From: Greg Aldering (aldering@panisse.lbl.gov)
Date: Fri Jan 16 2004 - 02:06:33 PST
Hi Serena,
I've made a few notes based on further thinking and examination of
the additional plots you have put on the webpage.`
Based on your figures of Imax versus chi^2 for the three high-z SNe,
and the 99Q fits for 89B and 99ac templates on your webpage, it is now
more clear to me what issue we are dealing with. Namely, unlike the
other two high-z SNe, the SN1999Q fits allow both 89B and 99ac
templates at similarly good chi^2, and these give peak magnitudes that
differ by about 0.2 mag (as you said in the telecon). This suggests
that, baring other information, one has to take an uncertainty of 0.14
mag (i.e., if the probabilty of 89B and 99ac are equal). One can use
the relative chi^2 to weight by the relative chi-sqr to get an improved
peak magnitude and uncertainty. (One might also consider the relative
likelihood of a 89B versus a 99ac.)
However, more can be done to try to determine whether 99Q is more like
99ac or 89B in other respects. If you can rule out (or estimate relative
probabilities) for 99ac or 89B as templates for 99ac then the
uncertainty can be further reduced.
I was able to fit a B-band lightcurve to the I + (B-I) data in Table 1
of Riess 2000 and get a good constraint on stretch. I estimate that
s = 1+/-0.05 based on a by-hand fit. I fixed the restframe dates wrt Tmax
using the "Age" given in Riess' Table 1; the rationale being that Riess
had other B-band data and so probably constrained the data of max fairly well
(as we did for 00fr). I also assumed that since the published restframe
B-band data were optical observations taken with HST, while the
restframe I-band is from noisy NIR data, the correct errors on the
I+(B-I) data points should be sqrt(sigma_BmI^2 - sigma_I^2). Under these
assumptions (which give very small, ~ 0.05 mag, error bars for each
point in B), I get excellent chi^2/DOF from my by-hand fits, with all
points within 1-sigma (0.05 mag) of the fit. (An appropriately
constrained fit in SNMINUT could firm up this numbers.)
So let's compare 89B and 99ac with 99Q. Below are the stretches for each:
89B has s_B = 0.89 s_I = 1.10 (s_B based on dm15 = 1.31)
99ac has s_B = 1.079 s_I = 1.23 (outside calibration range)
99Q has s_B ~ 1 s_I = unknown
It basically looks like 99Q has a stretch centered between these two.
Perhaps its magnitude is between as well. However, my fit was rough and
the stretch for 99Q could pull towards one or the other. After a better
fit of the B-band lightcurve this question should be reexamined.
(I originally started looking at this based on the low B-band stretch
you found, but my fit doesn't support such a low stretch).
Note that the fact that we can fit the stretch for 99Q further allows
us to use stretch correction for the high-redshift SNe! As you have
mentioned, this still may not improve the high-z Hubble diagram since
99Q appears to be fainter than expected.
Misc. coments:
Figures 3 and 4 are just continuations of Fig 2, so shouldn't be new figures.
I could not locate plots for SN 1989B through SN 1993O lightcurve fits
The 42 I-band templates all have uncertainties versus time - have these
been accounted for in high-z fits?
I'm still sorting through some of the issues, but wanted to get the news
of the B-band fitting to you. I'll send more later as things unfold.
Cheers,
Greg
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