*Astron. Astrophys. 340, 476-482 (1998)*
## Appendix: continuum renormalization
A procedure is described for the renormalization of échelle
spectra in which the blaze function has been incorrectly removed. It
is not valid for spectra in which the noise level is comparable to the
strength of the line spectrum. The procedure follows the following
steps.
1. The original spectrum is cleaned such that
, rejecting all x-values with
.
2. A spectrum is constructed in which all the
data gaps are replaced by the mean value .
3. is smoothed using a Gaussian filter
() to define a pseudo-continuum
.
4. is re-normalized using this pseudo-continuum
to obtain .
5. Step 1 is repeated with , where
. This defines a more restricted set of x-values
for which S(x) are more likely to be `true' continuum values.
6. The spectrum is constructed in which the
data gaps are replaced by the mean value .
7. This is multiplied by the pseudo-continuum
to restore valid values of to their original
values, , giving with
non-continuum points now replaced by a local mean rather than a global
mean.
8. An improved pseudo-continuum is defined as in step 3, to give
.
9. The renormalized spectrum is then computed from
.
Steps 5 - 9 may be repeated with a decreasing interval
until a satisfactory result is obtained. For
the current CASPEC data, with and
, the values and
, the above procedure was satisfactory without
further repetition.
The normalized spectrum obtained by this procedure improved the
goodness-of-fit statistics considerably, but was ineffective in
regions where the original continuum was incorrectly defined and where
the spectrum was extremely crowded. With considerable trepidation, a
second renormalization procedure was introduced, but only after the
majority of the stellar parameters had been well established. In this
case the following steps were taken.
1. The renormalized spectrum was divided by the
best available synthetic spectrum .
2. The result was cleaned in the same manner as before and smoothed
with a Gaussian filter to define a new pseudo-continuum
.
3. A completely renormalized spectrum is generated from
.
It should be noted that throughout these procedures the equivalent
widths of all absorption lines measured relative to a local continuum
are not altered. The object of this renormalization is to ensure that
this local continuum is normalized to unity throughout the spectrum.
The final step uses information from absorption lines whose properties
have already been deduced to correct regions of spectrum which may
contain information (e.g. as blended lines) that cannot be recovered
by other means.
© European Southern Observatory (ESO) 1998
Online publication: November 9, 1998
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