From: Serena Nobili (serena@physto.se)
Date: Mon Mar 01 2004 - 06:36:04 PST
Dear Chris,
I think you have a very reasonable worry about the choice of the fit of
Imax giving the minimum chisq. I think in general this is a good choice
since the best fit is the one matching the data better, so why would one
want to average "bad" results together?! The only problem is if one thinks
the chisq is not a good measure of the quality of the fit (this I believe
is the case of Andy program, due to the low signal to noise of the high-z
SN spectra. ) Given the low statistics we have (few data to be fitted and
a discrete distribution of templates) we should be careful. However, the
case of SN 2000fr is pretty clear to me. The only template giving a good
chisq is the one of 1992bc, because of the low value of the second point,
i.e. the template looks very different from other templates. I will try to
make this more clear by answering to your point:
On Mon, 1 Mar 2004, Chris Lidman wrote:
>
>In the lower half of figure
>
>http://www.physto.se/~snova/internal/papers/iband/figs/Imax_sb_00fr.jpg
>
>I note that the best fit template to 2000fr is also the template that
>makes it the brightest. All other fits with poorer Chi-sq (but still
>with chi_sq < chi_sq_min + 3) are systematically fainter.
>
The bottom plot shows the fit with chi_sq < chi_sq_min +9 and not chi_sq <
chi_sq_min + 3, as I have mistakenly written in the web page. This
becomes clear by looking at the scale of the x-axis. There are only 3 more
templates in the range < chi_sq_min + 3, which you can see in the plot:
http://www.physto.se/~snova/internal/papers/iband/figs/read_fitlog.ps
The best fit is: Imax= 23.42 +- 0.08 chisq_min=0.79
The second best fit is: Imax=23.58 +- 0.08 chisq = 2.34
The large difference in chisq values, makes me think that one fit is
actually better than the other.
>We should always be wary of choosing an analysis method which makes
>the data look better, but we may want to reconsider whether or not
>we should use the fit with the minimum chi_sq to define the peak magnitude
>of the SNe.
>
>If one was to define the peak magnitude as the average of all fits
>that satisfied chi_sq < chi_sq_min + 3, then 2000fr would be 0.15 to
>0.2 magnitudes fainter.
>
This was based on the plot up to chi_sq_min < 9.
The average of Imax giving chisq < chisq_min +3 is <Imax>=23.48, that is
very close to the Imax given by the best fit.
>We might want to think of this difference as a systematic error
>induced by choosing a different analysis.
>
>I can give you an example of where the chi_sq minimum value is not used.
>When Andy determines the SN epoch, he takes the average of the best five(?)
>fits. I've cc'ed this e-mail to Andy so he can explain to us why
>he chooses this method of analysis.
>
As I said above, I think this is due to the fact that the chisq is not a
good indicator for the goodness of the fit of SN spectra. This depends on
the signal-to-noise but also on the differences in the spectral features.
I hope Andy agrees with me about this point.
>Similarly, the fit to 1999ff is the second brightest of all fits with
>chi_sq < chi_sq_min + 3.
>
>http://www.physto.se/~snova/internal/papers/iband/figs/Imax_sb_99ff.jpg
>
Again, same problem as before about the x-axis being chisq_min + 9.
The best fit is: Imax= 23.25 +- 0.10 chisq_min=0.26
The second best fit is: Imax= 23.39 chisq= 1.30
The average value in chisq_min +3 is <Imax> = 23.37
You might notice that in the plot on page 4 of:
http://www.physto.se/~snova/internal/papers/iband/figs/read_fitlog.ps
there is at least one SN giving a lower value of Imax than the best fit
one. That is 1997cn, for which the B-band stretch factor is not defined
and therefore is missing in the next page plot.
>Note that these plots are quite flat, which would argue that the
>light curve shape is not all that important in determining the peak
>magnitude.
>
>
I must disagree with this point. The flatness of these plots is only
telling us that the I-band light curve shape is not correlated with the
B-band stretch factor, and not that the Imax is not correlated with the
I-band light curve shape. I would rather say, that there is some light
curve shape parametrization that we did not find yet. Do you see what I
mean?
>In relation to the numbered items.
>
>1) There was concern for the way the dispersion in the Hubble diagram
> is computed. Serena should compute the weighted r.m.s.
>
>Serena's reply ...
>
>I have done this. The weighted r.m.s. gives about the same values as
>the non-weighted r.m.s. due to the uncertainties, which are about the same
>for all the points. However, Table 4 now includes the weighted r.m.s. as
>well as the weighted average for each of the samples. I have also added a
>discussion in section 3 about the differences between the data sets.
>
>Chris' comment ...
>
>I think that we were also interested in seeing the RMS scatter about
>the individual Hubble lines and not the scatter about the Hubble line
>that is derived from the entire data set. Was the RMS calculated in
>this way? It is not 100% clear in the paper.
>
I think the mean value of the residuals for each data set (column 4 of
Table 4) should be taken as an indication that differences are not
important. Although I could run the fit on each data set separately, I
don't think this is really relevant, given the low statistics of each of
them separately, e.g. only 6 SNe are in the CfA sample. For the same
reason I think any claims on differences between the data sets
(which I don't clearly see anyway), should be done very carefully.
>2) Lifan computes different K-corrections than I. We should try to
> compare them and figure out why there are differences. Serena uses
> the spectral templates published in Nobili et al 2003. Lifan uses a
> sample of nearby spectral templates for which he computes the
> K-corrs and average them out. Lifan will try to compare them.
> As Ariel pointed out, we would like to use templates for computing
> K-corrections, as this is used for the high-z SNe, in order not to
> treat them differently.
>
>Chris' comment ...
>
>For this paper, I tend to agree. We should treat high and low redshift
>SNe equally. Nevertheless, the comparison should be done.
>
>I think that it is worth investigating if we can better constrain the
>spectral energy distribution from some observable, for example the
>B-band stretch, and hence derive a more accurate k-correction. This
>might reduce the scatter about the Hubble line. I am not arguing
>that it should be in this paper, but it is something that the
>collaboration should do.
>
>10) Serena will try to add the restframe B,V-band for 1999Q, reduced by
> Vitaliy, in the analysis presented in Section 6.
>
>Serena's reply ...
>
>This is interesting! It turned out that the fit obtained by SNMINUIT
>fixing the time of B-maximum to Tonry value, would give a color excess
>E(B-V) = 0.2 mag (see email by Vitaliy in the archive on Feb 12). Given
>that this SN is host-less, this value is very surprising. I have been
>playing with numbers and plots. If the B-band stretch factor was sB=0.82
>the colors would make perfectly sense (even in I-band). Unfortunately the
>stretch fitted by SNMINUIT is 1.061 instead. Check plots and discussion
>in:
>
>http://www.physto.se/~snova/internal/papers/iband/index.new.html#99q
>
>Giving all of this, I do not think we should add the B-V colors of SN1999Q
>in the analysis of section 6.
>
>Chris's comments
>
>Why is the horizontal axis ins these plots scaled with the stretch?
>I've seen this with the B-band lightcurve, but it is the first time I
>have seen this done with colour.
>
This was found in Nobili et al. 2003. The color dispersion decreases when
dividing the time axis by the B-band stretch factor for all colours. Note
that Rob found the same in his analysis.
>Would the colour of 99Q be normal if the date of maximum derived by
>Vitaliy was used instead?
>
I have added one plot about that in the web page (Figure B)
http://www.physto.se/~snova/internal/papers/iband/#99q
The situation does not look much better, unfortunately.
Please, let me know if you have more doubts or comments.
Cheers
Serena
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