, testing any effect of the Lipka m_eff on the shapes for N57.
Cube D May 17, 2022 Built another rejection sampled cube based on the 1sigma contours (instead of 2 sigma contours) to try to solve the issue bi-modality issue in Tmaj. Didn't seem to improve things that much.

Cube Diagnostics

Chi2 vs. Parameters for EVERY Model + Contours
n57_all_plus_lipka_plusD-1 n57_all_plus_lipka_plusD_coloredby_BH-1 n57_all_plus_lipka_plusD_coloredby_ML-1 n57_all_plus_lipka_plusD_coloredby_rho0-1 n57_all_plus_lipka_plusD_coloredby_T-1 n57_all_plus_lipka_plusD_coloredby_Tmajor-1 n57_all_plus_lipka_plusD_coloredby_Tminor-1
slice_with_all_points-1
Plots of the various cubes in chi2 vs. parameter space
CubeA1A2
A1 A2
CubeA1 CubeA2
Cube B + B'
B B'
CubeB CubeBPrime
Cube C
C
cubeC
Cube D
D
cubeD
Lipka Test
Lipka
cubeLipkaTest
A Scalings
A1 A_part1_scale0 A_part1_scale1 A_part1_scale2 A_part1_scale3 A_part1_scale4 A_part1_scale5 A_part1_scale6 A_part1_scale7 A_part1_scale8 A_part1_scale9 A_part1_scale10 A_part1_scale11
A2 A_part2_scale0 A_part2_scale1 A_part2_scale2 A_part2_scale3 A_part2_scale4 A_part2_scale5 A_part2_scale6 A_part2_scale7 A_part2_scale8 A_part2_scale9 A_part2_scale10 A_part2_scale11
B Scalings
B B_scale0 B_scale1 B_scale2 B_scale3 B_scale4 B_scale5 B_scale6 B_scale7 B_scale8 B_scale9 B_scale10 B_scale11
B' Bprime_scale0 Bprime_scale1 Bprime_scale2 Bprime_scale3 Bprime_scale4 Bprime_scale5 Bprime_scale6 Bprime_scale7 Bprime_scale8 Bprime_scale9 Bprime_scale10 Bprime_scale11
All Fiducials
fiducials
All Fiducials No Lipka
fiducials_no_lipka
Here's an old, naive version of the cornerplot where I simply throw all models at GPR + dynesty with a cutoff K = 30. This assumed a chi2 error of 0.5 which is what we have used in the past.
niter=1 niter=2 niter=4
Chi2 error = 0.5 cubeABprimeC_error0 5_nIter1_Ts_K30-1 cubeABprimeC_error0 5_nIter2_Ts_K30-1 cubeABprimeC_error0 5_nIter4_Ts_K30-1

Best Model Diagnostics

And here are the diagnostics of the best fitting model so far
Input 1 bh_5 5178e+09_mlfid_1 9982e+00_dmp1_2 2866e+09_theta1_83 465_theta2_56 626_theta3_-88 787 220516_minimization-01
Input 2 bh_5 5178e+09_mlfid_1 9982e+00_dmp1_2 2866e+09_theta1_83 465_theta2_56 626_theta3_-88 787 220516_minimization-02
Input 3 bh_5 5178e+09_mlfid_1 9982e+00_dmp1_2 2866e+09_theta1_83 465_theta2_56 626_theta3_-88 787 220516_minimization-03
Input 4 bh_5 5178e+09_mlfid_1 9982e+00_dmp1_2 2866e+09_theta1_83 465_theta2_56 626_theta3_-88 787 220516_minimization-04
Input 5 bh_5 5178e+09_mlfid_1 9982e+00_dmp1_2 2866e+09_theta1_83 465_theta2_56 626_theta3_-88 787 220516_minimization-05
Input 6 bh_5 5178e+09_mlfid_1 9982e+00_dmp1_2 2866e+09_theta1_83 465_theta2_56 626_theta3_-88 787 220516_minimization-06
Profiles 1 bh_5 5178e+09_mlfid_1 9982e+00_dmp1_2 2866e+09_theta1_83 465_theta2_56 626_theta3_-88 787 220516_minimization-15
Profiles 2 bh_5 5178e+09_mlfid_1 9982e+00_dmp1_2 2866e+09_theta1_83 465_theta2_56 626_theta3_-88 787 220516_minimization-16
Profiles 3 bh_5 5178e+09_mlfid_1 9982e+00_dmp1_2 2866e+09_theta1_83 465_theta2_56 626_theta3_-88 787 220516_minimization-17
Profiles 4 bh_5 5178e+09_mlfid_1 9982e+00_dmp1_2 2866e+09_theta1_83 465_theta2_56 626_theta3_-88 787 220516_minimization-18
Profiles 5 bh_5 5178e+09_mlfid_1 9982e+00_dmp1_2 2866e+09_theta1_83 465_theta2_56 626_theta3_-88 787 220516_minimization-19
Profiles 6 bh_5 5178e+09_mlfid_1 9982e+00_dmp1_2 2866e+09_theta1_83 465_theta2_56 626_theta3_-88 787 220516_minimization-20
Beta bh_5 5178e+09_mlfid_1 9982e+00_dmp1_2 2866e+09_theta1_83 465_theta2_56 626_theta3_-88 787 220516_minimization-36
Betaz bh_5 5178e+09_mlfid_1 9982e+00_dmp1_2 2866e+09_theta1_83 465_theta2_56 626_theta3_-88 787 220516_minimization-37
Menc bh_5 5178e+09_mlfid_1 9982e+00_dmp1_2 2866e+09_theta1_83 465_theta2_56 626_theta3_-88 787 220516_minimization-65
And lastly, here are the diagnostics broken down by bin and by moment (I quite like this plot!) to see if there are any obvious trends or features in our data driving our chi2 landscapes.
chi2_full-1 chi2_per_bin-1
chi2_per_moment-1

Recent Results from Thinning Models

  • Last time we were looking in detail at N57, we were playing around with a thinning routine to see if the "islands" we saw in our posteriors were real. We have done a good deal of work since then so I don't think this is necessarily the best approach, but I wanted to summarize what we have already done here:
    • I thinned the full set of points into 20 realizations of ~1200 model points, each containing ~150 points within the 1 sigma contours
      • It seemed like the 20 realizations all agreed quite well with one another, and combining these into a single chain produces a "nice looking" set of posteriors
Here's quick plots showing the number of models vs. confidence interval/Cutoff K value
vs. Delta Chi2 vs. Confidence Level
cutoff conf
Here's a single cornerplot with all the realizations plotted on top of each other
twenty_full_realizations-1
For completeness, here are all the cornerplots but plotted separately so that we can see the individual landscapes.
r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15 r16 r17 r18 r19 r20
full_fit_seed_0_error_0 5_iter_2-1 full_fit_seed_1_error_0 5_iter_2-1 full_fit_seed_2_error_0 5_iter_2-1 full_fit_seed_3_error_0 5_iter_2-1 full_fit_seed_4_error_0 5_iter_2-1 full_fit_seed_5_error_0 5_iter_2-1 full_fit_seed_6_error_0 5_iter_2-1 full_fit_seed_7_error_0 5_iter_2-1 full_fit_seed_8_error_0 5_iter_2-1 full_fit_seed_9_error_0 5_iter_2-1 full_fit_seed_10_error_0 5_iter_2-1 full_fit_seed_11_error_0 5_iter_2-1 full_fit_seed_12_error_0 5_iter_2-1 full_fit_seed_13_error_0 5_iter_2-1 full_fit_seed_14_error_0 5_iter_2-1 full_fit_seed_15_error_0 5_iter_2-1 full_fit_seed_16_error_0 5_iter_2-1 full_fit_seed_17_error_0 5_iter_2-1 full_fit_seed_18_error_0 5_iter_2-1 full_fit_seed_19_error_0 5_iter_2-1
Lastly, here's the results of combining all samples into a single chain and plotting the contours
test_n57_cornerplot_shapes-1 test_n57_cornerplot_angles-1

Things on the to-do list:

  • Emily's selection procedure for the scaled cases

    • We discussed last time that taking the best-performing chi2 from each mass model (instead of all the scaled versions) is likely a better approach than anything we have done so far, so I can go ahead and implement that.

  • Specific checks to see about sampling in T/Tmaj/Tmin or (u,p,q) as we have been discussing

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