From: Greg Aldering (aldering@panisse.lbl.gov)
Date: Sun Apr 27 2003 - 10:39:23 PDT
There were a few questions about the stretch-luminosity plot I sent
out. First, let me remind those who are interested in this that I
didn't perform any fits - I simply took residuals provided by Rob to
Fit 3, along with the stretch, host extinction, and alpha values
reported in the paper. So, one important caveat for the
extinction-corrected stretch-luminosity relation I showed is that there
could be a residual zeropoint offset between high and low redshift. The
zeropoints appear to me to be pretty consistent, but that can
assessed more directly once Rob gets back.
I can roughly estimate the chi-squares with and without stretch
correction, but note that I don't back-out the stretch errors or
stretch-peak covariance in doing so (these are fairly small). Also, in
the plot I sent, I did not add an "intrinsic" scatter" to the magnitude
error bars that are shown. The chi-squared values below are calculated
both with and without intrinsic scatter, using 0.17 mag for the cases
with no extinction correction and 0.11 mag for the cases where
extinction correction was applied. Note that of the high-redshift HST
SNe, SN1998aw is not included because I do not have its residual
(it suffers strong extinction).
Chi-Squared values for the 10 HST SNe:
No Ext. Cor. Ext. Cor.
-------------------------------------------------------------------
No stretch correction 226 9.0
and no intrinsic error
Stretch correction 214 12.4
and no intrinsic error
No stretch correction 12.8 10.6
and instrinsic error
Stretch correction 12.1 7.6
and intrinsic error
-------------------------------------------------------------------
People can interpret this for themselves, but to me it appears that for
the extinction-corrected case, the data prefer to be stretch-corrected
when a 0.11 mag instrinsic error is assigned (chi-squared drops from
10.6 to 7.6). But, that if there is no intrinsic error assigned, they
do not favor stretch-correction (chi-square increases from 9.0 to
12.4). The differences for the extinction-corrected cases differ by
less than 2-sigma (delta chi-square < 4). All the extinction-correction
cases pass a goodness of fit test (the DOF is really close to 10 since
many more SNe went into determining the fitting parameters).
- Greg
>On Sat, 26 Apr 2003, Greg Aldering wrote:
>Hi Greg,
>can you please provide the chisquare for the high-z data w.r.t
>1) the solid line 2) the no correlation case?
>Thanks,
> Ariel
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