On the Distances of Planetary Nebulæ

Mon. Not. R. Astron. Soc. 000, 000–000 (1994) Printed 4 April 2014 On the distances of planetary nebulæ Haywood Smith, Jr Department of Astronomy, University of Florida, Gainesville, Florida U.S.A. 32611 ABSTRACT Reconsidering calibration of statistical distance scales for planetary nebulæ leads nat- urally to examining precision and especially the systematic errors of other methods. Here we present a different calibration strategy based on the 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 tested various other methods against those and each other. The statistical scales tested – Cahn et al. (1992), Zhang (1995), Frew (2008), and Stanghellini et al. (2008) – all show signs of radius dependence (i.e. distance ratio [scale/true] depends on nebular radius). Almost all have overall systematic error; Frew’s mean statistical scale seems free of that and also perhaps a scale of Zhang’s based on brightness temperature. Systematic errors were introduced by choices of data sets for calibration, by methodologies used, and by assumptions made about the nebulæ. Some spectroscopic parallaxes published by Ciardullo et al. (1999) seem consistent with the trigonometric ones where the objects overlap in nebular radius. Pottasch’s (1996) earlier spectroscopic parallaxes, on the other hand, underestimate distance consistently by a factor of two, probably because of a calibration difference. ‘Gravity’ distances seem to be overestimated by 40-50 per cent for nearby objects but may be underestimated for distant objects. Angular expansion distances appear to be suitable for calibration after correction for astrophysical effects (e.g. Mellema 2004). In particular the measurements by Hajian and collaborators using the VLA seem to yield fairly accurate distances after correction by Frew. Extinction distances appear to be often unreliable individually though sometimes approximately correct overall. 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. The ultimate goal is an accurate and internally consistent set of distances for planetaries. However, some of our tools and analysis can also be applied in distance scale comparisons utilizing parallaxes and/or distances for other objects as well. Key words: stars:distances – ISM:planetary nebulæ – methods:statistical – astrom- etry 1 INTRODUCTION estimate so obtained is fairly insensitive to the value of Mi. Later the Shklovsky method was modified and refined, 1.1 Brief history of calibration of statistical as for example with postulated universal relations between distances. Mi (no longer assumed constant; cf. Pottasch 1980; Ma- By the mid-twentieth century, when accurate distances ciel & Pottasch 1980) and R or between 5 GHz brightness could not generally be obtained for planetary nebulæ with temperature Tb (presumably unaffected by extinction, un- the usual methods (e.g. trigonometric and spectroscopic par- like Sβ ) and R (cf. Daub 1982). Yet calibration remained allax), recourse was had to methods based on uniformity difficult because of a dearth of accurate individual distance assumptions about the physical properties of the nebulæ. estimates. For a long time one had only a small collection of The hope with these ‘statistical’ methods was that the in- miscellaneous data, some of dubious quality and hardly any dividual objects’ properties do not greatly deviate from the of high precision, to use for calibration. In addition to the assumed universal value. One was the Shklovsky (1956) inaccuracies inherent in each kind there can be systematic method, based on the assumption of identical ionized mass errors differing from one kind to another or even from one Mi for all planetaries; it used recombination-line theory to data set to another for the same kind. obtain a relation between Hβ surface brightness Sβ (presum- Because of the past scarcity of high-quality data the ably distance-independent except for extinction) and radius practice in calibrating statistical scales has usually been to R to be used with the angular diameter ϕ in estimating dis- follow one of two strategies: the inclusive strategy, where one tance. Shklovsky showed mathematically that the distance simply includes all (or almost all) the various kinds of data 2 H. Smith jr in the calibration set, or the eclectic strategy, choosing only the range is expected to be greatly extended because of the the ‘best’ determinations for the calibration set. With the Gaia observatory (Perryman et al. 2001; Manteiga et al. former strategy one hopes that the various errors, random 2012), but see the remark at the end of Section 8. and systematic, will average out. In fact the result is likely a Unfortunately five of the nineteen original Hipparcos substantially larger uncertainty than the formal errors lead central star parallaxes in A98 were negative, while the re- one to expect, and there may be some residual systematic mainder were not very precise, with a median relative par- ′ ′ ′ error also. The latter strategy is likewise potentially vulner- allax error λ ≡ σπ/π of 0.66. (Here as usual π is the ′ able to systematic error; indeed, the narrower the selection is measured parallax and σπ is the estimated standard error the less likely that systematic errors will cancel out. Histor- of the parallax.) The median λ for the three obtained by ically, then, different choices of data, differences in weights Gutiérrez-Moreno et al. was almost the same, 0.69, while the given to the various data, and different calibration meth- H07 ones were much better, with median λ of 0.34, but on ods have produced a sizeable range of calibrations for these the whole still not highly precise. The HST fine guidance scales, just as one would expect when there are systematic sensors are capable of very high precision but until very errors. recently had yielded only one parallax measurement for a Broadly speaking, statistical scales divide into ‘short’ planetary. and ‘long,’ the two groups typically differing by a factor While some of the notation we use is standard – e.g. the of the order of two (cf. e.g. Phillips 2002, hereafter Ph02). use of π for parallax – much is not and likely is unfamiliar An example of the former is the scale of Cahn, Kaler, & to the reader. At the end we have added an Appendix with Stanghellini (1992, hereafter CKS); the latter is exemplified a list containing definitions and locations in the text. by Zhang’s (1995, hereafter Z95) scale. This dichotomy can actually be traced back at least as far as O’Dell (1962; here- 1.2 Accurate parallaxes and the ‘anchor’ strategy after O62) for the ‘short’ scale and Seaton (1966; hereafter for calibration. S66) for the ‘long’ one. During the past few decades more and better data have In the past several years the situation has improved consid- become available. For example, already in estimating the erably. An expanded sample (N = 16) of high-quality paral- local space density of planetaries Pottasch (1996, hereafter laxes was published by the USNO group (Harris et al. 2007, P96) made use of (among others) eight spectroscopic paral- hereafter H07). These parallaxes have a median error of laxes of companions of central stars, six distance estimates 0.42 mas and a median λ of 0.17, an improvement of a fac- from angular expansion rates, and thirty from extinction (ei- tor of two over their previous work. More recently four of ther line or continuum) as a function of distance. Ciardullo these objects were studied using HST (Benedict et al. 2009, et al. (1999, hereafter C99) used the Hubble Space Tele- hereafter B09). The precision of those measurements is even scope to search for more central star companions, consid- greater, with median error 0.23 mas and median λ = 0.08. erably augmenting the number of spectroscopic parallaxes. The results of the two studies are in generally good agree- The angular expansion method, originally applied to op- ment: The median parallax ratio H07/B09 is 1.17 and the tical images, has been extended to radio images with the mean is 1.19 ± 0.09, indicating that there might be a slight VLA (Terzian 1980, Masson 1986; cf. Terzian 1997, here- systematic difference between the two. We will discuss this after T97); the optical version has been improved with the question in the next section, arguing that there is in fact no replacement of photographic plates by CCD’s and the use significant systematic difference. of HST (e.g. Reed et al. 1999, Palen et al. 2002). A new Our concept is that accurate trigonometric parallaxes astrophysical method based on fitting central star spectral can serve as a solid foundation on which to erect an inter- line profiles to those from stellar atmosphere models and locking structure of distance determinations. It really is not matching the properties to evolutionary tracks has been de- new; of necessity that is how stellar distances came to be veloped (Méndez et al. 1988) yielding what are termed ‘grav- determined in large part, and in O62 O’Dell lamented the ity’ distances (referring to surface gravity) that can be used absence of astrometric data to fill precisely this rôle with for calibration. Lastly, new techniques have been applied planetaries. For a long time it did not seem possible to to measuring central stars’ trigonometric parallaxes, finally pursue that approach; the inclusive and eclectic strategies bringing those within reach. Parallaxes have been obtained appeared to be the only choices. We contend that space using the Hipparcos satellite (Acker et al. 1998, hereafter observatories and CCD cameras have changed that.

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