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For the purpose of surface imaging, very high-resolution (about 170 000 at
6173Å), high S/N spectra (about 200 - 300) were obtained with the
high-resolution echelle spectrograph SOFIN (Tuominen 1992)
at the 2.56 m Nordic Optical Telescope (NOT)
at Roque de los Muchachos Observatory, La Palma, Spain.
The high resolution optical
camera was used. The entrance slit width
of 32
m is adjusted
to give a resolution element
of about 2 pixels FWHM, corresponding to
on the sky. The spectra
were recorded with an Astromed-3200 CCD camera (Mackay 1986) equipped
with
an EEV P88200 UV-coated
CCD with a pixel size of 22.5
m
and operating at the optimal working temperature of 150K.
Three observing runs for
Gem were conducted in late 1993,
1994 and 1995. Typical integration times were 30-40 minutes.
The reductions of the echelle spectra used the 3A-software package
(Acquisition, Archiving and Analysis; Ilyin 1996).
The reductions involved the usual procedures of cosmic spike removal, bias
subtraction, flatfielding, subtraction of scattered light, extraction of the
curved echelle orders and wavelength calibration. The result is for each
order the intensity normalized
to the local continuum vs. heliocentric wavelength.
Two steps deserve a more detailed description.
Flatfielding uses summed, merged flatfields, i.e. the slit height
is so large that the orders of the flatfield spectra
overlap; many of those images are summed in order to
improve the S/N ratio in the flatfields. Fringing is usually of
very low amplitude or absent. In some cases, however, an ordinary
flatfield image is available, taken with the same parameters and
immediately before or after the stellar exposure, which, after
flatfielding and filtering to improve S/N and retain only the
fringes, can be used to correct the corresponding stellar spectrum
for fringing.
In order to obtain the highest possible accuracy in the wavelengths, a
two-dimensional dispersion curve is determined from the
Thorium-Argon comparison spectrum; this has the main
advantage to use many comparison lines from many orders, as opposed to the
sometimes very low
number of comparison lines available in one individual echelle order. The
determination proceeds as follows:
- Many orders from the comparison spectrum image are extracted in the
same way as the orders from the stellar spectrum image and the
backgrounds are subtracted.
- The positions of the comparison lines are determined by fitting of
Gaussians.
- The wavelengths are identified semi-automatically using the Kitt-Peak
Atlas for the Thorium-Argon-spectrum (Willmarth 1987).
- After determination of the two-dimensional positions (
) for
many (100-200) comparison lines, all are transformed into one master
order, using the
-law, i.e.

where k is the order number in which the line with wavelength
has been measured and
correspond to
the master order.
- The merging of all lines in the master order is subsequently optimized
according to the model:

The first equation describes the rotation of the CCD rows with respect
to the lines perpendicular to the dispersion direction. The rotation
angle, and thus the curves
, are modified due to the
optical distortions as described by the second equation. It was found,
that this simple model works very well for our spectrograph, where the
incident and diffracted beams are in the same plane. a and b are
optimized by minimizing the
of all merged comparison lines
from a single polynomial describing the dispersion curve of the master
order.
- The polynomial is then transported along the lines
into each of the orders of the original image,
yielding a dispersion curve for each of them that is based on all the
comparison
lines distributed all over the original two-dimensional image.
- Finally, telluric lines are used to establish the accurate wavelength
zero point, correcting for tiny geometrical shifts between the
comparison and stellar images due to bending of the spectrograph.
The accuracy of the RVs is determined by the following factors:
- -
- The accuracy of the dispersion curve: typically, about 150
comparison lines are taken into account.
The dispersion curve within the master order is described
by a polynomial of 2nd degree; the rms deviation of the lines from
the final fit is generally about 2 mÅ at 6165Å or 0.1
.
Since
due to the large number of comparison lines used the error of the
coefficients is much less than that, we conclude that the
statistical error of the dispersion curve is negligible.
- -
- The stability of the RV across the chip: any systematical
error of the two-dimensional dispersion curve should show up as a
systematical variation of the RV across the different orders. This
was checked in the spectrum of the RV-standard
Oph: the
RV is stable across the chip to within 0.03
. Also for
Gem with its much broader lines due to fast rotation the
RV is stable to better than 0.1
.
- -
- The accuracy of the wavelength zero point: Each spectral image
is shifted geometrically with respect to the image containing the
comparison
spectrum. Strong atmospheric
O
and H
O lines are used to establish the wavelength zero
point. The standard wavelengths are taken from the solar catalogue
by Pierce & Breckinridge (1973). In the present spectra,
three different orders are available, each containing enough
atmospheric lines to
establish independently the wavelength zero point. They prove that
there is no significant systematic variation of the shift across
the image
and allow an
error estimate for the shift. Typically, the shift is determined
with an accuracy of 0.1 to 0.2 CCD pixels. Since in echelle
spectra in a good first
approximation the dispersion is proportional to the wavelength
this uncertainty transforms to a systematic error of the RV from
the whole image of about 0.1 to 0.2
.
- -
- The accuracy of the template's RV: The RV of
Gem is
measured by cross-correlating the wavelength region around
6175Å with the same region of a spectrum of
Oph
(K2III), taken with the
same equipment and reduced in the same way.
The spectrum has been filtered to mimic the
rotational broadening in the
Gem spectra.
Oph is a radial
velocity standard (see Astronomical Almanac 1995), a
candidate
for a list of primary standards; we can thus assume that both the
constancy and the value of its RV are established to high accuracy.
According to
the Astronomical Almanac (1995) its
RV = 
.
- -
- The accuracy of the cross-correlation: At present, this
cannot be determined independently. Therefore, we adopt an error
of another
0.1
from this procedure.
If we assume these error sources to be independent and add up the variances
from the different
contributions, the final RV-error is about 0.3
. Note that
although all the above error sources are also present in the template
spectrum only the second to last source enters into the RV-error of
Gem, since the literature value for the RV of
Oph is used to determine
the RV from the cross-correlation.
The RVs measured from the SOFIN spectra are given in
Table 1 (click here).

Table 1: The radial velocities (RVs) measured from the SOFIN
spectra.
The heliocentric Julian date is given for mid-exposure. A typical
error of the individual RV is 0.3

Table 2: The previously unpublished RVs measured by Eker.
The measurement procedure and the interpretation is given in
Eker (1986). He estimates the RV error to be 0.5

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