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 © Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System 114 HALLIDAY, HARDIE, FRANZ, PRISER 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 diam- eter 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 obser- vations 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 © Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System DIAMETER OF PLUTO 115 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 com- parator 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 ex- pected 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. © Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System 116 HALLIDAY, HARDIE, FRANZ, PRISER 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 dia- phragm 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 observ- ers using integrated light to retain the best signal-to-noise ratio. However, a Schott GG 3 filter was found to be beneficial in re- ducing 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 dia- phragm 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 © Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System DIAMETER OF PLUTO 117 mag., which is quite consistent with the estimate based on the smaller Dyer Observatory telescope. The observatories participating in this attempt to time the ex- pected 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.