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Planetary nebula distances re-examined: an improved statistical scale
The distances of planetary nebulae (PNe) are still quite uncertain.Although observational estimates are available for a small proportion ofPNe, based on statistical parallax and the like, such distances are verypoorly determined for the majority of galactic PNe. In particular,estimates of so-called `statistical' distance appear to differ byfactors of ~2.7.We point out that there is a well-defined correlation between the 5-GHzluminosity of the sources, L5, and their brightnesstemperatures, TB. This represents a different trend to thoseinvestigated in previous statistical analyses, and permits us todetermine independent distances to a further 449 outflows. Thesedistances are shown to be closely comparable to those determined using aTB-R correlation, providing that the latter trend is taken tobe non-linear.This non-linearity in the TB-R plane has not been noted inprevious analyses, and is likely responsible for the broad (andconflicting) ranges of distance that have previously been published.Finally, we point out that there is a close accord between observedtrends within the L5-TB and TB-Rplanes, and the variation predicted through nebular evolutionarymodelling. This is used to suggest that observational biases areprobably modest, and that our revised distance scale is reasonablytrustworthy.
| The relation between Zanstra temperature and morphology in planetary nebulae
We have created a master list of Zanstra temperatures for 373 galacticplanetary nebulae based upon a compilation of 1575 values taken from thepublished literature. These are used to evaluate mean trends intemperature for differing nebular morphologies. Among the most prominentresults of this analysis is the tendency forη=TZ(HeII)/TZ(HeI) to increase with nebularradius, a trend which is taken to arise from the evolution of shelloptical depths. We find that as many as 87 per cent of nebulae may beoptically thin to H ionizing radiation where radii exceed ~0.16 pc. Wealso note that the distributions of values η and TZ(HeII)are quite different for circular, elliptical and bipolar nebulae. Acomparison of observed temperatures with theoretical H-burning trackssuggests that elliptical and circular sources arise from progenitorswith mean mass ≅ 1 Msolar(although the elliptical progenitors are probably more massive).Higher-temperature elliptical sources are likely to derive fromprogenitors with mass ≅2 Msolar, however, implying thatthese nebulae (at least) are associated with a broad swathe ofprogenitor masses. Such a conclusion is also supported by trends in meangalactic latitude. It is found that higher-temperature ellipticalsources have much lower mean latitudes than those with smallerTZ(HeII), a trend which is explicable where there is anincrease in with increasing TZ(HeII).This latitude-temperature variation also applies for most other sources.Bipolar nebulae appear to have mean progenitor masses ≅2.5Msolar, whilst jets, Brets and other highly collimatedoutflows are associated with progenitors at the other end of the massrange (~ 1 Msolar). Indeed it ispossible, given their large mean latitudes and low peak temperatures,that the latter nebulae are associated with the lowest-mass progenitorsof all.The present results appear fully consistent with earlier analyses basedupon nebular scale heights, shell abundances and the relativeproportions of differing morphologies, and offer further evidence for alink between progenitor mass and morphology.
| Galactic Planetary Nebulae and their central stars. I. An accurate and homogeneous set of coordinates
We have used the 2nd generation of the Guide Star Catalogue (GSC-II) asa reference astrometric catalogue to compile the positions of 1086Galactic Planetary Nebulae (PNe) listed in the Strasbourg ESO Catalogue(SEC), its supplement and the version 2000 of the Catalogue of PlanetaryNebulae. This constitutes about 75% of all known PNe. For these PNe, theones with a known central star (CS) or with a small diameter, we havederived coordinates with an absolute accuracy of ~0\farcs35 in eachcoordinate, which is the intrinsic astrometric precision of the GSC-II.For another 226, mostly extended, objects without a GSC-II counterpartwe give coordinates based on the second epoch Digital Sky Survey(DSS-II). While these coordinates may have systematic offsets relativeto the GSC-II of up to 5 arcsecs, our new coordinates usually representa significant improvement over the previous catalogue values for theselarge objects. This is the first truly homogeneous compilation of PNepositions over the whole sky and the most accurate one available so far.The complete Table \ref{tab2} is only available in electronic form atthe CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/408/1029}
| Ionized haloes in planetary nebulae: new discoveries, literature compilation and basic statistical properties
We present a comprehensive observational study of haloes aroundplanetary nebulae (PNe). Deep Hα+[NII] and/or [OIII] narrow-bandimages have been obtained for 35 PNe, and faint extended haloes havebeen newly discovered in the following 10 objects: Cn 1-5, IC 2165, IC2553, NGC 2792, NGC 2867, NGC 3918, NGC 5979, NGC 6578, PB 4, andpossibly IC 1747. New deep images have also been obtained of other knownor suspected haloes, including the huge extended emission around NGC3242 and Sh 2-200. In addition, the literature was searched, andtogether with the new observations an improved data base containing some50 PN haloes has been compiled.The halo sample is illustrated in an image atlas contained in thispaper, and the original images are made available for use by thescientific community at http://www.ing.iac.es/~rcorradi/HALOES/.The haloes have been classified following the predictions of modernradiation-hydrodynamical simulations that describe the formation andevolution of ionized multiple shells and haloes around PNe. According tothe models, the observed haloes have been divided into the followinggroups: (i) circular or slightly elliptical asymptotic giant branch(AGB) haloes, which contain the signature of the last thermal pulse onthe AGB; (ii) highly asymmetrical AGB haloes; (iii) candidaterecombination haloes, i.e. limb-brightened extended shells that areexpected to be produced by recombination during the late post-AGBevolution, when the luminosity of the central star drops rapidly by asignificant factor; (iv) uncertain cases which deserve further study fora reliable classification; (v) non-detections, i.e. PNe in which no halois found to a level of <~10-3 the peak surface brightnessof the inner nebulae.We discuss the properties of the haloes: detection rate, morphology,location of the central stars in the Hertzsprung-Russell diagram, sizes,surface brightness profiles, and kinematical ages. Among the mostnotable results, we find that, as predicted by models, ionized AGBhaloes are a quite common phenomenon in PNe, having been found in 60 percent of elliptical PNe for which adequately deep images exist. Another10 per cent show possible recombination haloes. In addition, using thekinematical ages of the haloes and inner nebulae, we conclude that mostof the PNe with observed AGB haloes have left the AGB far from a thermalpulse, at a phase when hydrogen burning is the dominant energy source.We find no significant differences between the AGB haloes ofhydrogen-poor and hydrogen-rich central stars.
| Shaping Bipolar and Elliptical Planetary Nebulae: Effects of Stellar Rotation, Photoionization Heating, and Magnetic Fields
We present two-dimensional hydrodynamical and magnetohydrodynamicalsimulations of the evolution of planetary nebulae formed through theinteraction of two succeeding, time-independent stellar winds. Bothwinds are modeled according to a consistent physical prescription forthe latitudinal dependence of their properties. We propose that singlestars with initial masses above ~1.3 M_solar can achieve near-criticalrotation rates during their ``superwind'' phase at the tip of theasymptotic giant branch (AGB). We show that the resulting equatoriallyconfined winds and their subsequent inflation to a double lobe structureby the post-AGB wind leads to the typical hourglass shape found in manyplanetary nebulae, such as MyCn 18. Following Chevalier & Luo andRóżyczka & Franco, we then combine the effect of amagnetic field in the post-AGB wind with rotating AGB winds. We obtainhighly collimated bipolar nebula shapes, reminiscent of M2-9 or He2-437. For sufficiently strong fields, ansae and jets, similar to thoseobserved in IC 4593 are formed in the polar regions of the nebula.Weaker fields are found to be able to account for the shapes ofclassical elliptical nebulae, e.g., NGC 6905, in the case of sphericallysymmetric AGB winds, which we propose for single stars with initialmasses below ~1.3 M_solar. Photoionization, via instabilities in theionization-shock front, can generate irregularities in the shape of thesimulated nebulae. In particular, it leads to the formation of cometaryknots, similar to those seen in the Helix nebula (NGC 7293). This effectmay also be responsible for large-scale irregularities like those foundin Sh 2-71 or WeSb 4. We arrive at a scenario in which the majority ofthe planetary nebula with their diverse morphologies is obtained fromsingle stars. This scenario is consistent with the Galactic distributionof the different nebula types, since spherical and ellipticalnebulae-which have a distribution with a large scale height above theGalactic plane-are ascribed to progenitor masses below ~1.3 M_solar,with magnetic effects introducing ellipticities. Bipolar nebulae, on theother hand-which are on average closer to the Galactic plane-are foundto stem from progenitors with initial masses above ~1.3 M_solar.
| The kinematics of 867 galactic planetary nebulae
We present a compilation of radial velocities of 867 galactic planetarynebulae. Almost 900 new measurements are included. Previously publishedkinematical data are compared with the new high-resolution data toassess their accuracies. One of the largest samples in the literatureshows evidence for a systematic velocity offset. We calculate weightedaverages between all available data. Of the final values in thecatalogue, 90% have accuracies better than 20 km s(-1) . We use thiscompilation to derive kinematical parameters of the galacticdifferential rotation obtained from least-square fitting and toestablish the Disk rotation curve; we find no significal trend for thepresence of an increasing external rotation curve. We examine also therotation of the bulge; the derived curve is consistent with a linearlyincreasing rotation velocity with l: we find V_b,r=(9.9+/-1.3)l -(6.7+/-8.5) km s(-1) . A possible steeper gradient in the innermostregion is indicated. Table 2 is available in electronic form only, viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/Abstract.html
| Planetary Nebulae in the NRAO VLA Sky Survey
The 1.4 GHz NRAO VLA Sky Survey (NVSS) images and source catalog wereused to detect radio emission from the 885 planetary nebulae north ofJ2000 declination delta = -40 deg in the Strasbourg-ESO Catalogue ofGalactic Planetary Nebulae. We identified 680 radio sources brighterthan about S = 2.5 mJy beam-1 (equivalent to T ~ 0.8 K in the 45" FWHMNVSS beam) with planetary nebulae by coincidence with accurate opticalpositions measured from Digitized Sky Survey (DSS) images. Totalextinction coefficients c at lambda = 4861 Angstroms were calculated forthe 429 planetary nebulae with available H beta fluxes and low free-freeoptical depths at 1.4 GHz. The variation of c with Galactic latitude andlongitude is consistent with the extinction being primarily interstellarand not intrinsic.
| A Morphological Study of Planetary Nebulae
We have produced simulated images of 110 planetary nebulae using theellipsoidal shell model. This process has allowed us to remove theprojection effects from the morphological classification of planetarynebulae and has provided quantitative measures of the intrinsicasymmetries of the nebulae. It is shown that the morphology of mostplanetary nebulae can be reproduced with pole-to-equator density ratiosof 0.1-1. Many planetary nebulae also show a modest departure from axialsymmetry. Contrary to previous findings by Khromov & Kohoutek, thesky orientation of planetary nebulae in this sample is consistent with apurely random distribution. Extremely bipolar nebulae (e.g., those ofbutterfly shape) point to a steep density profile in the AGB envelopeand are more likely to be type I (high helium and/or nitrogen abundance)nebulae. We found evidence that these nebulae are likely to have moremassive progenitors and are at a more advanced stage of dynamicalevolution.
| A self-consistent determination of distances, physical parameters, and chemical composition for a large sample of galactic planetary nebulae: chemical composition
The relative abundances of He, C, N, O, Ne, Mg, Si, S, and Ar arepresented for, respectively, 185, 65, 212, 221, 180, 13, 41, 197, and205 Galactic planetary nebulae. The observed stages of ionization weretaken into account using the relations between the relative abundancesof different ions derived from a grid of photoionization models for thenebular emission. The chemical compositions of all the planetary nebulaewere determined using the same method and the same atomic data, so thatthe results have a high degree of uniformity; this is the first timethis has been done for such a large sample of Galactic planetary nebulae(221 objects).
| A self-consistent determination of the distances, physical parameters, and chemical composition for a large sample of galactic planetary nebulae: The distances and parameters of central stars and the optical depths of envelopes
The distances and parameters of the central stars and the optical depthsof the envelopes in the Lyman limits of neutral hydrogen and neutralhelium were determined in a self-consistent way for 170 Galacticplanetary nebulae (PNe). The distance to each PN was so chosen that thetheoretically calculated evolutionary age of its nucleus was equal tothe dynamical age of its expanding envelope. The effective temperatureof the central star and its related parameters were determined either bythe generalized energy-balance method or, where appropriate, byZanstra's method. The derived distance estimates lend support to a`long' distance scale for PNe and are generally in agreement withcurrent individual and statistical estimates of the distances to PNeavailable in the literature. The mean distance to the bulge PNe is 7.9+/- 0.3 kpc, in agreement with the distance to the Galactic center. Themasses of the central stars of PNe corresponding to the deriveddistances are closely correlated with the nebular nitrogen-to-oxygenabundance ratio.
| Properties That Cannot Be Explained by the Progenitors of Planetary Nebulae
I classify a large number of planetary nebulae (458) according to theprocess that caused their progenitors to blow axisymmetrical winds. Theclassification is based primarily on the morphologies of the differentplanetary nebulae, assuming that binary companions, stellar orsubstellar, are necessary in order to have axisymmetrical mass loss onthe asymptotic giant branch. I propose four evolutionary classes,according to the binary-model hypothesis: (1) Progenitors of planetarynebula that did not interact with any companion. These amount to ~10% ofall planetary nebulae. (2) Progenitors that interact with stellarcompanions that avoided a common envelope, 11^{+2}_{-3}% of all nebulae.(3) Progenitors that interact with stellar companions via a commonenvelope phase, 23^{+11}_{-5}% of all nebulae. (4) Progenitors thatinteract with substellar (i.e., planets and brown dwarfs) companions viaa common envelope phase, 56^{+5}_{-8}% of all nebulae. In order todefine and build the different classes, I start with clarifying somerelevant terms and processes related to binary evolution. I then discusskinematical and morphological properties of planetary nebulae thatappear to require the interaction of the planetary nebula progenitorsand/or their winds with companions, stellar or substellar.
| Planetary nebulae morphologies, central star masses and nebular properties.
We have constituted a sample of about 80 PN with defined morphologiesand well observed basic parameters (fluxes, angular radii, expansionvelocities and magnitudes of the central stars). For these PN, we havederived the central star masses by comparing the observed set ofparameters with those predicted by a simple evolutionary model of a PN,expanding at the same velocity as the observed one. We have thenexamined the relations between the PN morphological types and otherproperties, linked to the central star mass. Bipolar PN are shown tohave a wider distribution of central star masses than the rest of PN,and shifted towards higher values. They lie closer to the Galactic planeand tend to have larger N/O ratios. Point symmetric PN, which have notbeen much studied so far, are found to constitute an outstanding class.They show an almost perfect M_*_-v_exp_ correlation. They correspond toa rather short evolutionary stage of PN. They lie, on average, furtherfrom the Galactic plane than bipolar PN and tend to have lower N/O.Globally, PN with higher central star masses are found closer to theGalactic plane, and the observed relation between N/O and M_*_ isroughly consistent with the predictions from evolutionary models for AGBstars.
| A statistical distance scale for Galactic planetary nebulae
A statistical distance scale is proposed. It is based on the correlationbetween the ionized mass and the radius and the correlation between theradio continuum surface brightness temperature and the nebular radius.The proposed statistical distance scale is an average of the twodistances obtained while using the correlation. These correlations,calibrated based on the 1`32 planetary nebulae with well-determinedindividual distances by Zhang, can reproduce not only the averagedistance of a sample of Galactic Bulge planetary nebulae exactly at thedistance to the Galactic center, but also the expected Gaussiandistribution of their distances around the Galactic center. This newdistance scale is applied to 647 Galactic planetary nebulae. It isestimated that this distance scale can be accurate on average to35%-50%. Our statistical distance scale is in good agreement with theone recently proposed by Van de Steene and Zijlstra. The correlationsfound in this study can be attributed to the fact that the core mass ofthe central stars has a very sharp distribution, strongly peaked atapprox. 0.6 solar mass. We stress that the scatter seen in thestatistical distance scale is likely to be real. The scatter is causedby the fact that the core mass distribution, although narrow andstrongly peaked, has a finite width.
| H I and CO observations of the circumnebular envelopes of planetary nebulae
lambda=21 cm spectral-line and continuum observations of 10 compactplanetary nebulae (PNe) have been made with the Very Large Array.Circumnebular atomic hydrogen is identified in the PNe SwSt 1, M 3-35,and possibly in Hu 2-1. The possibility of an inverse correlationbetween the optical depth of circumnebular atomic hydrogen and thelinear radius of the ionized nebula is investigated, but shown not to bestatistically significant. Observations of J=2-->1 CO emission for 22PNe and J=3-->2 CO emission for 16 PNe taken with the James ClerkMaxwell Telescope are presented. J=2-->1 CO emission is detected inthe planetary nebula M 1-59, and previous CO detections in IC 5117, M1-16 and NGC 6302 are confirmed. J=3-->2 CO emission is detected inthe PNe IC 5117 and NGC 6302.
| Sweeping the Supergalactic Plane.
Not Available
| Elemental abundances for a sample of southern galactic planetary nebulae.
Abstract image available at:http://adsabs.harvard.edu/abs/1994MNRAS.271..257K
| Spectrophotometry of southern planetary nebulae.
Twenty-seven southern planetary nebulae of moderate to low surfacebrightness have been observed in one or various positions across thenebula with the 152cm and the 3.6m ESO telescopes equipped with the IDS(image dissector scanner) attached to Boller & Chivens spectrographsat spectral resolution between 8 and 13A. The purpose was to search forobjects chemically enriched in helium and nitrogen, according to theprediction of the stellar evolution theory of intermediate mass stars.The chemical abundances of He, N, O, Ne, S and Ar have been determinedin the individual positions, and averaged into values representative ofthe whole nebulae. No cases of objects displaying chemical gradientsacross the nebula have been detected. Eleven nebulae enriched in heliumand/or in nitrogen have been found, six of which detected as such forthe first time. They are: A 37, A 70, Fg 1, MZ 1, MZ 2 and NGC 6578.They increase the number of the objects, which can be classified of typeI of Peimbert.
| The gasdynamic evolution of spherical planetary nebulae. Radiation-gasdynamics of PNe III.
Using a radiation-gasdynamics code the evolution of spherical planetarynebulae is followed, while taking into account the evolution of centralstar and the fast wind. These models show the importance of ionizationfronts for the structure of planetary nebulae, especially for the socalled multiple shell nebulae (MSPN). It is shown that the outer shellis formed by the ionization front while the inner shell is swept-up bythe fast wind. These models explain the emission profiles of the outershells as well as their various kinematic properties. Because they areshaped by the ionization front these outer shells only give indirectinformation on the AGB mass loss history. The models indicate thattypical MSPN structures point to mass loss variations during the AGBphase. The ionization also leads to a stalling of the expansion of thenebula, leading to nebulae with expansion ages lower than theirevolutionary age. Values for ionized mass and Zanstra temperatures arederived from the models.
| A catalogue HeII 4686 line intensities in Galactic planetary nebulae.
We have compiled the intensities of the HeII 4686 lines measured inGalactic planetary nebulae. We present a few observational diagramsrelated to this parameter, and discuss them with the help of theoreticaldiagrams obtained from simple model planetary nebulae surroundingevolving central stars of various masses. We determine the hydrogen andhelium Zanstra temperature for all the objects with accurate enoughdata. We argue that, for Galactic planetary nebulae as a whole, the maincause for the Zanstra discrepancy is leakage of stellar ionizing photonsfrom the nebulae.
| Confrontation of theoretical tracks for post-AGB stars with observations of planetary nebulae
We have constructed a distance-independent diagram to test publishedtheoretical tracks for the evolution of post-AGB stars by comparing themwith the Galactic planetary nebulae data base. We have found noinconsistency between observations and the set of tracks computed bySchoenberner (1981, 1983) and Bloecker & Schoenberner (1990). On theother hand, observations do not seem support the large transition timesbetween the end of the AGB superwind and the beginning of the planetarynebula ionization phase adopted in the models of Vassiliadis & Wood(1994).
| The correlations between planetary nebula morphology and central star evolution
The morphology of 111 Galactic planetary nebulae has been studied inrelation to the evolutionary stage of their central stars. In order tolocate these stars on the log Teff - Log L/solar luminosityplane, we have calculated the Zanstra temperatures with the most up todate fluxes and magnitudes available in the literature. Distances to thenebulae were estimated with statistical methods. The different natureand evolutionary stages of central stars have been related to themorphologies of the surrounding nebulae in a statistical sense. We foundthat multiple shell nebulae contain stars that are at a differentevolutionary stage than those of single shell nebulae; we also foundthat bipolar and elliptical planetary nebulae very likely containcentral stars with a different mass distribution; furthermore, we buildan optical thickness sequence of morphological types.
| The Correlations Between Planetary Nebula Morphology and Central Star Evolution
Abstract image available at:http://adsabs.harvard.edu/abs/1993A&A...276..463S
| The features of chemical abundances in Galactic planetary nebulae
The chemical composition of 217 Galactic planetary nebulae isinvestigated; 203 of them are subdivided into four classes according tothe masses of nebulae and progenitor stars. The values of localabundances, Galactic abundance gradients and Galactic electrontemperature gradients are found for each class of nebula. Thecorrelations between the abundances of pairs of elements are alsocalculated for each class of nebula. The results are compared withtheoretical predictions. In particular, it is concluded that CN cyclingcan play a role in progenitor stars for all classes of planetary nebula.
| A catalogue of narrow band images of planetary nebulae
The paper presents a catalog of narrow-band images of 255 planetarynebulae (PNe) taken with the 3.5 m ESO NTT, using EFOSC2, the faintobject camera, and spectrograph. The results include properties ofseveral PNe which were previously listed as unresolved, show extendedstellar objects, list several new bipolar proto-PNe, and describe a fewpreviously unknown faint haloes. A new list is presented of sizes inH-alpha and forbidden OIII images, including information on all peculiarobjects and features which have not been seen previously.
| The extinction constants for galactic planetary nebulae
The extinction constants are determined from Balmer decrementmeasurements for over 900 planetary nebulae. Comparison with publishedextinction constants shows that the results from ESO are fairlyreliable. An analysis of the extinction constants derived from theBalmer decrement and from the radio/Hβ flux ratio indicates thatthe latter tends to be systematically smaller than the former forincreasing extinction. We suggest that the radio measurements ofPottasch's group probably underestimate the radio fluxes, at least forsome (faintest) objects.
| A catalogue of absolute fluxes and distances of planetary nebulae
The paper presents a complete list of averaged recalibrated absoluteH-beta fluxes, global (where possible) relative He II lambda 4686fluxes, 5 GHz radio flux densities, and H-alpha/H-beta interstellarextinction constants for 778 Galactic planetary nebulae. The catalogprovides much of the fundamental data required to generate Zanstratemperatures. When data with the lowest errors are selected, the opticaland radio/optical extinctions show a peculiar correlation, with theradio values slightly high at low extinction and notably low at highextinction. The data are used, along with the best estimates of angulardiameters, to calculate Shklovsky distances according to the Daub schemeon the scale used earlier by Cahn and Kaler (1971). Use of this distancescale shows approximate equality of the death rates of optically thickand optically thin planetary nebulae. The method gives the correctdistances to the Magellanic Clouds.
| Strasbourg - ESO catalogue of galactic planetary nebulae. Part 1; Part 2
Not Available
| The absolute H-beta fluxes for galactic planetary nebulae
The absolute H-beta flux measurements from spectrophotometricobservations of about 880 galactic planetary nebulae are presented. Thegalactic coordinates of PNe and the adopted diameters for the nebulae inarcsec are given. The final values of the H-beta flux, corrected for thenebular extension, are presented and compared to the results of othermeasurements.
| Chemical abundances in planetary nebulae - Basic data and correlations between elements
To form a critical compilation of the abundances of He, C, N, O and Ne,all the individual determinations of chemical abundances in PN obtainedwith linear detectors have been considered. The data cover allobservations of the Galactic PN made in the 20 years up to the end of1989. Average chemicql abundances have been evaluated separately fornebulae of type I and of types II-III of Peimbert. For the first, theyare He/H = 0.137, C/H = 8.72, N/H = 8.60, O/H = 8.66, and Ne/H = 8.05.For the second they are He/H = 0.103, C/H= 8.82, N/H = 8.07, O/H = 8.66,and Ne/H = 7.99, in the usual units. The data analysis suggests that theenrichment of nitrogen in type I PNs is due mostly to the ON cycle,while that in PNs of type II-III is due mostly to the CN cycle.
| The energy-balance temperature of central stars of galactic planetary nebulae. II
The color temperature of the central star of planetary nebulae iscalculated using data from the ongoing spectroscopic survey of galacticplanetary nebulae carried out by Acker and Stenholm in conjunction withan energy-balance (EB) method of Preite-Martinez and Pottasch (1983). Inthese calculations it was assumed that thermal equilibrium holds in thephotoionization nebula. The derived EB temperatures are found to beconsistent with the corresponding temperatures derived by the Zanstra(1931) method. The T(EB) values derived for six planetary nebulae alsoagree with those of Preite-Martinez and Pottasch.
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