From: Gabriele Garavini (garavini@in2p3.fr)
Date: Wed Dec 22 2004 - 06:45:27 PST
Hi Rob, Hi All
following your suggestion I've added a section to the evolution paper
regarding the technique to measure the EW and the possible systematics
involved in the measurement on low S/N ratio data. I still have to
implement the other changes that where suggested during the meeting but
I'd like to send you this new section now for Eric and Rob to have a
reference for their work. In this section I also include Fig 1 and Table
3 of Gaston's paper. The section reads like:
""""""""""""""""""""""""""""""""""""""""""""""
\subsubsection{Measurement technique and possible systematic effects}
The technique used to measure equivalent width in SN~Ia was extensively
described in the original works \citet{folatelliew} and
\citett{folatellithesis} together with a detailed study of the
possible involved systematic effects. For completeness in this section
we schematically summarize the topical points to the application of this
technique to high red shift supernova spectra.
To measure the {\sc ew} of a spectral feature the underneath continuum
must to be determined. The latter is computed as the straight line fit
through the two local maxima that bound a feature (see panel {\bf (b)}
in Fig.~\ref{fig:feat}). The wavelength location of the local maxima
at a given epoch may differ from supernova to supernova and a drift
with time is expected. To help the identification of SN features
Table~\ref{tab:limits} reports the typical wavelength span in which
the maxima are identified and shows the feature labels as in
Fig~\ref{fig:feat}.
For the fit of the continuum a small wavelength region is selected
around each maximum, always within the ranges of
Table~\ref{tab:limits}. The straight line is then fitted through the
identified regions. The wavelength span of these regions around the
maxima strongly depends on the signal to noise ratio (SNR) of the
spectrum. In high SNR spectra the maxima are easily identifiable and
small regions (typically 10{\bf????} \AA) give the best estimate of
the peak. In relatively low SNR spectra , as those presented in this
work, larger regions (typically 20-30{\bf????} \AA) are needed to
estimate at best the maximum flux hidden within the noise. This
approach was chosen as a practical one to be consistently used both to
high and low signal to noise ratio data.
Possible systematic error arising from the choice of the regions were
accounted for by randomly shifting these regions. This was the
dominant source of uncertainties when the signal-to-noise ratio per
resolution element was above $\sim$10. In the case of lower SNRs (e.g
as those of our data set) is found to be sub-dominant with respect
to the statistical uncertainties.
The systematic effect of low signal to noise ratio was also tested by
adding Gaussian noise to high-quality spectra with known {\sc ew}. No
significant bias was detected on the resulting \ew\ values.
Further systematic effects could arise from host-galaxy light
contamination. Residual galaxy light underlying the SN spectrum would
bias the {\ew} measurements toward low values. This effect must be
taken into account. We will come back on the this point in the next
section.
"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
Thank you all for the collaboration and Happy new year.
I'll fly to the hopefully sunny Rome tomorrow.
Ciao
Gabriele
On Tue, 21 Dec 2004, Robert A. Knop Jr. wrote:
> Eric (and others) --
>
> A summary of the discussion at the phone meeting.
>
> * It turns out that the way you've been measuring the endpoints is
> different from what Gaston and Gabriele have been done.
>
> The fact that we've proven it unclear makes it obvious that the brief
> description in Gaston's paper is insufficient, and needs to be
> clarified and properly specified (ideally in Gabriele's paper, if
> that's the next thing that will be published on this stuff). That's
> the first important point.
>
> The second point is that Eric, you need to make sure that you can
> reproduce what's done using the actual method. What is done is that
> a small region around the maximum on either side of the "line" is
> chosen. Data points within those two small regions are *together*
> fit into a single line, which defines the continuum. (QUESTION FOR
> GABRIELE AND GASTON: WHERE ARE THE "ENDPOINTS" DEFINED FOR THE LINE
> FLUX? I didn't get that out of our discussion, and it's not defined
> in the paper.)
>
> * Needed from Gaston ASAP (certainly by January 1):
>
> 1. The equivalent widths he gets for individual supernovae
>
> 2. The actual spectra used, in cases where galaxies were
> subtracted
>
> 3. description of prescription for defining the continuum
> (though I think I understand that, except that it's not clear
> how you choose the size of the region around the maximum, and
> *SOME* sort of prescription or at least guildlines need to be
> given for that)
>
> 4. description of prescription for choosing the endpoint
> wavelengths over which to integrate.
>
> * Eric: when you get back, first make sure you can reproduce Gaston's
> numbers using his method for defining the continuum and endpoints.
> Next, repeat your noise-adding, smoothing, and binning simulations
> using the new prescription to see if the systematics go away, or what
> happens with that.
>
> * The goal is to have all of this done by the second week of classes,
> before labs start again at Vanderbilt.
>
> -Rob
>
>
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