meeting 2026 01 15 gw - JacobPilawa/TriaxSchwarzschild_wiki_6 GitHub Wiki

Context

  • In addressing some of the open questions from the meeting, I discovered that I had the W1 k-correction computed incorrectly, and had been dividing where I should have been multiplying.
    • More specifically, in Section 5.1 of the J23 paper, they state that the flux gets "boosted" by a factor, which I intpreted as dividing by the factor they give, when it should have been multiplied.
  • I have verified that the W1-W2 k-correction is correct, however, so the only change needed is to fix this W1 k-correction. This bullet tries to bring the past few bullets up to speed and assess where we are at now.

K Correction Diagnostics

K-Correction Error and Sanity Checks

  • Here's a quick comparison of the stellar masses before and after the k-correction fix, plotted as a function of redshift.
    • Note that I had to slightly downsample the points here due to some memory constraints, but I can clean this up at a future point if we'd like:
Before and After One-to-One
[images/260115/quick_comparison.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260115/good_bad.png)
  • Here are two sanity plots showing that the updated k-correction is being done properly.
W1 K Correction W1-W2 K correction
[images/260114/w1_k_correction_sanity.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260114/color_k_correction_sanity.png)
  • I've also updated a few of the plots we've looked at in the past with the updated stellar masses, and have both here for comparison. Note that the old k-corrections greatly inflate both the stellar masses and the black hole masses.
    • Note that for consistency between the plots here, I'm including the intrinsic scatter when drawing the Mbh values.
Case Mstar Distributions Mbh Distributions K-band comparsion
New Mstar [images/260115/260114_mstar_distributions_jarrett23.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260115/260114_mbh_distributions_jarrett23.png) images/260115/260114_J23_versus_Kband.png
Old Mstar [images/260115/mstar_distributions.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260115/mbh_distributions.png) images/260115/J23_versus_Kband.png

Additional Diagnositcs

  • I'm trying to contain the k-correction information to be above this section since it's a bit different in spirit to the work below. I am now continuing on with what we were trying to do prior to discovering the k-correction error, including:

    • W1 vs. W1-W2
    • Comparison of dynamical Mbh vs W1-W2 Mbh without scatter
    • Tracking down the origin of the highest and lowest mass galaxies

  • Takeaway/Summary: *

W1 vs. W1-W2

  • One thing we wanted to investigate -- we wanted to see how correlated the W1 magntiude is with the W1-W2 color, so I have a few visualizations of this.
    • The punchline is that there doesn't appear to be a very strong trend between W1 and the color, either observed or absolute magnitude.
W1 vs. Color
images/260115/w1_versus_color.png

Comparison of dynamical Mbh vs W1-W2 Mbh without scatter

  • I've redone the comparison of the W1/W2 inferred masses vs. the MM13 and vdb16 samples. The nice thing is that, because the k-corrections are small for nearby objects, the general trend here remains the same as what we have seen before. Note that I removed the upper limit data from the VDB16 sample for a "fair" comparison:
Case 1-to-1 Residuals
MM13 [images/260115/comparison_plot_upperlimits_mm13_no_scatter.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260115/resid_mm13_no_scatter_no_upper_lim.png)
vdb16 [images/260115/comparison_plot_upperlimits_vdb16_no_scatter.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260115/resid_vdb16_no_scatter_no_upper_lim.png)

Highest and Lowest Mass Galaxies

Lowest Mass galaxies

  • I think the most major issue we wanted to make sense of were the galaxies with very large or very small inferred stellar masses (say, below 10^7 Msun and above 10^12 Msun).
  • First, here's a histogram of the stellar masses for the ~19.6 million galaxies in the catalog:
    • There are 4438 sources with Mstar < 10^7 Msun (about 0.2% of sources)
    • There are 343240 sources with Mstar > 10^12 Msun (about 1.75% of sources)
Stellar Mass Histogram
images/260115/mstar_dist.png
  • I then split these into three groups, with the goal of seeing whether grouping by mass reveals any trends with color or redshift.
    • Msun < 1e7
    • Msun > 1e7 & Msun < 1e12
    • Msun > 1e12 Msun
  • I then plotted the distributions of some of the relevant quantities for these groups:
Mass Group Distributions
images/260115/distributions_split.png
  • Immediately the redshift distribution for the lowest mass galaxies stood out to me, so I plotted this a bit more clearly:
    • It seems like the lowest mass galaxies are preferentially at z<0.01 or so, whereas the higher mass galaxies have very few galaxies in this region. More specifically:
      • $\log(M_\star) < 7$: 4547 galaxies with zPhoto_Corr < 0.011
      • $7 \leq \log(M_\star) \leq 12$: 10045 galaxies with zPhoto_Corr < 0.011
      • $\log(M_\star) > 12$: 0 galaxies with zPhoto_Corr < 0.011
Case Zoomed redshift distribtuion
diff. x-axis ranges images/260115/z_dist1.png
identical x-axis ranges images/260115/z_dist2.png
identical ranges, colored by sample images/260115/z_dist3.png
  • So at least for the lowest mass galaxies, we're probably fine to simply impose a lower bound of z=0.01 on the data,

Highest Mass Galaxies

  • It also seems like maybe of the very large galaxies (>10^12 Msun) have their masses reduced from the proper k-correction, so it's not clear we still have the popoulation of high mass galaxies which concern us:

    • $\log(M_\star) < 7$: 0 galaxies with zPhoto_Corr > 0.5
    • $7 \leq \log(M_\star) \leq 12$: 2081 galaxies with zPhoto_Corr > 0.5
    • $\log(M_\star) > 12$: 0 galaxies with zPhoto_Corr > 0.5

  • Here are some similar histograms for the high mass galaxy case:

Case Zoomed redshift distribtuion
identical x-axis ranges images/260115/z_dist2_highmass.png
identical ranges, colored by sample images/260115/z_dist3_highmass.png

Final Catalog

  • We can now start discussing what exactly we want to pass over to Maria and Nicco.

  • A quick summary of how this final catalog was constructed:

    • Start with 2MPZ data, from here. Most relevant columns are WISEX, WISEID, RA, DEC, W1MCORR, W2MCORR, ZPHOTO. This data should have 934,175 sources.
    • Also download WISExSCOS and the mask from here. The relevant columns here are wiseX, wiseID, w1mCorr, w2mCorr, zPhoto_Corr, ra, and dec.
      • After applying the HEALPIX mask to the WSCOS data, there should be 18,675,715 sources in that dataset.
    • I then cross-check the two catalogs for overlapping sources based on the wiseID columns, and I find that there are 5923 repeated sources in the two catalogs. I remove these from the 2MPZ catalog before merging both the 2MPZ and WSCOS catalogs. I am left with 19,603,967 sources from the two catalogs.

  • With the catalogs in hand, we can start calculating "value-added" quantities like the stellar mass and black hole mass. More specifically, we:

    • Start by converting the W1 and W2 magnitudes to fluxes. I'm assuming:
      • W1 zeropoint = 309.54 Jy
      • W2 zeropoint = 171.79 Jy
    • We then k-correct the W1 flux by multiplying the observed flux by e^(-2.614*z), where z is the redshift. This is from Table 2 of J23.
    • We also k-correct the W1-W2 color following the prescription in J23. Specifically, we calculate the observed color from the W1 and W2 columns, and also calculate the delta_color parmaeter from J23 (note: this prescription only extends to to z=0.5, and we have a handful of sources outside of this range).
      • important note: J23 specifies that colors should be clipped to be between -0.2 and 0.4; I am clipping the rest-frame (i.e., k-corrected) colors to be in this range, not the observed colors.
    • I then compute the W1 absolute magnitude and then luminosity using M_W1_SUN = 3.24 and the k-corrected W1 flux. Distances are computed as the luminosity distance to the object's given redshift assuming H0=70 and Omega_M0 =0.3.
    • The mass-to-light ratio is then computed from the J23 equation: ML = 10 ** (-0.376 - 1.053 * (W1-W2, rest frame)). Again, note that the W1-W2 rest frame colors are clipped to be between -0.2 and 0.4 in this expression.
    • The final stellar mass is then this M/L * L_{W1}.
    • Black holes are then "painted-in" based on their stellar mass using the mean relation from MM13: logMbh = 8.46 + 1.05*(logMstellar - 11)

  • Additional cuts done:

    • We saw that there was a number of sources with z<0.011 or so which had suspiciouslly small masses. As a first pass, I have cut out all sources below z<0.01. Doing so, I am left with 19,586,966 sources.

Diagnostics from this catalog

W magnitude distributions
images/260115/260115_w_distributions_horizonal.png
Mstar distributions for redshift bins
images/260115/260115_mstar_distributions.png
GSMF (in redshift bins) GSMF (single bin)
[images/260115/GSMF_260114-1.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260115/GSMF_260115_single_redshift_bin-1.png)
  • Note that the BH Mass functions here DO NOT introduce any scatter to the relation, which I think is part of the reason for the large disagreement between our curve and the curve from Emily.
BHMF (in redshift bins) BHMF (single bin)
[images/260115/BHMF_260115-1.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260115/BHMF_260115_single_redshift_bin-1.png)
  • And one last diagnostic -- here's the W1/W2 mass vs. K-band mass comparison for this filtered dataset:
    • Need to investigate this slope a bit, but putting this all together just prior to the meeting!
K-band vs. W1/W2 masses
images/260115/filtered_k_band_comp.png

A quick note on MM13 Comparison

  • I've also started to look into why we might not find any "matches" in the coordinate matching with the MM13 set of sources. This is still a work in progress.
  • I started with the 73 galaxies in the MM13 table, and was able to find coordinates (in my code) for 69 out of 73. The four missing are:
    • Milky Way
    • A1836-BCG
    • A3565-BCG
    • Circinus
  • I then plotted the search results for all the galaxies, rather than those that I found a match for only. It really does seem like ~half of the MM13 sources are simply not in the WSCOS/2MPZ catalogs for whatever reason, rather than the catalogs having the sources and me finding the matches incorrectly. Notice the jump in nearest separation in the titles -- we go from ~1.5" at worst to nearly 30 arcsec.
Full result of matching
images/260115/all_matches_combined_MM13_full.png
  • Trying to spot check a few now for why they didn't make the final catalog.