4 Data reduction and analysis

The IRAF software package was used to perform the reduction and analysis. For each night's spectra, an average bias frame was constructed and subtracted from the arc, flat and object frames. Orders were traced automatically using the GP Vel frames, as the object was relatively bright and its early-type spectrum does not contain many large absorption features which could complicate the tracing process. An optimal extraction algorithm was used to extract all the spectra in order to maximise the signal-to-noise ratio.

A wavelength calibration solution was found for the whole echelle frame using the arcs. A total of 1109 lines were identified from the thorium-argon arc spectrum (about 20 per order of the echelle) and the wavelength solution was fitted using a Chebyshev polynomial of order three in the wavelength direction plus another of order four in the spatial direction. The RMS of the fit was 0.005 Å, which is less than 10% of a pixel in all orders. The FWHM of the individual arc lines near the centre of the echelle about 0.1 Å.

Figure 1: An average spectrum of GP Vel. Horizontal bars indicate the regions used in the cross-correlation procedure. Many of the sharp lines peaking downwards are weak interstellar lines; most of the upward peaking lines are remaining sky features.

At the blue end, the signal-to-noise ratio was poor and there was also a problem with overlapping orders. Consequently only 53 orders were extracted from each echelle spectrum, spanning the wavelength range 3820 Å to 5958 Å (orders 148 to 96). The spectral resolution ranged from 0.06 Å pixel^-1 at the blue end to 0.1 Å pixel^-1 at the red end. All spectra were extracted onto a common log-linearised scale with a resolution of 4.86 km s^-1 per pixel. An average spectrum is shown in Fig. 1.

The spectra of GP Vel showed essentially the same set of absorption lines as were seen by van Kerkwijk et al. (1995). In particular we saw the Balmer series from H$\beta$ to H9, He I lines at 5015 Å, 4921 Å, 4713 Å, 4471 Å, 4387 Å, 4143 Å, 4121 Å and 4026 Å, and several lines due to Si III (4553 Å, 4568 Å, 4575 Å, 4820 Å, 4829 Å), Si IV (4089 Å, 4116 Å), O II (4591 Å, 4596 Å) and N II (4601 Å).

Before proceeding with the main cross-correlation, the stability of the detection system was checked by cross-correlating the various spectra of the radial velocity standards HR 1829 and HR 3694 against each other. Across the whole run, the mean shift in these spectra was only 0.46 km s^-1, which is negligible (<0.1 of a pixel). As a further check, regions of the GP Vel spectra containing the CaII 3934 Å and NaI 5890/5896 Å interstellar lines were cross correlated against themselves. No trends were apparent in these data either.

To extract the radial velocity curve of GP Vel, template spectra of $\epsilon$ Ori were cross correlated against the spectra of the target. Since these stars have similar spectral types, systematic errors in this process should be minimised. Regions of the spectrum containing the He I lines plus the Si III and Si IV lines were used to produce the radial velocity curve in Fig. 2 (see Appendix for the individual radial velocity values, relative to $\epsilon$ Ori). The radial velocities themselves were extracted using standard IRAF routines by fitting a Gaussian to the cross-correlation function in each case. The Gaussian fits were performed using the full shape of the Gaussian curve down to one-quarter of their height. Although radial velocities were also obtained from the Balmer lines, these lines were in general very broad and so it was difficult to obtain accurate velocities. Furthermore, there was some evidence that the radial velocity amplitude increased with the order of the Balmer line. We comment on this further below, but as a result did not use Balmer lines in the rest of our analysis.

Figure 2: Radial velocity curve for He I, Si III and Si IV lines showing the fitted curve (the first fit). Each cluster of radial velocity values represents a single night's data. The fit has a reduced chi-squared of 3.84.