Context

• Following up on some questions that came up in the meeting yesterday, in particular about k-corrections in the W1 band.

Karademir+23

• I found a paper with both Jarrett and Cluver as authors which has some additional information on the k-corrections and the use of the J23 stellar mass estimations. Check out Section B1 of the Appendix of Measurement of the evolving galaxy luminosity and mass function using clustering-based redshift inference for more information, but I'll summarize the most important information here:
  • Our understanding of the k-correction and my application of it appear to be correct -- it seems like there is quite a large k-correction of nearly 1.2 magntiude at a redshift of z=0.5
  • The "Mentari" lines are simulated k-corrections based on galaxy SEDs generated using Mentari (Triani et al. 2023). The Mentari tool uses simulated galaxies calculated from the Millennium simulation (Springel et al. 2005) and the semi-analytic model Dusty SAGE (Triani et al. 2020). Here Mentari focuses on simulated galaxies with stellar mass M∗ > 108 M and generates SEDs from far-ultraviolet to far-infrared wavelength which includes stellar emission, dust attenuation, and re-emission using the population synthesis code by Bruzual & Charlot (2003).
  • Addtionally, in this work, it appears that the authors trust the J23 relations over the Mentari results, as suggested in their Appendix B2: "It is seen that the scaling relation from Mentari shows a general offset to the resultsfrom Jarrett et al.(2023). Since the scaling relation from Jarrett et al. (2023) is based on observational data, we correct the results from Mentari by a scalar of −0.47log (M∗), which has been derived by a simple least squares analysis between the two relations, to account for this offset."

Figure B1
images/260116/b1.png

Huang+07 and Kettlety+17

• An older paper I came across that presents k-corrections for the W1/W2/W3 and W4 channels. An approximation for the W1 channel is given as -2.27*z, and this appears to be generally in agreement with the J23 and the Kettlety+17 approximations.

• Kettlety+17's Galaxy and mass assembly (GAMA): the consistency of GAMA and WISE derived mass-to-light ratios provide an extremely simple approximation for the k-correction that appears to agree quite while with the J23 relation.

• Specifically, they say the k_c = -7.1*log(1+z) is a good approximation, and this also seems to show a k-correction of ~1.2 mag at z=0.5:

Kettlety+17 K-correction
images/260116/kettlety.png

Chilingarian+10

• An older but very popular paper is Analytical approximations of K-corrections in optical and near-infrared bands which provides some polynomial approximations for various bands. They also provide an online calculator here: http://kcor.sai.msu.ru/

  • Unfortunately they did not include W1/W2 bands in their approximations, but they do have 2MASS J/H/K band measurements so we can get a general sense of how big of a k-correction there should be.

• I've extracted the J and K band measurements for our galaxies which are in 2MPZ, and have plotted their color distribution here, which has a median of something like J-K = 1 or so. Plugging this in to the k-correction calculator at a redshift of 0.5, I am finding a K-correction of ~0.92 magntiude, similar to the J23 k-correction:

J-K Colors	Result from K-Correction Calculator
[images/260116/j_k_colors.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260116/kcorr.png)

Duey+25

• The Baryonic Tully─Fisher Relation. II. Stellar Mass Models
• Interesting paper which compares the Cluver+14 and J23 mass relation to masses derived from Spitzer observations, and they claim (Figure 2 and in Section 3) that the J23 mass estimates are hard to reconcile with their models, instead landing in much better agreement with the Cluver+14 relation. They seem to prefer the Cluver estimation overall.
• In general they prefer slightly higher masses than the J23 masses, going in the direction we need.

Fig 2, Duey+25
images/260116/duey25.png

WISE2MBH

• It's noteworth to read Section 9 of the WISE2MBH Paper, which goes into detail about their process. They specify that they use the k-corrections presented in J23, but choose the C14 mass-estimation procedure using the W1-W2 colors. This is consistent with the Duey+25 paper, which seems to agree better with the C14 estimation method.
• They also state that their choice of C14 over J23 is because: "Our estimations of M∗ come from the method of C14, which presents a different dependence of M/L on W1−W2 compared to J23, which was the method for which the K-corrections were developed. Despite this, our most important goal with respect to the ETHER sample is not M∗ estimates, but rather MBH estimates. The latter showed better agreement with measured MBH values in the literature when using the method of C14."