From: Greg Aldering (aldering@panisse.lbl.gov)
Date: Wed Apr 16 2003 - 00:13:46 PDT
Earlier in this series I advocated using an intrinsic U-B color
dispersion of 0.04 mag, as this was most consistent with our own
observations of 10 z > 0.63 SNe Ia (5 with HST colors). This value is
also consistent with Peter's fit to the U-B versus stretch relation
from Jha's thesis after elimination of two 3-sigma outliers.
Since then Peter has provided me with the data on the two 3-sigma
outliers. One is too blue, and there is no SN in our HST sample as
blue as that object. Accounting for our measurement errors, our SN with
the bluest U-B (in residual space) is 2.3-sigma redder than this blue
outlier of Jha's. Our z > 0.63 SN with the reddest U-B (again, in
residual space) is within 1.6-sigma of being as red as the red Jha
outlier. So, there is a 5% chance that such a SN is among our 5 SNe
(i.e., the expectation is for 0.25 of such a SN in our sample).
Furthermore, the incidence of such a red SN is suppressed by an
additional factor of 1.4 due to flux selection effects. (It is
unusually faint in U, so is less likely to be found at the limits of
our searches.)
From this, I conclude that within our HST sample there is no sign of
color outliers like those in Jha's thesis. Given that the outliers in
Jha's thesis are so extreme, they really are not part of a
Gaussian-distributed distribution as the term "dispersion" would
imply. Taken together, I don't see a justification for a citing a
dispersion of 0.095 mag (i.e., the value when the outliers are
included), and again conclude that 0.04 mag is a choice that best
describes our data.
Although the choice of U-B color dispersion doesn't much affect the
OM,OL and OM,w fits, as Rob has shown, it does affect how well we can
measure the mean extinction in our highest redshift SNe. In particular,
using a U-B color dispersion of 0.095 versus 0.04 is statistically
equivalent to reducing our sample size at the highest redshifts by a
factor of 2 - quite a hit given the work and resources that went into
making these measurements. I feel that constraining the amount of
ordinary extinction in the highest redshift SNe is of interest,
independent of the cosmology fit parameters.
Cheers,
Greg
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