3 Fluctuations of the stellar beam at the output of the fiber feeding the ELODIE spectrograph

3.1 ELODIE spectrograph

A full description of ELODIE is given by Baranne et al. (1996). This is a fiber-fed spectrograph within a stable temperature-controlled environment, located at the 193-cm telescope of Observatoire de Haute-Provence, in France. Using a $102\times 408$ mm echelle and a $1024 \times 1024$ CCD, it samples a spectrum between 389 and 681 nm (67 echelle orders) with a spectral resolution of about 42000. The pixel velocity-width is about 3000 m/s. The 100 $\mu$m-core fiber input accepts 2 arcsec from the sky. The beam aperture is converted to f/5 by transfer optics in order to feed the fiber, located at the f/15 Cassegrain focus, and then brought back to f/15 at the spectrograph input. At the focus of the f/3 camera lens, the geometrical spot diameter is 60 $\mu$m corresponding to a velocity-width of about 7500 m/s. It is feasible to record simultaneously star and reference spectra with two fibers, the outputs of which are displaced by few pixels in the direction of cross dispersion, and orders for both spectra alternate over the CCD. For our observations, we introduce the channelled spectrum from a Fabry-Perot (FP) etalon illuminated by a white-light source (Fig. 1). With invar spacers and temperature stabilization within 10^-2 K, the FP-induced velocity error is about 3 m/s but appears only as a slow drift during a run. Two kinds of recordings are possible: FP/FP spectra (with the FP beam on both fibers) and STAR/FP spectra. We record simultaneously the two spectra, extract the echelle orders, and compute the RV change relative to a reference exposure. In order to get meaningful RMS errors within a few hours, and also to check the suitability of ELODIE for studying stellar oscillations, we used a large number (a few hundreds) of short exposures (60 s) on a given star. A full description of our RV measurements with ELODIE has been given by Connes et al. (1996).

  

Figure 1: ELODIE Calibration optical system: 1) tungsten lamp, 2) mirror and beam splitter, 3) pupil, 4) achromat (to put the pupil at infinity), 5) removable mirrors, 6) concave mirror with 2 holes. Fiber F3 takes FP beam to Cassegrain focus assembly (here highly schematized; for more exact diagram, see Fig. 4 of Baranne et al. 1996). Fibers F1, F2 are illuminated through holes in mirror 6. Mobile mirror system gives two possibilities: 1) FP light into F1 and F2; 2) star light into F1, FP light into F2. This system is standard; we added only the FP étalon

The autoguider is the common-user 193-cm-telescope device, the principle of which is standard: a tilted concave mirror pierced with a hole corresponding to 2 arcsec on the sky allows the fiber to be fed and, at same time, the outer part of the image to be reflected onto the VIDICON guiding camera (see Fig. 1). Initial image centering is done manually from the video-screen image; then the autoguider is locked on. An HP1000 computer calculates the coordinates of image centroid and triggers relays which operate the fine-guiding telescope motors (with step unit 0.1 arcsec) in order to return the image to the center position. In general, an average of many video images is used before making a correction, which reduces by integration the guiding-camera noise, smooths out the effect of seeing, and damps the telescope response. Corrections are performed once every few seconds, which means (in our case) at least 10 corrections per spectrograph exposure. The system does not measure seeing.

3.2 Observations and data reduction

In a previous study, Connes et al. (1996) have measured apparent fluctuations in stellar velocities with ELODIE. For bright stars, these were much higher than the photon noise. This effect did not appear when a spatially stable reference beam was used instead the star. An imperfect scrambling of the stellar beam ("scrambler noise'') was obvious. Here, we attempted to quantify the geometrical time-fluctuations of the output beam of the stellar fiber. For this experiment, about 30% of the output beam was taken with a beam-splitter located within the spectrograph, and the near- and far-fields of the stellar fiber output were re-imaged on the same $381\times 286$ CCD. A sketch of the optics is shown in Fig. 2, and a typical image in Fig. 3.

  

Figure 2: Fiber-output optical section (added by ourselves) for measurement of beam geometrical fluctuations at spectrograph input (simplified diagram, not to scale). System is located on an aluminium table suspended below spectrograph, and fed through hole in granite baseplate. The Kohler double-scrambler was not yet available

  

Figure 3: Fiber-output beam cross-section from a star (193-cm telescope, 100 mm fiber). Near-field: left; far-field: right. Two windows ($140\times 140$pixels and $190\times 190$ pixels) used for computation are shown. Pixel size: 23 $\mu$m; dynamic range: 12 bits. 100 $\mu$m and f/5 indicated dimensions are reduced to fiber output. A small portion of the far-field is cut-off on the left side by a holder within the spectrograph

In order to detect unusual problems in time to correct them during the observing run, an on-line data treatment was applied. Images were reduced directly after each exposure, and also saved on a PC disk for future analysis. The program computed for each field (limited to a specific window on the CCD) the XY photocenter, the first order momentum and the intensity average within the window. The differences between these parameters and those computed from a reference image taken at the beginning of the run were displayed on-line. Fluctuations are presented in nanometers for the near-field, in microradians for the far-field; relative changes are also given. We estimate that our system could measure CG motions of about 1/1000 pixel, which means about 1 nm on the output face of the 100 $\mu$m-fiber.

Acquisition of each field pattern was synchronous with spectrograph exposures, in order to compare the different image parameters with the RV measurements.

3.3 Results

3.3.1 Fabry-Perot étalon beam

Our first experiment used the white-light source and FP étalon only. Hence, the beam falling on the fiber input was geometrically stable during a run. We took simultaneous 62 seconds exposures with the spectrograph 1kx1k-CCD detector and with our Fig. 2 $381\times 286$-CCD detector. The lost time from readout plus computation was 40 s, hence the cycle time was 100 s and the sequence took about 5 hours. Figure 4a presents the X, Y near-field photocenter shifts in nanometers versus time. The slow drift is attributed to mechanical relaxations and temperature drifts mostly within the Fig. 2 optical system, hence is uninteresting. We fit our data with a 3rd-order polynomial and find a fluctuation of 5 nm RMS, roughly explainable by photon noise. Figure 4b presents the difference between the two spurious-RV curves, obtained with FP light on both fibers, relative to a previously exposed reference spectrum and computed from a single echelle order (centered at 571 nm, and covering 6.1 nm). Such a test is of course independent of any FP drift. The slow trend shows that the two-fiber setup does not compensate fully spectrograph drift (as already shown by Connes et al. 1996). The residual may arise from a nanometer-scale relative drift between the two fibers outputs; it may also involve data treatment and non-identical sampling of the two spectra by the CCD since the absolute drift (for both fibers) was about 100 times larger (see Fig. 3 of Connes et al. 1996). The best cure should be alternate use of the same fiber for both beams. The fast residuals (0.82 m/s RMS) come mostly from photon noise, as shown by the fact that they decrease as expected when the RV from many orders are averaged.

  

Figure 4: Output beam fluctuations from FP beam. a) Near-field photocenter X and Y shifts measured by Fig. 2 set-up. b) RV measured by ELODIE

3.3.2 Stellar beam

We now have star light on fiber F2 and FP light on F1. The star $\gamma$DRA (M_v=2.2, K5III) was selected because it could be observed all night. A sequence of 130 similar 62-s exposures with 111-s cycles was recorded. Figure 5a presents near-field X and Y photocenter shifts, Fig. 5b the radial velocity (from a single order, after subtraction of 2nd order polynomial, as only fast fluctuations are of interest here), Fig. 5c the mean intensity for the same order, plus star elevation. The seeing could not be monitored continuously, but did not seem to depart greatly from the usual OHP figure of 2 to 2.5 arcsec.

Two main remarks: 1) Missing data points correspond to electronic failures of the Fig. 1 removable mirror system; they are unrelated to guiding problems. 2) Even with the guider ON, the stellar image was invariably seen to drift relative to fiber input on the video screen, which indicates poor stability of something in the guider optics. Whenever this drift seemed excessive (i.e. approaching image size), the guider was stopped for few seconds, and the guiding point recentered, again from the video image. Major peaks (marked by arrows) indicate these operations.

These irregular and irreproductible guider incidents contribute a major part of the measured RMS, both for X, Y and for the RV. Here we get 9.26 m/s; in our older tests (Connes et al. 1996), with similar seeing, we had found 6.2 m/s.

Lastly, although a large part of the intensity fluctuations arose from changes in seeing and/or transparency, some peaks are correlated with those in Fig. 5a while the reduction of intensity is minimal. Hence, guiding errors not only decrease the intensity of the stellar beam but also change the geometry of the beam in the spectrograph, and degrade the RV results. If we suppose that the 100-$\mu$m fiber reduces the star image motions by a factor 100 (as in Sect. 2), this means that these motions are about 5 $\mu$m RMS, which corresponds to 0.1 arcsec; this is the step-size of the fine-guiding telescope motors.

3.3.3 More guiding problems

Two other severe drawbacks of the 193-cm telescope autoguider for our program were also noted:

First, the autoguider does not check nor correct focusing. The size of the video image is seen to drift, and manual focus corrections produce similar RV breaks.

Second, this autoguider fails to work with alternate illumination of fiber F1 by the star- and FP-beams; operation of the Fig. 1 removable mirrors is not possible within a sequence such as those of Figs. 4 or 5. We have seen that mere use of the second fiber F2 for the reference beam leaves uncorrected errors of a few m/s.

  

Figure 5: Output beam fluctuations with star. a) Near-field photocenter X and Y shifts. b) RV measured by ELODIE and corrected of the Earth motion. c) Intensity fluctuations and star elevation

As far as a search for stellar oscillations during a given night is involved, these problems are likely to find simple solutions. For instance, no obnoxious guider drift is mentioned by Brown et al. (1994), whose RV records also cover a few hours. Our 193-cm telescope has a Pyrex-type mirror; with a ZERODUR one, short-term defocusing might become negligible. However, irrespective of any guider improvements, similar difficulties are bound to arise during a long-term planetary search. For instance, the VIDICON will soon be replaced by an intensified CCD; this will mean a RV break. So far, within any very-long-term program, stellar image centering and focusing are performed from qualitative eye-only estimates.

The AAA technique involves use of a wavelength-sliding reference spectrum, reducing the spectrograph role to the classical one of a null-checking device. It eliminates all internal spectrograph problems; even a CCD replacement at spectrograph output should become irrelevant. However, a geometrically-stable stellar beam, alternating with the reference beam, is still essential at the spectrograph input. In order to guarantee that performance over the long term (several years), a sizeable effort was clearly required to solve the guiding problem. Altogether, an autoguider making use of the fiber input itself as a null-checker of stellar-image XYZ-position appeared best, as it should solve guiding and focusing difficulties simultaneously. Such a system is now to be described.