Mon. Not. R. Astron. Soc. 000, 1–?? (2002) Printed 24 November 2015 (MN LATEX style file v2.2) The Hα surface brightness – radius relation: a robust statistical distance indicator for planetary nebulae David J. Frew1,2⋆, Q.A. Parker1,2,3 and I.S. Bojiciˇ c´1,2,3 1Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China 2Department of Physics and Astronomy, Macquarie University, NSW 2109, Australia 3Australian Astronomical Observatory, P.O. Box 296, Epping, NSW 1710, Australia Accepted ; Received ; in original form ABSTRACT 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. Key words: techniques: photometric – circumstellar matter – stars: distances – ISM: bubbles –H II regions – planetary nebulae: general. arXiv:1504.01534v3 [astro-ph.SR] 22 Nov 2015 1 INTRODUCTION of Minkowski (1965), Gurzadyan (1970), Smith (1971) and Liller (1978). The PN distance-scale problem was nicely summarised by One of the greatest difficulties still facing the study of planetary Ciardullo et al. (1999, hereafter CB99) who stated that “it is un- nebulae (PNe) in our own Galaxy has been the problem of deter- fortunately less obvious . how one could devise a new ‘grand mining accurate distances to them. Due to the wide range of effec- unification’ calibration that simultaneously handles both the lower tive temperatures and bolometric luminosities seen in their ionising surface brightness objects that prevail among the nearby nebulae stars, they are not suitable as standard candles1, nor can their ex- and the brighter PNe that dominate samples like those in the Galac- panding PNe be used as standard rulers. Indeed, the most reliable tic bulge and extragalactic systems. We leave this daunting task to distances are for PNe located in external galaxies, such as M 31 and future workers.” the Large and Small Magellanic Clouds (e.g. Jacoby & De Marco 2002; Reid & Parker 2006). This problem has led to the applica- So far accurate primary distances (with uncertainties <10%) tion of a range of secondary distance methods for Galactic PNe, are known for less than one per cent of the more than 3400 Galactic which we will evaluate as part of this work. For reviews of the PNe that have so far been catalogued (Parker et al. 2015, in prepa- older Galactic distance scales, the reader is referred to the works ration), of which the most accurate come from trigonometric par- allaxes of their central stars (CSPNe; Benedict et al. 2003, 2009; Harris et al. 2007). Generally speaking, distance estimates to the ⋆ E-mail: [email protected] bulk of PNe are statistical in nature and rely on quantities which 1 However the well-known PN luminosity function (PNLF) works as an have a large observed dispersion (e.g. Cahn, Kaler & Stanghellini effective distance indicator for an ensemble of luminous PNe (see Ciardullo 1992, hereafter CKS; Stanghellini, Shaw & Villaver 2008, hereafter 2012, for a recent review). SSV). Uncertainties in the Galactic PN distance scale have been 2 D.J. Frew, Q.A. Parker and I.S. Bojiciˇ c´ significant, up to factors of three or more (e.g. Zhang 1995, here- The classical Shklovsky method was the first statistical after Z95; Van de Steene & Zijlstra 1995; CB99; Napiwotzki 2001; method to be applied that had any claim to veracity. It assumed a Phillips 2002; SSV). This uncertainty severely hampers attempts to constant ionised mass (typically 0.2 M⊙) for the PN shell and was derive meaningful physical quantities for most Galactic PNe. Al- first applied by Minkowski & Aller (1954) and Shklovsky (1956). most every quantity of interest, including nebular radii, masses, lu- Osterbrock (1960) applied this method to NGC 3587 and O’Dell minosities and dynamical ages, and the luminosities and masses of (1962) used newly-determined Hβ fluxes to derive an early distance their CSPNe, depends on accurate knowledge of their distances, as scale, based on emission theory and the assumption of constant do all statistical determinations of the PN scale height, space den- ionised mass; several calibrating nebulae were used to determine sity, and formation rate (Ishida & Weinberger 1987). the mean ionised mass for PNe. This was followed by the work of In this paper we develop and calibrate a new optical statisti- Abell (1966), using ‘photored’ fluxes for over 90 evolved PNe, be- cal distance indicator, the Hα surface brightness – radius relation fore being further developed by Cahn & Kaler (1971). This distance (SHα–r relation hereafter). Here we address the problem posed by scale was later utilised by Kaler (1983), Shaw & Kaler (1989), and CB99, and our results show that the controversy surrounding the Kaler, Shaw & Kwitter (1990). Other Shklovsky scales have used long-running PN distance scale problem has finally been put to the observed proper motions of the central stars, in combination rest. Our technique is relatively simple in its application, requir- with assumptions regarding their space motions (e.g. O’Dell 1962) ing an angular size, an integrated Hα flux, and the reddening of to fix the zero point. Cudworth (1974) undertook a statistical cal- the PN. From these quantities, an intrinsic radius is calculated, ibration of the PN distance scale using a large set of uniformly which when combined with the angular size, yields the distance obtained proper motions, obtaining one of the longest scales to directly. We have chosen Hα as the most optimum emission-line, date. However, as these are constant-mass scales, distances to the firstly as it best represents the nebular ionized mass, and secondly youngest compact PNe and the largest evolved PNe were in general because a number of narrowband Hα imaging surveys have re- overestimated and underestimated respectively. cently become available, from which large numbers of accurate In the simplest terms, and assuming a constant ionised mass, integrated fluxes, diameters, and surface brightnesses can be deter- the nebular radius (r) increases as the PN evolves, and the mean mined. These include the SuperCOSMOS H-alpha Survey (SHS; electron density (ne) falls in sympathy. If the mean electron density Parker et al. 2005; Frew et al. 2014a), the INT Photometric H- can be determined from measurements of [O II]or[S II] doublet in- Alpha Survey (IPHAS; Drew et al. 2005), the VST Photometric tensities, the intrinsic nebular radius can be calculated. Comparing H-Alpha Survey (VPHAS+; Drew et al. 2014), and the lower- this to the angular size of the PN leads directly to a distance via resolution Southern H-Alpha Sky Survey Atlas (SHASSA; Gaus- simple trigonometry. Variations on this technique, by assuming an tad et al. 2001) and Virginia-Tech Sky Survey (VTSS; Dennison, ionised mass derived from a set of calibration objects at known Simonetti & Topasna 1998). distance and using the observable electron density and Hβ flux to Our paper is arranged as follows: in §2 we review the vari- infer a distance, have been utilised by Kingsburgh & Barlow (1992) ous distance methods that have been used in the literature, while and Kingsburgh & English (1992). A more novel method has been we compile a sample of critically-assessed primary distances in §3, utilised by Meatheringham, Wood & Faulkner (1988), who found which underpins our new relation. In §4 we describe the SHα–r that Magellanic Cloud (MC) PNe fall on fairly tight plane in dy- relation in detail, and discuss the increase in accuracy obtained by namical age – density – excitation-class space. For a sample of using specialised sub-trends. We also examine the theoretical basis Galactic PNe the dynamical age was estimated from the observed for the relation in this section. We present our catalogue of SHα– electron density and excitation class, and once the expansion veloc- r distances in §5 (presented in full as an online supplement), and ity is measured, the intrinsic radius can be inferred. Comparing this in §6 we investigate the dispersion of the relation, before compar- number with the angular size leads directly to a distance. ing our final mean distance scale with previous work in §7. This An equally common approach in the literature is a variable- work refines the distance scales presented by Frew (2008; here- mass derivation of the Shklovsky method, as it is now known that after F08), and the earlier preliminary results given by Pierce et PNe have a range of ionised masses, and the standard method can al.