Calibration of the Wilson-Bappu Effect Using Trigonometric Parallaxes

Lutz, T. E.; Kelker, Douglas

doi:10.1086/129822

Cited by 18 publications

(12 citation statements)

References 8 publications

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“…bocki et al (2000). made to calibrate the WBR based on ground-based trigonometric parallaxes (Wilson 1959;Hodge & Wallerstein 1966;Lutz & Kelker 1975;Gle . bocki & Stawikowski 1978).…”

Section: Comparison With Other Resultsmentioning

confidence: 99%

The Wilson–Bappu effect: A tool to determine stellar distances

Pace

Pasquini

Ortolani

2003

A&A

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Abstract. Wilson & Bappu (1957) have shown the existence of a remarkable correlation between the width of the emission in the core of the K line of CaII and the absolute visual magnitude of late-type stars. Here we present a new calibration of the Wilson-Bappu effect based on a sample of 119 nearby stars. We use, for the first time, width measurements based on high resolution and high signal to noise ratio CCD spectra and absolute visual magnitudes from the Hipparcos database. Our primary goal is to investigate the possibility of using the Wilson-Bappu effect to determine accurate distances to single stars and groups. The result of our calibration fitting of the Wilson-Bappu relationship is M V = 33.2−18.0 log W 0 , and the determination seems free of systematic effects. The root mean square error of the fitting is 0.6 mag. This error is mostly accounted for by measurement errors and intrinsic variability of W 0 , but in addition a possible dependence on the metallicity is found, which becomes clearly noticeable for metallicities below [Fe/H] ∼ −0.4. This detection is possible because in our sample [Fe/H] ranges from −1.5 to 0.4. The Wilson-Bappu effect can be used confidently for all metallicities not lower than ∼−0.4, including the LMC. While it does not provide accurate distances to single stars, it is a useful tool to determine accurate distances to clusters and aggregates, where a sufficient number of stars can be observed. We apply the Wilson-Bappu effect to published data of the open cluster M 67; the retrieved distance modulus is of 9.65 mag, in very good agreement with the best distance estimations for this cluster, based on main sequence fitting.

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“…bocki et al (2000). made to calibrate the WBR based on ground-based trigonometric parallaxes (Wilson 1959;Hodge & Wallerstein 1966;Lutz & Kelker 1975;Gle . bocki & Stawikowski 1978).…”

Section: Comparison With Other Resultsmentioning

confidence: 99%

The Wilson–Bappu effect: A tool to determine stellar distances

Pace

Pasquini

Ortolani

2003

A&A

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“…The formula is independent of cutoff distance. Lutz and Kelker (1973, 1974, 1975 observed that, when a distance limited sample has been used for calibration, the Trumpler-Weaver bias will generate a systematic error in the luminosity distances of individual stars, and calculated the appropriate correction to magnitude (note that Binney and Merrifield 1998 do not correctly describe the bias discussed by Lutz & Kelker. See also Haywood Smith 2003).…”

Section: Trumpler-weaver Biasmentioning

confidence: 99%

Calibration of RAVE distances to a large sample of Hipparcos stars

Francis

2013

Monthly Notices of the Royal Astronomical Society

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A magnitude limited population of 18 808 Hipparcos stars is used to calibrate distances for 52 794 RAVE stars, including dwarfs, giants, and pre-main sequence stars. I give treatments for a number of types of bias affecting calculation, including bias from the non-linear relationship between the quantity of interest (e.g., distance or distance modulus) and the measured quantity (parallax or visual magnitude), the Lutz-Kelker bias, and bias due to variation in density of the stellar population. The use of a magnitude bound minimises the Malmquist and the Lutz-Kelker bias, and avoids a measurement bias resulting from the greater accuracy of Hipparcos parallaxes for brighter stars. The calibration is applicable to stars in 2MASS when there is some way to determine stellar class with reasonable confidence. For RAVE this is possible for hot dwarfs and using log g. The accuracy of the calibration is tested against Hipparcos stars with better than 2% parallax errors, and by comparison of the RAVE velocity distribution with that of Hipparcos, and is found to improve upon previous estimates of luminosity distance. An estimate of the LSR from RAVE data, (U 0 , V 0 , W 0 ) = (14.9 ± 1.7, 15.3 ± 0.4, 6.9 ± 0.1) km s −1 , shows excellent agreement with the current best estimate from XHIP. The RAVE velocity distribution confirms the alignment of stellar motions with spiral structure.

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“…(They were referring to the Wilson–Bappu effect, which relates absolute magnitude to the equivalent width of a reversal in the cores of the H and K lines of late‐type stars.) In that later paper (Lutz & Kelker 1975) they calibrated the relation using individual absolute magnitudes to which the Lutz–Kelker corrections had been applied, as indeed one would have expected. (Actually they used two methods to find the Wilson–Bappu relation, one of which involved grouping.…”

Section: The Original Lutz–kelker Papermentioning

confidence: 89%

Is there really a Lutz--Kelker bias? Reconsidering calibration with trigonometric parallaxes

Smith

2003

Monthly Notices of the Royal Astronomical Society

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In the recent literature there are indications of some confusion regarding the Lutz-Kelker bias: whether or not it exists, and if so, what it is and when it should be corrected. Here we carefully reexamine Lutz & Kelker's original work to understand what they actually did, and then look at their later papers and some other works on the subject. There is, properly speaking, no universal Lutz-Kelker bias of individual parallaxes. There is a bias for stars that are members of samples which is different from, but often has the same form as and is given the name of, the Lutz-Kelker bias. The overall bias for samples selected according to relative parallax error is sometimes given the name of Lutz-Kelker; in fact it is, or is very nearly the same as, that discussed by Trumpler and Weaver. The Lutz-Kelker corrections can, under certain conditions, be used to counter that bias. The Lutz-Kelker correction applied for an isolated star (independent of sample properties) is an incomplete refinement of the estimate of absolute magnitude calculated directly from the parallax, not a correction for bias.We reconsider the more general problem of calibration using only trigonometric parallaxes, and examine some of the maximum likelihood methods proposed for its solution. Of these, several are based on linear approximation and are therefore of limited validity. Three exact methods are all based on essentially the same form of the likelihood but are implemented in different ways. One of these is statistically flawed, as was originally pointed out by Jung. We test the other two using synthetic samples, compare their performance, and discuss their application. We also apply one (grid method) to the Feast-Catchpole high weight sample of Hipparcos Cepheid parallaxes as a test. The grid method is to be preferred over the approximate ones because it does not have a limited range of validity, should not require any a posteriori correction, and provides a more complete picture of the uncertainties, in the form of a contour diagram of log(likelihood).

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Calibration of the Wilson-Bappu Effect Using Trigonometric Parallaxes

Cited by 18 publications

References 8 publications

The Wilson–Bappu effect: A tool to determine stellar distances

The Wilson–Bappu effect: A tool to determine stellar distances

Calibration of RAVE distances to a large sample of Hipparcos stars

Is there really a Lutz--Kelker bias? Reconsidering calibration with trigonometric parallaxes

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