• My sanity checks for the k-corrections seem to check out.
  • Specifically, the Manucci+01 paper which has K-band k-corrections seems to suggest to me that the K-correction makes the K-band measurements fainter. This is in contrast to the J and H bands. The reason for this is (sort of) explained in the Jarrett+23 paper, stating: "Similar to the NIR K band (at 2 μm), the WISE W1 3.4 μm band gets brighter with (1+z) because the “peak” stellar bump at 1.6 μm shifts longward toward the K and W1 bands,increasing their flux (relative to rest, ignoring the 4πr2 flux dilution). As shown in Figure 9, upper-left panel, the expected change in flux with redshift is well behaved, an exponential function (or power law), similar for all galaxy types. This demonstrates how most normal galaxies have the same NIR (1–4 μm) spectrum (i.e., the stellar bump from evolved, luminous K/M-type stars), nearly a “standard candle” which may be exploited in photometric-redshift studies. The kcorrection is the scale factor shown on the Y-axis; it is less"
  • The Jarrett+23 paper also explains that the W1 k-correction should have the net effect of dimming the galaxies. They express the W1 k-correction in terms of the rest and observed frame fluxes. They ultimately give this plot, showing that (rest flux) = (obs flux)*(factor), where factor is always less than or equal to 1. So the W1 k-correction ends up reducing the flux, and thus making the objects fainter. This does trade off with the color k-correction as explained below, however.
• For the MASSIVE sample of galaxies:
  • It's not obvious to me that the MASSIVE survey galaxies are any different from other galaxies in the sample. I've included plots below showing the k-correction vs. non-k-corrected mass prescriptions, and the MASSIVE galaxies seem to be scatter sort of randomly (albeit at low redshif) among the other points.

• Seems to show to me that the rest frame Kband K(0) = K(z) - kcorr; because kcorr is always negative, we're always subtracting a negative and thus making the K-band fainter after applying the k-correction.
• Though the Chilingrian polynomial takes on slightly different values, it should be applied the same way.

• They express the W1 k-correction in terms of the rest and observed frame fluxes. They ultimately give this plot, showing that (rest flux) = (obs flux)*(factor), where factor is always less than or equal to 1. So the W1 k-correction ends up reducing the flux, and thus making the objects fainter as well.
• As we'll see below (and as we saw last week), the color k-correction is ~5x as strong as the W1 k-correction, so there is a bit of tradeoff between the W1 k-correction and the W1-W2 k-correction, so the combination of the two don't strictuly reduce or raise the overall mass; it depends on the color.

• Note that the upper right panel showing the "k-corrected vs. non-k-corrected" results, the data is plotted as 2d histograms but the points lie on a line defined by the product of the k-correction to W1 and the k-correction to W1-W2.

• This plot is a simple set of histograms showing some of the MASSIVE galaxy data vs. the rest of the distribtuions. Note that I am not techncially doing anything with the W2 obs --> rest frame conversion, so these panels are identical to one another.

After exchanging some emails, we wanted to look more closely at the missing set of MASSIVE galaxies to figure out why they never made it into our catalog.

I started by spot checking NGC 410, trying to trace where it dropped out of the data.

• I started by checking the 2MASS Extended Source Catalog which is the 2MASS parent catalog for 2MPZ. We expected the MASSIVE galaxies to be inside of this survey since they are local and bright, and I was in fact able to find NGC 410 inside of the 2MASS XSC.

The 2MPZ Catalog however is more than just the 2MASS XSC. They also required B, R and I photometry from SUPERCOMSOS for the photometric redshift determination.

• Crucially, the WISExSUPERCOMSOS paper only used the B and R data since the I band data has "low sensitivity and non-uniform sky coverage". So reading this made me suspect that the issue is not with the 2MASS or the WISE data, but rather with the I band data

This seems to be connfirmed in a number of ways:

• First, I was able to find all of the missing galaxies inside of 2MRS (except for 545 which is noted as being a special case in MASSIVE I).

I also have been spot checking that the I-band data really is the problematic spot. To do this, I have queried the original SuperCOSMOS photographic plate data to try to manually find the galaxies.

• For NGC 410 for example, I searched through all sources within 1 arcmin of NGC 410's coordinates, which returned this table:
• In the 2MPZ paper, they say that they only consider sources with meanClass=1 (galaxies), and sources which have all quality flags less than 2048 ("no strong warnings, nor severe defects, Hambly et al. 2001b"). The issue is that the I-band data has a ton of quality errors. There are only 2 rows for which the I-band data is good, and for those two rows, there are problems with the other photometric bands. So there are no valid sources for NGC 410, and thus this doesn't get passed into 2MPZ due to the lack of I-band coverage.
• I suspect this is true for the other MASSIVE galaxies, but it's a bit clunky to check the data in this way (since the SUPERCOMSOS data is basically a scan of photographic plates containg 1.9 billion sources).

So what do we do?

• Maybe it'd be helpful for me to make some plots look at 2MRS vs. 2MPZ vs. WISExSCOS? And I can try to find the sources that are in 2MRS but not in 2MPZ (since we only need W1 and W2 plus a redshift). I suppose I would need to find the corresponding W1 and W2 measurements from the AllWISE catalog, but in theory that should be possible?