From: Robert A. Knop Jr. (robert.a.knop@vanderbilt.edu)
Date: Wed Mar 19 2003 - 15:47:04 PST
WARNING -- use a monospace font to read this E-mail. (You should always
read your E-mail that way anyway.)
Just due to the U-band differences, you'd expect to see different m_b
values due to different K-corrections at redshifts of ca. 0.3-0.4 in
addition to at redshifts of >0.5.
Reason: suppose that the "intial" template spectrum, with whatever "too
red" U-B color, is this, where the general ranges of the different
filters have been indicated:
---------------------------------------------------
U B V R
Now, in order to increase the U-B color, what I've done is *smoothly*
deform the spectrum (reather than just stepping the U-band) so that the
integrated U-B colors have the new desired value (U-B = -0.4 at day 0).
Naively, you might expect this (exaggerated) to look like:
_
___
____
_____
_______________________________________
U B V R
However, that is *wrong* -- the reason being that because U and B
overlap, in so deforming the spectrum to get a higher U, you've also
changed the B-V color. However, we want the B-V color to stay the same
even when we put in a new U-B color. Thus, in practice the deformed
spectrum (exaggerated) looks something like:
_
___
____
_____
_____ __________________________
___ ___
__
U B V R
The total integral in B is the same, but because the left side was
enhanced, the right side needs to be supressed. In net, the integrated
B-V color stays the same.
A side effect of this is that for relativly low redshift supernovae,
where the R-band is systematically sampling the right side of the B-band
filter, you're *also* going to get an offset compared to previous
results (or compared to results with a different U-B color). It is
impossible to do a *smooth* deformation of the spectrm to change the U-B
color without this side effect.
(Note also, as I've said before, that I think our V-R and R-I color
measurements improved with this iteration on the K-corrections, which
also has implications for the low end of the high-redshift set.)
-Rob
-- --Prof. Robert Knop Department of Physics & Astronomy, Vanderbilt University robert.a.knop@vanderbilt.edu
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