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

Smith, Howard G.

doi:10.1046/j.1365-8711.2003.06167.x

Cited by 48 publications

(49 citation statements)

References 20 publications

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“…Finally, we also adopt the distance to the young, compact nebula K 3-35 , determined using VLBI Exploration of Radio Astrometry (VERA) array observations of a bright water maser in the nebula 2 . Note that the trigonometric method is susceptible to the socalled Lutz-Kelker (L-K) bias (Lutz & Kelker 1973;Smith 2003Smith , 2006Francis 2014) which causes measured parallaxes to be systematically greater than their actual values in a statistical sense, and is broadly related to the Trumpler-Weaver bias (Trumpler & Weaver 1953). As emphasised by van Leeuwen (2007) and Francis (2014), the L-K bias is a sample statistical correction, and has not been applied to individual distances.…”

Section: Trigonometric Distancesmentioning

confidence: 99%

The H surface brightness-radius relation: a robust statistical distance indicator for planetary nebulae

Frew¹,

Parker²,

Bojičić³

2015

Monthly Notices of the Royal Astronomical Society

172

127

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Measuring the distances to Galactic planetary nebulae (PNe) has been an intractable problem for many decades. We have now established a robust optical statistical distance indicator, the Hα surface brightness -radius or S Hα -r relation, which addresses this problem. We developed this relation from a critically evaluated sample of primary calibrating PNe. The robust nature of the method results from our revised calibrating distances with significantly reduced systematic uncertainties, and the recent availability of high-quality data, including updated nebular diameters and integrated Hα fluxes. The S Hα -r technique is simple in its application, requiring only an angular size, an integrated Hα flux, and the reddening to the PN. From these quantities, an intrinsic radius is calculated, which when combined with the angular size, yields the distance directly. Furthermore, we have found that optically thick PNe tend to populate the upper bound of the trend, while optically-thin PNe fall along the lower boundary in the S Hα -r plane. This enables sub-trends to be developed which offer even better precision in the determination of distances, as good as 18 per cent in the case of optically-thin, high-excitation PNe. This is significantly better than any previous statistical indicator. We use this technique to create a catalogue of statistical distances for over 1100 Galactic PNe, the largest such compilation in the literature to date. Finally, in an appendix, we investigate both a set of transitional PNe and a range of PN mimics in the S Hα -r plane, to demonstrate its use as a diagnostic tool. Interestingly, stellar ejecta around massive stars plot on a tight locus in S Hα -r space with the potential to act as a separate distance indicator for these objects.

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Section: Trigonometric Distancesmentioning

confidence: 99%

The H surface brightness-radius relation: a robust statistical distance indicator for planetary nebulae

Frew¹,

Parker²,

Bojičić³

2015

Monthly Notices of the Royal Astronomical Society

172

127

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“…However, rejection of such objects (or, in general, objects for which σ π /π is above some threshold) from the sample leads to a statistical bias, as it removes the stars from one wing of the error distribution only. See Smith (2003) for a thorough discussion of the bias and possible corrective procedures. We decided to use parallax values directly, without performing the inversion, and to keep stars with negative parallaxes in the sample.…”

Section: Parallaxesmentioning

confidence: 99%

The interstellar Ca II distance scale

Megier

Strobel

Галазутдинов

et al. 2009

A&A

100

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Aims. We attempt to extend the relation between the strengths of the interstellar Ca ii lines and the distances to early-type stars to objects beyond 1 kiloparsec, with the line saturation taken into account.Methods. We measure the Ca ii K and Ca ii H equivalent widths, and compute Ca ii column densities for 262 lines of sight towards early-type stars with available Hipparcos parallaxes (π). The targets are located within a few hundred parsecs of the Galactic plane, and span all the range of Galactic longitudes. We fit the N Ca ii -parallax relation with a function of the form π = 1/(a · N Ca ii + b), using a maximum-likelihood approach to take account of errors in both variables. We use the resultant formula to estimate distances to stars in OB associations and clusters, and compare them to those found in the literature, usually estimated by spectrophotometric methods. 1.3, we obtain the following approximate formula for the distance: D Ca ii = 77 + (2.78 + Results. For lines of sight with EW(K)/EW(H) > EW(K) EW(H) −0.932 )EW(H), where the equivalent widths EW(K) and EW(H) are in mÅ, and the distance D Ca ii in parsecs.The errors in D Ca ii , resulting from the uncertainty in the fit parameters and errors in the equivalent widths, are typically about 15% of the distance. We can also expect the equation not to hold for objects situated farther than a few hundred parsecs from the Galactic plane. We find several cases of significant column density differences between association or cluster members, especially notable in the Trumpler 16 cluster, indicating either a local contribution to the Ca ii column density, or background/foreground stars being confused with members. The ratio D Ca ii /D assoc appears to depend on the Galactic longitude, being highest in the range 70 • < l < 120 • and lowest for 200 • < l < 300 • . This effect may be due to large-scale structure being present in the Ca ii layer, or to the nonmember confusion being enhanced in these directions.

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“…Individual values of log R are of interest in connection with both any possible radius dependence of distance ratios and their relation to log T b or log S. Estimates of log R based on parallaxes are affected by transformation bias (through the log function acting on distance d ′ ) together with a double truncation bias, a combination sometimes mistakenly thought of as universal for absolute magnitudes M : Lutz-Kelker bias (Lutz & Kelker 1973). As the author pointed out (Smith 2003) the effect of the combination is not intrinsic and universal as originally claimed but rather depends on the characteristics of the particular sample; this fact is clearly demonstrated by figs. 3 and 4 of that paper.…”

Section: Some General Considerationsmentioning

confidence: 99%

On the distances of planetary nebulae

Smith

2015

Monthly Notices of the Royal Astronomical Society

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Past calibrations of statistical distance scales for planetary nebulae have been problematic, especially with regard to 'short' vs. 'long' scales. Reconsidering the calibration process naturally involves examining the precision and especially the systematic errors of various distance methods. Here we present a different calibration strategy, new for planetaries, that is anchored by precise trigonometric parallaxes for sixteen central stars published by Harris et al. (2007) of USNO, with four improved by Benedict et al. using the Hubble Space Telescope. We show how an internally consistent system of distances might be constructed by testing other methods against those and each other. In such a way systematic errors can be minimized.Several of the older statistical scales have systematic errors that can account for the short-long dichotomy. In addition to scale-factor errors all show signs of radius dependence, i.e. the distance ratio [scale/true] is some function of nebular radius. These systematic errors were introduced by choices of data sets for calibration, by the methodologies used, and by assumptions made about nebular evolution. The statistical scale of Frew and collaborators (2008, 2014) is largely free of these errors, although there may be a radius dependence for the largest objects. One set of spectroscopic parallaxes was found to be consistent with the trigonometric ones while another set underestimates distance consistently by a factor of two, probably because of a calibration difference. 'Gravity' distances seem to be overestimated for nearby objects but may be underestimated for distant objects, i.e. distance-dependent. Angular expansion distances appear to be suitable for calibration after correction for astrophysical effects (e.g. Mellema 2004). We find extinction distances to be often unreliable individually though sometimes approximately correct overall (total sample).Comparison of the Hipparcos parallaxes (van Leeuwen 2007) for large planetaries with our 'best estimate' distances confirms that those parallaxes are overestimated by a factor 2.5, as suggested by Harris et al.'s result for PHL 932. There may be negative implications for Gaia parallaxes for these objects. We suggest a possible connection with the much smaller overestimation recently shown for the Hipparcos Pleiades parallaxes by Melis et al. (2014).

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

Cited by 48 publications

References 20 publications

The H surface brightness-radius relation: a robust statistical distance indicator for planetary nebulae

The H surface brightness-radius relation: a robust statistical distance indicator for planetary nebulae

The interstellar Ca II distance scale

On the distances of planetary nebulae

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