Cross-correlation and maximum-likelihood analysis: a new approach to combining cross-correlation functions

Zucker, S.

doi:10.1046/j.1365-8711.2003.06633.x

Cited by 149 publications

(169 citation statements)

References 15 publications

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“…According to the Appendix in Zucker et al (1995), the error estimate of the component RVs derived from multi-dimension cross-correlation techniques can be obtained from a one dimensional (1D) error analysis carried out on each dimension. In this version of the program, we therefore applied a relation deduced by Zucker (2003) from the maximum-likelihood theory that provides reliable estimates of the uncertainty as long as the errors are dominated by random processes.…”

Section: Hd 93146 Amentioning

confidence: 99%

Physical properties of seven binary and higher-order multiple OB systems

Mayer

Harmanec

Chini

et al. 2017

A&A

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Analyses of multi-epoch, high-resolution (R ∼ 50000) optical spectra of seven early-type systems provided various important new insights with respect to their multiplicity. For HD 93146 A, which was hitherto assumed to be SB1, lines of a secondary component could be discerned. HD 123056 turns out to be a multiple system consisting of a high-mass component A (≈ O8.5) displaying a broad He ii 5411 Å feature with variable radial velocity, and of an inner pair B (≈ B0) with double He i lines. The binary HD 164816 was revisited and some of its system parameters were improved. In particular, we determined its systemic velocity to be −7 km s −1 , which coincides with the radial velocity of the cluster NGC 6530. This fact, together with its distance, suggests the cluster membership of HD 164816. The OB system HD 318015 (V1082 Sco) belongs to the rare class of eclipsing binaries with a supergiant primary (B0.5/0.7). Our combined orbital and light-curve analysis suggests that the secondary resembles an O9.5 III star. Our results for a limited sample corroborate the findings that many O stars are actually massive multiple systems.

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Section: Hd 93146 Amentioning

confidence: 99%

Physical properties of seven binary and higher-order multiple OB systems

Mayer

Harmanec

Chini

et al. 2017

A&A

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“…We refer to it hereafter as the standard method. Its last significant reformulation is from Zucker (2003), who derives it from a maximum likelihood argument that enables him to provide a consistent estimate for the actual random error in a given measurement. He also shows how to combine the information from different orders of a spectrum without merging them.…”

Section: Historical Backgroundmentioning

confidence: 99%

“…the orders of an echelle spectrogram, different CCDs (as in the case of Gaia) or disjoint wavelength regions (e.g. to eliminate interstellar or atmospheric spectral features); afterwards these C-functions can be averaged (Zucker 2003) or, for those of Sect. 2.3.3, summed.…”

Section: Observed Fluxmentioning

confidence: 99%

“…Therefore a method based on the ML principle is also a minimum distance method, which is a more significant name in the present context. Zucker (2003) assumes exclusively that the distribution is Gaussian and that the dispersions σ n are all equal but unknown; he determines this unknown value σ s from the data along with the other parameters. However, in Sect.…”

Section: Maximum Likelihood/minimum Distancementioning

confidence: 99%

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

David

Blomme

Frémat

et al. 2014

A&A

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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.

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“…Indeed, the cross-correlation function is calculated between the position spectrum and the derivative of the intensity spectrum. The mathematical evaluation of the cross-correlation errors has been discussed by Zucker (2003) who proposes using a likelihood estimator. This approach to estimating the errors was studied in our simulations.…”

Section: Cross-correlation Extractionmentioning

confidence: 99%

Determination of the position angle of stellar spin axes

Lesage

Wiedemann

2014

A&A

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Context. Measuring the stellar position angle provides valuable information on binary stellar formation or stellar spin axis evolution. Aims. We aim to develop a method for determining the absolute stellar position angle using spectro-astrometric analysis of high resolution long-slit spectra. The method has been designed in particular for slowly rotating stars. We investigate its applicability to existing dispersive long-slit spectrographs, identified here by their plate scale, and the size of the resulting stellar sample. Methods. The stellar rotation induces a tilt in the stellar lines whose angle depends on the stellar position angle and the orientation of the slit. We developed a rotation model to calculate and reproduce the effects of stellar rotation on unreduced high resolution stellar spectra. Then we retrieved the tilt amplitude using a spectro-astrometric extraction of the position of the photocentre of the spectrum. Finally we present two methods for analysing the position spectrum using either direct measurement of the tilt or a cross-correlation analysis.Results. For stars with large apparent diameter and using a spectrograph with a small plate scale, we show that it is possible to determine the stellar position angle directly within 10 • with a signal-to-noise ratio of the order of 6. Under less favourable conditions, i.e. larger plate scale or smaller stellar diameter, the cross-correlation method yields comparable results. Conclusions. We show that with the currently existing instruments, it is possible to determine the stellar position angle of at least 50 stars precisely, mostly K-type giants with apparent diameter down to 5 milliarcseconds. If we consider errors of around 10 • still acceptable, we may include stars with apparent diameter down to 2 mas in the sample that then comprises also some main sequence stars.

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Cross-correlation and maximum-likelihood analysis: a new approach to combining cross-correlation functions

Cited by 149 publications

References 15 publications

Physical properties of seven binary and higher-order multiple OB systems

Physical properties of seven binary and higher-order multiple OB systems

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

Determination of the position angle of stellar spin axes

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