The distances of highly evolved planetary nebulae

Transcription

1 Mon. Not. R. Astron. Soc. 357, (2005) doi: /j x The distances of highly evolved planetary nebulae J. P. Phillips Instituto de Astronomía y Meteorología, Av. Vallarta No. 2602, Col. Arcos Vallarta, C.P Guadalajara, Jalisco, Mexico Accepted 2004 November 24. Received 2004 November 24; in original form 2004 June 15 1 INTRODUCTION The distances of planetary nebulae (PNe) are very poorly known. More or less direct estimates have been evaluated using trigonometric parallax (e.g. Harris et al. 1997; Acker et al. 1998; Gutierrez- Moreno et al. 1999), kinematic parallax (e.g. Liller & Liller 1968; Hajian, Terzian & Bignell 1993; Hajian & Terzian 1996; Reed et al. 1999), radial velocities (Acker 1978; Phillips 2001a), spectroscopic parallax (Méndez & Niemela 1981; Ciardullo et al. 1999), trends in nebular extinction (e.g. Kaler & Lutz 1983; Gathier, Pottasch & Pel 1986; Martin 1994), values of Na D line absorption (Napiwotzki & Schönberner 1995), and determinations of central star gravity (e.g. Napiwotzki 2001; Méndez et al. 1988b; Méndez, Kudritzki & Herrero 1992). These procedures have been applied to only very limited numbers of PNe, however, and are subject to uncertainties of order σ (D) 0.3D. A larger number of distances have been evaluated using so-called statistical procedures, although the uncertainties in these values are even larger. They are also, in certain cases, dependent upon the assumed physical characteristics of the outflows. The earliest of these methods proposed that the ionized masses of the PNe were constant (Minkowski & Aller 1954). This is now known to be incorrect (Pottasch 1980; Maciel & Pottasch 1980), however, and is in conflict with much recent modelling of shell expansion (e.g. Okorokov et al. 1985; Schmidt-Voigt & Köppen 1987; Mellema 1994; Marigo et al. 2001). Other procedures have assumed that the absolute magnitudes of compact PNe are constant (Vorontsov-Veljaminov 1950; Aller 1965; Acker 1978). However, whilst most younger and higher jpp@cencar.udg.mx ABSTRACT The central stars of highly evolved planetary nebulae (PNe) are expected to have closely similar absolute visual magnitudes M V. This enables us to determine approximate distances to these sources where one knows their central star visual magnitudes, and levels of extinction. We find that such an analysis implies values of D which are similar to those determined by Phillips; Cahn, Kaler & Stanghellin; Acker, and Daub. However, our distances are very much smaller than those of Zhang; Bensby & Lundstrom, and van de Steene & Zijlstra. The reasons for these differences are discussed, and can be traced to errors in the assumed relation between brightness temperature and radius. Finally, we determine that the binary companions of such stars can be no brighter than M V 6 mag, implying a spectral type of K0 or later in the case of main-sequence stars. Keywords: ISM: jets and outflows planetary nebulae: general. surface brightness PNe are likely to be optically thick, it is unlikely that their central star (and nebular) luminosities are similar. Other, more recent analyses, have explored trends of brightness temperature T B (5 GHz) with radius R, and of ionized mass M I with θ 2 /S (5 GHz) [where θ is the angular diameter and S(5 GHz) is the observed flux; see e.g. Daub 1982; Cahn et al. 1992; Zhang 1995; Bensby & Lundstrom 2001; Phillips 2002]. Both these procedures can be shown to be equivalent. However, Ciardullo et al. (1999) have noted that most such distances appear to be in conflict with trigonometric estimates. The procedures also appear to yield markedly differing mean distances, even when compared to each other. Phillips (2004a) has recently addressed these inconsistencies in discussing a new distance calibration based upon 5-GHz luminosities. He finds that most of the problem is likely to reside in a nonlinearity between T B and R. Itfollows that whilst the scales of Bensby & Lundstrom (2001) and Zhang (1995) appear to be applicable for higher brightness temperature PNe [i.e. those having log(t B ) > 0.5], they are extremely poor when it comes to calculating the distances of lower T B outflows. By contrast, the procedure of Phillips (2002) appears to lead to excellent results where log(t B ) < 0.5, but is inadequate for larger values of this parameter. We shall note, in the following, a further way in which the distances of lower brightness temperature PNe may be determined. It will be pointed out that the absolute magnitudes of highly evolved central stars are expected to be closely similar. This prediction is confirmed through an analysis of PNe at known distance. It follows that distances may be determined where certain central star properties (visual magnitude, extinction) are known, and shells have low brightness temperatures. We have used this procedure to calculate distances to a broader range of evolved shells, and have compared the results with those C 2005 RAS

2 620 J. P. Phillips of other statistical scales. It is found that whilst the distances of Acker (1978), Daub (1982), Cahn et al. (1992) and Phillips (2002, 2004) are in accord with our results, those of Zhang (1995), van de Steene & Zijlstra (1995) and Bensby & Lundstrom (2001) differ appreciably. Finally, we shall note that such an analysis permits us to place constraints upon the likely spectral types of binary companions. M V COMPARISON BETWEEN OBSERVED AND THEORETICAL ABSOLUTE VISUAL MAGNITUDES IN HIGHLY EVOLVED PNe M M 2 THE EVOLUTIONARY CHARACTERISTICS OF PNe CENTRAL STARS There is now a general acceptance that most PNe central stars follow H-burning tracks within the Hertzsprung Russell (HR) plane (see, for instance, Henry & Shipman 1986; Schönberner 1989). After an initial evolution to higher temperatures, during which their luminosities are more-or-less constant, a point is reached at which H- burning declines, and temperatures and luminosities decrease, leading to a terminal phase of evolution dominated by gravothermal heating (Schönberner 1979, 1981, 1983; Blöcker & Schönberner 1990; Vassiliadis & Wood 1993, 1994). A recent analysis of such tracks within the T B R plane suggests that this occurs where log(t B ) < 0.5, and where envelopes are optically thin to Lyman continuum radiation (Phillips 2004a). It follows that shell brightness temperatures would be expected to decline very rapidly indeed, as approximately T B R 5. This latter phase of evolution is particularly interesting in the context of the present discussion, because evolutionary tracks are likely to be closely similar within the HR plane. Where 0.6 < M CS / M < 0.7 (a regime which is likely to include a large fraction of PNe; see e.g. the discussion of central star mass functions in Phillips 2001b), then the tracks are displaced from one another by only very small amounts. The range in stellar effective temperatures is only of order log(t EFF ) dex, for instance, depending upon the metallicity of the progenitor stars, and given any particular evolutionary period t EV. This similarity between evolutionary trajectories has various consequences for the observed properties of the stars. In particular, it can be shown that their absolute magnitudes should be restricted to avery narrow range of values (Schönberner 1981; Napiwotzki & Schönberner 1995). We have, in studying these trends, somewhat modified the procedures of Schönberner (1981) and Napiwotzki & Schönberner (1995), wherein the tracks of Schönberner (1983) and Blöcker (1995) were used to evaluate M V (t EV ). This analysis was open to several uncertainties, not least in the assumption that velocities of expansion are constant that is, that the sizes of the ionized regimes increase at a constant rate. This is unlikely to be the case during optically thick phases of expansion, and may not even be true during later optically thin expansion (see e.g. the evolutionary modelling cited in Section 1, and the discussion of Phillips 2000a). Marigo et al. (2001) have recently undertaken an extremely detailed analysis of PNe shell evolution. This includes synthetic modelling of asymptotic giant branch (AGB) stars and winds, and takes account of the differences in shell mass, and the evolution in central star ionizing fluxes. All of these aspects, together with an interacting winds hydrodynamic code, permit them to plot the evolution of a wide range of parameters as a function of t ev. Phillips (2004a) has recently used these results (including their treatment of ionization front velocities) to evaluate the variation of T B (5 GHZ) as a function of R. The results appear to be closely consistent with observations. We have therefore used the functions NGC A M -1.5 A35-2 PHL LoTr 5 LOG(T B (5 GHz)) M Figure 1. A comparison between absolute visual magnitudes M V, and 5-GHz brightness temperatures T B (5 GHz) for highly evolved PNe. The curves represent the trends to be expected for various central star masses M CS, and under the assumption that the luminosities of the stars are dominated by gravothermal heating. The solid discs correspond to the values determined for various low brightness temperature nebulae. It will be noted that there is a close correspondence between the observed and theoretical trends. The open circles represent sources which have binary central stars, or are otherwise anomalous. The open squares correspond to PG 1159-type stars. for T B (t EV )ofphillips (2004a), and those of M V (t EV )owing to Napiwotzki & Schönberner (1995), to yield trends of M V with T B for various central star masses. The results are illustrated in Fig. 1 for 4.0 < log(t B ) < 0.5. It will be noted that the tracks are again very closely similar where < M CS /M < Note that as T B is closely correlated with R (e.g. Phillips 2004a), our limits upon T B also imply that log(r/pc) > 0.8. Not all sources having log(r/pc) > 0.8 also possess log(t B ) < 0.5, however, and there are an appreciable number of sources having both larger radii R, and log(t B ) > 0.5. Some of these, at least, are likely to be of low mass (M CS < 0.6 M ), and to be less evolved (see below). Although He-burning evolutionary tracks differ from those of H-burning stars, the final values of M V are expected to be closely comparable. Such stars are therefore expected to have a distribution similar to those of the curves illustrated in Fig. 1. By contrast, higher mass stars would be expected to possess larger values of M V,of order 6.5 < M V < 8. Given the steep gradients in central star mass functions (Phillips 2001b), however, the proportion of such sources is expected to below. Lower mass stars tend to evolve very much more slowly. By the time that they approach the white dwarf (WD) sequence their shells are likely to have very low values of T B pushing them off the right-hand side of Fig. 1, and beyond the point at which they can sensibly be detected. It is also possible that certain lower mass PNe possess low T B,but also have high central star luminosities L CS sources in which the shells are highly evolved, but for which the central star is still descending towards the WD sequence. These do not appear to be detected in the present nebular sample. An analysis such as this comes with various advantages. It enables us to make a comparison between observed parameters, rather than evaluating dubiously determined expansion periods. It also permits us to identify a specific class of highly evolved source on the basis of shell brightness temperatures alone

3 It follows that where 3 < log(t B ) < 0.5, a range which includes most of the standard sources of Phillips (2002), then central stars should possess absolute visual magnitudes in the range 6.2 M V 7.2. This latter result is open to several uncertainties. The expansion characteristics of nebular shells are far from well established, for instance. Although the properties deduced by Marigo et al. (2001) appear consistent observed trends between T B and R (see the discussion above), such an analysis is still open to considerable uncertainties. It is unclear at what stage the shells become optically thin, for instance, and how this might vary with M CS. Similarly, it remains unclear how the kinematics of the shells vary between phases of optically thick and thin expansion, as well as as a function of central star mass. Finally, the so-called transition periods t TR, which determine the zero points of the evolutionary tracks, appear to be essentially unknown (although see also the further comments of Marigo et al. 2001). Most of these uncertainties are likely to have only a minor effect upon our present analysis, however. Errors in predicted ionization front velocities V I (t EV )would likely cause a horizontal shift in the placement of our curves (i.e. along the T B axis in Fig. 1). Similar consequences are likely to occur as a result of uncertainties in t TR. Neither of these factors are therefore likely to be critical in biasing our estimates of M V. It is therefore clear that most evolved PNe are expected to be associated with closely similar values of M V, and that this may act as a useful tool in constraining the distances to these sources. It is important first, however, to establish just how reliable this analysis might be. How similar are these trends to those of sources at known distance? 3 THE OBSERVATIONAL DATA BASE Various procedures have been employed to determine the distances to galactic PNe, including trigonometric parallax, expansion distances and a raft of other methods summarized in Section 1. Of these values, the most reliable and consistent appear to be those for sources within 1 kpc of the Sun, and we shall heretofore confine our analysis to these local outflows alone. We have also, following the discussion in Section 2, restricted our analysis to sources having log(t B ) < 0.5. Most (if not all) of these appear to be optically thin, and are likely to be evolving along gravothermal evolutionary tracks. They should therefore have absolute magnitudes comparable to the trends noted in Fig. 1. Any departures from these assumptions will likely result in strong variations in M V, and marked disparities between observation and theory. Although we have preferred to use the standard source distances of Phillips (2002), these have been carefully filtered and modified so as to yield the most realistic estimates of M V. Thus, the trigonometric results of Pottasch & Acker (1998) have been deleted, as these depend upon highly uncertain Hipparchos measurements. The distances have less than a 2σ level of significance. A further worry concerns the fact that most (60 per cent) of our distances depend upon measures of central star gravity. This is problematic for several reasons. Not only does our analysis appear to be unhealthily dependent upon this single distance method, but these distances are also sensitive to various modelling uncertainties. This can cause inconsistencies between independent estimates of D. Thus, the gravitational distances of Méndez et al. (1988b) are 20 per cent greater than those of Méndez et al. (1992). Similarly, it appears that the distances of Napiwotzki (2001) are =23 per cent greater than those The distances of PNe 621 quoted by Pottasch (1996) (a difference which rises to 27 per cent where only lower T B, highly evolved outflows are considered). These differences in scale arise from a variety of causes. The Méndez et al. (1992) results take account of the spherical extension of the central stars, and the effects of stellar winds, for instance; features which were not included in their earlier analysis. The effects of ion-dynamical effects upon Stark broadening of the Balmer lines was investigated by Napiwotzki & Rauch (1994), although the authors concluded that this has only a modest effect upon estimates of g.a more serious bias may arise from the contribution of metals to atmospheric opacity (Werner 1996). Finally, such evaluations of g depend upon the quality of the spectra, their resolution and signal-to-noise (S/N) ratios. Where any of these factors are deficient, as was the case in several earlier analyses, then this may lead to appreciable biases in the evaluation of distance. We have preferred, in the following, to use the more recent results of Napiwotzki (2001). These appear to be closely consistent with trigonometric measures, and correspond to detailed non-local thermodynamic equilibrium (non-lte) spectral modelling. We have also used the values of Traulsen et al. (2005) for the sources NGC 1360 and A36. This leaves just seven nebulae (RX J2117, PG , Jn 1, IW 2, Sh 2 176, VV 47 and WDHS1) for which more recent distances appear to be unavailable, and for which we have used the values quoted by Pottasch (1996). Five of these outflows represent PG 1159-type sources (see below). Given the likely bias in the Pottasch distances (see our comments above), it is likely that their absolute magnitudes will be too high. It is apparent that various of the central stars are members of close binary systems. The apparent luminosities of these systems will therefore be greater than those of the central stars alone, and will lead to departures from predicted luminosities. Similarly, it appears that certain field stars may have been misidentified as PNe central stars, whilst PHL 932 appears to be associated with a nonpost-agb-type star (Méndez et al. 1988a). All of these sources have been deleted from our present analysis. Finally, a large subset of our sources appear to contain PG type stars (see e.g. Werner et al. 1996; Dreizler et al. 1997, for discussion of these sources). These tend to be hydrogen deficient, and have likely undergone a phase of born-again evolution they have experienced a late He flash during post-agb evolution, and are now retracing somewhat differing paths within the HR plane. A discussion of this phenomenon may be found in Iben et al. (1983). The evolutionary tracks of these stars are far from being well determined, although it is likely that they differ from those illustrated in Fig. 1. We have therefore excluded these sources from the evaluation of mean absolute magnitudes, and separately identified them in Fig. 1 (as open squares). Our list of distance estimates, extinctions, apparent and absolute magnitudes, and 5-GHz brightness temperatures are summarized in Table 1, together with the associated references. Values of m v have, where possible, been determined using weighted means of several independent estimates. The mean error in m v appears to be of order =0.13 mag. The range of independent extinction estimates is very much more restricted, although it appears that errors are also relatively modest [of order σ (C) ]. By far the most substantial error in evaluating M V derives from uncertainties in distance, however. Comparison between independent, non-gravitational estimates of distance suggests that σ (D) 0.3D. However, the gravitational distances of Napiwotzki (2001) and Pottasch (1996) appear to have errors which are very much larger; and as these constitute a large fraction of the distances used

4 622 J. P. Phillips Table 1. Reference PNe having low 5-GHz brightness temperatures. Source PNG Distance Log(T B /k) V σ (V) Refs c Refs M V Note(Ref) (pc) (mag) (mag) Sh , PG 1159 NGC , 3, 4, 5, , A , RX J p PG 1159 PG p PG 1159 Jn p , , PG 1159 IW pN , , DeHt Sh pN Sh , EGB , 4, PHL NPAGB(32);LG Sh , 4, NGC , 3, 4, 5, 6, , HDW , IW p PG 1159 HDW Sh , PuWe , VV p , PG 1159 WDHS , A , , 10, PG 1159 A , 6, A , 24, CM A , NGC , 21, , B(31) A B(33) A , , LG LoTr , B(34) Notes: B, binary; NPAGB, non-post-agb central star; PG 1159, PG 1159-type star; LG, low-gravity star; CM, conflicting published magnitudes. We have used the most recent results of Tylenda et al. (1991), although the results of Abell (1966) would suggest V = The quoted error represents a mean value; in reality, 0.1 <σ(v ) < 0.25 mag. References: 1, Napiwotzki & Schönberner (1995); 2, Perek & Kohoutek (1967); 3, Kaler (1983); 4, Tylenda et al. (1991); 5, Kaler & Jacoby (1989); 6, Shao & Liller (quoted in Acker et al. 1992); 7, Kaler & Feibelman (1985); 8, Abell (1966); 9, Drummond (1980); 10, Pottasch (1996); 11, Ishida & Weinberger (1987); 12, Greenstein (1974); 13, Ellis, Grayson & Bond (1984); 14, Arp & Scargle (1967); 15, Kwitter, Jacoby & Lydon (1988); 16, Hartl & Weinberger (1987); 17, Walsh & Walton (1996); 18, Cheselka et al. (1993); 19, Liebert et al. (1988); 20, Weinberger et al. (1983); 21, Shaw & Kaler (1989); 22, Tylenda et al. (1989); 23, Jacoby (1981); 24, Cahn et al. (1992); 25, Tylenda et al. (1992); 26, Shaw & Kaler (1985); 27, Kaler, Shaw & Kwitter (1990); 28, Acker et al. (1991); 29, Pollacco & Bell (1994); 30, Lutz & Kaler (1987); 31, Méndez & Niemela (1977); 32, Méndez et al. (1988a); 33, Gatti et al. (1998); 34, Graham et al. (2004); 35, Borkowski et al. (1993). here, they are likely to be of considerable importance in defining the scatter in our results. Pottasch (1996) has noted that estimates of g sometimes differ from each other appreciably, and may lead to errors σ (D) D. In addition, Pottasch sometimes evaluates gravity on the basis of similarities between central star spectra; a procedure which is likely to lead to rough-and-ready values of this parameter. Finally, he notes that values of g determined from X-ray spectra are often significantly greater than those evaluated in the visible. It is clear that these various doubts should place us on alert, and it seems possible that overall errors in D may be very large indeed. More concretely, Napiwotzki (2001) estimates errors in distance for all of his gravitational measures, whence we determine a mean value σ (D)/D = ± Using these latter values for σ (D), we determine that gravitational distances may lead to errors in M V of order σ (M V ) = ± mag [increasing to σ (M V ) ± in the case of Sh 2 188]. This size of error is indicated by the vertical arrow in Fig. 1, and appears roughly consistent with the observed scatter in our results. 4 COMPARISON BETWEEN OBSERVED AND THEORETICAL TRENDS It is apparent, from Fig. 1, that non-pg 1159 stars (represented by the solid circles) cluster about the trend expected from our theoretical analysis. This agreement is further illustrated in Fig. 2, where it is apparent that 90 per cent of central stars fall within one magnitude of the range expected for highly evolved nebulae. The mean value for all of the sources combined is M V =7.05 ± 0.26; a value which differs by only 2σ from theoretical trends. The PG 1159-type stars, on the other hand, are displaced to somewhat lower values of M V, and possess a mean absolute magnitude M V =5.99 ± Such a disparity in trends may imply a difference in evolutionary tracks and/or lifetimes. It may also reflect the systematic biases in distance mentioned in Section 3. Given that the distances of PG 1159 sources are biased towards older gravitational measurements, it is possible that their value of M V may require decreasing by up to 0.5 mag. We have also illustrated the distribution of evolved sources investigated by Napiwotzki & Schönberner (1995). Several cautionary

5 NUMBER OF STARS OBSERVED DISTRIBUTIONS OF EVOLVED CENTRAL STARS WITH RESPECT TO M V NAPIWOTZKI RESULTS (PG1159 STARS OMITTED) <M V(N)> <M V(P)> EXPECTED RANGE M V PRESENT RESULTS (PG1159 STARS OMITTED) DISTRIBUTION OF PG1159 STARS Figure 2. The distribution of observed sources with respect to central star absolute magnitude. The solid lines correspond to the trend for non-pg 1159-type stars, determined using our present results. The dotted lines correspond to the distances of Napiwotzki & Schönberner (1995). Finally, the dashed lines represent the variation for PG 1159-type stars. Field stars, binaries, low-gravity stars and a single non-post-agb central star have been eliminated. M V (N) represents the mean magnitude of Napiwotzki & Schönberner (1995), whilst M V (P) corresponds to the value determined using our present results. remarks require to be stated about these, however. The first is that the distances of these authors are based upon measures of D line absorption, at least some of which were taken from maps of galactic sodium line strengths owing to Binnendijk (1952). These latter strengths are likely to be very approximate indeed, and may result in considerable errors in their estimations of D. Similarly, levels of extinction are evaluated using a model of galactic interstellar extinction in Arenou, Grenon & Gómez (1992). Although Napiwotzki & Schönberner (1995) suggest that the extinctions of these sources are modest, and that errors in c should therefore be of little consequence, it is possible that the procedures they employ lead to uncertainties as great as σ (M V ) 0.5 mag. Placing these uncertainties aside, however, it is clear that their magnitude distribution is very similar to that deduced here. Both sets of data are centred close to the M V = 7 mag bin, although the trend for Napiwotzki & Schönberner (1995) is skewed towards lower values of M V, and implies a mean value M V (N) = 5.89 ± 0.33 mag. Note that here, yet again, we have excluded the PG 1159-type stars. Taking all in all, it is therefore clear that the observed distribution of central stars is just what would be expected from theory, and that the scatter is not very much different from what might be anticipated given the variation in central star masses, and errors in D. The distances of PNe 623 Although individual distances may therefore not be well determined, the error is certainly no greater than can be claimed for most other statistical procedures. Our analysis also enables to assess which of the alternative distance scales are likely to be correct. We have calculated the distances to be expected for a further 17 PNe using a value M V =7.05 mag (see Section 4). The results are indicated in Table 2, where also give details of extinction and apparent magnitudes. It is clear that our present values of D are closely similar to those determined using previous methods. More specifically, we may define a scaling factor κ = D i(p) i D i i(a), (1) where D(P) corresponds to the distances derived here, and D(A) refer to those of alternative distance procedures. The results are listed in Table 3 for both M V =7.05 and = 6.5 mag (the latter value close to the mean expected from our theoretical trends). We have again excluded a single PG 1159 star, a low-gravity star (located in A36), various binary systems, and two likely born-again outflows (A30 and A78; see for instance Borkowski et al. 1993). It is clear from Table 3 that both values of M V lead to similar conclusions. If one uses M V = 7.05, then the present distances appear most similar to those of Cahn et al. (1992), and are slightly discrepant with those of Phillips (2002, 2004a). If one employs M V = 6.5, on the other hand, then the closest agreement appears to be with Phillips (2002), whilst the distances of Cahn et al. (1992) and Phillips (2004a) are more at variance. All in all, and taking the uncertainties in M V into account, one may state that the scales of Phillips (2002, 2004a) and Cahn et al. (1992) appear to be in reasonable agreement with our results. The distances of Zhang (1995), however, are discrepant, and by avery wide margin indeed a margin which can only be reduced where M V is unrealistically high. Such an analysis is not possible for the distances of Acker (1978), Daub (1982), van de Steene & Zijlstra (1995) and Bensby & Lundstrom (2001) as they have few sources in common with the present results. However, their values of κ can be assessed using the analysis of Phillips (2004a). It is clear from this that van de Steene & Zijlstra (1995) and Bensby & Lundstrom (2001) give similar distances to those of Zhang (1995), whilst those of Acker (1978) and Daub (1982) are similar to the distances of Phillips (2004a). It is therefore clear that our present results confirm the shorter distance scales of Acker (1978), Daub (1982), Cahn et al. (1992) and Phillips (2002, 2004a), but are inconsistent with those of Zhang (1995), van de Steene & Zijlstra (1995) and Bensby & Lundstrom (2001). 5 THE DISTANCES TO FAINTER NEBULAE It is apparent from Section 4 that the intrinsic distribution of central star absolute magnitudes is likely to be highly peaked. Although the variation of source numbers with M V (see Fig. 2) suggests a typical range M V 3 mag, the intrinsic distribution will be significantly narrower, and probably not much greater than is implied by the theoretical tracks (σ (M V ) ±0.5 mag). This, in turn, would imply that we may use a specific mean value of M V in evaluating the distances to these sources, and that the random error in these distances should be of order σ (D) 0.3D. 6 CENTRAL STAR BINARITY One further point worth making is about the binarity of PNe central stars. Phillips (2000b) noted that the observed magnitudes of the central stars permit us to place constraints upon the spectral characteristics of any binary companions. Such a result is of considerable interest, given that many central stars may be associated with binary companions (De Marco et al. 2004). An even stronger constraint upon binarity is possible in the case of the present sources, because they are at a phase of their evolution during which M V is small. Any binary companion will therefore

6 624 J. P. Phillips Table 2. Distances and central star parameters for faint PNe. Source PNG Log(T B /k) V σ (V) Refs C Refs D Notes(ref) (mag) (mag) (kpc) IC A , EB(17) A , 8, A A , 8, , EB(29) A , NGC , , PG 1159, LG A , BA(35) A A A FS? A A A PU A B(30) A A , 8, BA(35) A , 24, A K A , 8, , 24, A K Notes: B, binary; EB, eclipsing binary; LG, low gravity; PG 1159, PG 1159-type central star; BA, born again. References: see footnote to Table 1. Table 3. Comparison between distance scales for faint PNe. Comparative distances N M V =7.05 M V =6.5 κ κ Phillips (2002) ± ± Cahn et al. (1992) ± ± Phillips (2004a) ± ± Zhang (1995) ± ± stand out particularly strongly, and may cause appreciable deviations from our deduced trends. It is clear from Fig. 1 that this does not occur for most of our present sample, however. Excluding sources having known central star binarity, or which may be characterized by differing evolutionary tracks (e.g. the PG 1159 stars), there are really no sources in our list which appear in any way anomalous. We therefore conclude that most evolved PNe central stars are unlikely to have companions with magnitudes M V 6, which is equivalent to a main-sequence spectral type of K0 or later. Note, finally, that this constraint is likely to represent a strict upper limit, because M V 6 main-sequence stars might be expected to be spectroscopically detectable. It is possible that spectroscopic upper limits are deeper by at least a couple of magnitudes or so (i.e. that M V < 8 mag). 7 CONCLUSIONS We have noted that the evolutionary tracks of PNe central stars are expected to be closely similar where 0.6 < M CS /M < 0.7, and where sources are also highly evolved. This mass range is likely to include the majority of observed galactic outflows, and imply closely similar central star absolute magnitudes. We have shown that PNe with 5-GHz brightness temperatures log(t B ) 0.5 have magnitudes which are consistent with these predictions, implying that M V =7.05 ± 0.25 mag. The intrinsic scatter in M V is likely to be of order ± 0.5 mag. We have therefore used this estimate to evaluate the distances to a further 17 low surface brightness PNe. We find that these new distances are consistent with those of Acker (1978), Daub (1982), Phillips (2002, 2004) and Cahn et al. (1992). However, they differ (by factors of 3) from the estimates of Zhang (1995), van de Steene & Zijlstra (1995) and Bensby & Lundstrom (2001). This latter disparity arises because of non-linearities within the T B R plane, and confirms the recent analysis of Phillips (2004a). We also note that similarities between observed and predicted values of M V enable us to place strong constraints upon any binary companions, and that such stars must have magnitudes M V 6. This corresponds to a spectral type of K0 or later for main-sequence stars. ACKNOWLEDGMENTS I would like to thank Dr Ralf Napiwotzki, whose constructive and perceptive comments have enabled me to improve the analysis. REFERENCES Abell G. O., 1966, ApJ, 144, 259 Acker A., 1978, A&AS, 33, 367 Acker A., Stenholm B., Tylenda R., Raytchev B., 1991, A&AS, 90, 81 Acker A., Ochsenbein F., Stenholm B., Tylenda R., Marcout J., Schohn C., 1992, Strasbourg-ESO Catalogue of Planetary Nebulae. ESO, Garching

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