On the estimation of distances from trigonometric parallaxes

Smith, Howard G.; Eichhorn, Heinrich

doi:10.1093/mnras/281.1.211

Cited by 65 publications

(59 citation statements)

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“…1 1 As we are working with individual stars, we do not correct for statistical biases (Smith & Eichhorn 1996). In any case, for the stars in our sample the Smith–Eichhorn corrected parallaxes do not differ significantly from those measured. …”

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confidence: 99%

A catalogue of young runaway Hipparcos stars within 3 kpc from the Sun

Tetzlaff¹,

Neuhäuser²,

Hohle³

2010

Monthly Notices of the Royal Astronomical Society

253

277

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Traditionally, runaway stars are O‐ and B‐type stars with large peculiar velocities. We would like to extend this definition to young stars (up to ≈50 Myr) of any spectral type and to identify those present in the Hipparcos catalogue by applying different selection criteria, such as peculiar space velocities or peculiar one‐dimensional velocities. Runaway stars are important for studying the evolution of multiple star systems or star clusters, as well as for identifying the origins of neutron stars. We compile the distances, proper motions, spectral types, luminosity classes, V magnitudes and B−V colours, and we utilize evolutionary models from different authors to obtain star ages. We study a sample of 7663 young Hipparcos stars within 3 kpc from the Sun. The radial velocities are obtained from the literature. We investigate the distributions of the peculiar spatial velocity and the peculiar radial velocity as well as the peculiar tangential velocity and its one‐dimensional components and we obtain runaway star probabilities for each star in the sample. In addition, we look for stars that are situated outside any OB association or OB cluster and the Galactic plane as well as stars for which the velocity vector points away from the median velocity vector of neighbouring stars or the surrounding local OB association/cluster (although the absolute velocity might be small). We find a total of 2547 runaway star candidates (with a contamination of normal Population I stars of 20 per cent at most). Thus, after subtracting these 20 per cent, the runaway frequency among young stars is about 27 per cent. We compile a catalogue of runaway stars, which is available via VizieR.

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confidence: 99%

A catalogue of young runaway Hipparcos stars within 3 kpc from the Sun

Tetzlaff¹,

Neuhäuser²,

Hohle³

2010

Monthly Notices of the Royal Astronomical Society

253

277

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“…However, in practice only the measured parallax Π′ is available together with the corresponding estimated distance r ′= 1/Π′ and the derived absolute magnitude . Obtaining true distance and true absolute magnitude from a measured trigonometric parallax is not a straightforward task (Smith & Eichhorn 1996; Kovalevsky 1998b; Arenou & Luri 1999) because of the non‐linear relation. Whereas this obstacle cannot generally be avoided, its effect can be limited if data with small relative errors are considered.…”

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confidence: 99%

Statistical biases in stellar astronomy: the Malmquist bias revisited

Butkevich

Berdyugin²,

Teerikorpi³

2005

Monthly Notices of the Royal Astronomical Society

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A unified analytical treatment of the Malmquist bias is presented. Depending on the data under consideration and on the way the mean values of absolute magnitude are calculated, three different types of Malmquist bias appear: integral bias, and magnitude‐ and distance‐dependent ones. An analytical consideration of the distance‐dependent bias, previously studied in extragalactic astronomy, is given in terms of the trigonometric parallax. In a quantitative treatment of the Spaenhauer diagram, in which the derived absolute magnitude is plotted versus the true parallax, we developed an easy‐to‐use method for determination of the region unaffected by the bias (‘unbiased plateau’). Considering spectroscopic distance indicators, we point out that for any magnitude‐limited sample spectroscopic distance and parallax approach constant limits as the true distance increases. We draw some examples from luminosity calibrations of stellar classes. A brief outline is also given of a tentative course of investigations, anticipating future space astrometry missions.

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“…For the record, the transformation method developed by Smith & Eichhorn (1996) and improved by Smith (2001) gives essentially the same bias with λ‐truncation as the direct method. The reason is that for small values of λ the transformation has virtually no effect; it only becomes important when the error is comparable to, or somewhat greater than, the true parallax π.…”

Section: Truncation By Both λ and M With The Direct Methods And Varimentioning

confidence: 95%

Beware -truncation! Sample truncation and bias in luminosity calibration using trigonometric parallaxes

Smith

2006

Monthly Notices of the Royal Astronomical Society

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The common practice in luminosity calibration of sample truncation according to relative parallax error λ can lead to bias with indirect methods such as reduced parallaxes as well as with direct methods. This bias is not cancelled by the Lutz–Kelker corrections and in fact can be either negative or positive. Making the selection stricter can actually lead to a larger absolute amount of bias and lower accuracy in certain cases. The degree to which this bias is present depends upon whether the sample is more nearly specified by the relative parallax error or by the limiting apparent magnitude when both limits formally apply; when the latter limit dominates it is absent. The difference between the means for the two extreme cases is what is customarily termed the Malmquist bias. However, it is not truly bias, but rather what we call here an offset. For a sample to be effectively magnitude‐limited, there is a lower bound imposed on the mean absolute magnitude which depends on the limiting magnitude. If a wide‐ranging luminosity relation such as the Wilson–Bappu relation is to be calibrated, some portion of the relation may be magnitude‐limited and the rest not. In that case there will be offsets between the different parts of the relation, including the transition region between the two extremes, as well as bias outside the magnitude‐limited part. Another, less common, practice is truncation according to weight, specifically with the reduced parallax method. Such truncation can also bias the calibration with one variant of the method. Indeed, the weighting scheme used with that variant introduces bias even without truncation. For calibration it is probably best to use a general maximum likelihood method such as the grid method with a magnitude‐limited sample and no limit on relative parallax error. The Malmquist shift could then be applied to obtain an estimate of the volume‐limited mean.

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On the estimation of distances from trigonometric parallaxes

Cited by 65 publications

References 0 publications

A catalogue of young runaway Hipparcos stars within 3 kpc from the Sun

A catalogue of young runaway Hipparcos stars within 3 kpc from the Sun

Statistical biases in stellar astronomy: the Malmquist bias revisited

Beware -truncation! Sample truncation and bias in luminosity calibration using trigonometric parallaxes

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