meeting 2025 10 20 gw - JacobPilawa/TriaxSchwarzschild_wiki_6 GitHub Wiki

Context

  • Toward the end of last week, we had finalized the matching between MASSIVE and Zou/WISE, and we wanted to explore the stellar masses a bit more. Specifically, we had a "de-trended" comparison in the previous bullet that we'll build off of, and we'll also try to compute stellar masses from W1 and W2 photometry following some of the references in the GW catalog proposal.
  • Takeaways:
    • I can reproduce the DESI/WISE2MBH masses to within reasonable accuracy trying to implement my own M* calculations from the Cluver14 and Jarret+13 papers (crudely). Trying to use the updated Jarrett+23 method leads to quite a large M* disagreement due to the M/L treament being different in J23 compared to C14 and J13.
    • I can try to refine the details and make this more accurate, but since we're ultimatley going to be using the full WISE2MBH or DESI M* catalogs, it's probably good to call it here and go back to "correcting" either of those catalogs.

Quick Offset Question

  • One very quick detail -- last time, I had fit a line to the stellar masses to "correct" them; we had wanted to try a fixed offset approach rather than a linear fit to the data, so I've done that here:
    • The long-story-short is that there's a ~0.5 dex offset that we can apply that roughly brings everything into agreement!
Fixed Offset Question

Mass Estimator Diagnostics

  • I started by getting the photometry from the DESI DR9 catalog for the massive galaxies. Here are some histograms of the observed magnitudes:
Magntiude Distributions

Comparing Mass Estimators

  • There are a number of papers/updates which try to extract the stellar masses from the photometry. I've computed the stellar mass using a few of the estimators below, and this section compares those estimators.

  • Important note on WISE2BH:

    • One question we had -- what does WISE2BH use for the estimators? It seems like it's roughly a combination of a few parts of the methods below, outlined in WISE2BH's Section 7.
    • It seems like their final M* estimates use the relation from C14 (full sample), but they obtain the k-corrections for both W1 and the W2-W2 colors from Jarret+23 (an updated paper with updated coefficients).
    • They also clip W1-W2 colors to be [-0.2, 0.6] corresponding to high and low M/L values.

  • A very short summary of the methods:

    • All methods essentially get M* from (M/L) * L = M.

    • Jarrett+13:

      • No k-correction mentioned; derived from 17 galaxies
      • log(M/L) = -0.246 - 2.1*(W1 - W2)

    • Cluver+14:

      • Gets k-correction via template fitting
      • log(M/L) = -0.030 - 1.96*(W1 - W2) [FULL SAMPLE]
      • log(M/L) = -0.170 - 2.54*(W1 - W2) [low-z SOURCES]

    • Jarrett+23:

      • Gives k-correction approximations that they use
      • IMPORTANT: W1-W2 (rest frame) colors get clipped to be within [-0.2, 0.4] which is a problem for MASSIVE
      • log(M/L) = -0.376 - 1.053*(W1-W2)

    • WISE2MBH

      • Uses K-corrections from J23
      • Uses stellar mass estimator from C14
      • Clips colors to be in the range (-0.2, 0.6)

    • I have a plot near the bottom of this page showing these different relations.

Expand for some more detailed explanations of the various methods:

Jarrett+13

  • Ref. 56 in the GW catalog proposal.

    • Seems like they obtained their relations from 17 resolved galaxies. I'm using their "full sample" relations, which are the same that are quoted in the GW catalog proposal.
    • It doesn't appear they convert to rest-frame colors or anything via K-corrections.

  • The quick procedure is:

  1. Compute L(band) from
$$L(band)/L_\odot = 10^{-0.4(M(band) - M_\odot(band))}$$

where the value is 3.24 for the sun in W1. Note that I'm taking the absolute magnitude from the DESI catalog which reports both apparent and absolute magntiudes.

  1. Compute mass-to-light ratio from their equation (9):
$$log(M/L) = -0.246 - 2.1*(W1 - W2)$$
  1. Compute total mass from product of the two above.

Cluver+14

  • Reference 57 in the GW proposal.

    • Note that they use SED fitting to get rest frame magnitudes (i.e., they're using template results to find the k-correction, so I am ignoring that here). Given that the MASSIVE galaxies are all very low-z, this should be fine for the comparison we have here.

  • Their general process is essentially the same as Jarrett+13, but with a much larger sample (calibrated to the Taylor+11 masses):

  1. Compute L(band) from
$$L(band)/L_\odot = 10^{-0.4(M(band) - M_\odot(band))}$$

where the value is 3.24 for the sun in W1. Note that I'm taking the absolute magnitude from the DESI catalog which reports both apparent and absolute magntiudes.

  1. Compute mass-to-light ratio from their equation (2):
$$log(M/L) = -0.03 - 1.96*(W1 - W2)$$
  • Note that this relation is their full sample; they have another relation for the "low-z" sources, but I'm using their full-sample since it'll be most analogous to what we end up using.
  1. Compute total mass from product of the two above.

Jarrett+23

  • This work essentially builds off of Cluver+14 and Jarrett+13, deriving three scaling relations (W1 luminosity, W1-W2 color, and W1-W3 color) for M* estimation. For our purposes, only two of these scaling relations are relevant.
Simplest Case
  • The first case mentioned in Jarrett+23 is simply a relation between W1 luminoisty and stellar mass:
$$log(M) = A_0 + A_1 log(L) + A_2 (log(L))^2 + A_3 (log(L))^3$$
  • And the cofficients are given in Equation (2). The resulting slope of the line implies a global mass-to-light ratio of 0.35.
With W1-W2 colors
  • Jarrett+23 goes a bit further and fits for the M/L from the W1 and W2 colors, obtaining the equation:
$$log(M/L) = A_0 + A_1 C12$$
  • where A_0 = -0.376 and A_1 = -1.053, and C12 = W1-W2. Note that they also clip the colors to be in [-0.2, 0.4]. This impacts nearly all of the MASSIVE galaxies which have W1-W2<-0.2 for basically all galaxies. Also note that I'm ignoring k-corrections here (though they give a prescritpion for such). I just suspect that the k-corrections are small for the MASSIVE galaxies since they're all at such low z.

Plots of Comparisons

  • With these calculated, I can now compare our masses vs. the ones reported in the various catalogs. There are a few things that I mentioned above that I want to once again bring up here:
    • I'm not doing ANY k-corrections here, though I anticipate the effects for this are small for the MASSIVE galaxies since we're at such a low redshfit here. In theory for the full calculation, I'll likely want to take the k-correction information/approximations from Jarrett+23.
Case Plot
Comparing w Emily's Masses
Comparing with Zou+22
Comparing with WISE2MBH

Some comparisons on why the estimates

  • Aside from minor differences arising from k-corrections on both the W1 and the W1-W2 colors, the largest difference between the mass estimates is how we get the mass-to-light information. Here's a quick plot showing the M/L curves vs. galaxy color for the different results I showed above. I've also included a histogram of the MASSIVE galaxy colors below.
    • The punchline is that the massive galaxies' W1-W2 are well into the "clipped" range, which is driving the large difference when using the Jarrett+23 approach (which clips to "reasonable M/L values").
    • Note that in the cases, above, we can effectively write:
$$log(M) = log(L) + log(M/L)$$
  • And the luminosities are the same in all cases, so we're really just changing the mass based on the derived mass-to-light relations. In particular for the non-clipped MASSIVE colors, this leads to ~1.0 dex differences since our W1-W2 colors are as negative as they are:
ML Relations

Attempting to exactly reproduce WISE2MBH

  • In the examples above, I had neglected any k-corrections; in this section, I was trying to reproduce as best I can the Mstar estimates presented in WISE2MBH (specifically following Section 7 of the WISE2MBH paper and section 5.1 of Jarrett+23). The idea is that, in this calculation, I do the following (taken from the Jarrett+23 paper):
    • Note one potential place where the two might differ -- I'm grabbing the W1 and W2 photometry from the Zou+22 DESI catalogs; assuming that they're using the same between Zou+22 and WISE2MBH.

  1. Convert W1 Magnitude to Flux Density
    Convert the observed W1 magnitude (total magnitudes are preferred) to flux density.

    • Use the zero-point correction of 309.68 Jy for W1 Vega magnitudes.
    • Reference: Jarrett et al. (2011).

  2. Correct W1 Flux to the Rest Frame

    • Determine the scale factor relevant to your source redshift from the k-correction figure or apply the exponential law relation (Eq. A1, Table 2). This is typically ~0.95 for our galaxies.
    • Scale the observed flux to obtain the rest-frame flux:
$$f_{\rm W1}[{\rm rest}] = \frac{f_{\rm W1}[{\rm obs}]}{f_0} \times f_{\rm W1}[{\rm obs}]$$

  1. Compute the W1 In-Band Luminosity ($L_{\rm W1}$)

    • Convert the rest-frame flux to absolute magnitude using the distance modulus (from redshift → luminosity distance).
    • Apply Eq. 1 to compute $L_{\rm W1}$.

  2. Apply W2-Based K-Correction (Optional)

    • If you have a W2 detection and the resulting W1–W2 color uncertainty is < 0.2 mag, apply a k-correction:
      • Use the k-correction figure or the polynomial in Eq. A2 / Table 2.
    • Compute the rest-frame color:
$$[W1-W2]_{\rm rest} = [W1-W2]_{\rm obs} - \delta[W1-W2]$$
  • Note: The polynomial coefficients vary across two redshift ranges (see Table 2).
  1. Estimate Stellar Mass
    • Basic method: Use $L_{\rm W1}$ with Eq. 2.
    • Preferred method: If you have a reliable W1–W2 color, use Eq. 3 (or a weighted combination of Eq. 2 and 3) to better constrain the mass-to-light ratio.
    • Stellar mass is then computed as:
$$M_\star = L_{\rm W1} \times \Upsilon_{\rm W1}$$
  • The result is this plot, which is showing my attempt at replicating the WISE2MBH masses vs. the reported masses from the catalog. There's an approximately ~0.25 dex offset, as well as some scatter. Note that the WISE2MBH paper does sampling account for uncertainties, but that doesn't really explain my offset I don't think:
WISE2MBH vs. Replication
⚠️ **GitHub.com Fallback** ⚠️