A multi-method approach to radial-velocity measurement for single-object spectra

Abstract

Context. The derivation of radial velocities from large numbers of spectra that typically result from survey work, requires automation. However, except for the classical cases of slowly rotating late-type spectra, existing methods of measuring Doppler shifts require fine-tuning to avoid a loss of accuracy due to the idiosyncrasies of individual spectra. The radial velocity spectrometer (RVS) on the Gaia mission, which will start operating very soon, prompted a new attempt at creating a measurement pipeline to handle a wide variety of spectral types. Aims. The present paper describes the theoretical background on which this software is based. However, apart from the assumption that only synthetic templates are used, we do not rely on any of the characteristics of this instrument, so our results should be relevant for most telescope-detector combinations. Methods. We propose an approach based on the simultaneous use of several alternative measurement methods, each having its own merits and drawbacks, and conveying the spectral information in a different way, leading to different values for the measurement. A comparison or a combination of the various results either leads to a "best estimate" or indicates to the user that the observed spectrum is problematic and should be analysed manually. Results. We selected three methods and analysed the relationships and differences between them from a unified point of view; with each method an appropriate estimator for the individual random error is chosen. We also develop a procedure for tackling the problem of template mismatch in a systematic way. Furthermore, we propose several tests for studying and comparing the performance of the various methods as a function of the atmospheric parameters of the observed objects. Finally, we describe a procedure for obtaining a knowledge-based combination of the various Doppler-shift measurements.

TheGaiamission

“…The calibrations are subsequently used to stack the noise-dominated transit spectra of faint objects and derive mission-average radial velocities through crosscorrelation techniques (Sect. 8.3;David et al 2014). For the brightest subset, epoch spectra and epoch radial velocities will be available.…”

Properties and nature of Be stars

“…To meet the requirements of the FFT algorithm (see e.g. David et al 2014), the spectra were rebinned to a smaller, constant, log λ bin size and apodised at both edges by means of a cosine-bell function. David & Verschueren (1995) showed that the combination of an even and uneven number of points correctly chosen around the CCF summit allows reducing the impact of discretisation on the measurement of its location, hence on the RV determinations.…”

A test field forGaia

“…The latter value being used to assess the bias significance using a two-tailed test (Eq. (20), David et al 2014). At the 1% significance level, it implies for what follows that an offset between two collections of measurements will be judged significant if the corresponding ∆RV/σ > 2.57.…”

“…In this way, the median sky line shift obtained for the dataset is +0.19 km s −1 with a dispersion (measured as half the interquantile range from 15.87% to 84.13%, see Eq. (19) in David et al 2014) dispersion will be used throughout the text. The scatter reflects the mean precision and stability level of the wavelength calibration over the 3 years of observation.…”

“…The correlation of observed spectra with theoretical ones is performed by computing the Pearson correlation coefficient (David et al 2014, and references therein) for different radial velocity shifts. To derive the star's RV, we have reduced the step around the top of the Pearson Correlation Function (PCF) to 1 km s −1 , then we combined the solution of 2 parabolic fits through 3 and 4 points taken on both sides of the maximum as described in David & Verschueren (1995).…”