The Hα surface brightness–radius relation: a robust statistical distance indicator for planetary nebulae

MNRAS 455, 1459–1488 (2016) doi:10.1093/mnras/stv1516 The Hα surface brightness–radius relation: a robust statistical distance indicator for planetary nebulae David J. Frew,1,2‹ Q. A. Parker1,2,3 and I. S. Bojičić1,2,3 1 Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China 2 Department of Physics and Astronomy, Macquarie University, NSW 2109, Australia 3 Australian Astronomical Observatory, PO Box 296, Epping, NSW 1710, Australia Accepted 2015 July 7. Received 2015 April 7; in original form 2014 August 18 ABSTRACT Key words: techniques: photometric – circumstellar matter – stars: distances – ISM: bubbles – H II regions – planetary nebulae: general. 1 I N T RO D U C T I O N One of the greatest difficulties still facing the study of planetary nebulae (PNe) in our own Galaxy has been the problem of determining accurate distances to them. Due to the wide range of effective temperatures and bolometric luminosities seen in their ionizing stars, they are not suitable as standard candles,1 nor can their expanding PNe be used as standard rulers. Indeed, the most reliable distances are for PNe located in external galaxies, such as M 31 and the Large and Small Magellanic Clouds (LMC and SMC; e.g. Jacoby & De Marco 2002; Reid & Parker 2006). This problem has led to the  E-mail: 1 However the well-known PN luminosity function (PNLF) works as an effective distance indicator for an ensemble of luminous PNe (see Ciardullo 2012, for a recent review). application of a range of secondary distance methods for Galactic PNe, which we will evaluate as part of this work. For reviews of the older Galactic distance scales, the reader is referred to the works of Minkowski (1965), Gurzadyan (1970), Smith (1971), and Liller (1978). The PN distance-scale problem was nicely summarized by Ciardullo et al. (1999, hereafter CB99) who stated that ‘it is unfortunately less obvious . . . how one could devise a new “grand unification” calibration that simultaneously handles both the lower surface brightness objects that prevail among the nearby nebulae and the brighter PNe that dominate samples like those in the Galactic bulge and extragalactic systems. We leave this daunting task to future workers.’ So far accurate primary distances (with uncertainties <10 per cent) are known for less than one per cent of the more than 3400 Galactic PNe that have so far been catalogued (Bojičić et al., in preparation), of which the most accurate come from trigonometric parallaxes of their central stars (CSPNe; Benedict et al. 2003,  C 2015 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society 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 SHα –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 SHα –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 SHα –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 SHα –r plane, to demonstrate its use as a diagnostic tool. Interestingly, stellar ejecta around massive stars plot on a tight locus in SHα –r space with the potential to act as a separate distance indicator for these objects. 1460 D. J. Frew, Q. A. Parker and I. S. Bojičić if appropriately calibrated. In this section we briefly review the standard statistical techniques previously used in the literature. The reader is referred to the review of Smith (2015) for a fuller discussion of the limitations and biases of each distance technique. The classical Shklovsky method was the first statistical method to be applied that had any claim to veracity. It assumed a constant ionized mass (typically 0.2 M ) for the PN shell and was first applied by Minkowski & Aller (1954) and Shklovsky (1956). Osterbrock (1960) applied this method to NGC 3587 and O’Dell (1962) used newly determined Hβ fluxes to derive an early distance scale, based on emission theory and the assumption of constant ionized mass; several calibrating nebulae were used to determine the mean ionized mass for PNe. This was followed by the work of Abell (1966), using ‘photored’ fluxes for over 90 evolved PNe, before being further developed by Cahn & Kaler (1971). This distance scale was later utilized by Kaler (1983), Shaw & Kaler (1989), and Kaler, Shaw & Kwitter (1990). Other Shklovsky scales have used the observed proper motions of the central stars, in combination with assumptions regarding their space motions (e.g. O’Dell 1962) to fix the zero-point. Cudworth (1974) undertook a statistical calibration of the PN distance scale using a large set of uniformly obtained proper motions, obtaining one of the longest scales to date. However, as these are constant-mass scales, distances to the youngest compact PNe and the largest evolved PNe were in general overestimated and underestimated, respectively. In the simplest terms, and assuming a constant ionized mass, the nebular radius (r) increases as the PN evolves, and the mean electron density (ne ) falls in sympathy. If the mean electron density can be determined from measurements of [O II] or [S II] doublet intensities, the intrinsic nebular radius can be calculated. Comparing this to the angular size of the PN leads directly to a distance via simple trigonometry. Variations on this technique, by assuming an ionized mass derived from a set of calibration objects at known distance and using the observable electron density and Hβ flux to infer a distance, have been utilized by Kingsburgh & Barlow (1992) and Kingsburgh & English (1992). A more novel method has been utilized by Meatheringham, Wood & Faulkner (1988), who found that Magellanic Cloud (MC) PNe fall on fairly tight plane in dynamical age – density – excitation (...truncated)