EXPANSIONS of PLANETARY NEBULAE William Liller Harvard

EXPANSIONS OF PLANETARY NEBULAE

William Liller

Harvard College Observatory

INTRODUCTION

Expansion rates1 of 11 planetary nebulae, predicted by Vorontsov-Velyaminov on the basis of Campbell and Moore's velocity measurements,2 suggested that of this group only NGC 2392 (radius increase rate = 2/./7/century) grew at a sufficient speed to be measurable. Vorontsov-Velyaminov, however, did not consider the nearest planetaries, such as the great Aquarius Nebula NGC 7293, the Dumbbell Nebula NGC 6853, the Owl Nebula NGC 3587, and NGC 246. For example, for NGC 6853 Wilson finds a radial expansion velocity, Vr ~ 27.9 km/sec.3 Adopting the distance d — 300 parsecs, given by Vorontsov- Velyaminov for NGC 6853, one finds a rate of increase in the radius equal to

d^ 100 Vr 0//rw , -di = T74T=2'0/century'

or a rate of increase in the diameter of the nebula equal to 4^0/century. Schatzman and Kahn have shown4 that a planetary which is an optically thick hydrogen ionization sphere (Strömgren sphere) might expand at twice the rate expected for an optically thin nebula. This conclusion follows from a time-differentiation of the equation for the radius of an ionization sphere with four assumptions, viz., (1) the central star remains constant in size and energy output for a period of the order of a hundred years,

(2) within the ionized sphere Νε = iV(H+), (3) the density of the nebular gas is uniform throughout, and (4) the outward velocity of material is everywhere proportional to its distance

This paper was presented in Pasadena on May 25, 1964, at a symposium on "Planetary Nebulae" in honor of Dr. Ira S. Bowen, retiring director of the Mount Wilson and Palomar Observatories.

from the center. This last assumption receives support from Wilson5 whose spectroscopic observations confirm it approxi- mately for several planetaries. Therefore, one should, in principle, be able to determine whether or not the planetary is optically thick by comparing the rate of expansion of a nebula, as derived from measurements of its angular rate of growth, with the rate of expansion of the nebular gas at the edge of the visible nebula, as derived spectroscopically. An optically thin nebula will expand at exactly the spectroscopically predicted rate. On the other hand, because of the time decrease of electron density within an expanding optically thick nebula, the radius of the ionization sphere will grow at twice the outward rate of motion of the gas. We are prevented from making this comparison by the well-known filamentary and inhomogeneous structure of many planetaries, and by our uncertainty concerning their distances. The central stars of some planetaries may still be ejecting gas into space. If the rate suffices to maintain a constant electron density, the nebular radius would remain constant with time. An increasing rate of ejection of material could even produce a shrinking nebula ! The presence of magnetic fields might alter the gas motions and vitiate our results. Indeed, loops of nebular material reminis- cent of solar prominence loops appear in a number of planetaries,6 and Gurzadian7 has given convincing theoretical arguments for the existence of such fields. Interaction between the edge of the expanding gas and the interstellar medium might be severe enough in some instances to decelerate the nebular material appreciably. Minkowski8 and Osterbrock9 suggest that the resulting pileup of the nebular gas might explain the sharp edges of those planetary nebulae which seem to be optically thin to radiation below 912 A.

THE OBSERVATIONAL MATERIAL

Between the years 1896 and 1918 several astronomers secured excellent plates of the brighter planetaries with the Crossley reflector (see Pub. Lick Obs. 8, 1908, and Curtis10).

The plate scale is such that photographic grain often competes with seeing as the limiting factor in image definition, even for slow, fine-grain emulsions. Thanks to the kindness of Director A. E. Whitford of Lick Observatory, Mrs. Liller and I were able to obtain a new series of direct photographs of planetary nebulae with the Crossley reflector. On November 5-8, 1961, we observed 28 planetaries that would be expected to show the largest angular expansions. In order to match as closely as possible the spectral response of the first-epoch plates (usually Seed 23 and 27 emulsions) we employed Kodak Ila-O emulsions. These are probably more sensitive to the green nebular [O m] lines than the older emulsions. Furthermore, the aluminized Crossley mirror enhances the contributions of the [On] λ 3727 lines and other ultraviolet emissions which the low ultraviolet reflectivity of a silvered mirror weakened or suppressed. These response differences might engender spurious effects, since images of different excitation often differ in size. That the green [O in] lines overwhelm the contributions of the other lines, even on the older emulsions, may be seen by combining relative line intensities of representa- tive planetaries (of e.g. Liller and Aller11) with the response curve, given by Seares and Joyner,12 of a Seed 23 emulsion plus one silver reflection. For example, the calculated contributions of the λ 4959, λ 5007 pair of lines to the images of NGC 2392, NGC 7009, and NGC 7662 are 51, 61, and 66 percent respec- tively. (Most of the remaining radiation, e.g. 31 percent for NGC 2392, arises from [Nein] and the Balmer series which very possibly radiate in precisely the same volume of space as [Oui].) There are a few objects of rather low excitation, such as NGC 40, that have little [O in] in their spectra, and in which the total contribution is shared fairly equally by the Balmer series and by [On]. Clearly, for such nebulae, comparison of old and new plates should be carried out with considerable care. Other systematic effects that might affect the final results include emulsion "creep," differential atmospheric refraction and dispersion, and the increase in sky brightness caused by the growth of the city of San Jose.

To test the first effect, I measured the position of twelve stars on a pair of plates centered on NGC 6720 taken in 1899 and 1961. On the average these stars appeared to undergo a contraction of 0.16 microns (0^006) ; the standard error of the result was 0.60 microns (0^023). As will be seen, the standard deviations of the nebular measures are an order of magnitude larger than this latter value. This random check shows that the emulsion distortion is negligible, as the experience of others, e.g., Gollnow and Hagemann13 would suggest. Differential atmospheric refraction causes a circular nebula to appear elliptical at all zenith angles ; atmospheric dispersion shifts an ultraviolet image relative to a green one. Because most planetaries are substantially monochromatic, the latter effect is all but nonexistent; Table I lists as a function of zenith distance the apparent vertical width of a nebula whose true diameter is 100^ and demonstrates that above a zenith distance of about 45° differential refraction is not important. Only for a few low- declination objects were the zenith angles greater than this, and in those instances particular care was taken to observe the nebulae at the same local hour angle at which the first-epoch plates were taken. On no pair of plates is there a contraction in the vertical diameter more than 0^05 per 100", according to Table 1.

TABLE I Vertical Diameter of a Nebula 100" in Diameter as a Function of Zenith Distance Zenith Vertical Zenith Vertical Distance Diameter Distance Diameter 0° 99'.'971 30° 99'.'961 10 99.970 40 99.950 20 99.967 50 99.929

Systematic effects from the increase in sky brightness at Lick are difficult to estimate. A filament lying perpendicular to a radius from the central star with a steep intensity gradient on the outside edge and a gentle one on the inside might, all motions excluded, appear to be farther from the central star on the new plate because of the loss of faint detail. The error would be in the

opposite direction if the nebula appeared as a more or less uniform disk of light with a moderately well-defined edge. However, such effects would hold true only for nebulae of very low surface brightness for which long exposures were necessary. Quantita- tive evaluation of these errors must await further tests in which an artificial background fog will be added to one plate of identical pairs taken of suitable nebulae.

THE REDUCTION PROCEDURES

Initially, distances between well-defined filaments and edges were measured by eye on a precision one-screw measuring engine. However, occasionally a comparison of measurements showed conflicting results. In an effort to eliminate uncertain- ties, we made microdensitometer tracings along selected diame- ters of the more interesting objects and on these tracings we measured the distances between the centroids of filaments and of central stars or of other diametrically located filaments. The extension to sky level of a linear slope of the intensity dropoff or the position of the mid-density point at the edge of a nebula also served as objectively defined points from which distances to the central star or to the opposite edge could be measured. The results were consistent. As a consequence, the standard deviations of all eye measures have arbitrarily been doubled to allow for the intrusion of subjectivity. Because we realized that the measured diameter or radius of a nebula might depend upon the density of the nebular image, we made several exposures of each nebula. In the reduction of the densitometer and microscope measures, the following pro- cedure was adopted : For each radius or diameter, the measure- ment was plotted against the emulsion density as determined at some convenient point. A sample "growth curve" appears in Figure 1. Least-squares straight-line solutions were put through both first- and second-epoch points, and a weighted mean slope for the two lines determined. The best straight line with this weighted mean slope was placed again through each set of points. The vertical separation of these lines was then adopted as the measured expansion (or contraction) with the standard deviation measured relative to these two parallel straight lines.

PHOTOGRAPHIC DENSITY (arbitrary scale) Fig. 1.—The diameter of the "face" of the Eskimo Nebula, NGC 2392, as measured on plates of different density taken 46 years apart. The parallel lines show the diameter expected on the basis of the distances indicated.

THE RESULTS

Because the measurements are still not complete, the following results are intended to serve only as a progress report. From the 28 planetaries that we photographed, 13 were selected for study on the basis of large expected angular expansion. In this paper the measurements of three will be described in detail. In the discussion below, the distances given by Vorontsov- Velyaminov14 and Shklovskiï15 will be used for the prediction of angular expansions. Because Vorontsov-Velyaminov has assumed that the bolometric luminosities of the central stars are known, his distances will apply most accurately to nebulae optically thick to radiation below 912 Â. On the other hand, Shklovskiï takes as his basic assumption that the masses of all nebulae are equal; thus, his distances apply to optically thin nebulae. O'Dell16 has given distances based upon Shklovskiï's method17 but refined by the use of accurate flux measures.

NGC 2392 (The Eskimo Nebula). Wilson18 finds the [O in] Doppler expansion velocity of this nebula to be 52.7 km/sec—higher than that of any other nebula. This value com- bined with Vorontsov-Velyaminov's distance of 460 parsecs yields a predicted angular rate of growth in the radius of 2'/4/century. On the other hand, Shklovskiï's distance of 930 parsecs gives a corresponding value of l"2/century. Because Vorontsov-Velyaminov's distances should be more reliable for optically thick nebulae, one would expect a radial expansion rate of twice the quoted value, namely 4//8/century, since the nebula would, in fact, be an ionization sphere. Figure 1 shows that these high expansion rates do not exist. Our measures yield a centennial increase in radius of O'/OS ± (Y.'IO (estimated error). The measured radius is that of the "face" of the Eskimo, position angle 95°. The estimated error is twice the derived value of the standard deviation. Visual measures of the center of the most conspicuous section of "fur" surrounding the Eskimo's face and a few densitometer measures of both the face and the fur show similar results. The visual measures of the fur yield an expansion in the radius of 0^05 ± 07.¾ per century. The densitometer measures average out to a small contraction (OVOZ/century) with an estimated error of O'/S. Perhaps the best explanation for the small or nonexistent expansion rate of NGC 2392 is that over the past 62 years the central star of NGC 2392 has maintained a constant gas density within its surrounding nebulosity. This idea receives support from Wilson's spectroscopic study of the central star,18 which reveals emission components on the short wavelength side of the major absorption lines. Such features confirm that the star is currently ejecting material. Another possibility is, of course, that NGC 2392 is some 20 times farther away than hitherto suspected. A distance of 10 or 20 kpc at the galactic coordinates of this object (/11 = 198° ; b11 = 18°) would, however, place it in a rather unlikely position in space and require it to have an extremely high mass and luminosity.

NGC 6853 (The Dumbbell Nebula), Unpublished spectro-

graphie observations of Wilson3 assign a radial expansion velocity of 27.9 km/sec to NGC 6853. Vorontsov-Velyaminov and Shklovskiï give for it distances of 400 and 150 parsecs, corresponding to centennial expansions in the radius of 2 χ l'.'S and 3^9. Chudovicheva reports an expansion of the radius of 6^8 ± 1//8 per century.19 A cursory eye examination of the available Crossley plates (see Plate I) shows that this last result cannot be correct. Densitometer measurements along four diame- ters made by Barbara L. Weither yield an average expansion of the radius of 0^64 ± 0^24 per century. In the case of NGC 6853 it would appear that either (1) it is about five times farther away than expected, or (2) Vorontsov- Velyaminov's distance is correct; the central star is still ejecting material, but not at a large enough rate to maintain a constant gas density. Certainly NGC 6853 is larger in linear diameter than ΝGC 2392 ; possibly it is more advanced in its evolution, and the central star is no longer emitting material at the rate of the central star of NGC 2392. A high-quality spectrum of NGC 6853^ central star should resolve this dilemma. NGC 7009 (The Saturn Nebula). For this complex object Wilson gives a radial expansion velocity of 20.5 km/sec.20 The distances given by Vorontsov-Velyaminov and by Shklovskiï are 500 and 550 parsecs; the corresponding angular expansion rates are 2 χ 0^9 and 0^8 per century. Table II summarizes the visual and the densitometer measurements and lists the centennial expansions in the radius of various features. There is quite good agreement between the visual and the densitometer results. The data for the outer ring, which from photographs appears to be a complete spheroid (unlike the inner ring), show excellent agreement with the expansion rates predicted from Wilson's spectrographic work. If this ring is optically thin, then Shklovskiï's distance is appropriate and the expected expansion per century of 0^8 falls comfortably within the standard deviation of the result. If the outer ring is optically thick, then from Vorontsov-Velyaminov's distance, one must conclude either that NGC 7009 is about twice as far away as expected or that the central star still remains somewhat active.

1961

A composite photograph of NGC 6853, the Dumbbell Nebula. The two sections were made from enlargements of Crossley plates taken in 1899 and 1961. The indicated plate scale is precisely the same for the two halves.

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There is some question, of course, as to whether Wilson's spectroscopic observation refers to the outer ring. The only positive evidence is the good agreement between the observed and predicted expansions for the optically thin model. The remarkable ansae of NGC 7009 show expansion more clearly than any feature in any nebula yet measured (see Plate II). If the adopted expansion rate of 1//6 for the ansae has remained constant, then they, and very possibly the entire nebula, were ejected from the central star in the year 420 A.D. ±: 280 years. Neither Hsi Tsê-tsung21 nor Ho Peng Yoke22 lists a nova within 25° of the position of NGC 7009 during the first millenium A.D. An interesting question that remains is how have these very condensed features remained so condensed for 1500 years? From our data, it would seem that the material of NGC 7009 moves outward at a velocity proportional to its distance from the central star, and this gives further justification for our earlier assumption. Other Nebulae. Although the reductions of the 13 planetaries selected for initial study are not complete, it can be stated that features in five planetaries, including NGC 7009, show expansions that are more than three times their standard deviations. Three more nebulae exhibit expansions greater than twice their standard deviations. The expansions of the remaining five objects can be considered as undetectable.

My wife and Miss Barbara L. Weither assisted me in carry- ing out the tedious measurements described here, and I am very grateful to them both. I wish to thank Director A. E. Whitford for permission to work with the Crossley reflector and with the excellent first-epoch plates of the Lick Observatory collection. Also, my thanks go to Drs. O. C. Wilson and C. R. O'Dell for supplying me with the expansion velocities for NGC 6853.

1 Β. A. Vorontsov-Velyaminov, Gaseous Nebulae and Novae (Mos- cow: Academy of Sciences U.S.S.R. Press, 1948). 2 W. W. Campbell and J. H. Moore, Puh. Lick Obs., 13, 75, 1918. 3 O. C. Wilson, private communication transmitted by C. R. O'Dell. 4 E. Schatzman and F. D. Kahn, in Gas Dynamics of Cosmic Clouds (Amsterdam: North-Holland, 1955), p. 163.

5 O. C. Wilson, Revs. Mod. Phys., 30,1025, 1958. 6 R. Minkowski, reported by L. H. Aller, Gaseous Nebulae (London: Chapman and Hall, 1956), p. 242. 7 G. A. Gurzadian, Planetary Nebulae ( Moscow : State Publishers for Physics and Mathematics, 1962), Chapter 9. This chapter has been trans- lated into English by Professor Leo Goldberg; preprint available from Harvard College Observatory librarian. 8 R. Minkowski, in Gas Dynamics of Cosmic Clouds (Amsterdam: North-Holland, 1955), p. 11. 9 D. E. Osterbrock, Annual Rev. Astronomy and Astrophysics, 2, 95,1964. !<> H. D. Curtis, Pub. Lick Obs., 13, 55, 1918. 11 W. Liller and L. H. Aller, Proc. Nat. Acad. Sei., 49, 675, 1963. 12 F. H. Seares and M. C. Joyner, Ap. /., 98, 302, 1943. 13 H. Gollnow and G. Hagemann, A. J., 61, 399, 1956. 14 B. A. Vorontsov-Velyaminov, Astr. Zhurnal U.S.S.R., 27, 285, 1950. 15 I. S. Shklovskiï, Astr. Zhurnal U.S.S.R., 33, 222, 1956. ie C. R. O'Dell, Ap. J., 135, 371, 1962. 17 The so-called "Shklovskiï method" was first suggested by Minkow- ski and Aller in Ap. J., 120, 261,1954. 18 O. C. Wilson, Ap. J., 108, 201,1948. 19 O. N. Chudovicheva, Izv. Astr. Obs. Pulkova, 23, 154, 1964 (No. 20 O. C. Wilson, Ap. J., Ill, 279, 1950. 174). 21 Hsi Tsê-tsung, Smithsonian Contr. to Astrophysics, 2, 109, 1958. 22 Ho Peng Yoke, in Vistas in Astronomy, Vol. 5, A. Beer, ed. (London: Pergamon Press, 1962), p. 127. 23 A. A. Latypov, Pub, Astr. Obs. Tashkent (2) 5, 31, 1957.