Publications of the Astronomical Society of the Pacific

PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF THE PACIFIC

Vol. 78 April 1966 No. 461

AN UPPER LIMIT FOR THE DIAMETER OF PLUTO®

IAN HALLIDAY AND R. H. HARDIE^ Dominion Observatory Ottawa, Canada

AND

OTTO G. FRANZÎ AND JOHN B. PRISER U.S. Naval Observatory

Received February 14, 1966

The determination of the diameter and mass of the planet Pluto is made difficult by its extremely small angular diameter as seen from the earth and by the lack of any known satellite. Kuiper (1950) measured an apparent diameter of 0^723 which leads to a diameter of 5900 km for the planet. The estimated mean error of this observation is about 5 percent. If, however, there were a need for certain corrections which were not applied, Kuiper suggested that a value as small as 4900 km might be obtained. The mass of Pluto can be estimated from its gravitational effects on the orbits of Uranus and Neptune. The conventional value is given by Brouwer and Clemence (1961) as 0.90 earth masses (360,000 reciprocal solar masses) although they stress the unrelia- bility of the result which depends on old observations at times of conjunction of Pluto with Neptune or Uranus. A combination of the separate determinations of diameter and mass yields a mean density for Pluto of 50 gm/cm3 which is un- reasonable and indicates a serious error in at least one of the mass or diameter values. It has been suggested by Alter (1952) that the surface of Pluto may reflect light in a semi-specular manner which

# Contributions from the Dominion Observatory, Vol. 4, No. 20. t On leave from the Dyer Observatory, Vanderbilt University, 1964-65. J Now at Lowell Observatory, Flagstaff, Arizona.

113

would result in an underestimate of the diameter in any direct measure of the image. The asymmetry in the light curve has been interpreted by Hardie (1965) to be due to limb-darkening, and this direct evidence appears to cast doubt on the small value of the measured diameter. Precise observations of occultations of stars by Pluto appear to provide the best means of solving the problem.

Occultation Predictions

A proposal to use large reflectors to detect possible occultations of very faint stars by means of photoelectric photometry was ad- vanced recently by Halliday (1963). An important aspect of this proposal is that if the same occultation is observed from two or more observatories, then the difference in the parallax of Pluto as seen from the different observatories can be used to derive the actual diameter and not merely a lower limit. The effect is quite sensitive and is capable of even greater accuracy if the true diameter of Pluto is significantly less than that of the earth. An accuracy of about one percent can reasonably be expected. The season during which observations are currently possible extends roughly from October, when Pluto is observable in the east before sunrise, through opposition in March, until May or June when Pluto is in the western sky at sunset. Conclurent observations near either end of the observing season are restricted to a narrow belt of terrestrial longitude. Near opposition, on the other hand, observatories within a belt of at least 8 hours of longitude could attempt observations. The path of Pluto among the faint background stars has been followed at the Dominion Observatory during the oppositions of 1963-64 and 1964—65 with the help of several plates kindly taken for us with the 48-inch Schmidt telescope at Palomar Observatory, sup- plemented by plates taken with the Seyfert 24-inch telescope (in its Baker-corrector configuration) of the Dyer Observatory. Since the image of Pluto was secured on all these plates, it was possible to measure its position relative to a network of Yale Zone Catalogue stars, having applied appropriate proper motion corrections. This was required to determine the corrections to the ephemeris positions of Pluto which are listed in Table I. Mean corrections in a and δ of +0^52 and —(^/9 respectively were subsequently applied

TABLE I

Observed Corrections to Pluto Ephemeris Ephemeris Corrections ( O — Ε ) Date (UT) Telescope Δα Δδ 1963 May 20.2 S +0^55 —OTT 1964 Jan 14.4 S +0.54 -0.7 1964 Feb 4.3 S +0.50 -0.8 1964 May 4.1 R +0.55 -0.9 1964 May 5.1 R +0.53 -0.9 1964 Nov 11.5 R +0.48 —0.6 1964 Dec 14.5 R +0.46 —1.1 1965 Jan 27.4 R +0.52 -0.8 1965 Jan 31.4 S +0.53 -1.5 S: 48-mch Schmidt telescope, Palomar Observatory R: 24-inch Seyfert reflector, Dyer Observatory

to the ephemeris path in order to seek potential occultations of stars. It must be emphasized that neither the Palomar 48-inch Schmidt nor the Seyfert 24-inch Baker-corrector telescopes were designed or intended to yield positional results of high astrometric quality, and accordingly the mean corrections derived from the data of Table I may be reliable to only about 0.3 second of arc. Positions of the faint stars lying close to the predicted path of Pluto on the plates were measured on the Mann two-screw comparator at the Dominion Observatory, again using Yale Zone Catalogue stars for reference. A short computer program was then used to determine the minimum separation between the planet and any star lying close to its predicted path, together with the time of closest approach. The results from this program over two years yield a better estimate of the expected frequency of occultations than has been available from sample star counts. For the 1963-64 seasôn some 16 stars were found to lie within 10 seconds of arc of the path of Pluto, and for 1964-65 another 9 stars were within the same range. The limiting visual magnitude for this survey is estimated to be 17. If these two years are representative, then Pluto can be expected to pass within 10 seconds of arc of about a dozen stars per year, or within 0.8 second of arc of a star once per year, the stars being brighter than 17th magnitude.

A possible occultation was predicted for the night of April 28/29, 1965 (Halliday 1965). The star involved has a visual magnitude of 15.3, and the predicted time of occultation (511 UT) was suitable for observations from North America. The reader is referred to the illustration in the last reference for identification of the particular star. Numerous observatories cooperated in the observing program, and the photoelectric and photographic results are summarized below.

Photometry

At the time of closest approach, Pluto was expected to have an apparent visual magnitude of 14.1. The combined magnitude of Pluto and the star would be 13.8 outside of occultation, and the drop in intensity during an occultation would be about 25 percent. Since the light level was fairly low, it was essential to consider the sky brightness and to use as small a diaphragm as seeing and guiding facilities would permit. Under typical dark-sky conditions, a diaphragm of 15 seconds of arc in diameter or smaller was considered advisable, since a sky brightness of about 21 mag. per square second of arc would then add about as much light as the star in question. An occultation would then result in a net reduction in the total signal of about 20 percent. Since the star happens to have virtually the same color as Pluto, no advantage could be gained from the use of filters, and measures were secured by most observers using integrated light to retain the best signal-to-noise ratio. However, a Schott GG 3 filter was found to be beneficial in reducing the sky light without significant loss of intensity for Pluto and the star. Naturally, refrigeration of the photomultiplier was required to make its dark current negligible. Results from actual measurements of the event show that a time of occultation could have been secured with the Dyer Obser- vatory 24-inch telescope for a star of 16.2 mag. and with a diaphragm of 10" in diameter in the photometer. This is about one magnitude fainter than the star under discussion; and the accuracy of timing, based on signal-to-noise ratio, would be about 3 seconds (m.e.) in this extreme case. Examination of a photometer tracing made of the same event with the 84-inch Kitt Peak telescope re- veals that this telescope could do likewise for a star as faint as 17.8

mag., which is quite consistent with the estimate based on the smaller Dyer Observatory telescope. The observatories participating in this attempt to time the expected occultation included virtually all in North America possess- ing telescopes of adequate aperture and photoelectric photometers. The spread in latitude was from Victoria, British Columbia, to Fort Davis, Texas, and there was adequate duplication to cover such contingencies as cloudy skies. No occultation was observed at any observatory. Of particular interest were the negative results from the southernmost points since, as will be shown in the following section, the event was a very close miss, Pluto passing south of the star. In Tucson, Arizona, where observing conditions were excellent, the observers reported definitely negative results, and in Fort Davis, Texas (slightly farther south) where the conditions were less favorable, the observers reported probably negative results. It is unfortunate that no observations were secured from lower latitudes, as it is quite probable that an occultation could have been observed not far south of Texas.

Astrometry

The 61-inch astrometric reflector of the U.S. Naval Observatory Flagstaff .Station was used to carry out photographic astrometry as part of the total observing program. Fourteen plates of astrometric quality, each containing two exposures centered upon the star to be occulted, were obtained between April 23 and May 6 (UT). Kodak 103a-D was used in combination with a Schott GG 14 filter, and the exposure times ranged from four to eight minutes depend- ing on seeing conditions. No exposures were made duripg a three- hour interval, centered on the expected time of closest approach, in order to avoid proximity effects when the images would have been closer than 3". All plates were measured (by O.G.F.) simultaneously in the direction of right ascension and declination on the Mann two- screw comparator of the U.S. Naval Observatory's Astrometry and Astrophysics Division. The two exposures on each plate were treated as separate plates in the subsequent reductions. No cor- rection was made to account for differential refraction, since its effect upon the results of this investigation is negligible.

Six reference stars of suitable brightness were used to first reduce by plate constants all plates to the system defined by a single plate that contained a star trail for orientation purposes. All sets of reduced reference-star coordinates were then combined into a mean standard plate. Reduction by plate constants was then repeated to refer all measures to this mean standard plate. The reduced coordinates of Pluto and the star yielded directly the linear rectangular coordinate differences Δα cos δ and Δδ which, together with the respective epochs of observation, provided data for determining the angular separation of the planet and star at the time of closest approach. Least-squares solutions were carried out to represent the coordinate differences Δα cos δ and Δδ as functions of time by a third- order and a second-order polynomial, respectively. Each exposure entered into these solutions with a weight assigned according to an estimate of the photographic image quality, made before meas- uring the plates or reducing the data. The epochs of observation, the observed coordinate differences, their weights, and their residuals from least-squares fits of poly- nomials are given in Table II. The observed motion of Pluto with respect to the star during the period of astrometric observation is illustrated in Figure 1. The power series representing the observed coordinate differences as functions of time were interpolated to obtain coordinate differences and thus separations of the planet and star at epochs near that of closest approach. Precise interpolation was carried out at time intervals of one thousandth of a mean solar day for a period of about 20 minutes centered upon the approximate time of closest approach. The interpolated values of Δα cos δ and Δδ, the resulting separations, and the corresponding epochs are listed in Table III. A representation of the separations obtained from interpolated coordinate differences is given in Figure 2. The data show that closest approach, as observed from the Naval Observatory Flagstaff Station, occurred at April 29.217 (UT), when Pluto passed to the south of the star at a minimum separation of 0.0106 mm =b 0.0010 (m.e.) as imaged at the focal plane of the 61- inch reflector. For a plate scale of ISYS/mm, the angular separation at the time of closest approach (^12111 UT on April 29) was 0^/143.

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The mean error is conservatively estimated as itiK/OlS and is based upon an evaluation of the dispersion among the reduced coordinates of each reference star and of the residuals from least-squares fits of power series to the observed coordinate differences between planet and star. Photographic observations of the event were carried out also by Sanders (1965) with the 36-inch refractor of the Lick Observatory. Using a linear formula to represent the measured relative positions of Pluto and the star, and thus not accounting for the slight curva- ture definitely exhibited by his observations, Sanders obtained a minimum separation of 0^094 =b 0^020, a value incompatible with that determined from our observations. If, however, one applies to the Lick observations the same method of evaluation used in our work, and, more importantly, if one represents the observed y coordinates more accurately by a

TABLE III

Interpolated Separations

Epoch (UT) Δα COS δ AS 1965 (mm) (mm) ρ April 29.2110 +0.0201 —0.0109 0.0229 .2120 +0.0166 -0.0108 0.0198 .2130 +0.0130 —0.0107 0.0168 .2140 +0.0095 —0.0107 0.0143 .2150 +0.0059 —0.0106 0.0121

April 29.2160 +0.0024 —0.0105 0.0108 .2170 —0.0012 —0.0105 0.0106 .2180 -0.0047 -0.0104 0.0114 .2190 -0.0083 -0.0103 0.0132 .2200 —0.0119 —0.0103 0.0157

April 29.2210 —0.0154 -0.0102 0.0185 .2220 —0.0190 —0.0101 0.0215 .2230 —0.0225 —0.0100 0.0246 .2240 -0.0261 —0.0100 0.0280 .2250 —0.0296 —0.0099 0.0312

Plate Scale; 13''5/mm quadratic formula, one obtains a value of 0/163 for the minimum photocentric separation of Pluto and the star as observed from the Lick Observatory. Referred to the latitude of Flagstaff, this separa-

APR 29.212

Fig. 2 — The computed separation, p, of Pluto and the star around the time of closest approach.

Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System 122 HALLIDAY, HARDIE, FRANZ, PRISER

tion becomes 07154 and is in excellent agreement with that derived from our observations.

Discussion

In Figure 3 we have represented the essential results of this investigation. The star position is represented by the dot; the solid line, labeled FlagstafiE, represents the photocentric path of Pluto at a distance of (^/143 from the star. The dashed lines represent the corresponding geocentric path and those paths appropriate to the latitudes of several other observatories. The minimum photocentric separation for the most southerly observatory (McDonald) is reduced to 0^125, corresponding to a diameter of Pluto of 5800 km for a grazing occultation. The circle represents the projected disk of the planet as seen from the McDonald Observatory if Pluto were 5500 km in diameter. Considering the mean error, estimated at 0^/013, one can assign an extreme upper limit of 6800 km to the diameter with a confidence of 95 percent (based on an expectation of 5 percent that a positive error will exceed 1.6 times the mean error). While these results do not confirm Kuiper s estimate of the diameter since they are merely upper limits, they do increase substan- tially the confidence one may place in his result. It appears that any conjecture, such as Alter's or Hardie's, which attempts to ex-

for explanation.

plain the density discrepancy by assigning a diameter significantly larger than about 6000 km can now be eliminated. Although the orbit of Pluto is known with reasonably good ac- cracy, we know very little about its physical properties. From consideration of its apparent magnitude and distance, the diameter must be at least 2000 km, the diameter corresponding to unit albedo. However, such a small value is hardly compatible with Kuiper's measures of the diameter, or physically likely. On the basis of our extreme upper limit of 6800 Ion for thß diameter of Pluto, an extreme lower limit of 0.1 for its albedo can now be assigned. Considering the limit derived here for the diameter of Pluto, it is clear that the mass determined from orbital perturbations must be greatly in error. An upper limit to the mass of Pluto may be derived by assuming: (1) the density of Pluto is equal to the great- est known planetary density in the solar system, viz., that of the earth, and (2) a diameter of 6800 km. These assumptions yield an upper limit of 1/7 of an earth mass, corresponding to 2,200,000 reciprocal solar masses. Since there is very little physical reason for assuming that Pluto's density can be as high as that of the earth, and since the diameter is very probably less than 6800 km, there can be little doubt that the mass is considerably smaller than the upper limit just derived. A value of 4 gm/cm3 for the density would appear more plausible, and this, combined with a possible value of 5500 km for the diameter, would lead to a mass of 1/17 of an earth mass (5,700,000 reciprocal solar masses) or about five times the mass of the moôn. Such orders of magnitude for the mass would not account for the perturbations in the motion of Uranus and Neptune that were used in deriving the mass of and predicting the existence of Pluto. We interpret the results of this investigation as substantiating independently Kuiper's conclusions that Pluto's mass has heretofore been greatly overestimated. There appears to be no escape from a mass estimate as small as 0.1 earth mass or smaller, unless the density deviates markedly from values permitted by current physical theory. Neptune will not pass again near Pluto for several centuries, but Uranus will pass close to Pluto late in 1967. Positional observations of Uranus of extreme precision before and after that time

may provide new insight into Pluto's mass, but positional observers should expect very small perturbations. The occultation prediction program will be continued and inten- sive efforts will be made to observe probable events. Since the diameter of Pluto is now known with confidence to be considerably smaller than that of the earth, we may point out again that fairly short spacings between observatories will produce significant changes in the duration of an occultation and that the diameter may ultimately be known with an accuracy of about one percent.

This project, by its very nature, depends on the cooperation of many astronomers. The interest shown in observing the event of April 1965 was most encouraging. We would like to record our indebtedness to all who participated in these observations and par- ticularly to the Palomar Observatory for providing the plates on which the predictions were based, to Dr. R. L. Sears for securing supplementary plates at the Dyer Observatory, and to Mr. A. A. Griffin of the Dominion Observatory who carried out much of the computing and programming of the positional data from these plates.

REFERENCES

Alter, D. 1952, /.R.A.S. Canada 46, 1. Brouwer, D., and Clemence, G. M. 1961, in Planets and Satellites, G. P. Kuiper and B. M. Middlehurst, eds. (Chicago; University of Chicago Press), chap. 3. Halliday, I. 1963, J.R.A.S. Canada 57, 163. Hallíday, I. 1965, Sky and Tel. 29, 216. Hardie, R. 1965, A.]. 70, 140. Kuiper, G. P. 1950, Pub. A.S.P. 62, 133. Sanders, W. L. 1965, Pub. A.S.P. 77, 298.