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1We take the typical wavelength coverage of an optical spectrograph used for RV measurements.
The Doppler Method for the Detection of Exoplanets
A P Hatzes
Chapter 4
Simultaneous Wavelength Calibration
You are an eager exoplanet hunter, and you want to find exoplanets using the radial velocity (RV) method. Taking everything you have learned from the previous chapter, you design a spectrograph with enough resolution, wavelength coverage, etc. to achieve an RV precision of, say 10 m s−1. You prepare a target list of suitable stars, i.e., bright, late-type, and slowly rotating stars. You start making measurements, and after a time, you realize that the scatter of your measurements, even for stable stars, is far worse than your estimated uncertainty. What went wrong? Most likely, instrumental shifts have introduced an unwanted and large source of errors.
A CCD detector only records the intensity of light as a function of pixel location. To measure a Doppler shift, you need to know the intensity of light as a function of wavelength. Thus, you have to put a wavelength scale on your spectrum using a suitable calibration source. A good wavelength calibrator should have a high density of spectral features with measured wavelengths well spread across the spectral range of your Doppler measurements. The more features you have, the better the mapping between pixel location and wavelength will be.
But that is not the whole story. We have seen in Chapter 3 that a Doppler shift is a tiny displacement on your detector. It does not take much of a mechanical shift to mimic a shift of the spectral line. The problem is that you most likely observed the calibration source at a different time than when you made your stellar observation. Furthermore, the light from the hollow cathode lamp always goes through a different optical path than your starlight, and this might introduce a systematic error. If you are getting large uncertainties in your Doppler measurements, much higher than is predicted by photon statistics, then the likely cause is instrumental shifts.
If you want to minimize the effects of instrumental shifts on your Doppler measurement, it is essential that you observe your wavelength calibration at the same time as your stellar observation. Unless your spectrograph is extremely stable, there is a good chance that something has moved—optical elements, the detector, etc.—between the time you observed your star and the time you observed your calibrator.
In this chapter, we examine the various methods of simultaneous wavelength calibration, both historic and modern, that have been employed to minimize the effects of instrumental shifts on the RV measurement.
