From: Greg Aldering (aldering@panisse.lbl.gov)
Date: Wed May 07 2003 - 01:11:59 PDT
Hi Rob,
I downloaded your new SN data table and residuals tables, and took a
look. So far I have only examined the extinction-corrected fit which
includes 72 SNe. (I could use only 71 because 92O was not in the
residuals table).
First, all the high chi-squared comes from just a few SNe, as you
noted. Most of these are low-redshift, extincted SNe with good error
bars (also as you noted). 1996bo is 4-sigma, 1995bd is 3.3-sigma,
sn9855 is 2.9-sigma, and 1992bs is 2.8-sigma wrt the best fit. These
are outliers on the residuals histogram, and their chi-squared accounts
for the poor fit (chi-squared of 104 drops to 61 in going from 72 to 68
SNe after these 4 are removed).
Next, as we discussed on the phone, I examined whether a different
value of R_B would help the situation, and indeed it does. I simply
step through R_B, recalculate the weighted mean offset, and then
calculate the new chi-squared. I explore the range 1 < R_B < 6.
Although my program is a little crude in how it adjusts the best-fit
when R_B is changed, it should be indicative.
Here's what I found:
Sample chi^2/DOF R_B
--------------------------------------------------------------
all 71 0.87 2.3 +0.3 -0.3
all but 0.88 2.4 +0.3 -0.3 (this shows that
sn9855 signal not from 9855)
all but (this is similar to
96bo, 95bd, 0.82 3.0 +0.5 -0.4 Phillips 1999)
sn9855
z > 0.1 0.76 2.8 +0.6 -0.5
w/o 9855
(or 96bo, 95bd)
This shows that the high-redshift SNe like R_B close that of the
low-reshift SNe, that this value is lower than the canonical value, but
that the outliers would like a slightly lower value still. In
the last two cases, R_B = 4.1 is still allowed, giving delta-chi^2
around 3.
I haven't explored any further than this. It is clear that adopting the
Phillips R_B will improve the situation for the three worst outliers.
If one includes all 72 SNe, then chi^2 improves by about 22.1 in going
from R_B=4.1 to R_B=3.4 (the latter being the Phillips values). Chi^2
improves by 15 more, in going down to R_B = 2.3. However, I don't know
of anything we could cite to support such a low value. Using the
Phillips R_B might be quite reasonable though. (This value is
strangely similar to the CMAGIC and Nicolas' color slope!)
Note that these finding, while more detailed, are similar to what
I was finding prior to the HST aperture correction correction and
the color-zeropoint correction.
Cheers,
Greg
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