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Astron. Astrophys. 340, 476-482 (1998)

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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 [FORMULA] is cleaned such that [FORMULA], rejecting all x-values with [FORMULA].
2. A spectrum [FORMULA] is constructed in which all the data gaps are replaced by the mean value [FORMULA].
3. [FORMULA] is smoothed using a Gaussian filter ([FORMULA]) to define a pseudo-continuum [FORMULA].
4. [FORMULA] is re-normalized using this pseudo-continuum to obtain [FORMULA].
5. Step 1 is repeated with [FORMULA], where [FORMULA]. This defines a more restricted set of x-values for which S(x) are more likely to be `true' continuum values.
6. The spectrum [FORMULA] is constructed in which the data gaps are replaced by the mean value [FORMULA].
7. This is multiplied by the pseudo-continuum [FORMULA] to restore valid values of [FORMULA] to their original values, [FORMULA], giving [FORMULA] 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 [FORMULA].
9. The renormalized spectrum is then computed from [FORMULA].
Steps 5 - 9 may be repeated with a decreasing interval [FORMULA] until a satisfactory result is obtained. For the current CASPEC data, with [FORMULA] and [FORMULA], the values [FORMULA] and [FORMULA], 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 [FORMULA] was divided by the best available synthetic spectrum [FORMULA].
2. The result was cleaned in the same manner as before and smoothed with a Gaussian filter to define a new pseudo-continuum [FORMULA].
3. A completely renormalized spectrum is generated from [FORMULA].
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.

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© European Southern Observatory (ESO) 1998

Online publication: November 9, 1998
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