Photometry of Faint Asteroids and Satellites

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PHOTOMETRY OF FAINT ASTEROIDS AND SATELLITES

proefschrift

ter verkrijging van de graad van Doctor in de Wiskunde en Natuurwetenschappen aan de Rijksuniversiteit te Leiden, op gezag van de Rector Magnificus Dr. O.J. Kuenen, hoogleraar in de Faculteit der Wiskunde en Natuurwetenschappen, volgens besluit van het College van Dekanen te verdedigen op vrijdag 1 december 1978 te klokke 14.15 uur

door Johan Degewij geboren te Amsterdam in

Sterrewacht Leiden Promotores: Prof. T. Gehrels en Prof. H.C. van de Hulst

The research described in this dissertation was supported by Leiden University and the National Aeronautics and Space Administration. Voor mijn ouders Voor Leonne CONTENTS page SUMMARY CHAPTER I INTRODUCTION 1.1 Background and Purpose 1 1.2 Detection of Faint Objects in the Solar System 6 1.3 Photometry of Asteroids 8 1.3.1 Definitions 8 1.3.2 Photographic Photometry 11 1.3*3 The Precision and Usefulness of Photographic Photometry 18 \.k Spectroscopy 19 1.5 Polarimetry 19 1.6 Infrared thermal Radiometry 20

CHAPTER II ASTEROIDS IN THE MAIN BELT 2.1 Studies of Photographic Lightcurves 25 2.1.1 Photographic Lightcurves obtained in 1973 27 2.1.2 Photographic Lightcurves obtained in 197^ 3*» 2.1.3 Rotation Periods and Body Shapes 42 2.2 Photoelectric Photometry 2.2.1 UBV Photometry of Faint Asteroids *»7 2.2.2 Compositional Types and Orbital Parameters 57 2.3 Size Distributions 2.3.1 Absolute Magnitude Distributions 60 2.3.2 True Size Distributions 63 2.3.3 Revised Size Distributions 65 2.4 Variations of the Composition over the Surface 2.4.1 Observations 71 2.4.2 Uniformity of Asteroid Surfaces 74 CHAPTER IN DISTANT ASTEROIDS 3.1 Asteroids with Hilda-type Orbits 3.1.1 VBV Colors 80 3.1.2 Radiometric Albedos and Diameters 80 3.2 Trojan Asteroids 3.2.1 UBVRI Reflectances 82 3.2.2 Variability and Body Shapes 88 3.2.3 The Phase Function 90 3.2.4 Radiometric Albedos and Diameters 90 page CHAPTER IV FAINT SATELLITES ' 4.1 Outer Jovian Satellites 3k U.I Saturns' Satellite S9 Phoebe 98 < CHAPTER V HISTORY OF SMALL BODIES IN THE i SOLAR SYSTEM I 5-1 Collisional Processes 101 \ 5.2 Similarities between Distant Asteroids ' and Faint Satellites 107 T 5.3 Where are the Dead Comets? 109 SAHENVATTING 115 STUD IE OVERZICHT 117 ACKNOWLEDGEMENT 118 SUMMARY

I began this work in Leiden in 1974 by measuring on photographic plates the 1ight variations of small asteroids as they rotate about their axes. The years 1976-1978 I spent at the University of Arizona making photoelectric observations of faint asteroids, the satellites of Jupiter and faint cometary nuclei. The following general insights were obtained into physical parameters, interrelations, and origin. The smaller asteroids, having diameters of about 1 km, appear to rotate faster than do the larger asteroids (-v-200 km diameter). Most of the bodies may be nearly spherical, probably due to a collisional erosion process in the Main Belt of asteroids. The distributions of diameter versus number were studied for low albedo (C, for carbonaceous) and high albedo (S, for silicaceous) type asteroids in the main belt, down to diameters of 25 km. Among the smaller bodies the S type asteroids are relatively more abundant, probably due to greater crushing strength for S type asteroids. This indicates that both optical types have also different properties in the in- terior of the body. Areas with slightly different reflectivity over the surface of an asteroid were detected; the rotational light varia^- tron of asteroid 4 (Vesta) was found to be caused by spots on Its surface. The spots may be due to differences in composition, or to partial excavation to deeper layers by meteoritic impact. In general, however, the surfaces of asteroids are quite uniform. Impact events result in the excavation of much more than the impacting mass and each asteroid blankets itself by a well-mixed layer of its own debris. Colorimetry and infrared radiometry of some Hilda asteroids, Trojans and the fainter satellites of Jupiter and Saturn, all having diameters between 100 and 200 km, show that a mixture of types exist. However, the resemblances of reflectance spectrum, albedo, phase function, rotation period and body shape among the majority of Trojans and J6 strongly suggest the possibility of dynamical interrelation during the history of the solar system. If some asteroids are nearly expended nuclei of comets that have lost most of their volatile gaseous material, then their cometary activity is expected to be extinct or at least weak. A dozen asteroids y

1.1 Background and Purpose

. Small bodies in the solar system (0.5-500 km) are of three ; types: asteroids, satellites, and comets. A comet differs from an asteroid by the appearance of a coma and/or a tail due to f outgassing, as the comet approaches the sun. KresSk (1972) 1 showed that a plot of semi-major axis a and orbital eccentri- ; city e (Fig. 1.1) distinguishes the asteroids from the comets. ' Only SUU Hidalgo is in a cometary orbit and does not show come- : tary activity. The relation between apparent magnitude, distance and diameter of a solid body without an atmosphere, is given in Fig. 1.2. With a 1.5 meter telescope (V,. = 18) bodies that have albedos of 0.05 can be observed phoioelectrically with sizes down to 5 km in the main asteroid belt and down to 30 km at Ju- piter distance. Objects smaller by a factor of 10 can still be observed photographically with large Schmidt telescopes. The location of these bodies (Fig. 1.1) is mainly in the asteroid belt (2 AUearth. The lifetime, before a collision with the planets takes place, may be on the order of 107 years (Wetherill ^) i All detailed information about magnitudes and orbital ele- j merits of asteroids was obtained with systematic photographic I surveys. The Yerkes-McDonald Survey (MDS), published in 1958 by ; Kuiper, Fujita, Gehrels, Groeneveld, Kent, van Biesbroeck, and - van Houten, provided magnitudes for asteroids down to blue ap- \ parent magnitude 16. The Palomar-Leiden Survey (?LS), published :: in 1970 by van Houten, van Houten-Groeneveld, Herget, and I Gehrels, sampled only 2% of the belt. It yielded orbital ele- k ments and an absolute magnitude distribution down to blue appa- ll rent magnitude 20. With an estimate for albedo and density, the 2 3

3 2

2 1

3 1

Fig.l.l The distribution of orbital elements a and e for asteroids (•), librating asteroids (A), well observed comets (O), and lost comets (o). Every object to the right side of the curved lines, representing the aphelia of Earth and Mars, crosses the orbit of the planet. Also the orbital resonances with Jupiter are shown. Adapted from KresSk (1972). derived mass distribution provided an idea about the total mass in the main-belt, namely about twice the mass of the largest asteroid, Ceres, or 2.Jt*102ltg, or O.^IO-3 the mass of Earth (Schubart 1972). The mass distribution at the faintest end gave reasonable agreement with the nieteroid mass distribution, sugges- ting a meteoroid origin from crushed asteroids (Oohnanyi 1969). A series of papers (see Chapter 2.3) was devoted to the interpretation of a non-linearity or "hump" at 9.5

Fig.1.2 The relation between the apparent visual magnitude V, semi-major axis a, and diameter D for an asteroid in opposition with the sun. Circular orbits and an albedo of 0.05 are assumed. Table 1.1 Terminology and Symbols

Asteroid A moving object of stellar appearance, without any trace of cometary activity. k Vesta Asteroid moving in the main belt of asteroids between Mars and Jupiter; this one is the fourth discovered, numbered k in the asteroid catalogue, and named Vesta. J6 Himalia Sixth satellite of Jupiter.

Albedo Geometric albedo ». Angle between the rotation axis of the body Aspect and the radius vector to the earth. Ratio between the longest and shortest axis Body shape of the body. An asteroid which occurs in a stable region Hilda at a-3-9 AU. The orbital period is in resonance with that of Jupiter. Lightcurve Magnitude values plotted as a function of time. This plot does not necessarily have to show variability. Lightcurve Peak to peak value in magnitudes of a light- amplitude curve showing variability. The angle at the asteroid between the radius Phase (angle) vectors to the earth and to the sun. The relation between phase angle and magnitude Phase function at unit distance to Sun and Earth. Also called phase relation. Seeing The width in arcseconds of a stellar intensity profile, measured at half-maximum intensity on a photographic image. Size Average diameter. In this dissertation only diameters are used. Trojan An asteroid which occurs in stable regions at a-5.2 AU either preceding or following Jupiter by -60° (p. 2). Blue magnitude, in the UBV system, reduced to 5(1,0) a distance of 1 AU between the asteroid and Earth and also between asteroid and Sun, with a phase angle of zero degrees. Mean opposition apparent blue magnitude. B(a,0) Table T.I Terminology and Symbols (cont.) cdf central density /og; photographic density parameter of the center of an image as defined for measurements with the ASTROSCAN (p.13 ) minus the surrounding background fog density. The unit is 0.01 d.

P(1,0). Absolute photographic magnitude. Geometric albedo.

P Photographic magnitude. X __=0.42 um. P Value of the polarization. The value is given as an estimate or can be variable.

Table 1.2 Location of Tables and Figures TabU: page Figure page Figure paqe 1.1 4 1.1 2 2.20 67 1.2 5 1.2 3 2.21 67 1.3 10 1• 3 7 2.22 73 1.4 14 1.4 9 1.5 15 3.1 82 2.1 26 1.6 17 3-2 86 2.2 28 3.3 87 2.3 32 2.1 27 3.4 89 2.4 37 2.2 30 3.5 90 2.5 41 2.3 30 2.6 49 2.4 33 4.1 95 2.7 52 2.5 34 4.2 96 2.8 68 2.6 36 4.3 97 2.9 72 2.7 38 4.4 99 2,8 39 3.1 81 2.9 40 3.2 83 2.10 43 3.3 84 2.11 45 3.4 85 2.12 51 3.5 85 2.13 57 3.6 87 2.14 58 3.7 91 2.15 59 2.16 60 4.1 94 2.17 61 4.2 96 2.18 64 .3 98 2• 1966 Because of their faintness it is difficult to study the smaller (<30 km) asteroids, beyond the non-linearity, in detail. The magnitude is generally fainter than 13 or 15 for the inner and outer parts of the belt resp. Much time with large telescopes is needed to obtain for these faint objects information about physical parameters such as: a) size distribution; b) body shape and rotation period; c) albedo and its variation over the surface; d) surface mineralogy and its variation over the surface; and e) surface texture. The basic philosophy of this dissertation is to bring together as many as possible physical parameters for objects of the smallest size in different locations of the solar system. A search for groupings of these parameters, related with the type of orbit, may improve the insight into the interrelation between the objects. With the 122 cm Palomar Schmidt telescope and the large telescopes of the University of Arizona efficient observing techniques were developed to observe faint asteroids. Also faint satellites of Jupiter and Saturn were observed and experience was obtained with the observation of cometary nuclei. This work was done to improve the insight into the following problems concerning the origin and history of the solar system: - Are the smaller asteroids fragments of catastrophic collisions between larger bodies? - Where are the dead comets? Or, which asteroids are the most likely candidates for being extinct cometary nuclei? - How did the Trojans and the faint satellites of Jupiter and Saturn originate? What are their interrelations, if any? Are they captured asteroids or comets, or were they formed in. situ! The presentation of the observational work related to these questions is given in the Chapter 11-IV, and is arranged according to distance to the sun: II Asteroids in the main- belt with 3-5 AU; IV Faint satellites of Jupiter and Saturn; and V History of Small Bodies in the Solar System. I have summarized the often used symbols and terminology in Table 1.1. The figures and tables can be located with Table 1.2.

1.2 Detection of Faint Objects in the Solar System

Faint objects in the solar system can be detected and dis- tinguished by their apparent motion, which is mainly a reflex of the earth's motion. It takes on the average 6 minutes for an object in the main belt to move its own apparent image diameter (3 arcsec) with respect to the surrounding stars. This means that longer exposures on photographic plates will not record fainter objects, unless the telescope is guided with the asteroid's motion. The corresponding limit for Trojans (a*5 AU) is 9 minutes and 2.2 hours for a possible new planet at 100 AU; such a planet would have a minimum size of 20G0 km

To detect as many and faint as possible objects, instruments have to be used that combine a wide field coverage with a deep limiting magnitude obtained in a few minutes. The most suitable instrument that has both these qualities is a large Schmidt telescope like the 122 cm Schmidt of the Hale Observa- tories on Palomar Mountain. It has a 6?4x6?4 field, and it re- cords in 5 minutes about 100 asteroids down to apparent magnitude 18-19 in the main-belt when at opposition to the sun. A survey for objects beyond the main-belt requires a care- ful choice of the time interval between the blink plates. Figure 1.3 gives the relation between the time interval between the blink plates and the displacement of the object relative to the stars. Very distant objects will be missed if the time interval is too short. This may be the reason why so few distant objects beyond Saturn have been reported in the literature. A big Schmidt telescope is also the most suitable instrument for detecting faint satellites at large distances (1-5 degrees) from a planet. Proper precautions have to be taken to reduce the scattered light from the planet in the telescope.

Fig.1.3 Displacement on blink pairs for objects in opposition with the earth, as a function of semi-major axis a, and time interval between the blink pairs. The diameter D of a faint object with F=21 is given. Circular orbits 0.5 1 5 10 and an albedo of 0.05 Time interval in hours are assumed. By using a piece of cardboard in front of the filter, Kowal et al.1*975) reduced the scattered Jupiter light in the 122 cm Paiomar Schmidt telescope, and he discovered J13 and, possibly, 4 Devices with much higher quantum efficiency are needed at long focus telescopes to detect faint moving objects. A relatively inexpensive image acquisition system consisting of an RCA 8857 image intensifier coupled to a VARO k8Ok SIT Vidicon, was used with the 154 cm telescope of the Lunar and Planetary Labo- ratory. Objects down to 17-18 mag were visible in a second on a TV screen that has a field of 5 arein in diameter. This device is invaluable for locating fainter objects, with magnitudes beyond =14.

1.3 Photometry of Asteroids

1.3.1 Definitions

Because my observations were mainly directed at faint objects (15<7<17), only broad-band (AA=0.05-0.2jim) filters were used. The photoelectric observations were always made in the UBVRI system (Johnson 1965), and the photographic photometry was made in a closely similar system. The relations between the instrumental system {ubvri) in which the measurements were obtained, and the standard system {UBVRI) are as defined by Hardie (1962):

V = Vo + e(B - V) + ?y (1)

B - V = V(b - V)Q * Cfa> (2)

a - B = *(« - b)o * ^ (3)

V - R = <.(» - r)Q + cw W

R - I - &(r - i)o + t,^ (5)

The terms with index zero are instrumental magnitudes and colors corrected for atmospheric extinction. Bodies in the solar system have UBVRI colors not too different from those of the sun. The domains are: 0.60<(B - 7)<1.00 and 0.1<(6 - B)<0.6. This facilitates the transformation from the instrumental system to the standard system. The observed magnitude 7 is related to the absolute magnitude 7(1,0) at unit distances to Sun and Earth and zero phase by

V ' 7(1,0) + 5Iogr + 51ogp - ^ (6)

Further we define

7(a,0) = 7(1,0) + 51og(a-1) + 51oga (7)

With r: distance Asteroid-Sun in AU, p: distance Asteroid-Earth in AU, a: phase angle; angle between ! in and Earth as seen from the object, the sign is - before and + after opposition, a: semi-major axis of the orbit of the object.

V(a,Q) is called the mean opposition magnitude, and Fj/a) is the phase function expressed in magnitudes. The phase function contains information about the surface texture of the body. The study of the phase function is, however, complicated by the variation in cross-section of a non-spherical body. For accurate studies of the phase function it is necessary to obtain lightcurves of the object, so that the same cross-section of the object can be recognized. As a "recognition point" sometimes the maximum of the Iightcurve (V ), or the magnitude level of c •; 1ightcurve cycle with equal°areas above and below this levei is used. F(a) is wavelength dependent.

Figure 1.4 shows 7o(1,a)= (i.O)-Fp(a) for asteroid 6 Hebe, and this curve represents the phase function Fjr(a) for this asteroid with the zero-point 7(1,0) added to it. In the following we will describe how 7(1,0) is defined in practice.

T T vo(i.o) 6.0 r\ © Hebe

6.5 -

i i i i 1 I I I i I 1 I i I I I 10 15 2C Solar Phase Angle a Fig.1.4 Phase function of asteroid Hebe. For A see the text. Adapted from Gehrels and Taylor (1977). TO

The linear part (|o|-t 7°) of the phase function has a o slope called the phase coefficient or -phase factor. For |a|£7 the phase function shows an excess brightness above the straight line and this is called the apposition effect. The absolute magnitude F(1,0) is defined as the extrapolation to zero phase of the 1inear part of the phase function (point A in Fig. Hi). If only incidental measurements are available and an absolute magnitude is needed, then this definition requires an assumption about the phase coefficient and the opposition effect. Gehrels (1967band Table 1.3) adopted the mean phase function of many bright asteroids as a standard curve to reduce all absolute blue magnitudes in the Yerkes-McDonald Survey (Kuiper et al. 1958), and recommended the use of this standard curve for all asteroids for which no detailed observations are available. Bowel 1 (1976) found however, that C-type objects have a mean phase coefficient of O.OAO mag/degree and S-type objects have a mean phase coefficient of 0.029 mag/degree. From this dependence on compositional types, it is clear that errors up to 0.2 mag can be made if a single observation is extrapolated to zero phase in deriving the absolute magnitude. I recommend, therefore, to publish single observations of an object together with the phase angle. In that case, corrections of the absolute magnitude can be made if future observations reveal its true phase function and/or surface compositional type. Such improved absolute magniyudes are proposed by Gehrels and Gehrels (i978;Chll).

Table 1.3 '

Average Correction to Zero Phase

Phase(a) ,(•>

0° +0.40 mag 1 + .22 2 + .12 k 00 6 - .10 8 18 10 - .23 12 - 28 14 - .32 16 -0.37

For larger phase angles, use 0.023 mag/deg. Adapted from Gehrels(1967b, 1970). 11

Photographic observations are often tied in photometrical- ly to standard sequences in Selected Areas. The objects in these areas were often measured long ago and the international photographic magnitude P was used. It is centered at 0.42 ym, and can be transformed to the Johnson B magnitude (Gehrels 1970) by:

B = P - 0.090(B - V) + 0.176 (8)

and, since the asteroid colors range over

0.60<(B - y)<1.00 (9)

the asteroids have

B = P + 0.10 (10) which is precise to within + 0.02 mag.

1.3.2 Photographic Photometry

This section is to give the definitions of photometric parameters, derived from stellar density profiles, and I will discuss basic error sources and how I dealt with them. The spe- cific reduction techniques for the transformation of photometric parameters into a standardized photometric system are dependent on the observational circumstances and are therefore given in Chapter 2.1.

Definition of Photographic Density The photographic density is defined by the ratio of the intensity IQ of the light incident on an emulsion and the intensity I- of the light transmitted by the emulsion. 'o d = 10log-i- (11) 'T I designate photographic density values in this dissertation with d (e.g. 0.2 d). The photographic density depends on the type of emulsion, the measuring system, and the wavelength of the light beam. This dependence is mainly caused by the substantial amount of light scattered in the emulsion. 12

Stellar Density Profiles

Borgroan (1956) discussed microdensitometer scans of stellar images obtained with the 122 cm Palomar Schmidt telescope. He showed that the emulsion is saturated at the center of the relatively brighter stars (K£i6), and that the width of their profiles increases with increasing brightness. Near 7=16 there is no saturation in the center of the stellar images, and both central density and profile width decrease with decreasing brightness. For Vi.\f the width of the profile does not change with brightness anymore. In this magnitude domain the image diameter depends on the quality of the seeing and is about 30-50 Vim, equivalent to 2-4 arcsec.

The Center of the Image For photographic photometry it is necessary to know the center of the image. Some definitions are: a) the center of qravity; and b) the center obtained with the "Iterative Rota- tion Algorithm" (Zorn pers.comm.). Method b) is an algorithm applied to the matrix with density values obtained from a measuring machine. This matrix is roughly centered at the object. The algorithm compares the original matrix with the same matrix rotated over 180 degrees. Both matrices are translated in X and Y until a best fit between the original and rotated matrix is obtained. The translation gives an insight into the accurate position of the center but weighted over the whole image. This method is in particular suited for grainy images obtained with Schmidt telescopes.

Microdensitometers and Photometric Parameters

A brightness dependent parameter has to be defined after the center of the image is found. For many years the iris photometer (Siedentopf 1934, Stock and Williams 1962) was the most effective tool for the determination of a photometric parameter. This is still true for programs with not too many stars. In this instrument the object is centered by eye in the iris diaphragm, which is then adjusted in diameter, often automatically, until the transmitted light is equal to a constant reference light- level. So,

2TT r. % r e de f ) 'T( » ) **" = constant (12) o o In this definition of the photometric parameter p., being the radius of the iris opening, the central density anS the width of the image are involved, and in practice the curve of 13

r. against magnitude is nearly linear. The iris photometer is especially suited for circular images and for faint objects with densities close to the background fog. Faint images of asteroids on Schmidt plates are irregular and the centering process is difficult, it is possible to search for a position with maximum rv (Kwee, pers. comm.), but this does not necessarily give the optimum solution. In the last decade, with the introduction of small com- puters, several types of measuring machines were developed. Basically they are microdensitometers, of which the table movement or the position of the 1ightbeam are controlled by a computer. The fastest machines need hardware and/or software to detect the image, to reject plate-faults, and to derive the position and a photometric parameter. This is done on-line and reduces the amount of data that has to be stored. The machines used for the photographic photometry presented in this dissertation were the Sartorius Iris photometer of Leiden Observatory, and the Ret icon array machine ASTROSCAN (Blansjaar and van Kuilenburg 1975), developed in a cooperative program between Leiden Observatory and NIWARS (Netherlands Interdepartmental Working group for the Application of Remote Sensing Techniques). Also some experience was gained with the POS microphotometer of Kitt Peak National Observatory and the VAMP microphotometer (Heintze et al. 1975) of Utrecht. Observa- tory. With the exception of the iris photometer, the off-line reduction recognizes the image and provides the position and a photometric parameter. An object is detected if the density difference between the center of the object and the background fog is equal to or larger than a preset value.

The ASTROSCAN

At the ASTROSCAN the photometric parameter is defined as the mean of the 5 highest densities measured in 10 x 10 micron squares situated around the center of the image and is called central density. The center of the image is found with the Iterative Rotation Algorithm. In this parameter, also information about the inner wings of the smaller images is incor- porated. The central density minus the average background fog density is designated in this dissertation as adf (central density minus surrounding fog density).

The PDS Microdensitometer

For density matrices measured with the POS microdensitometer of Kitt Peak National Observatory, a reduction program ASP (Area Stellar Photometry) is available (Newell and O'Neil, Jr. 1976). It is assumed that the center of the object is near the center of the density matrix, and the center is found 14

with the Center of Gravity Method. Newell and O'Neil define a parameter, K, equal to the integral of the density of the top and the inner wings of the stellar profile. The off-line reduction gives this parameter as a function of the grid size used for the integration. By using a rectangular density matrix and comparing the photometric parameter of two matrices perpendicular to each other, an optimum matrix-size can be selected providing: a) minimum influence of the difference between the adopted center and the true center of the image; b) rejection of nearby contaminating stars. I found however, that this program, designed for smooth and circular electronographic images was not very suited for small and grainy images obtained with a Schmidt telescope.

The Magnitude Scale and its Precision

The relation between the photometric parameter and the photoelectric magnitude of the star, for the same effective wavelength as the effective wavelength of the telescope- filter-emulsion combination, is called the calibration-eurve. Some curves are given in Fig. 1.5 (ASTROSCAN), and Fig. 2.7 (PDS). If colors are available, then it is possible to minimize the standard deviation of the residuals by adjusting the effective wavelength and using the corrected stellar magnitudes.

Table 1.4 Photometric Repeatability of the ASTROSCAN

Measurements on several dates with the ASTROCAN of 8 stars in selected Area 68 on plate PS 20401 Standard Measurements in adf units/ dev.t Star B 11 11 12 12 13 13 14 14 15 15 18 18 cdf mag 122 15.4 87 86 86 85 86 84 84 83 84 85 85 88 0.96 0.06 110 15.4 89 87 89 88 90 84 86 86 86 87 87 92 1.50 0.09 85 16.6 62 61 62 62 63 60 63 62 62 63 62 65 0.87 0.04 129 16.7 68 67 69 66 69 68 66 67 68 73 68 73 1.41 0.07 27 17.3 49 49 50 48 49 48 48 49 50 50 50 50 0.82 0.04 60 17.9 36 36 36 34 36 33 36 36 36 37 38 38 1.01 0.05 64 19.2 16 16 17 17 17 16 15 11 15 22 17 17 1.87 0.13 965 19.8 6 4 6 5 3 6 5 5 6 7 7 6 1.31 0.12 Fog| 163 162 163 160 161 160 c t Corrected for shift in the calibration curves. / The numbers heading the data, are dates in July 1976 that the ;• measurements were done. *' I Background fog value of the photographic plate in units of \. 0.01 density. i 15

mog/cdf 0.08 0.06 0IW 0.05 0.05 007 0.12 cdt

Fig.1.5 Relation between the photometric parameter adf and the photoelectric blue magnitude B for stars in Selected Area 68. The scale at the top gives the slope of the curve fitted through the measurements, for integer values of B. The 103a-0 plate was exposed by Prof.L.Plaut on Sep 28 1956 with the 122 cm Palomar Schmidt telescope.

In order to compare the precision of the photometric parameter obtained with the Sartorius iris photometer and the ASTRO- SCAN, Selected Area 68 was measured with the Sartorius Iris photometer on a 103a-E plate, and with the ASTROSCAN on a 103-0 plate (Fig. 1.5). The standard deviation of the residuals between the data and the fit were 0.14 mag (n=Ht) and 0.11 mag (n=3S) respectively. It is difficult to compare the two instruments with two different plates. I expected that the iris photometer had a lower photometric precision with respect to the ASTROSCAN. This is caused by the difficulties in centering grainy stellar images in the iris of the iris photometer. The results are not convincing and a better test with the same plate is needed in the future. An insight into the photometric repeatability of the ASTRO- SCAN is given in Table 1.4. The plate with the photometric sequence was measured after the measurement of a field plate, and the intensity of the measuring lamp was monitored with a photocell showing small variations not larger than 2%. It can 16

be seen that the calibration curves obtained with time intervals of many hours, are shifted with respect to each other. The maximum shift between two curves for the brighter stars is 5.5 adf (July 18(2) - July 13 (2)), which corresponds to 0.33 mag. I shifted each curve to the average of all curves and I computed the standard deviation of the corrected measurements for the same star. This standard deviation is called repeatability and is given in the last column of Table 1.4. It is on the average equal to 0.06 mag for stars with S<19, and suggests that the photometric quality of the ASTROSCAN should be improved, because it contributes significantly to the total photometric calibration error (0.11 mag). The photometric quality of the ASTROSCAN can be improved by: a) higher read out accuracy for the higher density values, this can be achieved with a logarithmic amplifier; b) better stability of the measuring lamp; and c) higher intensity of the measuring lamp. A time consuming alternative is to do the measurements more than once, or to make the integration time longer.

The Magnitude Calibration Obtained from a Second Plate

For the calibration of the Fainter magnitude domain beyond 16, it is difficult to find photoelectric maQfsitudes for objects on the field plate. For that purpose a second plate was exposed of a calibration area with known photoelectric magnitudes and colors. The field plate and the calibration piate were exposed and processed under circumstances as equal as possible. The background fog level was, however, difficult to equalize because of different directions in the sky. Systematic errors in the photometry can be expected if there is a difference in background fog between field plate and calibration plate. Some results of Chapter 2.1.2 are: if the field plate is only 0.1 d darker than the calibration plate, then the magnitudes are 0.1 mag too faint. If the background fog difference is O.k d then the magnitudes of the brighter objects are O.k mag too faint, and the magnitudes of objects close to the plate limit are off by as much as 1 mag.

Sensitivity Fluctuations in tlse Photographic Emulsion

I looked into the existence of periodic density patterns on photographic emulsions. Fourier analysis was made of micro- | photometer scans of several emulsions on glass plates and sheet- [ film. Also, several density levels were studied. No significant | sinewaves with wavelengths between 50 micron and 5 cm were Pound. 17

Fig.1.6 Prof.L.Plaut used an occulting sector to expose each quadrant of the 355x355 cm plate with Selected Area 68.

An insight into sensitivity fluctuations over larger distances could be obtained from a plate taken by Dr. L. Plaut, with the 122 cm Palomar Schmidt telescope. He exposed four quadrants of one plate with an occulting sector (Fig. 1.6) to study vig- netting effects in the telescope. This is an elegant way to expose, with circumstances as equal as possible, several areas on the same plate. I measured this plate with the ASTROSCAN. Selected Area 68 with 38 objects was used as a photometric standard area. The sensitivity over the plate is surprising- ly homogeneous. There might be a small systematic magnitude difference between the four exposures, about 18 cm apart on the emulsion, equal to =0.06 mag.

Elongated Images

With exposure times of 5 minutes, the object moves a distance between 30 (Jupiter satellites) and 60 ym (asteroids) on a plate taken with the 122 cm Palomar Schmidt telescope. This is comparable to the mean image diameter and therefore care has to be taken with the photometry. Van Houten et at. (1970) found corrections up to 0.^1 mag for the brighter objects of about 16 mag with a trail length of 100 pm. I tried to do precise photometry with the ASTROSCAN for the outer Jupiter satellites only. Their mean motion is 30 urn per 5 minute exposure and their magnitude is generally fainter than 18, so the effect is expected to be negligible. For the 1ightcurve runs of asteroids that move up to 60 ym per 5 minute exposure, a small systematic error in the magnitude will be present. The standard deviation of the Iightcurves is not affected by this problem, because the motion during the night is constant. Some influence from guiding errors can be expected. The Effect of Variable Seeing Conditions

Seeing influences the density profiles of the stellar images (Roemer 1976), and if these profiles change during the night, then this will affect the photometric parameter. I never did no- tice, however, that the photometric parameter for the comparison 18

stars deviated suddenly or slowly from an average airmass curve, due to varying seeing conditions. I was in a good position to test any such deviations because the photographic lightcurves of the asteroids and satellites are referred to five nearby comparison stars of comparable magnitude. The magnitude difference and distance generally did not exceed one magnitude and two centimeters on the Schmidt plate, respectively.

1.3.3 The Precision and Usefulness of Photographic Photometry

Absolute Photometry

In order to determine magnitudes of faint objects on photographic plates, one is often forced to use photoelectric magnitude sequences that occur on different plates. In this case systematic errors up to 0.5 mag can easily be made, or even worse, if the background fog density levels are different. It is clear that this kind of work, with large differences in fog level, has to be used with caution. !f one has, however, a magnitude sequence on the field plate, then systematic errors are absent because the background fog and processing are the same. It must be possible to determine magnitudes in this case, with a precision better than 0.1 mag, if more than two plates are used.

Relative Photometry, Lightcurve Surveys

For lightcurve surveys of faint asteroids one is forced to use photographic techniques for detection and photometry, because there are no ephemerides. It is clear that large Schmidt telescopes are especially suited for this purpose, mainly by their large field coverage and short exposure times for recording objects with blue magnitudes down to 21. It is shown (Ch. 2.1.1) that standard deviations in the magnitudes of about 0.1 mag can be obtained for these very small images, if one selects comparison stars nearby with magnitudes not too different from the object. I conclude that there is not yet a photoelectric device or observing technique available to do this kind of work with a comparable efficiency. 19

1 .h Spectroscopy

Faint objects in the solar system, moving in orbits around the sun, are called asteroids if no cometary activity is observed. Usually the objects are discovered by direct photography, and an obvious question relevant to the interrelation between comets and asteroids is: do asteroids show weak cometary activity not detectable with direct photography? A spectrograph is needed to detect weak cometary activity, and to study the physical processes in detail. I observed several faint comets by direct photography using an image intensifier, and a low dispersion (-0.2 ]im/m\) spectrograph at the cassegrain focus of the 228 cm telescope of Steward Obser- vatory. For faint (7^15) comets, the coma consists of a dustcloud and a gascloud. The dustcloud, of unknown composition, contains the majority of material within roughly 10,000 km diameter (=10 arcsec). The gascloud composed of CN and sometimes C3 extends much further out and I did not see a change in line intensity over the slit-length of 20 arcsec for several faint comets (Ch. V). A comparison between direct photography and simultaneous spectroscopy showed that the dustcloud can be detected with both techniques. The gascloud, however, with its well-defined emission lines, was with the spectrograph still detectable at large (=10-20.arcsec) distances from the nucleus, where the direct photography failed to detect it. With this equipment, a program was initiated to look for cometary features in asteroid spectra. The results are given in Ch. V.

1.5 Polarimetry

Reflected sunlight from bodies without atmospheres in the solar system is slightly polarized. The polarization is dependent on the refractive index, the degree of porosity or com- paction, and the opaqueness of individual grains on the surface. Pioneering work on polarization measurements of Mercury, the moon and laboratory samples was done by Lyot (1929). Work by Dollfus (1961) gave a correct identification of the surface textures of the moon and Mars. Recent reviews are published by Gehrels (197*0 and Zellner (1978). 20

The position angle of the dominant electric vector is for a spherical object constrained to lie parallel or perpendicular to the plane of scattering. Denoting the corresponding intensity components by I,, and lx , we may define the degree of polarization by:

P = (l± - I,, )/{\J_ + I,, ) (13) which can be positive, negative, or zero. The polarization for bodies without atmospheres in the solar system varies only with the phase angle a. A plot of P as a function of a is called the polarization curve. It shows P=0 for ot=0, and negative polarization until some value, o0, between 18° and 25°. This effect is generally interpreted to arise from multiple scattering in the grains close to the surface with shadowing to spoil the symmetry. Beyond the inversion angle ct0 the polarization is positive. An empirical relation between the albedo and the slope of the polarization curve at the inversion angle was independently found by Kenknight et al. (1967) working with laboratory samples, and Widorn (1967) interpreting the polarization studies of moon and planets by Lyot (1929) and Doilfus (1961). A first application to an asteroid, Icarus, was made by Gehrels et al. (1970). Under certain plausible assumptions it can be shown that for any o, a change in albedo is inversely proportional to a change in polarization, and this principle can be used to study the variation in albedo over the surface of an asteroid. For this purpose high precision polarimetry has to be perfor- med during a rotational lightcurve cycle (Ch. 2.4).

1.6 Infrared thermal Radiometry

A body in the solar system receives radiation from the sun. The reflected radiation appears as the visual brightness of the object, while the absorbed energy is re-emitted as thermal infrared radiation.

If it were possible to measure: a) £y£s,being the energy of the reflected radiation per unit time integrated over visual wavelengths and over all space angles; and b) L^r, being the energy of the emitted radiation per unit time integrated over infrared wavelengths and over all space angles, then it would be possible to determine the Bond albedo Aj^s from the simple relation: 21

In practice the energy radiated by the object is measured by a single detector in space and therefore the coverage of space angle and wavelength is limited. Let Sy and Sg denote the quantities corresponding to Lv^8 and L^p, but now measured per unit of solid angle. V and N are standard wavelength bands in the visual (0.55 u"i) and infrared (10.0 tim) domains of the spectrum. With srFa2Svis an<*S lTa2'ir* vie can wr'te: WiV«7 05) and Lir ^B^B (16) in which q is the phase integral and Oj and s«> are constants. If we further define Ay^Pyq^, then we can rewrite (14) as:

It is known (e.g., van de Hulst 1979) that qy varies between 1.45 and 1.64 for different models. The value is dependent on the surface texture and the distribution of craters over the surface. The value of qg depends on the rotation of the body and the heat conductivity at the surface, and also on the surface texture and cratering (Hansen 1977). All references cited below contain models for the visual end infrared (black body) radiation, which amount to implicit estimates of the phase integrals, although it is not customary to present the formulae in this form. With measured values of Sy and Sfl, reasonable estimates of Ay and qg, and a value of C based on calibration, we can use equation (17) to find the visual geometric albedo py. It is called the radiometric albedo to distinguish it from the value determined with the polarimetric technique (Ch.1.5) called: polarimetria albedo. Similar expressions exist between the radiative area of the body and the quantities mentioned previously. From the radiative area an average diameter can be computed. Allen (1970) determined for the first time the albedo and diameter of Vesta. Ke used a simple model of a non-rotating smooth spherical black body, and obtained a diameter of 570 km. This value is 50% larger than the value determined by Barnard (1902) with a disk micrometer. Matson (1971) obtained for 26 asteroids albedo values between 0.03 and 0.3. Recent work about asteroid albedos and diameters derived with this method, is published by Hansen (1977) and Morrison (1977). 22

A discrepancy existed between radiometric and polarimetric albedos measured for the same objects. The radiometric albedos were on the average smaller -than the polarimetric ones by about 20%, and the discrepancy increased strongly for albedos below 0.06 (Chapman et at. 1975)- The discrepancy decreased to 10% by the use of better models (Hansen 1977» Morrison 1977), and measurements in the laboratory showed that the polarimetric calibration suddenly deviated from a straight line for albedos below 0.06 (Zellner et al. 1977)- This means that the radiometric albedos below 0.06 can be trusted. I applied the radiometric technique to some asteroids in peculiar locations of the solar system, like Hildas and Trojans. The infrared radiometer as described by Low and Rieke (1974) was used together with the 154 cm Catalina reflector of the Lunar and Planetary Laboratory. The albedo py and diameter were computed according to the model of Morrison (1973) and Jones and Morrison (1974). The transformation from the instrumental system (X^^J=10.6 pm) to the standard system (A-,ff=10.0 ym) is given by GriMe (1978). JJ

References Allen, D.A. 1970 Infrared diameter of Vesta Nature 227, 158 Barnard, E. 1902 On the dimensions of the planets and satellites AN 157, 260 Blansjaar, P.W.H., and Kuilenburg, J. van 1975 The computer controlled comparator ASTROSCAN Image Processing Tech- niques in Astronomy p247 (Eds. C. de Jager and H. Nieuwen- huijzen) 0. Reidel Publ. Co. Dordrecht Holland Borgman, J. 1956 Electronic scanning for variable stars Publ. Groningen Observatory 58, 25 Bowel 1, E. 1976 Physical properties of asteroids from UBV photometry; paper presented at the Division of Planetary Sciences Meeting Austin Texas (march 1976) Chapman, C.R., Morrison, D., Zeliner, B. 1975 Surface properties of asteroids: A synthesis of polarimetry, radiometry and spectrophotometry Icarus 25, 104 Dohnanyi, J.S. 1969 Collisional model of asteroids and their debris Journ. Geophys* Res. 74, 2531 Dollfus, A. I96I Polarization studies of planets Planets and Satellites p343 (Ed. G.P. Kuiper) Univ. Chicago Press Gehrels, T. 1967a Minor planets. I The rotation of Vesta Astron. J. 72, 929 Gehrels, T. 1967b Minor planets. II Photographic magnitudes Astron. J. 72, 1288 Gehrels, T. 1970 Photometry of asteroids Surfaces and Interiors of Planets and Satellites p317 (Ed. A. Dollfus) Academic Press London Gehrels, T. Editor of Planets, Stars, and Nebulae Studied with Photopolarimetry University of Arizona Press 1974 23

Gehreis, T., Roemer, E., Taylor, R.C., Zellner, B.H. 1970 Minor planets and related objects. IV Asteroid (1566) Icarus A8tron. J. 75, 186 Gehreis, T., and Taylor, R.C. 1977 Minor planets and related objects XXII Phase functions for (6) Hebe Astron. J. 82, 229 Gradie, J.C. 1978 An astrophysical study of the minor planets in the Eos and Koronis asteroid families Ph.D. thesis University of Arizona Hansen, O.L. 1977 An explication of the radiometric method for size and albedo determination learus 31, 456 Hardie, R.H. 1962 Photoelectric reductions Astronomical Techniques p178 (Ed. W.A. Hiltner) University of Chicago Press Chicago Houten, C.J. van, Houten-Groeneveld, I. van, Herget, P., Gehrels, T. 1970 The Palomar-Leiden survey of faint minor planets Astron. Astrophys. Suppl. Ser. 2, 339 Hulst, H.C. van de 1979 Multiple scattering and radiative transfer Academic Press New York N.Y. Johnson, H.L. 1965 Interstellar extinction in the galaxy Astrophys. J. 141, 923 Jones, T., and Morrison, D. 1974 Recalibration of the photometric/radiometric method of determining asteroid sizes Astron. J. 79, 892 KenKnight, C.E., Rosenberg, D.L.,Wehner, G.K. 1967 Parameters of the optical properties of the lunar surface powder in relation to solar-wind bombardment J. Geophys. Res. 72, 3105 Kowal, C.T., Aksnes, K.,Marsden, B.G., Roemer, E. 1975 Thir- teenth sateli iteof Jupiter Astron. J. 80, 460 Kres.5k, L. 1972 On the dividing line between cometary and asteroidal orbits The Motion, Evolution of Orbits, and Origin of Comets p503 (Eds. G.A. Chebotarev and E.I. Kazimirchak-Polonskaya) 0. Reidel Leningrad 1970 Kuiper, G.P., Fujita, Y., Gehrels, T., Groeneveld, I., Kent, J., Biesbroeck, G. van, and Houten, C.J. van 1958 Survey of Asteroids Astrophys. J. Suppl. Ser. 3, 289 Low, F., and Rieke, G. 1974 The instrumentation and techniques of infrared photometry Methods of Experimental Physics 12 (Ed. N. Carl ton) Academic Press p4i5 Lyot, B. 1964 Research on the polarization of light from planets and from some terrestrial substances Ann. Obs. Paris VIII no. 1, 1929 NASA TT F-187 Matson, D.L. 1971 Infrared observations of asteroids Physical Studies of Minor Planets p45 (Ed. T. Gehrels) NASA SP- 267 Morrison, D. 1977 Asteroid sizes and albedos Icarus 31, 185 Morrison, D. 1973 Determination of radii of satellites and asteroids from radiometry and photometry Icarus 19, 1 Newell, B., O'Neil, Jr. E.J. 1976 The KPNO ASP program System User's Manual 24

Roemer, E. 1976 Luminosity and astrometry of comets: a review in The Study of Comets p380 (Eds. B. Oonn, M. Mumma, W. Jackson, M. A'Hearn, and R. Harrington) NASA SP-393 Schubart, J. 1972 Asteroid masses and densities Physical Studies of Minor Planets p33 (Ed. T. GenreIs) NASA SP-267 Siedentopf, H. 197^* Photograph!sch-photometrische Untersuchungen I AN 254, 33 Stock, J., and Williams, A.O. 1962 The measurements of focal stellar images Astronomical Techniques p392 (Ed. W.A. Hiltner) The University of Chicago Press Wetherill, G.W. 1974 Solar system sources of meteorites and large meteoroids Ann. Rev. of Earth and Planetary Sc. 2y 303 Widorn, T. 1967 Zur photometrischen Bestimmung der Durchmesser der Kleinen Planeten Ann. Univ. Sterroaarte Wien 27, 3 Zellner, B., Leake, M., Lebertre, T., Duseaux, H., and Dollfus, A. 1977 Laboratory polarimetry of meteorites and the asteroid albedo scale Proceedings 8th Lunar Science Conf. pi 044 Zellner, B. 1978 Optical polarimetry of paniculate surfaces Optical Polarimetry-Instrumentation and Applications 112 Proceedings of the Society of Photo-optical Instru- mentation Engineers 25

CHAPTER II ASTEROIDS IN THE MAIN BELT

2.1 Studies of Photographic Lightcurves

Very little is known about the rotation properties and body shapes of the smallest asteroids in the size domain of some kilometers. Some of these asteroids cross the orbit of Mars, and come sufficiently close to the earth to be observable. They generally have elongated shapes and some have the fastest rotation periods known among asteroids. The only information concerning the brightness variation of small main belt asteroids was from studies of photographic plates. On these plates, faint asteroids with apparently large amplitudes were reported (van Houten 1962). These observations were intuitively interpreted as being caused by very elongated chunks, ripped off from a parent body by a catastrophic collision. Kuiper et al. (1958) found that the histogram of number of asteroids versus absolute magnitude for about 2000 asteroids is not continuous but has a non-linearity near absolute magnitude 10 (50-100 km), especially for the asteroids in the inner part of the belt. This histogram (Fig. 2.16) will be discussed in more detail in Chapter 2.3. By assuming that the absolute magnitude is a measure of size, they suggested that the non-linearity separates two modes of asteroid formation: original accretion and collisional fragmentation. The smaller asteroids thus are believed to be debris arising from the collisional shattering of a few or a few hundred original condensations, some of which may still survive today among the larger asteroids. Any observational clue to the correctness of this hypothesis clearly is important for the understanding of the evolution of the solar system.

If the smallest asteroids are collisional fragments, then they may have short rotation periods (if they have enough tensile strength), and elongated shapes, which may be detected in their rotational lightcurves (Gehrels 1971). However, in order to work on the faint side of the non-linearity where exclusively the fragments occur, one needs to obtain lightcurves for aster- roids usually fainter than apparent magnitude 16 where photoelectric photometry for sufficiently large samples is not fea- sible. Large samples can be obtained with a photographic telescope that combines a wide field and a faint limiting magnitude in an exposure of some minutes, like the 122 cm Paiomar Schmidt telescope. Photographic photometry of the small Schmidt images seldom gives precision better than 0.1 mag for a measurement of one stellar image and this means that shapes less elongated than 10% in body axes are not detectable with short photographic runs during one night. Prof. T. Gehrels got the first opportunity with the Palo- mar Schmidt telescope for exposing a series of plates of a field in opposition with the sun on 2 November 1973 (the re- 26

suits are reported in Ch.2.1.1). A second run was done on 15 August 1974 (Ch.2.1.2); these plates actually were taken for outer Jovian satellites, but some information can be extracted also for the foreground asteroids. Table 2.1 gives the circumstances for both runs.

Table 2.1 Photographic Lightcurve Runs with the 122 cm Palomar Schmidt Telescope

Date 2 Nov 1973 15 Aug 1974 Objects aimed at main belt Jovian asteroids satel1ites Time UT 6*23 - 10*13 5*06 - 11*46 Right Ascension 2* 36m 23* 08m Declination 15° 13' - 6° 131 Eel. Long. 41?5 345°6 Eel. Lat. (1950) - 0?1 - 0?6 Number of plates 11 19 Number of exposures 44 57 Exposure groups 4x3 rain 3x4 min Distance between the 36-36-48 48-60 exposures in arcsec Photographic emulsion 103a-E 103a-0 Filter WR4 WG-2 Background fcg 1 .Id 1.7-2.6d Calibration area SA68 SA68 Exposure groups 4x3 min 3x4 min Limiting magnitude -calibration area 7=18.5 5=19-5 -plate field 7=18.5 5=19.0-19.5 Surface blinked in 42.6 20.9 square degrees Number of objects 106 50 asteroids found 6 satel1ites Number of objects 96 43 asteroids measured 6 satel1ites 27

2.1.1 Photographic Lightcurves obtained in 1973

Introduction

On 2 November 1973 UT as many exposures as possible were obtained with the 122 cm Palomar Schmidt telescope of a field opposite to the sun (see Table 2.1). I found 106 moving objects with the Nijmegen blink comparator (de Kort 1968), and used the S3rtorius iris photometer of the Leiden Observatory for the photometry of 96 asteroids and 108 reference stars. I limited this reconnaissance to the most homogeneous set of plates, covering a period of k hours. Even so, there were 60,000 measurements which were reduced by referring the photometric measurement of each asteroid to the mean of 5 comparison stars. For each asteroid the range of magnitudes of the comparison stars was less than one magnitude and included that of the asteroid.

Measurements and Reductions

Every image of the asteroid and the five comparison stars was measured and near it a measurement of the background fog was made. From the iris value r^ of each image, the mean of eight background fog iris values was subtracted. The differences Aj-£ for the asteroid and S^-fc for the comparison stars were plotted in the manner shown in Fig. 2.1. The measurements of the four exposures offered a possibility to suppress photometric noise compared with single exposure plates. As can be seen from Fig. 2.1 and Fig. 2.7, the images exposed after the first image are systematically brighter. This is called the pre-exposure effect. The analysis showed a straight line relation between the number of the exposure and its photometric

Magnitude

Ins value »• Fig.2.1 The measurements with the iris photometer of the asteroid (*) and five comparison stars plotted against the exposure 3 on one plate. Formula 18 fits with least-squares five parallel lines with slope m^=tga through the measurements of the comparison stars. 28

parameter, and parallel lines were fitted through the measurements of a set of comparison stars for one asteroid at each plate (Fig. 2.1). I determined m^ and S^ so that

5 i» 2 , error- £ J. CSv7-fe-(S£4fe-m^(j-l})] - minimum (18) I- t-*1 3ml i in which i is the number of the comparison star; 3 the number f of the exposure; and k the number of the plate. For the small stellar images an optimum iris value was determined for which the rms value of error was minimal. The measurements for this purpose were done on one plate and the results are shown in Table 2.2. An optimum iris value setting of 650 units for the background fog was adopted.

Table 2.2 Determination of optimum iris setting and photometric errors for plate PS 9537, taken Nov 2, 1973

Iris error/ Settingt V ' 17 18 19 mk = 0.25 0.20 0.02 average 400 0.10 0.08 0.08 0.09 650 0.07 0.08 0.07 0.07 650 0.07 0.09 0.09 0.08 725 0.08 0.08 0.08 0.08 800 0.08 0.10 0.08 0.09

t Refers to a plate area without stars. The number is proportional to the surface of the iris. / See formula 18 .

; The successive steps to derive relative lightcurves in J units of iris setting were: i 1. The reduction to the overall (nightly) mean. I 1 ! 1.1 Compute the average of S^fc from all plates I- — " . { Hi - 1/11 I Htk i - 1.-...5 (19) I k=\ 29

1.2 Compute for each plate • T" ik m z^k ' il 'f«"»»3 | k * 1,...,11 (20) i I: and F 1/5 f fc * 2! Fife (21)

1; f 1.3 Correct each measurement of an object on plate k to y the mean

hk ~%k Fk (23) 2. The correction for the pre-exposure effect.

DFfe (25) The reduction to relative 1ightcurves. The magnitude of a comparison star is referred to the mean of the magnitude of the other four comparison stars. The magnitude of the asteroid is referred to the mean of the magnitudes of the five comparison stars. Sifk " Hok ~ V* ? Hjk (26)

- 1/5 I S^ (27)

All reductions to relative 1ightcurves were done with this algorithm. It was proven that the use of the pre-exposure effect as extra information to reduce noise was indeed effective. The standard deviation in the comparison star 1ightcurves (Fig. 2.2) increases by 20% if the reductions are made with the assumption that hh single-exposure plates were measured.

The Magnitude Scale The measurements were transformed into an apparent magnitude (Table 2.3, column 2) with measurements of standard stars in Selected Area 68, using photoelectric magnitudes of Baum 30

RMS 1 1 1

02 o o oo o 0.1 ° o o o o

n 1 1 1 15 16 17 18

Fig.2.2 The average rms error RMS of the lightcurves of five comparison stars plotted against their magnitude B. (pers.comm.). The plate and filter combination gives an effective wavelength of 0.585 um (103a-E + Mrk, see Fig. 2.3). This was obtained with the following method: B-V colors were known for the standard stars and the magnitude at an intermediate wavelength was obtained by a linear interpolation. For many values of the wavelength the corresponding photoelectric magnitudes were used for the fit against the iris value and a standard deviation of the residuals was computed. The wavelength with a minimum value of the standard deviation was called the effective wavelength. A B-V color of 0.75 was assumed for the asteroids and with effective wavelengths for the B and V response curves of 0.45 v"> and 0.55 vwi (Allen 1973) resp. a correction of 1.0 mag was obtained. This correction is added to the apparent magnitudes to obtain B. For each asteroid the distance from Earth was estimated from an opposition path of 3.2 hours,which corresponds to a movement on the plates of -2000 vim,while the precision of the measurements is -25 um. Assuming the orbits of the asteroids to have zero eccentricity and inclination and taking corrections for the observed phase angles from Gehrels (1970b), I de-

Log S - 2 /—- v I03O-D WO-2 / \ Fig.2.3 Spectral sensi-

1 / 1 I 1 1*1 I 1 1 tivity S of the photographic emulsion and LogS filter combinations used in this disser- WG-2 / tation. Adapted from /WR; a WR i.l Kodak publication P-315 (1973). 0L3 0.4 0.5 0.6 07 31

rived B(1,0) magnitudes; this transformation to absolute magnitude has a maximum uncertainty of about±1 magnitude. The correction for trailing is expected to be negligible. The correction for the effect that the objects were preferentially observed in their perihelion was made by adding 0.7 to their magnitudes (van Houten et al. 1970).

The Detection of Variability

The detection limit for variability, RMS, is shown plotted against apparent magnitude in Fig. 2.2. It is equal to the average of the rms errors in the lightcurves of the five comparison stars. The comparison stars were selected as close as possible to the asteroids. Sometimes larger distances could not be avoi- ded (Table 2.3, column 9). I measured an rms error in the lightcurves of some test stars of 1.3 times MS if the distance actually is as large as 70 mm. Fourier analysis indicates, however, that the increase in noise of the lightcurve due to the separation of an asteroid from its comparison stars did not introduce spurious periods. On the average I consider the detection limit of amplitudes to lie near 0.2 mag. The detection limit can be improved by choosing reference stars closer by. This, however, can only be realized by considerably increasing the number of comparison stars. In the following text a shorter notation of the relative lightcurves Aj^ and S^jfc of asteroid and comparison star resp. is adopted, being m^(t^) with Z=1,2,...,kk. These magnitude points were transformed into a power spectrum:

(28) with

FS, (29) m and 41* m T i (30) 1=1 where k^ runs from one period per 8 hours until one period per *» minutes, with equal steps of one period per k minutes. A sine wave was said to be detected if P(k^) of the power peak was h times larger than the mean noise in r(k ). The power-spectrum analysis allowed sine waves to be detected in the lightcurves of 22 of the 96 asteroids in our sample; they are shown in Fig. 2.k. For a typical asteroid the lightcurve has two maxima and two minima in one rotation period. 32

The periods given in columns (6) to (8) of Table 2.3 are these rotation periods, which are double the periods found from the power-spectrum analysis. The amplitudes in column (5) are peak- to-peak amplitudes of the sine waves. For only two objects (16 and 27) power-spectrum analysis revealed periods smaller than 2 hours. Both these objects have an rms deviation significantly larger than the EMS of the comparison stars. Because of the relatively poor signal-to-noise ratio of the Fourier power peak, the periods of these and also two other objects are indicated with colons in Table 2.3. The last two columns of Table 2.3 give the average distance between the asteroid and the comparison stars and the RMS of the reference stars.

Table 2.3 Sine-wave variations found by power-spectrum analysis for 22 asteroids observed on 2 Nov 1973-

No V a 5(1,0) Ampl. Double-sine Period At RMS mag AU mag mag first 3 total last 3 mm mag (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) 90 15.3 1.9 15.9 0.22 3*0 3h5 !?4 95 ±0.14 60 15.4 2.2 15.3 .50: - 4.7 5.0 20 .11 95 15.5 2.2 15.2 .30 - 4.1 3.3 155 .16 104 16.1 2.0 16.7 .36 11.6 9-5 8.4 155 .16 8 16.6 2.5 15.5 .22: - 8.9 75 .14 100 16.6 2.0 17.1 .58 4.5 4.7 5.0 0 .11 27 17.2 2.1 17-3 .30 - 0.9: 50 .15 28 17.3 2.8 15.5 .28 5.4 4.7 4,.6 140 .16 2 17.4 2.8 15.6 .52 2.8 2.9 3.2 6G .16 9 17.6 2.0 18.0 .62 5.0 4.7 4.• 9 0 .14 32 17.6 2.3 16.9 .24 3.3 2.8 2..6 0 .14 36 17.6 2.3 17.0 .66 5.0 4.9 5..0 110 .20 63 17.6 2.2 17.4 .42 6.0 5.0 5..0 50 .17 40 17.7 2.3 17.0 .38: 5.8: 9-1: 30 .15 91 17.7 1.7 19-2 .26 6.6 4.6 4..1 70 .17 16 17.8 2.1 18.1 .20 - 2.0+0.2 70 .20 68 17.8 2.7 16.4 .38 3.7 3.5 3-3 0 .14 29 17.9 2.4 17.0 • 56: 5.6: 8.8: 40 .18 7 18.0 2.4 17.2 .30 3.8 3.5 25 .17 10 18.0 2.5 16.9 • 32 4.3 3.4 2.6 40 .18 57 18.0 2.0 18.6 .44 4.8 3.9 3.5 25 .17 85 18.0 2.5 17.1 0.68 3.0 3-3 3.9 0 ±0.15 +Distance between the asteroid and the comparison stars. 33

Some insight into the precision of the periods was obtained by applying the Fourier analysis to the first three hours of observation and also to the last three hours (columns 6 and 8). I conclude that about 16 of the 22 objects have well established periods to within 20 percent.

1 1 i i _ i i j 32

6 36 — •^ „, "V-\- •

• • • 100

• *• 27 • . • •"•*• • * ." - - 58 •. ; '

*•* 7

'""•^\ y ITJD E S7 rI j f-'r'" 15 16 s * _ • •" .. .''••* •* \- -'' " \. • •

(0 91 • •

10 % . ••..•.

f- ;- —^ -'•*" *• • • • • 29

. • *•• • • .

i i * 1 i , 0 HOURS

Fig.2.4 Photographic lightcurves of 22 asteroids during the 1973 lightcurve run. The sinewaves are obtained by power-spectrum analysis. The conclusions are listed in Table 2.3. 2.1.2 Photographic Lightcurves obtained in

During the 1974 photographic lightcurve run, for which the observing conditions are given in Table 2.1, Prof. Gehrels included for the first time Jupiter in the field to study the lightcurves of the outer Jovian satellites together with foreground asteroids. Care was taken to suppress scattered light from Jupiter at the surface of the emulsion by suspending before the plate a piece of dark felt at the position where Jupiter Mould be during the exposure. The photographic density was still between 2.5 and 1.8 (Fig. 2.5) near Jupiter and in the plate- corners, respectively. We realized beforehand that this background fog gradient would impair the consistency of the photographic lightcurve analysis of the asteroids in the field. The main aim of this run was, however, the outer Jovian satellites and any information about the asteroid lightcurves could be used as a confirmation of the results obtained from the 1973 data (Ch. 2.1.1). By blinking these plates 50 asteroids and 6 Jovian satellites were found. Because the photometry was planned with the ASTROSCAN, preset coordinates were needed with a precision of about 0.1 mm. These were obtained with the projection blink comparator of the Nijmegen University (de Kort 1968) providing

Fog

- 2.5 d

- 2.0 d

1.5 d Distance to Jupiter in cm Fig.2.5 Background fog density versus distance to Jupiter on plate PS 20394 (airmass=3.9) and PS 20406 (airmass=1.3). The fog level without Jupiter in the field is about 1.6 d. 35

coordinates for the beginning and end points of the paths of the objects during the observing night. The use of an automized measuring machine made it possible : to increase considerably the total number of comparison stars. I Also other precautions could be taken to improve the quality ; of the photometry: Five photometric comparison stars were se- [ lected and surrounded each object. The distance between the ob- t ject and a comparison star was often less than 1 cm. It was 'f tried to get the magnitude difference between object and com- : parison star as small as possible. This difference was always • less than 0.5 mag. A set of 10 photometric comparison stars : was selected for the Jovian satellites 8, 9, 10, and 12, in : order to have a better control over the problem caused by the . background fog gradient.

Object Recognition

The ASTROSCAN measured density matrices with a size of 2.0 x 0.4 mm centered at the mid-exposure. Each matrix con- '• tained 200 x kO adjacent elements and each element represented the density of an area of 10 * 10 microns on the photographic emulsion. It took 65 hours to measure the 19 plates with 318 matrices each centered on faint objects. The density matrices together with the positions were written on about 30 magnetic tapes of 720 meter. With the off-line reduction an average • _ number of 10 objects was found per matrix and for each object the position, mean central density, and background fog level were given. The next reduction step was to recognize with great certainty the 3 exposures out of the mean number of 10 objects per •~ matrix. For this purpose I wrote Fortran programs for making ::. combinations of objects and to reject objects if a set of three ; did not pass the following criteria: a) The objects must be :, located in sub matrices of which the sizes were determined by V. the coordinates of the easily detectable brighter stars; •: b) The deviation of each object from a straight line through •- the three objects must be less than 65 pm; c) The difference p, in adf value for each combination of three objects must be less ! than 16. : With these criteria I defined a recognition routine that ; provided the three exposures for about all matrices. I needed \' in particular criterion c to solve the recognition problem if I, the asteroid or satellite moved near a background star. This f criterion excludes, however, the detection of 1ightcurves with f large amplitudes and rotation periods of some minutes. This is \f not a severe restriction because with the present knowledge of f tensile strenght of rocks such rotation periods are impossible i in view of the excessive centrifugal forces. Also, the blink I comparator provided photographs on which I marked the path of the object during the observing period. With these photographs it was easy to see if the object was approaching a star too closely and affecting the photometry. If we should have had single exposure plates, then a much higher precision (less than 50 um) in the preset coordinates would have been necessary for a safe recognition. In case of astrometry and photometry of objects near the plate limit I recommend to use multiple exposure plates for the blinking and measuring because the criteria for both position and density of the exposures provide more certainty in the identification.

Photometry

The straightforward reduction method for photographic photometry (Ch. 2.1.1), with the basic assumptions of similarity of emulsion characteristics and background fog level between calibration plate and field plate, provided for J6 a brightness about 2.5 mag too faint compared with photoelectric measurements. The object was situated close to Jupiter (2.5 cm) am embedded in a heavy background fog. It was also clear that the 1ightcurve amplitudes for all objects were too small.

Fig.2.6 The influence of background fog on the calibration curves, from data given in Table 2.4. The magnitude scale E is close to V. 37

To study the influence of the background fog level on the relation between the photometric parameter and the magnitude, I measured five 103a-E plates of Selected Area 68, taken with the Palomar Schmidt telescope in 1973 and 1975. The measurements are given in Table 2.4 and Fig. 2.6. We see clearly from the data of the plates taken during consecutive nights in 1975 that the higher background fog level makes the calibration curve flatter. This explains the trend to find the objects too faint on plates with a high background fog level, as in the case of J6. In order to solve this calibration problem I had to per- form photometry of at least one comparison star near each object. These stars were,however, too faint for a photoelectric program, and this meant that the photometry had to be done in a photographic way. C.T. Kowal was so kind to take on December 12 UT 1976 a plate of Selected Area 68 and of our field, but now without Jupiter to guarantee that the background fog levels of both plates were as equal as possible. The platenumbers were PS23431 and PS23430.

Table 2.4 The Influence of Background Fog on Calibration Curves

Plate PS9409 PS9414 PS9521 PS22002 PS22016 Date UT 5 Oct 1973 5Oct 1973 2Nov 1973 29 Oct 1975 30 Oct 1975 | Time UT 8.69 10.18 3.10 4.12 2.54 1 Exp. min 12 12 2x3 2x5 2x5 Airmass 1-15 1.47 1.22 1.10 1.35 Emulsion 103a-E 103a-E !03a-E 103a-E 103a-E Filter WG-2 WG-2 WR-4 WR-2C WR-2C i Star Ef 122 14.55 102 106 98 97 89 110 14.82 99 104 89 95 86 85 15.73 85 87 70 79 72 129 15.98 88 88 60 85 76 27 16.33 74 73 54 66 58 60 16.90 65 66 35 58 49 64 18.08 35 34 8 36 31 965 18.68 22 23 5 18 14 993 18.91 21 17 13 9 916 19.89 10 7 7 9 Fog/ 172 179 132: 162 177

t Magnitude value for the effective wavelength of 103a-E + WR-4 (58508). / Background fog value of the photographic plate in units of 0.01 density. 38

The objects on both plates were measured with the PDS microdensitometer of the Kitt Peak National Observatory. The off-line reduction of the density scans gives with the Area Stellar Photometry program (p. 13) an instrumental magnitude value K. The calibration curve for plate PS23*»31 is given in Fig. 2.7, and it can be seen that the third exposure gives systematically brigher values by 0.1-0.2 mag, in agreement with the earlier findings in Table 2.2. The measurements of all comparison stars (=200) on the field plate without Jupiter (PS231»30) were transformed into magnitudes with the calibration given in Fig. 2.7. The adf value averaged during the night for every comparison star was plotted against its magnitude, and this was done for four intervals of the background fog density. One set of data points is given in the upper half of Fig. 2.8. The substantial noise is caused by the cumulative noise of three steps of photographic photometry: a) Photometry of the standards on the calibration plate; b) Photometry of the comparison stars on the field plate without Jupiter; and c) Photometry of the comparison stars on the field plate with Jupiter. Fig. 2.8 gives also the final calibration curves, to be applied to the measurements made on plates taken during this night, for different values of the background fog density. The curve with background fog density 1.6 d was obtained from measurements of comparison stars on the plate without Jupiter (PS23'»3C ).

Fig.2.7 Calibration curve of plate PS 23431 obtained with the Kitt Peak National Observatory PDS microdensitometer. The lower line is fitted through the data of the first exposure (»),'and the upper line through the third exposure (•). 39

These relations show that differences of 0.15 and 0.4 in background fog density between the field plate and the plate with a photometric sequence (background fog-1.6 d) gives systematic errors in the photometry of 0.1 mag and 0.4 mag, respectively, for the brighter stars. For fainter stars, about 1 mag above the plate limit, the errors are 0.2 mag and 0.8 mag resp. It is of interest that 1ightcurve amplitudes are fiardly affected by the aforementioned differences in background fog level, if the object is about 2 mag above the plate limit. The lightcurves t — cdt

— 20

Fig.2.8 The calibration curve in the upper figure is used for measurements in 1974. The substantial noise is caused by the cumulative noise of three steps of photographic photometry. This curve is again given in the lower figure together with curves for different levels of the background fog density. of fainter objects will be influenced seriously: the amplitudes will be measured too small by a factor between 2 and 5 if the object is 1 mag above the plate limit. The final reduction to lightcurv s was done by the proce- dure explained in Ch. 2.1.1. As a photometric parameter the for background fog corrected central density value, cdf, was used. The measurements, referred to the five comparison stars and given in cdf units, were transformed into magnitudes with the relations given in Fig. 2.8. The rms errors of the 1ightcurves of the 5 comparison stars were averaged, and this value was called EMS.

1 1 1 1 1 1 1 I 1 1 1 1 1 I 31 . ;\ A J\ •

•• *

35 J6 • • •

• • • • 39 • • • • • / A 7. ^.// \ .-/.

# 1 1 r 1 1 1 1 1 fifii 0 1 HOURS Fig.2.9 Photographic lightcurves of nine asteroids and of Jupiter satellite 6 (Himalia) during the 1974 run. Light- curves with much noise are for objects close to Jupiter and embedded in a heavy background fog. The curves are hand-drawn and the conclusions are listed in Table 2.5. Table 2.5 Photometry of Asteroids and Satel 1 ites on 15 Aug 1974. (1) (2) (3) (4) (5) U± (7) (8) Object Fog adf B ft ~RMS Ampi. Period d mag mag mag hours 2 2.0 20 18.1 2.5 0.24 3 1.9 16 18.6 3.6 0.36 4 2.0 12 19-5: 4.0 0.40 5 2.0 19 18.2 2.0 0.19 1.2 3.4 6 2.1 44 16.7 1.0 0.05 0.4 9: 7 1-9 13 13-5: 4.0 0.40 8 2.0 29 17.6 1.0 0.09 0.4 7: 9=J9 2.0 11 19-5: 4.0 0.40 10 2.0 12 19-5: 4.0 0.34 11=J12 2.1 8 19.5: 4.0 0.40 12 2.1 15 18.6 3-4 0.43 13 2.1 10 19.5: 4.0 0.40 18 2.4 8 19.5: 4.0 0.34 19=J8 2.5 11 19.5: 4.0 0.44 20 2.2 15 18.3 3.4 0.34 21 2.0 18 18.2 2.2 0.24 22 2.0 10 19.5: 4.0 0.37 2.3 3.0 23 1.9 11 19-5: 4.0 0.37 24 1.9 25 17.8 1.4 0.17 25 1.9 24 17.8 1.5 0.14 26 2.0 6 19-5: 4.0 0.37 28=J11 2.0 17 18.5 2.7 0.30 30 1.9 32 17.4 1.0 0.08 0.7 11: 31 Z.O 22 17.9 2.0 0.19 0.3: >24 32 1.9 14 19.2 4.0 0.37 33 1.9 12 19-5: 4.0 0.37 34 2.0 53 16.6 1.0 0.11 1.4 12: 35=J6 :2.2 59 15.8 1.0 0.10 0.2: 6: 36=J10 :2.3 15 18.2 3.4 0.23 37 I2.5 16 17.8 2.2 0.19 39 :2.2 13 18.6 4.0 0.47 1.2: > 8 40 .9 39 17.1 1.0 0.08 ? 41 1 .9 14 19.2 4.0 0.34 42 1 .9 9 19.5: 4.0 0.34 43 • 9 18 18.3 3.1 0.34 45 .9 17 18.6 4.0 0.47 50 .9 11 19.5: 4.0 0.27 51 .9 10 19-5: 4.0 0.34 55 .9 37 17.2 1.0 0.08 56 .9 10 19-5: 4.0 0.34 tFactor between the magnitude scale of the object and the magnitude scale without the heavy background fog caused by Jupiter. Table 2.5 gives the results for all measured objects. The background fog gradient gives a strong variation of RMS over the plate, therefore no Fourier analysis was used. Some lightcurves showed variability by "eye ball" analysis; these are given in Fig. 2.9. A colon means that the B magnitude can be in error by as much as 0.5 mag and the lightcurve amplitudes and periods can be in error by as much as 30 percent.

Photoelectric Checks

In order to obtain an insight into the quality of the photographic photometry I measured photoelectric B and V magnitudes of two comparison stars of J6 on September 19 UT 1977 with the 15** cm telescope of the Lunar and Planetary Laboratory. These results show that the photographic magnitudes are too faint by 0.5 mag. This check refers, however, to stars embedded in a very strong background fog of 2.20 d. For these circumstances zero-point errors of 0.5 mag can apparently be expected. The photographic lightcurve of satellite J6 showed an amplitude of 0.1-0.2 mag, and at the telescope a photoelectric amplitude of 0.12 mag was measured (Ch. IV). Indeed, the 1iqhtcurve amplitude for this relatively bright object is not affected by the heavy background fog.

Comparison with the Quality of the 1973 Run

The quality of the results in this 137k run is poor compared with the 1973 run. The major problem is the high value of the photometric noise , 0.3-0.4 mag, but more serious is its variation over the field The results are: a) The first lightcurves of 6 outer Jovian satellites (the results are discussed in Ch. IV);b) An insight into the limitations imposed on the accuracy of photographic photometry by the presence of a varying background fog.

2.1.3 Rotation Periods and Body Shapes

It is assumed that a periodic lightcurve with two maxima and two minima during one rotation period is caused by a solid body having: a) no atmosphere; b) an elongated body shape; c) an uniform reflectivity over its surface; and d) rotation around the shortest axis. With these assumptions the total sample (1973+197*0 of 130 asteroids yielded rotation periods for 27 (21+6) asteroids, and lightcurve amplitudes larger than 0.2 mag for 30 (22+8) asteroids. Rotation Periods

Fig. 2.10 gives the histogram for the rotation periods of the asteroids listed in Table 2.3 and 2.5. The histogram shows an average period of 5.6 hours indicated by a dashed line. It is evident that these asteroids with small sizes,of the order of 1 km on the average,rotate faster than do the much larger objects for which the period histogram is given in Fig. 2.10a. This effect has also been noted by Harris and Burns (1978), from a study of periods in published literature. The smallest asteroids in their sample had diameters of about 10 km and the faster rotation for these compared to larger bodies was barely detectable. The present work shows the effect with more clarity. Selection effects are, however, present and concern mainly: a) the rather short observing periods of A hours in 1973 and 6.k hours in 1974; b) the insensitivity to detect a variability less than 0.2 mag by using photographic photometry; c) the inability of Fourier analyses to provide correct periods and amplitudes for lightcurves strongly deviating from a sine wave; and d) the possibility that there is a relation between rotation period and body shape.

20 Asteroids oop. Size 200 km

- s

r n .

- -i— - 20 27 Asteroids opp. Size 1-10 km

- 10 |~L Fig.2.10a-c Distributions • of lightcurve periods. The periods in Fig.b are "1 i taken from Table 2.3 and 2.5. The dashed vertical line indicates the mean period for each distribu- 9 Mars-orbrt Crossers l-10km tion. Published by Degewij (1977). 20 25 Rotation Period Ihours) kit

Effect c) will in particular provide wrong periods and amplitudes for peculiar lightcurves with a partial coverage only. A comparison between the period obtained from a part of the lightcurve and that of the full lightcurve may give an insight into this selection effect. For that purpose I did Fourier analysis of the first three hours and last three hours of the lightcurves obtained in 1973 and the results are given in Table 2.3 column (6) and (8). No systematic deviation was found between the periods obtained for the pieces of three hours and the period obtained from the total lightcurve. This indicates that for this case the use of sine waves is a reasonable approximation. In the period histogram for the asteroids with about 1 km sizes (Fig. 2.10b)21 periods are determined with the k hour run of 1973, and with such a time coverage sine wave periods up to about 5 hours (corresponding with rotation periods of 10 hours) can be determined with sufficient precision. The histogram shows a peak value at about 3 hours and falls off rapidly towards the 10 hour level. From the previous discussion it can be concluded that the shape of this curve is probably real. At the short period side the detection limit is about 0.5 hours. I did not find with certainty a period shorter than 1 hour. This is probably a real effect due to limited tensile strength for asteroids, so that the centrifugal force in the mid-plane of the asteroid will disrupt the body if it rotates too fast (Napier and Dodd 197*0. The critical period for this mechanism is dependent on size (Degewij and Gehrels 1976), but we have not yet enough data to confirm this relation. The conclusion that these smaller asteroids spin faster than do the larger asteroids, is not necessarily valid for the remaining 80% of the sample (1973), for which no variation lar- qer than 0.2 maq was seen. We have no insight into the rotation periods of asteroids with lightcurve amplitudes smaller than 0.2 mag, but there is no physical argument why their distribution of periods will differ. Photoelectric surveys (Ch. 2.2) show that the rms deviation in the magnitudes of asteroids measured many times during an apparition is comparable with the rms deviation found in our surveys. This indicates the practical absence of slowly rotating asteroids with lightcurve amplitudes larger than »0.2 mag. An interesting explanation of the shape of the period histo- grams is given by Harris and Burns (1978).They studied the histogram of numbers versus (period)'1 and concluded that it had a maxwellian shape, as expected from a population originated t by col Visional fragmentation. • It can be concluded that my results are firm for the pe- \ riods between 1 and 10 hours, but a future lightcurve run with emphasis on longer periods is needed. An attractive possibility would be a cooperative progran between the 122 cm Schmidt telescopes at Palomar Mountain and Siding Spring in Australia, to obtain a more continuous time coverage.

Body Shapes and Orbital Eccentricity

I define the body shape as the ratio between the longest and shortest axes of the body. If the body rotates around the shortest body axis, then the relation between the lightcurve amplitude and the body shape of the asteroid is influenced by the aspect. The distribution of 1ightcurve amplitudes is for a sufficient large sample indicative for the distribution of body shapes,with the assumption that the rotation axes are randomly oriented in space. It is possible to determine the orientation of the rotation axis of an asteroid from lightcurves obtained during many apparitions. The method is discussed by Gehrels (1970). Some

1 / , 25 Asteroids / \ App. size 200 km 1 i 1 I \ \ _ \ - 5 \ \ \ Fig.2.11a-c Distributions of \ lightcurve amplitudes. Fig.b \ shows the amplitudes obtained in the 1973 run and are taken from Table 2.3. The dashed box 96 Asteroids contains 74 asteroids for which App. size 1km the photographic technique did not detect variability. The dashed Gaussian-like curve 20 gives the shape of the distribution given in Fig.a and is copied in Fig.b. Published by Degewij (1977).

16 Mars-Orbit Crosses App. size K km H 0.5 1.0 1.5 Lightcurve Amplitude in Mag results about the orientation of asteroid rotation axes (Vesely 1971) do not contradict this assumption. It is of interest to study if there is for a given sample a relation between the body shape and average body size. For that purpose I give in Fig. 2.11b the distribution of lightcurve amplitudes obtained during the 1973 run and given in Table 2.3. These asteroids have sizes between 1 and 10 km. The lightcurves for large asteroids are well documented and brought together in the TRIAD (Bender et al. 1977) compu- terfile for asteroid lightcurves maintained by E. Tedesco. The lightcurve amplitudes obtained during the 1973 run are "first discovery" results and for a fair comparison with larger asteroids I used the amplitudes of the first published 1ightcurves of the numbered asteroids 1 to 25. The distribution of these amplitudes is given in Fig. 2.11a. Some information concerning lightcurves for Mars-orbit crossers is available in TRIAD. These lightcurve amplitudes together with recent values obtained from IAU Circulars are plotted as a histogram in Fig. 2.11c. An apparently significant observational effect is shown by the three figures 2.11a-c.The tail with amplitudes >0.2 mag for the amplitude histogram obtained in 1973 (figure in the middle) appears to lie between the other distributions. The deficit of amplitudes above 0.3 mag for the 200 km asteroids can be explained by gravity in very weak objects (Johnson and McGetchin 1973). There may be evidence that the weaker C-type asteroids in this sample are nearly spherical in shape, and the stronger S-type asteroids in this sample are more elongated (Chapman 1976). However, more lightcurve observations for more objects are needed. If I assume: a) the fragments just after a catastrophic collision in the main belt have elongated shapes comparable with the Mars-orbit crossers; and b) the Mars-orbit crossers have their origin in the main belt, then the lack of elongated 1 km objects in the main belt can be explained by an erosion process with noncatastrophic collisions by smaller asteroids. It would tend to make the elongated pieces more spherical and to increase their rotation rate. This discussion was first published by Degewij (1977). Dohnanyi (1972) predicted that these 1 km main belt asteroids originate from about five catastrophic collisions of larger parent bodies since the age of the solar system. The last catastrophic collision that determined their birthdate occurred about 109 year ago according to iohnanyi. It may have occurred even more recently if recent determinations of asteroid collisional cross-sections are taken into account (Mor- rison 1977). The Mars-orbit crossers also have extensive parts of their orbits in the main belt, but their lifetime and thus exposure time to the erosion process is relatively short. Wetherill (1972*) predicted short dynamical lifetimes of about 107 year for Earth-orbit crossers. If we assume a comparably short life time for Mars-orbit crossers, then they are relatively young and hardly eroded elongated pieces perturbed out of the main belt. A selection effect, affecting the reality of the amplitude distributions, is the possibility that a substantial number of slowly rotating asteroids (periods >10 hours) with large amplitudes exists. Some additional facts are available from the photoelectric surveys for the 25-50 km size domain by Bowel 1 (1976) and by Degewij et al. (1978 and Ch. 2.2), with a time- base of several hours, days and longer. Degewij et al. found for k% minor planets a mean magnitude difference of 0.15 mag and no differences exceeding 0.18 mag. Bowell found from multiple observations of 88 asteroids with diameters larger than 100 km a mean magnitude difference of 0.17 mag. He found a mean magnitude difference of 0.19 mag for 85 asteroids with sizes between 20 and 100 kin. From these data it can be concluded that slow rotators with large amplitudes are not abundant and that our amplitude distributions probably are real.

2.2 Photoelectric Photometry

2.2.1 UBV Photometry of Faint Asteroids

Photometric data on the UBV system were presented by Zellner et al. (1975) for 91 minor planets. They demonstrated that, although little compositional information can be directly extracted from B-V and U-B colors, it is usually possible to

;•_• recognize the principal optical types identified by more sophis- ticated techniques (e.g., Chapman et al. 1975; Zellner and Gradie 1976; Morrison 1977; McCord and Gaffey 197^; Gaffey and McCord 1978; Bowell et al. 1978). Ferrosilicates generally have reddish colors in this spectral region due to the broad wings of ultraviolet charge-transfer absorptions; the colors are variously muted by components of spectrally neutral silicate, free metal, and opaques such as finely divided carbon. In UBV colors asteroids of type S (ferrosilicate plus metal) are well separated from other types, while the domains of type C (silicate plus opaques), M (metal, or metal plus neutral silicate), and E (neutral silicate) overlap somewhat. Objects of exceptional type usually stand out from the population in UBV colors. The power of UBV photometry lies in its great sensitivity, which permits observations of almost any numbered asteroid with a 2-meter telescope. This makes it possible to classify, at least provisionally, large numbers of small and distant objects for statistical studies of the distributions of types over diameter and heliocentric distance (Zellner and Bowel 1 1977)• Also, the smaller members of dynamical families can be observed, which are now showing indications of compositional homogeneity for each family (Gradie and Zellner 1977; Gradie et at. 1977) in accordance with old suggestions that they are fragmentation remnants of discrete parent bodies. ZelIner et al. (1977a) presented additional UBV data for 65 objects, with emphasis on the distant Hildas and Trojans and main-belt asteroids down to 6 km diameter. In this chapter new observations of faint asteroids are presented, most of which have not been previously observed by any technique which is sensitive to differences in composition. The text is mainly from Degewij, Gradie, and Zellner (1978). Observations

Asteroids were selected according to: 1) mean opposition blue magnitudes between 14.5 and 15.5, for improvement of the classification statistics in this poorly sampled magnitude range; 2) poorly known absolute magnitudes as indicated by Gehrels and Gehrels (1978); and 3) membership among the Hunga- rias, Hildas, Trojans, and the dynamical families associated with Zk Themis, and V* Nysa (Arnold 1969; Williams 1978). The program is complementary to the extensive UBV photometry of Bowell (1977) for the brighter asteroids. Circumstances of the observing nights are given in Table 2.6. With few exceptions as noted, the measurements were made with standard UBV filters and the computerized photon-counting polarimeter MINIPOL described by Frecker and Serkowski (1976) Standard stars exclusively from the list of Purgathofer (1969) were observed each night, and the reductions were done by standard techniques (see Ch. 1.3 and Zellner et al. 1977a). An analysis of the standard star measurements showed no indications of variability. Some checks for possible systematic deviations between the Purgathofer standards and primary UBV standards (Gehrels and Owings 1962) showed no indication for any significant deviation. For 12 objects, measured in common with E. Bowell, in both colors a mean of the residuals ("Tucson- Flagstaff") of -0.01 mag and an rms error of±0.03 mag was found. Generally filter sequence WBBUUUUBBW with integration time 20 seconds and a sky measurement at each filter was used for a total integration time of 6 minutes per observation. The rms error of an observed magnitude or color as derived from the internal noise level of the data is shown in Fig. 2.12. Some objects were observed with longer integration times to achieve higher precision. These more accurate values are indicated by a + sign in Table 2.7. Table 2.6 Photometric Quality of the Observing Nights

Date UT t / Standard stars Standard star observ.| N °V °B-Va U-B CV-I 76 10 29 Z/D M.154 SA94-16-18-29-30 8 11 20 28 76 11 26 G/D " SA71-7-11-14-17 14 6 15 18 77 02 20 Z/D " SA54-18-20-21-22 9 11 41 16 -24-26 77 02 21 D " SA54-18-20-24-26 9 9 12 17 77 04 13 D " SA54-18-20 k 6 4 12 77 04 14 D " SA54-18-20-24-26 6 }J 3 16 77 05 15 D SA54-18-20-24-26 12 7 7 26 SA54-18-20-24-26 8 40 35 44 77 05 16 D " AQUILA-15 SA54-18 12 15 20 29 77 06 12 D " AQU ILA8-1l»-15-24 SA54-18-20 13 19 24 25 77 06 13 D " AQUILA8-14-15-24 SA54-18-20 10 26 41 30 77 06 14 D UBV,15k AQUILA8-14-15-24 AQUILA8-14-15-24 11 27 17 45 77 06 15 D/G " SA54-15 10 24 10 40 77 06 16 G/D " AQUILA8-14-15-24 77 09 18 D M.154 AQU1 LAI 5-24 5 4 13 11 77 09 19 D " AQUILAI 5-24 10 8 20 25 SA71-14-17 77 10 16 D M.152 SA71-14-17 4 10 10 10 77 10 1/ D " SA71-14-17 k 40 7 8 77 10 19 0 M.154 AQUILAI 5-24 4 2 6 8 77 10 20 D " AQUILAI 4-12-24 6 18 10 32 M34-1-2-3 3 77 11 16 D " SA71-14-17 4 4 21 16 SA94-251-300-305 6 M34-1-2-3 77 11 17 0 " SA71-14-17 16 k 9 12 77 11 18 D " 50

Table 2.6 Photometric Quality of the Observing Nights (cont.) Date UT t Standard stars Standard star observ.| N

t D: J. Degewij G: J. Gradie W: W. Wisniewski Z: B. Zellner

/ M: MINIP0L photopoiarimeter with UBV filters (Frecker and Serkowski 1976) UBV: UBV-photometer (Johnson and Mitchell 1962) 100: 100-cm Mount Lemmon reflector of the Lunar and Plane- i tary Laboratory S-; 152: 152-cm Mount Lemmon reflector of the Lunar and Plane- I tary Laboratory - 154: 154-cm Catalina reflector of the Lunar and Planetary Laboratory . I Number of times that standard stars were observed. a is the standard deviation of the residuals between the observations and the transformed values. The transformations were done with the formulae given in Ch. 1.3.1. 51

Fig.2.12 Standard deviation of V, B-V, and V-B measurements in the instrumental sys- I tem.

Identification at the telescope of faint and slowly moving objects, which are not always near the predicted positions, can be difficult. Finding charts were made in the form of 35 mm negatives covering 55><35 arcminutes from Palomar Observatory Sky Survey glass plates. Faint circles indicating the predicted position of the asteroid were superimposed on the negatives. At the telescope a 30X microfiche projector gives a scale and illu- mination close to that of the star background at the eyepiece. Recently a TV system with an intensified-silicon intensified- target vidicon was used at the 154 on telescope showing in some seconds objects down to visual magnitude 18 in a field of 5 arcmin diameter (Ch. 1.2). This device was invaluable in locating the fainter objects. Asteroid motion is checked by plotting the position of the asteroid and nearby stars on a plastic over- lay in front of the TV screen. The image scale (1 mm=k arcsec) allows motion to be visible in 5 to 10 minutes. Table 2.7 gives the resulting magnitudes and colors and multiple observations give some indications of variability. Measurements separated by an hour or more for 48 minor planets show a mean magnitude difference of 0.15 mag. Apparently many of these small objects are not very elongated, in agreement with the photographic 1ightcurve studies reported in Ch.2.1. An exception is asteroid 1595 for which a large-amplitude 1ightcurve was clearly demonstrated on June 12 and 13, 1977. Observations a few weeks apart suggest a large-amplitude Iightcurve for 1390. The standard correction to zero degrees phase was made by means of the magnitude-phase relation adopted by Gehrels (1967b) (Ch. 1.3.1). No corrections were applied for possible phase effects in the colors, because they are not yet sufficiently documented. 52

Table 2.7 UBV Photometry of Faint Asteroids.

Number .' Date UT a B-V U-B V V a) 7(1,0) 37 76 11 26.48- 23?96 0.84 0.40 11.17 8.26 7.71 40 77 11 16• 45 9.70 0.83 0.47 9.88 7.64 7.42 69 77 10 16• 37 6 0.66 0.18 11 .47 7.49 7.36 b o 77 10 16• 39 6 VA ) 0.65 0.20 11 .45 7.47 7.34 76 78 05 9• 37 3.52 0.73 0.23 13.22 8.39 8.42 OOO O L A 89 77 10 16.43 23 0.83 0 11 .48 7.78 7.23

77 10 16• 45 23 0.88 0 0 O N 11.46 7.76 7.21 166 77 06 L A .40 11 .89 0 .74 0.40 14.15 10.63 10.36 77 06 • 45 11 .87 0.71 0.45 14.09 10.57 10.30 C M • - . C M i- P A . - 184 Th 77 09 18. C M PAS O 0.20 0 .66 0 12 • 95 8 .32 .70 77 10 20. 9.62 0.71 0 13.68 8 • 92 -70

77 10 20. 9.62 0.66 0 13.73 8 • 97 0 .75 P A L A C M P A C M ONO O 186 77 10 16.34 11.47 0.71 0 11 9.72 9.46 77 10 16.36 11 .47 0 .78 0 11 9.61 9.35 0 C M L A 279 76 11 26.20- 11 .94 0.76 0 O L A .21 O N .18 .91 76 11 26.22- 11 .96 0.73 0 .25 .22 .95 310 78 05 9-39 6.48 0.84 0.39 13.36 10,.53 10.41 313 11 26.42 16.19 0.70 0.35 11 .78 O N .85 9.48 0 O N V J 05 9.47 16..40 0 .72 0 .44 13. 07 .81 9.44 323 77 02 21.47- 11..40 0• 90 0.43 13-.80 10..43 10.18 413 77 06 13.28 11.29 0.68 0..22 14..00 10..88 10,.62 448 Ny 77 11 17.18 8..40 0. 0..32 14.63 10.87 10..68 O N 77 06 13.33- 11.31 0. v n 0..24 14.01 10.89 10.63 455 78 05 9.44 6.62 0.79 0..48 13.33 10.00 9.88 461 Th 77 10 17-46 3.21 0.59 0.32 14.87 11.18 11.22 468 Th 77 10 16.51 11.46 0.,64 0.32 13.59 10.11 9.85 522 77 09 18.21 6.82 0.66 0.24 14.13 9.64 9.48 525 77 04 14.36- 14.76 0.95 0.56+ 15.55 13.35 13.02 533 77 06 13-43- 14.49 0.85 0.50 14.58 10.55 10.22 77 06 13.45- 14.48 0.86 0.40 14.51 10.48 10. 15 542 77 06 12.16- 13.08 0.80 0.40 14.56 10.19 9.89 77 06 12.26 13.10 0.79 0.36 14.44 10.07 9.77 C M P A L I 546 77 02 21.13 16.98 0.76 0.P A L A S O 13.30 10.63 10. 77 02 21.35 16.98 0.79 0. 13.32 10.65 10. 53

Table 2.7 UBV Photometry of Faint Asteroids (cont.) Number / Date UT a B-V V-B V 7(1,a) 7(1,0)

i 617 TF 77 09 IS.39 8.65 0.68 0.26 15.04 8.79 8.59 77 09 IS.45 S.65 0.68 0.18 15.03 8.78 8.58 r 77 10 2G .25 2.53 0.68 0.18 14.80 8.65 8.73 77 11 17.21 4.91 0.67 0.27 14.80 8.59 8.54 i. 78 01 13.18 11.93 15• 49 8.87 8.60 rt - 643 77 02 20.25 9.19 0.75 0.29 14.46 10.37 10.16 77 02 21.24 9.46 0.74 0.29 14.45 10.35 10.13 664 77 10 17.51 7.25 0.69 0.54 15.65 10.63 10.48 77 10 19.26 6.79 0.67 0.23 15.47 10.46 10.32 : 77 10 19.31 6.79 0.70 0.15+ 15.55 10.54 10.40 692 77 02 20.32- 13.89 0.88 0.41 13.46 9.81 9.49 77 02 21.29- 13.90 0.87 0.45 13.42 9.76 9.44 729 77 06 12• 34 11.06 0.79 0.39 13.03 9.98 9.73 77 06 12.39- 11.05 0.77 0.36 13.06 10.01 9.76 750 Ny 76 10 29.44 12.80 0.65 0.22+ 15.49 12.77 12.48 754 77 06 13.27- \2.56 0.69 0.33 14.21 10.04 9-75 77 06 13.32- 12 57 0.70 0.34 14.05 9.88 9.59 814 77 11 16 53 15 96 0.69 0.36 12 55 9.63 9.27 11 17 50 15 60 0.67 0.32 12 69 9.77 9.41 T 77 824 i 77 04 14 39- 4 48 0.82 0.41 13 70 10.48 10.46 857 77 02 21.38 11 46 0.63 0.14 14 75 12.04 11.77 883 77 06 16.44 13.88 0.86 0.48 14.68 13.40 13.08 ,; 884 TF 77 09 19.42 6.09 0.68 0.17 16.11 9.26 9.16 77 10 19.21 2.28 0.74 0.12+ 15.80 9.03 9.13 77 10 19.23 2.28 0.76 0.23 15.85 9-08 9.18 77 10 20. 21 2.29 0.74 0.27+ 15.75 8.93 9.03 77 11 17.34 6.13 0.65 0.32+ 16.13 9.22 9.12 78 01 13.15 10. 5 16.63 9.34 9.10 ^ - 78 02 04.12 9.8 16.64 9.20 8.98 78 02 09-11 9.4 16.61 9.13 8.92 887 2 77 10 17.42 44.61 0.94 0.42 14.95 15.62 14.59 899 77 06 12.37 3.52 0.67 0.20 14.42 10.52 10.55 77 06 12.43 3.50 0.65 0.26 14. 24 10.34 10.37 77 06 13.40 3.18 0.67 0.28 14. 46 10.57 10.62 911 TP 77 02 21. 22- 1.96 0.77 0.20 14. 80 8.15 8.27 b 78 06 06.20 10.86 16. 21 9.00 8.75 !" 920 77 05 16.34 6.78 0.80 0.30+ 15. 16 11.71 11.58 t 944 2 76 10 29-14 7.34 0.74 0.23 13. 57 11.18 11.02 i r 954 Th 77 10 17.33 2. 06 0.61 0.34 14. 36 10.31 10.43 t 958 Hi 78 04 08.18 16. 90 0.841- 1b. 4f 10.97t 10.58t Table 2.7 UBV Photometry of Faint Asteroids

Number / Date UT B-V U-B T'(i,tt) ,0) 966 77 04 14 .14- 16 .00 0.85 0.42 14.04 10 .77 10 .40 77 04 14 .23- 16 .00 0.87 0.43 14 .00 10 .73 10 .36 991 Th 77 09 19 .29- 11 .26 0.66 0.37 15 .18 11 .83 11 .57 1004 77 04 14 .32- 1.01 0.72 0.12 15 .16 10 .12 10 .34 1012 Ny 77 10 19.16 13 .60 0.73 0.17+ 15.72 12.81 12 .49 77 10 19.25 13 .60 0.56 0.33+ 16 .49 13.58 13 .26 1015 77 05 15.41 3.71 0.68 0-37 14 .00 9.38 9.36 77 06 12 .24 8.37 0.71 0.30 14 .31 9.64 9.45 77 06 12 .30 8.39 0.69 0.29 14 .30 9.63 9.44 1019 Hu 77 02 20 .42 16 .43 1.00 0.52+ 15 .00 13.54 13 .16 77 02 21 .45- 16 .09 0.96 0.49+ 15 .01 13 .56 13 .19 77 04 13 • 32- 24 .43 0.97 0.57+ 15.27 13 .76 13 .19 1031 77 06 13..29 7.85 0.68 0 .30 14.05 10 .10 9.93 77 06 13 .35 7.86 0.68 0 .35 14.11 10 .16 9.99 1076 Ny 77 11 17..51 16 .97 0.67 0.34 15.18 13 .03 12 .69 1082 Th 77 10 17..49 11 .40 0.74 0.33 15 .08 11 .21 10 • 95 1093 77 11 16. 52 10,.77 0,.70 0 .30 14.55 9.43 9-19 77 11 17..48 10..57 0 .66 0.33 14 .56 9.45 9.21 77 11 17. 52 10..57 0..65 0 .42 14 .57 9 .46 9.22 1127 77 06 13.,41 11..06 0..73 0 .30 15 .48 11,.70 11 .45 77 06 13.,44 11..05 0..67 0..30 15 .32 11,.54 11 .29 1143 TP 77 02 20. 26- 3.89 0..82 0..23 15 .06 8..68 8,.68 1162 Hi 77 02 20. 19- 8. 13 0.,80 0..40 15.71 9.49 9..76 78 05 9.24 13.99 o;60 0..14 16. 07 10. 57 10.25 1172 TF 77 10 19. 19 3.01 0.78 0. 27+ 15.24 8.55 8.59 77 10 19. 22 3.01 0. 71 0.,28 + 15.34 8.65 8.69 77 10 20. 23 2.88 0. 67 0.,22 15.27 8.59 8.64 77 11 17.36 4.96 0.73 0.30+ 15.38 8.64 8.59 78 01 13. 12 10.81 15.96 8.86 8.61 1173 TF 77 10 19. 30 6.37 0.83 0. 18 + 16. 10 9-32 9.20 77 10 19. 33 6.37 0.65 0.24 16. 12 9.34 9.22 77 11 17.46 1.64 0.74 0.29 + 15.68 8.94 9. 15 78 01 13.21 9.34 16.31 9.31 9. 10 1208 TF 77 11 17.37 3.29 0.67 0.38+ 15.61 9. 18 9.21 78 01 13.19 11. 14 16.46 9.67 9.42 78 02 4.18 11.40 16.72 9.77 9.51 1235 Hu 76 10 29.40 30. 14 0.75 0.33 14.61 13.98 13.29 1241 77 02 21. 43- 2. 11 0.75 0.29 14.26 9.68 9.80 1247 Th 77 10 17.47 5.64 0.68 0.24+ 15. 19 10.98 10. 90 55

Table 2.7 UBV Photometry of Faint Asteroids (cont.) Number / Date UT a B-V U-B V VO,a) v(1,0) 1252 77 02 21.14 13.97 0.89 0.40 14.63 11.67 11.30 77 02 21.26 13.97 0.89 0.45 14.77 11.81 11.44 1317 77 02 21.50- 5.05 0.74 0.34 15.10 10.40 10.35 1326 77 06 13.30 5.72 0.79 0.43 15.16 11.40 11.31 77 06 13.36 5.74 0.78 0.52 15.16 11.40 11.31 1328 77 10 20.11 8.12 0.64 0.12 15.03 11.04 10.86 77 10 20.17 8.12 0.75 0.21 14.83 10.84 10.65 1330 77 06 12.17 14.47 0.65 0.18 15.29 11.06 10.73 77 06 12.28 14• 79 O.69 0.16 15.19 10.96 10.63 1341 77 05 15• 39 7.58 0.71 0.22 14.22 11.23 11.06 77 05 16.35 7.71 0.71 0.27 14.29 11.30 11.13 77 06 12.19 15.12 0.68 0.28 14• 57 11.44 11.09 77 06 12.31 15.15 0.70 0.24 14.44 11.31 10.96 77 06 14.25- 15.71 0.63 0.30 14• 51 11.36 11.00 1345 Hi 77 11 17 39 4.70 0.73 0.32+ 14-98 10.09 10.05 1359 77 04 14 15- 13.46 0.66 0.35+ 15• 94 11.35 11.04 77 04 14 26- 13.46 0.76 0.36+ 15.91 11.32 11.01 1390 77 04 13 34- 1.06 0.72 0 28+ 14.32 9.54 9.75 77 04 14 31- 1 16 0.69 0 18 14 15 9.36 9.56 77 05 16 18 10 12 0.80 0 19 14 40 9.48 9.24 1391 77 05 15 23 18 37 0.92 0.45+ 15 32 13.12 12 76 77 05 16.22 18 37 0.91 0.69 15 39 13 19 12 80 1437 TP 78 01 13.4? 9 60 15.46 8 73 8 51 78 02 4.50 6.49 15.09 8 48 8.36 78 04 5.30 6.76 15.19 8 56 8.43 78 05 12.21 10.96 15.63 8.77 8.52 78 06 6.21 11.52 15-74 8.70 8.44 '* 1453 Hu 77 02 20.39- 16.08 0.91 0.56+ 14.96 13.53 13.16 77 02 21.39- 16.02 0.98 0.52+ 14.94 13.51 13.14 1456 77 06 14.44- 15.37 0.69 0.34 15.22 11.78 11.43 1461 77 02 21.16 5.10 0.72 0.21 14.58 10.43 10.37 77 02 21.41 5.10 0.73 0.23 14.60 10.45 10.39 1474 MC 77 02 20.20 16.93 0.61 0.26 15.26 13.59 13.20 77 02 21.20 17.22 0.63 0.23 15.26 13.56 13.16 1512 Hi 77 02 20.22- 3.30 0.70 0.16 15.45 9.95 10.00 '.] 78 05 9.35 9.61 0.70 0.25 14.90 10.10 9.80 ;<= 1529 Hi 76 10 29.35 8.25 0.76 0.17 15.06 10.61 10.42 ;j 1583 TP 78 01 13.00 7.80 16.09 9.36 9.19 >J 78 04 8.00 10.40 15.B5 8.95 8.71 56

Table 2.7 UBV Photometry of Faint Asteroids (cont.) Number / Date UT a B-V U-B V v(1,o) 7(1,0) 1595 77 06 12.18 12.64 0.72 0.45 15.83 12.91 12.62 77 06 12.29 12.68 0.59 0.51 15.48 12.56 12.27 1602 77 05 16.28 10.73 0.93 0.55+ 15.25 13.19 12.94 1625 77 11 17.44 5.09 0.69 0.28+ 16.37 11.03 10.97 1658 77 05 15.27 15.51 0.96 0.67+ 15.03 12.34 11.99 77 05 16.24 15.86 0• 96 0.55 15.19 12.50 12.14 1669 Th 77 06 15.19- 10.12 0.73 0.46 15.32 11.63 11.40 1693 77 04 13.46- 7.75 0.76 0.41 14.52 11.35 11.18 77 05 16.29 9.38 0.83 0.35 14.61 11.64 11.43 1702 77 06 15.42 12.06 0.72 0.27 14• 99 11.75 11.47 77 06 15.46 12.04 0.75 0.14 15.07 11.83 11.55 1754 Hi 77 09 18.20 6.01 0.62 0.26 15.15 10.30 10.20 1755 77 04 13.40- 4.93 0.91 0.44+ 15.34 11.31 11.26 77 05 16..20 9• 93 0.92 0.28 15.46 11.33 11.10 1765 77 05 15.35- 7.00 0.73 0.26 14.81 10.41 10.27 77 05 16..26 7.23 0.77 0.28 14.91 10.51 10.36 1830 76 10 29..50 14.92 0.91 0.50 15• 39 13.28 12.94 1867 TF 77 09 19..20 6..25 0.78 0.23 15.60 8.88 8.77 77 09 19..32 6..25 0.71 0.29 15.64 8..92 8.81 77 11 17.27 9..57 0,.76 0.23 15.93 9..05 8..83 78 01 13., 14 10..4 16.44 9..20 8.96 78 02 4..10 9..0 16.50 9..14 8..93 1916 MC 77 09 19.,24 12..70 0..86 0.48 14.39 15.83 15..54 77 09 19.36 12,.70 0..89 0.38 14,.16 15.,60 15..31 77 10 17.37 19..19 0..82 0.36 15.53 15.97 15.53 77 11 17.08 27..66 0..84 16..85 16.08 15..44 1980 MC 77 10 20.47 53.34 0.95 0..44 15..52 15.89 14.66 77 10 20.49 53.34 0.96 0,.47 15-.21 15.58 14.35 976UA EC 76 10 29.28 32.09 0.77 0.50+ 15..85 21.62 20.88 1977RA MC 77 09 18.16 17.29 0..84 0,.48 14.03 16.22 15.82 77 09 19.25 17-26 0.83 0..56 14.28 16.45 16.05 77 11 17.07 29.19 0.82 16.07 16.07 15.40 1977VA MC 77 11 16.37 9.56 0.78 0..19+ 16.37 20.12 19.90 77 11 16.41 9.56 0.68 0..03+ 16.05 19.80 19.58 77 11 17.28 9.68 0.65 0..22+ 16.16 19.88 19.66 77 11 17.42 9.68 0.71 0.,10+ 16.04 19.76 19.54 1977VB MC 77 11 17.14 0.96 15.91 77 11 17.32 0.69 0.35+ 16.01 1977VC 77 11 16.39 0.83 0.40 14.16 77 11 17.16 0.80 0.43 14.21 57

Table 2.7 UBV Photometry of Faint Asteroids (cont.) / Members of dynamical families or other orbital groups are designated by: Ny, kk Nysa family; Th, Ik Themis family; Hi, Hildas; Hu, Hungarias; TP Trojans preceding Jupiter; TF, Trojans following Jupiter; EC, earth-crosser; MC, Mars- crosser; and Z, unique orbit.

+ The error indicated in Fig. 2.12 for U-B is to be divided by /2.

f Magnitude and color computed relative to J6Himalia.

An "-" indicates that the asteroid identification was not confirmed by visible motion in the expected direction.

2.2.2 Compositional Types and Orbital Parameters

Asteroid colors from Table 2.7 and from other sources are plotted in Figs. 2.13 through 2.15 together with the domains of the predominant c and s compositional types as described by Bowel 1 et al. (1978 and see also Fig. 2.18). The observing program to obtain UBV colors was made in conjunction with J. Gradie. He observed the asteroids in the Eos and Koronis family, and I concentrated on faint asteroids not belonging to any family. In the following paragraph some results of Gradie's published work is summarized. His conclusions about the clustering of UBV colors for objects in both families could be made by comparing with the UBV colors of objects with about the same size and not belonging to any family.

Fig.2.13 U-B vs B-V colors for asteroids in the 221 Eos family < •), and the 158 Koronis family (*) (Degewij et al. 1978). The asteroids marked with open circles are field objects from Table 2.7. Solar colors are indicated at B-V=0.63 and U-B=0.10. Domains for the S and C compositional types are as defined by Bowell et al. (1978). 58

The Eos and Koronis families are both located in the outer parts of the main-belt, where the field population is about 90% of type C(Zellner and Bowel) 1977). Fig. 2.13 shows that members of the Koronis family seem to be all of the S type (Gradie and Zeliner 1977), a result confirmed in the thermal radiometry of Gradie et al. (1977). The Eos objects are more problematical, forming a color group not characteristic of any common type (Gradie and Zeliner 1977) and with albedos near 0.08 according to Gradie et al. (1977). Such combinations of color and albedo are hardly,if ever,seen outside the Eos family. The Nysa objects also form a discrete unit, as plotted in Fig. 2.14 and discussed by Zellner et al. (1977b). The hypothesis that asteroid families are formed by collisional focussing of unrelated field objects (e.g. Alfven 19&9) is clearly incon- sistent with the modern observational data presented in these figures.

Fig.2.14 U-B vs B-V colors for asteroids in the 434 Hungaria group (o), the 44 Nysa family (•), the 24 Themis family (•) and Mars-orbit crossers (O). Data from Table 2.7, Zellner et al. (1975), Zellner et al. (1977a), and Degewij et al. (1978).

Hansen (1977) noted that seven members of the 24 Themis family are classified as type C. In Table 2.7 we find C-type colors for 8 additional Themis members. It is unlikely (proba- bility -21%) that 15 out of 15 objects randomly picked from the Themis family would all be of the type C if this family were to follow the field population distribution of -90% type Cat 3.14 AU. Morrison (1977) and Zellner et al. (1977b) have reported that asteroid 434 Hungaria at a=1.94 is of the rare E type. Three Hungarias from the listing by Pilcher and Meeus (1973) show colors that scatter widely (Fig. 2.14), but none of these are from the Hungaria dynamical family identified by Williams (pers.comm.). Other possible members of his Hungaria family re- main unsampled at this writing. 59

Neither the Mars-orbit crossers 1W Beira, 1977RA, 1980= 1950LA and 1977VA nor the earth-orbit-crosser 1976UA in Table 2.7 belong to any of the common main-belt types. The Mars-orbit- crossers 1953RA, 1977VB, and 1977VC appear to be typical S objects, like 433 Eros, 1036 Ganymed, and 1620 Geographos.

Fig.2.15 U-B vs B-V colors for asteroids in the 153 Hilda group (°), the Trojan cloud preceding Jupiter (•), and following Jupiter (*), 9<+4 Hidalgo (+), and 279 Thule (x). Data from Table 2.7, Taylor (1971), Zellner et al. (1975), Taylor et al. (1976), Zellner et al. (1977a), and Degewij et al. (1978).

Figure 2.I5 illustrates colors for the Hildas, Trojans, and other objects beyond the main-belt. Trojans in the preceding cloud were already known to form a spectral reflectivity group distinct from the main-belt population (McCord and Chap- man 1975; Zellner et al. 1977; Ch. Ill); I can now add to this group six Trojans following Jupiter. The distant orbitally unique objects 279 Thule and 9^ Hidalgo show the same unusual colors. The Hildas also have generally neutral UBV colors, but with wider scatter. Finally, it can be seen in Fig. 2.13 that the small main- belt objects in our survey are not so closely confined to the typical C and S classes as are the larger asteroids initially surveyed; compare, for example, Fig. 2 of Zellner et al. (1975). Some of the scatter may be due to noise in the observations of fainter objects, but the exceptional colors of 1330, 1595, and 1658 are well established. The asteroid populations hold beyond doubt a greater variety than one would conclude from only the larger representatives. 60

2.3 Size Distributions

2.3.1 Absolute Magnitude Distributions

The distribution of sizes of bodies in the asteroid belt is the primary observational clue to theories about accretional and collisional processes. The size of the body can be computed if the absolute magnitude and albedo are known. A survey of asteroid magnitudes and distances will therefore provide a size distribution under certain assumptions about the albedo. A major survey was undertaken in the fifties (Kuiper et at. 1958) and is known as the Yerkes-McDonald Survey (further called: MDS). It covered the ecliptic belt nearly twice around in 19*»9- 52 with a 6.5>«8.1 field photographic refractor, to a width of 40 degrees and a blue limiting apparent magnitude between 16 and 17. About 2000 objects were recorded, and great care was taken to derive precise photographic magnitudes. The mean of the residuals in a comparison with photoelectric values for 30 objects was+0.18 mag, and no magnitude-related systematic error in the domain 10

Diom in km(p = 0.05 \ 100 50 10

Fig.2.16 Numbers of asteroids counted per half-magnitude interval as a function of absolute magnitude g=B(l,o)- 0.1, for various zones in the main belt. The analyses was revised (from that by Kuiper et al. 1958) by van Houten (1971b). 15 61

the two methods. A revision of the completeness factor for the outer zone with 3-0<«<3.5 was published by van Houten (1971b), together with the final figures for the distributions of absolute magnitude in the different zones (Fig. 2.16). The absolute photographic magnitude g is no longer in use. It is converted to B(i,0)-g+0.1. We see marked differences in the distributions in the three distance zones. In particular, the non-linearity in the inner zone for 10

4.0 logN 2.0

00 3<0

2.0

Fig.2.17 Numbers of asteroids 0.0 2.6

The main results for the fainter objects covered by the PLS compared to the brighter objects of the MDS are (van Houten ; 1971a):"No significant differences for distribution functions of eccentricity, inclination, and semimajor axis exist, and the statistical relations found in the MDS have a continuous extension into the PLS". This is illustrated for the magnitude distribution in Fig. 2.17. There has been some discussion about possible selection effects in the PLS and the validity of the comparison with the MDS: a) Dohnanyi (1971) studied the cumulative distributions for both surveys and disputed the "continuous extension" from the MDS into the PLS. Van Houten (1971b) published a revision of the MDS absolute magnitude distributions and showed that the disagreement, between MDS and PLS in the overlap domain 11.2512) of the absolute magnitude distributions. -: The total number of asteroids and thus the comparison with the MDS may be uncertain, caused by the aforementioned selection ; effects and the coverage of only 2% of the belt, but apparently -, i the slope of the distributions may be trusted. The differences " i' in this slope for the distributions in the MDS in the three zones in the belt (Fig. 2.16) are not confirmed by the PLS (Fig. 2.17), which gives about equal slopes. ; For lack of data on albedos, it was necessary until recent- I Iy to assume that asteroids have the same albedo in order to i interpret the absolute magnitude distribution as a size distri- f button. The non-linearity for 9.5

than 100 large accretional objects, and numerous smaller collisional fragments.

2.3.2 True Size Distributions

A breakthrough in the knowledge of asteroid albedos and diameters took place in recent years. From polarization studies it was possible to derive albedos (Ch. 1.5). An independent method is by measuring the infrared flux together with the flux at optical wavelengths. This makes it possible to derive an albedo and diameter (Ch. 1.6). An unexpected discovery was that the distribution of albedos is bi-modal with preferred values of the albedo at 0.035 and 0.15. This means that the details of an absolute magnitude distribution might differ significantly if transformed into a size distribution. In recent years the amount of physical information increased rapidly. For the brighter asteroids physical information obtained with several techniques was available for the same object, and it was possible to classify the asteroids into compositional groups and to look for similarities with meteorite types. A first synthesis of all available physical data for 110 asteroids was made by Chapman, Morrison, and Zellner (1975). They found: a) 901 of the asteroids to fall into two broad compositional groups designated by the symbols C and S; b) the comparison with meteorite spectral albedo curves suggests that the two groups are compositionally similar to carbonaceous and stony-metallic meteorites; and c) C-type asteroids predomi- p nate in the belt, especially in the outer half. 'I ' A more recent study of asteroid compositional groups and i'c an analysis of the relation with diameter and heliocentric dis- [ tance was given by Zellner and Bowell (1977). The availability ij of the TRIAD computer file (Bender et al. 1978) in which all |--' reliable physical information for asteroids is available, was ?,;"" a necessity for this study. The name TRIAD means: Tucson Re- 'i^, vised Index of Asteroid Data, and it is maintained at the Uni- l.'; versity of Arizona by B. Zellner. Contributors and their areas I* of responsibility are: D. Bender, osculating orbital elements; If- E. Bowell, UBV colors; C. Chapman, spectrophotometric parameters; I;: M. Gaffey, digital reflection spectra; T. Gehrels, magnitudes; |i D. Morrison, radiometric diameters; E. Tedesco, rotational ele- E? ments; and B. Zellner, polarimetric parameters. fe The important corrections for observational selection ef- £ fects ("bias-corrections") in the different zones of the main- |E belt were applied by Zellner and Bowell to a sample of 359 asteroids with information about physical parameters, in order to get the best estimate for the properties of the whole asteroid population. The major results of Zeliner and Bowel 1 were: a) besides the C and S groups as defined by Chapman et al. (1975), two new groups exist: M-(metal-rich) and E-(metal-free; enstatite?) type asteroids; b) of the 560 main-belt asteroids with diameters >50 km, 76% are of type C, 16% of type S, 5% M, and 3% of other types; c) the shapes of the diameter-frequency relations for C- and (S-+ M-)types are statistically indisting- uishable, both showing a change of slope at 160 km diameter; d) the proportion of S-type bodies, referred to the total number of objects, decreases exponentially with heliocentric distance. The most recent study about asteroid compositional groups was by Bowel 1 et al. (1978), in which the classification system as published by Chapman et al. and Zeliner and Bowell was aug- mented to five classes, precisely defined in terms of seven parameters obtained from physical information for 521 asteroids. Fig. 2.18 shows which domains in the UBV diagram correspond with these classes. Furthermore, reliable diameters from thermal radiometry or polarimetry or else from albedos adopted as typical for the types were listed for 481 asteroids. A redis- cussion of the relation between compositional types and diameter, as described by Zellner and Bowell, has not yet been at- tempted for this larger sample. I will do that in the following section.

1 1 ' 1 1 1 1

U-B

0.5

/ S / - 04 1' y - C *

0.3 - - Fig.2.18 Adopted do- i—i mains in the UBV dia- ! C.M.E 7 E| - gram of asteroids i i with compositional 0.2 _i - ! M types C, S, M, E, and R. Adapted from Bowell et al. (1978) 0.6 0.7 0.8 0.9 B-V 65

2.3.3 Revised Size Distributions

This section gives new size distributions and the reasons > are: a) The sample of asteroids published by Bowel I et al. I (1978) with known physical parameters is k5% larger than the f. sample used by Zeilner and Bowel); and b)We now have UBV colors I for 145 faint asteroids with i4.5 were taken in order to make an easy comparison possible. Bias factors were defined in the same way as by Zellner and Bowel 1. If f [S(a,0)] is the distribution for all asteroids and f&[s(a,0)] is the distribution for the objects with known albedos, then the bias factor, F2> was defined in 0.5 magnitude intervals in each zone z by F_[B(a,0)] = f[B(a,0)]M[B(a,0)J (31)

This implies the assumption that in each zone the bias factor is a function of B(at0) only, and independent of the type or diameter. The completeness-corrected number of objects, \f{t,d,z), per type, t, per log diameter interval of 0.05, d, and the zone, s, i s C N (t,d,3) = ^T F2lBia,0)] Nlt.d.s) (32)

mi 2.0

nXt,d,z) is given in Table 2.8a-b in the columns headed c as the corrected number of asteroids. The observed number of asteroids for which information about albedo was available is given in the columns headed o. N\t,d,z) for all asteroids in the three different zones is given in Fig. 2.20 and for C and S type asteroids in the whole belt in Fig. 2.21. I shall now try to estimate how large the errors in the slope of the size distributions could be. The points marked + in Fig. 2.20 for 2.6

® 20

100

10 12 14 16 8 10 12 14 16 6(0,0) eio.o)

Fig.2.19 Number of asteroids in the TRIAD computer file (upper, solid line) and asteroids with assigned albedo (lower solid line} per Q.5 mag interval in B(a,0) for different zones in the main belt. The dotted line indicates an extrapolation with the slope found in the Palomar Leiden Survey. The correction factor for completeness (dashed line) is computed as the ratio between the two solid curves. For A and B see text. 67

9 10 11 12 13 9 « (o) 100 ' 1 1 N 50 o

unoo1-

5 •

H100-

- 1 / /

/ Fig.2.20 Completeness - corrected size distributions for three zones o 20

1 1 I , , A and B see Fig.2.19. 200 100 50 25 12 5 Oiameter km

i v Fig.2.21 Completeness corrected size distributions for all known C- and S-type asteroids. 200 100 50 25 Diameter km 68

Table 2 8a Observed o) and corrected (c) numbers of asteroids of various diameter ranges

C-type S-type

Diam 2. 24 1 14 7 47 5 6 6 16 11 22 56- 63 3 6 J» 38 5 31 12 75 2 2 4 9 3 4 9 15 ", 63- 71 4 7 I> 38 7 22 15 67 4 4 8 14 1 1 13 19 71- 79 1 2 i! 40 10 26 19 68 2 2 3 4 3 4 8 10 79- 89 4 5 Li 15 7 18 15 38 3 3 4 6 7 9 •! 89-100 5 6 12- 25 7 16 24 47 7 7 4 4 11 11 ' 100-112 6 7 11 20 8 14 25 41 1 1 1 1 2 2 112-126 2 2 1C 12 9 14 21 28 4 4 5 5 9 9 J 126-141 2 2 £ 10 10 14 20 26 2 2 2 2 J 141-159 3 3 c, 6 3 4 11 13 5 5 1 1 6 6 « 159-178 11 12 7 8 18 20 1 1 1 1 1 1 3 3 1 178-200 1 1 6 7 7 8 2 2 2 2 ; 200-224 2 2 3 3 4 4 9 9 1 1 1 1 • 224-252 1 1 2 2 1 1 4 4 3 3 3 3 252-283 ,; 283-317 2 2 2 2 317-356 4 4 4 4 356 1 1 1 1 J 69

Table 2.8b Observed (o) and corrected (c) numbers of asteroids of various diameter ranges

M-type Total Asteroid Population

Diam. 2

9- 10 1 27 10- 11 1 27 11- 13 2 35 13- 1^ 4 69 14- 16 7 60 16- 18 2 16 18- 20 2 5 20- 22 i» 59 22- 25 2 11 25- 28 2 3 28- 32 1 14 1 14 3 17 4 89 7 93 32- 35 1 1 1 1 2 3 3 31 7 40 35- 40 1 7 1 7 9 40 12 100 13 261 40- 45 1 5 1 5 11 19 4 34 10 79 45- 50 1 3 1 3 10 14 8 49 10 85 50- 56 1 2 1 2 9 15 10 43 5 24 56- 63 4 8 4 8 6 9 13 55 10 4! 63- 71 1 1 1 1 8 11 15 56 8 24 71- 79 5 6 12 49 15 33 79- 89 1 1 1 1 6 7 7 18 11 24 89-100 1 1 1 1 12 13 17 31 9 19 100-112 6 7 12 21 10 15 112-126 1 1 1 1 2 2 7 7 16 19 10 15 126-141 k k 11 17 10 17 141-159 9 9 8 9 3 k 159-178 1 1 13 14 8 9 178-200 1 1 1 1 2 2 2 2 6 7 200-224 3 3 3 3 4 4 224-252 1 1 5 5 1 1 252-283 1 1 1 1 1 1 283-317 2 2 317-356 4 4 356 1 1 1 1 70

Size distributions for Different Zones

The size distributions for all asteroids in the three I zones (Fig. 2.20) show clearly different slopes in the inner j and outer zones. The intermediate zone is apparently surveyed |: incompletely beyond B(a,0)=13 (Fig. 2.19), and this could be I a reason for the scatter in the resulting size distribution. I In a comparison of the corrected MDS distributions (Fig. [ 2J6 ) and the PLS (Fig. 2.17) with the true size distributions f of Fig. 2.20, I confirm the difference in slopes for the inner |: and outer zone in the domain 25-100 km (913).

Size distributions for Different Types

The size distribution for S-type asteroids in Fig. 2.21 differs significantly from the results of Zellner and Bowell (1977J, such that Fig. 2.21 is steeper for smaller sizes, and : a non linearity at 150 km is not so pronounced; the distribu- '•- tion might even be a straight line. Error sources in the clas- : sification of S-type asteroids are unlikely because of the j- unique relation between reddish colors and high albedo, with only one or two cases as exceptions. The size distribution for C-type asteroids in Fig. 2.21 differs slightly from the results of Zellner and Bowell. Between diameters of 60 and 140 km I find 20% more C-type asteroids, but this may be due to misclassification. High albedo M- and E-type asteroids are close together in UBV colors with low albedo C-type asteroids as can be seen in Fig. 2.18. An asteroid for which the UBV color is a little bit more in error than expected might enter the wrong UBV area so that a wrong type and albedo might be attributed to it. i. 71

l.k Variations of the Composition over the Surface

2.4.1 Observations

l> All minor planets have undergone intense surface bombard- | ment both in ancient and in more recent epochs, and for all |- an irregular shape resulting from collisions is revealed by at P- least some brightness variations over a rotational cycle. Under f; such conditions we may expect to see a local variation of the 4 composition over the surface due to contamination by impacting |: material, or due to distinct geological units within the pa- *-• rent body. If the latter type of variations could be establish- ;\, ed , then the compositional patterns revealed would provide r constraints on models of the parent bodies of meteorites. !•; For bodies sufficiently far from the sun, and with conse- y quently low surface temperatures, frosts (frozen volatiles) ." or local deposits of sublimates can be expected. A review Y of the stability of frosts in the solar system is given by >v Lebofsky (1975;. Albedo spots on the 10 km Martian satellite P Deimos were observed with the Mariner 9 satellite (Veverka % 1977). 1 The asteroids are too small and too distant for direct ; imaging of surface features, but any significant large-scale i variation of the composition over the surface should be re- ;>" vealed by changes in the apparent albedo or spectral reflectan- j} ce as the object rotates. The albedo may be taken inversely ; proportional to the optical polarization, which can be measured i' to very high precision for bright objects. Color differences '::.' as small as 0.01 mag can be detected by conventional photo- !•; electric techniques and with special care this can be improved p, to_+ 0.003 mag. The major surveys of color, polarization, and i; spectral reflectance by Zellner and Gradie 1976, McCord and ;; Chapman 1975, Zellner et al. 1977, Veeder et al. 1978, I. Degewij et al. 1978, and Ch. 2.2, have demonstrated remarkably • repeatable resul ts for individual minor planets. ? Dunlap (1972) studied 'lightcurves of artificial asteroids i; in the laboratory and concluded from peculiarities in the jV lightcurves of real asteroids that albedo changes can not be [ ignored for 16 out of kk asteroids. Both, albedo and/or color ;.;-:" changes are present. In view of the fact that they are small, '; I tried to obtain the highest precision with special obser- ; ving techniques for some selected asteroids. \'\ Recently we monitored 1 Ceres for polarization, and 3^9 [-, Dembowska for color variations, over one or more complete H rotations (Degewij and Zellner 1978). The color of Dembowska &•' in the V-I spectral range (the I filter falls within the strong I pyroxene absorption band for this unusual object) was constant | within +_ 0.01 mag. The polarization of Ceres was found to be 72

Table 2.9 Evidence for Spots on Asteroids

Asteroid Type/ D/ Ampl.j AP/Py Colorl Date or km mag r V mag Base Reference

1 Ceres C-U 1020 0.04 SO.005 31.111.77 4 Vesta U 549 0.08 0.08 +0.015 U-V 12-14.11.77 6 Hebe S 195 0.15 -0.02 U-V (1) 15 Eunomia c 246 0.50 50.01 B-V (2) 16 Psyche M 252 0.21 <0.10 13.11.77 19 Fortuna C 221 0.25 <0.03 <0.01 B-V (3) 25 Phocaea S 65 0.20 +0.02 B-V (2) 39 Laetitia S I6

/ From Bowel 1 et al. (1978). Last two objects from IAUC 3193. | Observed lightcurve amplitude. K + sign means redder and - sign means bluer at maximum brightness. References: (1) Gehrels and Taylor (1977); (2) Groeneveld and Kuiper (1954); (3) Zellner and Gradie (1976a); (4) Wamsteker and Sather (1974); (5) Mi His et al. (1976;; (6) Zellner and Gradie (1976b); (7) Tedesco and Bowel 1 (1979).

constant to a precision of better than 0.005 of the measured polarization value (1.6%). This indicates that the lightcurve for this 1000 km body is fully attributable to a slightly elongated shape. A list of asteroids for which color and polarization studies have been made is given in Table 2.9 . The observing date is given if the object was studied with one of the telescopes of the University of Arizona. The computerized photon-counting polarimeter MINIPOL (Frecker and Serkowski 1976) was always used, providing simultaneously the information about the colors and the polarization. The results for the variation in polarization during a lightcurve cycle are given under &pv/pv in Table 2.9 . For instance for 349 Dembowska Ap^/p^O.12 means that the rms error in the polarization measurements was equal to 0.12 times the value of the polarization; albedo variations larger than 12% during a lightcurve cycle can be excluded. 73

Albedo Spots on Vesta

Vesta has unique optical properties among the minor planet population, and has been firmly identified as the parent body of the basaltic achondrite meteorites by comparing its spectrum between 0.3-1-1 nm with meteorite spectra (McCord et al. 1970, Chapman et al. 1975)- The rotation period was given as 5.3^ hours by Gehrels (1967), with one photometric maximum and one minimum and Gehrels reported further that Vesta is slightly redder at maximum light. Taylor (1973J, however, found evidence for two maxima and two minima and hence a period twice as long. He used pieces of 1ightcurves observed 10 days apart and therefore a confirmation at approximately the same aspect is needed. New observations were made in February 1977 and the photo- polarimetric results from three nights (Fig. 2.22) show polarization changes with a period of SO'thours that exactly mirror the brightness variations. Evidently Vesta may be regarded as spherical, and the 1ightcurve variations due to albedo features. We also confirm the slight color changes, Vesta being slightly redder at maximum light, initially reported by Gehrels. I can not make a firm statement about the value of the rotation period from my data, because the noise in the polarization curve is too large to distinguish different maxima and minima. I consider a body with one spot to be more likely than a body with two spots having similar albedo variation, so that the shorter period of 5.3^ hours should be preferred.

1 1 1 —i —i

MAG

01 • * • rva *

•035

•0.40

HOURS Fig.2.22 The visual lightcurve and polarization curve for 4 Vesta on Feb 12 (<>), 13 (*), and 14 (•) UT 1977 observed by J.Degewij and Th. Le Bertre with the 100 cm telescope at Mount Lemmon. The lightcurve is re- peated as a dashed line on the polarization measurements to show that the brightness variations are essentially attributable to albedo spots on a nearly spherical body. A period of 5.34 hours is used. 2.4.2 Uniformity of Asteroid Surfaces Geochemically the basaltic achondrites are magma products (Consolmagno and Drake 1977J, and it can be speculated that the color and the albedo differences on Vesta are due to discrete lava flows, or to partial excavation to a deeper layer. The lava layer on Vesta can not be deeper than 10 km (M. Drake pers. comm.). Table 2.9 also indicates the strong color variations for 944 Hidalgo, as observed by Tedesco and Bowell (1979). Hidalgo, 10 times smaller than Vesta, is the only object without comet3- ry activity in the typical cometary a,e domain (Fig. 1.1), and its origin may have little to do with the asteroids in the main belt. Notwithstanding the results for Vesta and Hidalgo, the degree of uniformity of most asteroid surfaces is remarkable in view of the well-known hemisperical differences for the moon, the Galilean satellites, and lapetus. If an asteroid exists with large, discrete domains of ferrosilicate, metallic, or carbonaceous material together on its surface, it is yet to be identified. Even on the high-albedo, strongly-colored surface of 349 Dembowska, there appears to be no major contamination by the dark, neutrally-colored C-type material which do- minates in its vicinity in the main belt. We can conclude that impact events apparently result in the excavation of much more than the impacting mass, and each asteroid blankets itself with a well-mixed layer of essentially its own debris from the locale of the impact.

References Alfve'n, H. 1969 Asteroidal jet streams Astrophys. Space Sai. 4, 84 Allen, C.W. 1973 Astrophysical quantities University of London The Athlone Press Anders, E. 1965 Fragmentation history of asteroids Icarus 43 399 Arnold, J. 1969 Asteroid families and "jet streams" A.J. 74, 1235 Bender, D., Bowell, E., Chapman, C, Gaffey, M., Gehrels, T., Zellner, B., Morrison, D., and Tedesco, E. 1978 The Tucson revised index of asteroid data (note) Icarus 33. 630 Bowell, E. 1976 Physical properties of asteroids from UBV photometry; paper presented at the Division of Planetary Sciences Meeting Austin Texas (March 1976) 75

Bowell, E. 1977 UBV photometric survey of asteroids Bull. Am. Astron. Soc. 9, 459 Bowell, E., Chapman, C.R., Gradie, J.C., Morrison, D., and Zellner, 8. 1978 Taxonomy of asteroids Icarus in press Burns, J.A., and Harris, A.W. 1978 Asteroid rotation: I. Tabu- lation and analysis of data; submitted to loams Chapman, C.R. 1976 Asteroids as meteorite parent-bodies: the astronomical perspective Geoohim. Cosmockim. Aata. 40, I 701 Chapman, C.R., Morrison, D., Zellner, B. 1975 Surface properties of asteroids: a synthesis of polarimetry, radio- met ry and spectrophotometry Icarus 25, 104 Consolmagno, G.J. and Drake, M.J. 1977 Composition and evolution of the eucrite parent body: evidence from rare earth elements Geoohim. Cosmochim. Aota. 41, 1271 Oegewij, J. 1977 Lightcurve analyses for 170 small asteroids Proc. Lunar Soi. Conf. 8th, 145 Pergamon Press Degewij, J., and Gehrels, T. 1976 Spin and strength of small asteroids Bull. Amerio. Astvon. Soo. 8, 459 Degewij, J., and Zellner, B. 1978 Asteroid surface variega- tion (abstract) p235 Ninth Lunar and Planetary Science Conference Houston Degewij, J., Gradie, J., and Zellner, B. 1978 Minor planets and related objects. XXV. UBV photometry of 145 faint asteroids A.J. 83, 643 Dohnanyi, J.S. 1972 Interplanetary objects in review: statistics of their masses and dynamics Icarus 17, 1 Dunlap, L. 1972 Laboratory work on the shape of asteroids M. So. thesis University of Arizona Frecker, J., and Serkowski, K. 1976 Linear polarimeter with rapid modulation, achromatic in the 0.3-1.1 pm range Appl. Opt. IS, 605 Gaffey, M.J., and McCord, T.B. 1978 Asteroid surface materials: mineralogical characterizations from reflectance spectra Space Sci. Rev. 21, 555 Gehrels, T. 1967a Minor planets. I. The rotation of Vesta Astron. J. 72, 929 Gehrels, T. 1967b Minor planets. II. Photographic magnitudes Astron. J. 72a 1288 Gehrels, T. 1970 Photometry of asteroids Surfaces and Interiors of Planets and Satellites p317 (Ed. A. Dollfus) Academic Press London Gehrels, T. 1971 Physical parameters of asteroids and interrelations with comets From Plasma to Planet Nobel Sym- posium 21 (Ed. A. Elvius) Stockholm 1971 Gehrels, T., and Owings, D. 1962 Photometric studies of asteroids IX. Additional light curves Astrophys. J. 135, 906 Gehrels, T., and Taylor, R.C. 1977 Minor planets and related objects XXII. Phase functions for (6) Hebe Astron. J. 82, 229 76

Gehrels, T.f and Gehrels, N. 1978 Minor planets and related objects XXVI. Magnitudes for the numbered asteroids '. A.J. submitted Gradie, J., and Zeliner, B. 1977 Asteroid families: observational evidence for common origins Saienae 197, 25k Gradie, J., Rieke, G., and Zellner, B. 1977 UBV and 10 ym photometric observations of Eos and Koronis family members Bull. Amer. Astron. Soc. 9, 503 Groeneveld, I., and Kuiper, G.P. 195*» Photometric studies of asteroids I Ap.J. 120, 200 Hansen, O.L. 1977a Search for correlation between asteroid families and classes Icarus 32, 229 Hartmann, W.K.,and Hartman, A.C. 1968 Asteroid collisions and evolution of asteroidal mass distribution and meteoritic \ flux Icarus 8, 361 Houten, C.J. van 1962 An investigation of asteroid light-curves I on Franklin-Adams plates Bulletin of the Astronomical :- Institutes of the Netherlands 16, 160 Houten, C.J. van, and Houten-Groeneveld, I. van, Herget, P., Gehrels, T. 1970 The Palomar-Leiden survey of faint , minor planets Astron. Astrophys. Suppl. Ser. 23 339 Houten, C.J. van 1971a The Palomar-Leiden survey Physical studies of Minor Planets pi83 (Ed. T. Gehrels) NASA SP- • 267 Houten,C.J. van 1971b Discussion about correction factors for completeness of the MDS Physical studies of Minor Pla- nets p292 (Ed. T. Gehrels) NASA SP-267 : Houten, C.J. van 1971c Discussion about orbital selection ef- \ fects in the PLS Physical studies of Minor Planets p209 j (Ed. T. Gehrels) NASA SP-267 I Johnson, H.L., and Mitchell, R.I. 1962 A completely digitized f, multi-color photometer Comm. Lunar and Planetary Lab. r-- 1, 1*. P73 I Johnson, T.V., and McGetchin, T.R. 1973 Topography on satellite . surfaces and the shape of asteroids Icarus 18, 612 A Kort, S.J. de, J.J. 1968 Societa Astroromica Italians Atti • dell' XI Convegno Padova Trieste j KresSk, L.1971 Orbital selection effects in the Palomar- ? Leiden asteroid survey Physical studies of Minor Planets H p197 (Ed. T. Gehrels) NASA SP-267 H Kuiper, G.P., Fujita, Y., Gehrels, T., Groeneveld, I., Kent, J., * Biesbroeck, G., and Houten, C.J. van 1958 Survey of As- ;j teroids Astrophys. J. Suppl. Ser. 3, 289 | 77

Lebofsky, L.A. 1975 Stability of frosts in the solar system Icarus 25, 205 McCord, T.B., Adams, J.B., Johnson, T.V. 1970 Asteroid Vesta: Spectral reflectivity and compositional implications Science 168, 1445 McCord, T.B., and Gaffey, M.J. 1974 Asteroids: Surface composition from reflection spectroscopy Science 186, 352 McCord, T.B., and Chapman, C.R. 1975 Asteroids: Spectral reflectance and color characteristics II Astrophys. J. 197, 781 Mi 11 is, R.L., Bowell, E., and Thompson, D.T. 1976 UBV photometry of asteroid 433 Eros Icarus 28, 53. Morrison, D. 1977 Asteroid sizes and albedos Icarus 31, 185 Napier, W.McD., Dodd, R.J. 1974 On the origin of the asteroids Monthly Notices Roy. Astron. Soc. 166, 469 Pilcher, F., and Meeus, J. 1973 Tables of minor planets private printing Purgathofer, A.T. 1969 UBV sequences in selected star fields Lowell Obs. Bull. 73 98 Taylor, R.C. 1971 Photometric observations and reductions of 1ightcurves of asteroids Physical studies of Minor Planets p117 (Ed. T. Gehrels) NASA SP-267 Taylor, R.C. 1973 Minor planets and related objects XIV. Asteroid (k) Vesta Astron. J. 78, 1131 Taylor, R.C., Gehrels, T., and Capen, R.C. 1976 Minor planets and related objects XXI. Photometry of eight asteroids Astron. J. 81, 778 Tedesco, E., and Bowell, E. 1979 in preparation Veeder, G.J., Matson, D.L., and Smith, J.C. 1978 Visual and infrared photometry of asteroids Astron. J. 83, 651 Vesely, CD. 1971 Summary on orientations of rotation axes Physical studies of Minor Planets pi33 (Ed. T. Gehrels) NASA SP-267 Warnsteker, W., and Sather, B. 197^ Minor planets and related objects XVII: Five-color photometry of four asteroids Astron. J. 79, 1465 Wetherill, G.W. 1974 Solar system sources of meteorites and large meteoroids Ann. Rev. of Earth and Planetary Sc. 2, 303 Williams, J.G. 1978 in preparation Z'lllner, B., Wisniewski, W.Z., and Andersson, L. 1975 Minor planets and related objects XVIII UBV photometry and surface composition A.J. 80, 986 78

Zellner, B., and Gradie, J. 1976a Minor planets and related objects XX Polarimetric evidence for the albedos and compositions of 3k asteroids Astron. J. 81, 262 Zellner, B., and Gradie, J. 1976b Polarization of the reflected light of asteroid ^33 Eros Icarus 28, 117 Zellner, B., Andersson, L., and Gradie, J. 1977a VBV photometry of small and distant asteroids Icarus 31, kkij Zellner, B., Leake, M., Morrison, 0., and Williams, J.G. 1977b The E asteroids and the origin of the enstatite achondrites Geochim. Cosmochim. Acta 41, 1759 Zellner, B., and Bowel 1, E. 1977 Asteroid compositional types and their distributions Comets, Asteroids, Meteorites pi85 (Ed. A.H. Delsemme) University of Toledo

I It 79

CHAPTER III DISTANT ASTEROIDS

; Figure 1.1 shows with increasing semi-major axis three t groupings of asteroids: a) the main belt between about 2.2 and f" 3.5 AU; b) the Hilda asteroids at 3-9 AU; and c) the Trojans - in the orbit of Jupiter preceding and following it. The two :, distant groupings, Hildas as well as Trojans, have compared O with the main belt a strong gravitational interaction with >:•; Jupiter. y. Very little is known about the physical parameters of the - asteroids in the two distant groupings. 26 Hildas, 12 Trojans ; preceding, and 10 following Jupiter are listed in the annual • asteroid ephemerides of the Institute of Theoretical Astronomy f: in Leningrad. The detection of objects in both locations is Q-: difficult. The use of the 122 cm Palomar Schmidt telescope - aimed towards the center of the Trojan cloud, shows that on ;; one plate exposed for 10 minutes, 300 main belt asteroids, 20 • Trojans and 4 Hildas can be found based upon apparent motion i (van Houten, pers. comm.). By assuming a radiometric albedo of - 0.03, 75% of the 26 known Hildas have diameters larger than '-• 50 km, and the same applies to the 27 Trojans that are present- ;i ly known. / The published studies concerning physical parameters of f these distant objects resulted in: a) the magnitude distribution for 45 Trojans, with unknown orbits, has the same slope as the magnitude distribution for asteroids in the main belt (van Houten et al. 1970); b) the apparent number of Trojans down to a certain magnitude limit in the cloud preceding Jupi- [•- ter appears to be 2 times higher than that in the following cloud (van Houten, unpublished; see Gehrels 1970,1977); c) there appear to be two distinct groupings with small (5°) and large (17°) orbital inclination in both Trojan clouds (van t Houten et al. 1970); d) extensive 1ightcurve studies for Trojan :\ 624 Hektor (Dunlap and Gehrels 1969) showed a very elongated -* (2.75:1) body shape and a rotation period of 6 hours and 55 •" minutes. The same paper reports small amplitudes (0.2-0.4 mag) %• for 2 other Trojans. 911 has a fairly short period (6-10 hours) % and 1437 has a longer one (18-24 hours); e) UBV colors for I Trojan 624 Hektor (Dunlap and Gehrels 1969), 911 and 1437 (Tay- £ lor 1971), 588, 1143, and 1583 (Zellner et al. 1977) all in K. the cloud preceding Jupiter, indicate very similar colors near t: the ambiguous lower right edge of the C-domain. In this domain >; asteroids of different type cluster together (see Fig. 2.18); F f) Cruikshank (1977) measured radiometric albedos and diameters i; for one Trojan preceding and three following Jupiter. Similar t low albedos between 0.02 and 0.03 were found; g) spectrophoto- [ metry of 624 Hektor and 911 Agamemnon (McCord and Chapman 1975) t yieided unique reflection spectra with a steep rise between K 0.7 and 0.9 m. The spectrum of 1173 Anchises (Chapman 1976) I v 80 was, however, flat in this domain; h) UBV colors of one Hilda (Taylor et at. 1976) and four Hildas (Zellner et at. 1977) are located in the ambiguous lower part of the C-type domain, and Zellner et at. commented that preliminary polarization measure- merits of Hilda-type asteroid 361 Bononia are not consistent with the polarization curve of a typical C-type asteroid in the main belt. It can be seen from these results that little insight has been obtained: mixing of compositional types exist in the Tro- jan clouds but it does not show up in the albedos. Concerning the Hildas too little is known and additional data are urgent- ly needed. The TV system with an image intensifier (p. 8 ), now together with a self-made mirror device, made it possible to center the faint (15.0<7<17-5) objects in the diaphragm of the photometer. In the following sections new UBVRI photometry and also infrared radiometry is presented for Trojans and Hildas. I will discuss the resemblance of physical parameters of the objects in both locations and how these parameters compare with the extensive physical information about objects in the main belt.

3.1 Asteroids with Hilda-type Orbits

3.1.1 UBV colors

New UBV colors for six more Hildas (Table 2.7) together with colors for five Hildas measured previously, appear to cluster in the ambiguous lower edge of the C-type domain (Fig. 2.18). The ultraviolet drop-off, as represented by the U-B color is very similar to that for the Trojans. The reflection spectra towards the red, as represented by the B-V color, might differ in such a way that Trojans are slightly redder than Hildas in B-V. This small effect indicates that supplementary information in red light is needed. It is possible that Tro- jans and Hilda reflection spectra differ towards the red.

3.1.2 Radiometric Albedos and Diameters

With a small radiometric program I measured 10.6 pm fluxes of 3 Hildas (Table 3.1). A description of the instrumental system and the radiative model are given in Ch. 1.6. The rms errors in albedo and diameter are derived from the noise in the observations at 10.6 pm and 0.55 pm. N is the infrared magnitude for A.eff=10.6 pm, with AM] it can be transformed to the standard system (Gradie1978, Morrison 1977). 81

Tablei 3.1 10 um Radiometric Albedos for Asteroids in Peculiar Orbits

4 Date iN R D 17 at PV AU AU km x 10~3 887 MC 9 Jan 78 0.24 14 .54 3.49 1.15 0.36 -53 4± 0 156± 8 51 MB ,, 0.24 7.98 0.08 2 .22 1.57 -22 162 43 1362 MB ,i 0.24 11 .70 3.96 2 .57 1.62 + 7 29+ 1 43± 2 958 Hi i 0.35 10,.97 6.47 3.32 2 .36 - 4 20± 4 171+65 624 T ii 0.35 7,.89 4.52 5.02 4.52 -10 201 + 8 30± 2 .1 "•s 1437 T 0 .35 8,.68 4,.60 5.02 4.47 +10 190+10 17± 2 ) 911 T II 0 • 35 8.,26 5..46 5.30 4.90 +10 159±10 34± 5 617 T II 0.35 8.,60 4.52 4.71 4.41 +12 172+ 5 21± 1 313 MB 6 Apr 78 0.25 9.30 2.,22 2 .50 2.05 -23 84+ 0 47± 0 76 MB " 0.35 8.,41 3.,01 3.53 2 .60 - 7 117± 4 55± 4 1512 Hi ,, 0.35 9.92 3.56 3.53 2 .53 - 1 83+ 2 27± 1 51 MB 7 Apr 78 0.25 7.98 -0.33 2,.21 1.37 +18 148 51 1162 Hi i, 0.35 9.77 5.98 3..85 2 .98 + 8 42+ 5 123±31 1512 Hi 0 .35 9.92 3.58 3.52 2,.52 - 0 83+ 2 27± 1

js,- -f-"—" before opposition; "+" after opposition ft HOrbital groups are designated by: MB, main belt; MC, Mars-orbit f.j-: crosser; Hi, Hilda; T, Trojan (i

b An interesting result for these distant bodies is the high g. albedo for both asteroids 958 and 1162. The B-V color of 958 U was measured and computed (Table 2.7) relative to Jovian satel- [| lite 6, for which the B-V color is well established (Table 3-7). H; 958 shows a B-V color similar to that of S-type asteroids, but ij~ a confirmation is needed. The Jow albedo of 0.03 for 1512 was I? confirmed in a second night. ii For these faint objects it is very difficult and time con- fix suming to measure reliable infrared fluxes, and measurements re from one night cannot be trusted. The visual absolute magnitude p P(1>0), used for the computation of the albedo, is not obtained fji simultaneously with the measurement of the infrared flux, but P measured in a different night. This visual magnitude gives a P wrong albedo if the object has a lightcurve with a large ampli- |; tude. Little can be said about this problem because only single f; measurements for the majority.of observed Hildas exist. The I F(1,0) data for 1162 Larissa (Table 2.7) differ by 0.5 mag. The I low albedo for 1512, confirmed in a second night, and the two p high albedos for the objects 958 and 1162, also measured in a | different night, make it unlikely that the two albedo groupings I were accidently caused by large amplitude lightcurves. 82

3.2 Trojan Asteroids

3.2.1 UBVRI Reflectances

UBV Photometry

Table 2.7 Jists new UBV colors for 6 Trojans following Jupiter and for 2 preceding ones. The colors for the 2 preceding Trojans confirm the colors obtained previously. The spread in UBV colors for all objects with colors known in the literature (Fig. 2.15) is less for the objects in both clouds than for the Hildas, and the Trojans preceding Jupiter might be slightly (2 times error in the mean) redder in B-V than the following Trojans. This might indicate that the reflection spectra of the Trojans in both clouds differ towards the red.

Near-infrared Photometry

The similarity in UBV colors of Hilda and Trojan asteroids, suggests similar compositional types. This is contradicted by the two Hildas (958 and 1162) with high values for the radiometric albedos. It can be concluded that UBV photometry alone, with the purpose of classifying distant asteroids, has to be applied with caution. A photometric program was done to study if the small but possibly meaningful difference in B-V between Hildas and Tro- jans following and preceding Jupiter indeed indicates a difference in colors towards the near infrared. For that purpose 1.0 0.9 0.8 0.7 0.6

Q8 10 12 U 1.6 1.8 2.00 2.2 ff/X

Fig.3.1 Transmission curves of two filters (Coyne pers. comm.) used for photometry at visual and near infrared wavelengths. The maxima are scaled to transmission 1.0. The red cut-off of an RCA C31034 photomultiplier with an GaAs cathode cooled to -75°C (Cole and Ryer 1972) is shown to indicate the likely extent of the band in the near infrared. 83

a computerized photon-counting photopolar.imeter MINIPOL (Frecker and Serkowski 1976) was used as a photometer with green ("G") and red ("R2") filters and dry-ice cooled RCA C31034 photomultipliers having GaAs cathodes. Both a simultaneous mode in which the filters were mounted behind the Wollaston prism in front of the tubes, and a mode in which the filters were moved in a filter-slide in front of the Wollaston prism, were used. For these faint objects the brightness of the sky is dominant and noise in the colors obtained in both modes did not differ very much. A sky chopping photometer would be necessary to improve the quality of the results. The response curves of the used filter-cathode combination (Fig. 3.1) are similar to those by Kron et at. (1953), and Weistrop (pers. comm.). From Fig. 3-1 it can be estimated that the effective wavelengths of the response curves for the v (G) and r bands are 0.52 v>m and 0.80 ym resp. The response curve for the r band is defined by the passband of the R2 filter and the sensitivity cut-off towards the red of the GaAs cathode. Weistrop kindly provided 7-ti colors for the standard stars (Table 3-2} used fur the transformation

V-R = (33)

in which V and r are the magnitudes in the instrumental system. The transformation coefficient y, determined from the standard stars given in Table 3.2 with 0.44«F-i?<1.41, was 0.92 with an rms error of 0.03. The deviation from 1 might be caused by small differences with the response curves used by Weistrop. Golay (197*0 and Allen (1973) give 0.55 um and 0.83 um as effective wavelengths for the V and R bands, if objects are observed with colors close to those of the sun. A tie-in to a standard system will be useful for comparison with measurements from other observers. More important, however, is to observe bright main belt asteroids in the same instrumental system. For these objects reflection spectra are known down to 1.05 um, and how the observations for the Tro- jans and satellites are referred to it is given in the following sections.

Tabla 3.2 Standards used for VR photometryf

Star V R V-R M34- 89 11.13 10.10 1.03 M34-113 11.09 10.65 0.44 M34-119 11.97 11.22 0.75 SA94-251 11.21 9.98 1.23 SA94-300 11.53 10.47 1.06 SA94-305 8.89 7.48 1.41

tWeistrop (pers. comm.) Table 3.3 VRI Observations of Trojans and Faint Satellites in 1977 and 1978+

V-R V-l

Object Oct 20 Jan 13 Feb 4 Feb 9 Mar 10 Apr 5 Apr 8 May 8 May 12 11 6 0.80 0.82 1.29 22 0.75 0.70 1.1 0.70 0.73 i: 51 52 0.65 0.68 0.95 0 .8; 196 0.84 0.82 617 Q.98±12 0.92±3 884 1.07±2 1.19±3 1172 .35+18 1.40±6 1867 0.79±5 621* 0.92±2 0.95±1 0.95±2 1.22+ 4 1437 0.82±3 0.75±2 0.85±3 1.O6±18 1583 0.97±5 1.14±4 J6 0.72±1 0.80±5 0.97±4 0.87±4 S7 0.78+ 3 S9 0.66+2

tErrors in the mean of the measurements of a given night are expressed in units of 0.01 mag, and are computed in the instrumental system. The errors in the measurements of the five bright asteroids are generally on the order of±fl.02 mag. lIFrom Hansen (1976) 85

UBVRI Reflectances

Spectral information of solid bodies in the solar system is expressed in units of spectral reflectance. It is the ratio between the fluxes of object and Sun, integrated across the effective spectral response of the filter. Extensive work has been done by Chapman et at. (1973) and McCord and Chapman (1975a,b) to derive spectral reflectance curves for 98 bright asteroids. They used 22 narrow band filters in the wavelength domain 0.32-1.10 ym. I selected 5 bright asteroids ss standards for the UBVRI photometry. Table 3.3 gives the measurements for these bright

Table 3.4 Spectral Reflectances R for 5 Bright Asteroidst

0 0 Aeff m 0.38 .45 0.55 0.83 i.90 Fi1terband Vf B V R J 6 Hebe 0.71 0.80 0.96 1.16 1.08 22 Kalliope 0.82 0.90 0.98 - - 51 Nemausa 0.68 0.85 1.00 1.06 1.13 52 Europa 0.89 0.95 1.00 1.06 1.07 196 Philomela 0.70 0.76 0.98 1.17 1.21

t From Chapman et at (1973), McCord and Chapman (1975a,b). Scaled to unity at 0.57 pm.

asteroids for which spectral reflectance curves were determined by Chapman et at. From these curves reflectances at 0.38 \im, 0.^5 urn, 0.55 ym, O.83 um, and 0.90 ym were obtained and are 1isted in Table 3.4 .

Table 3-5 UBVRI Colors for 5 Bright Asteroidst

Type B-V SB]/ U-V V-R S V-I S VR VI 6 Hebe S 0.83 0.63 1.23 0.90 0.81 0.60 1.29 1.16: 22 Kalliope M 0.71 0.62 0.98 0.79 0.73 - 1.19 - 51 Nemausa C? 0.79 0.61 1.25 0.83 0.72 0.66 - 52 Europa C 0.68 0.62 1.03 0.90 0.67 0.61 0.92 0.85 196 Philomela S 0.83 0.55 1.26 0.89 0.83 0.64 1.06 0.98

Sy7=0.86±5; S^-0.63+3; (n-2) t UBV colors are from the TRIAD UBV file maintained by E. Bowel 1. VRI colors are from Table 3.3. The errors in the S-factors are rms errors expressed in 0.01 mag. 86

The reflectances can be used to compute colors in magnitude units by taking logarithms:

in which S12 is the color of the sun for the corresponding wavelength difference and R^ is the reflectance at wavelength \. The values are given in Table 3-5 for the k colors. The average values of S12 are used to transform all measurements given in Table 3.3 to the system used by Chapman et at. (1973) and McCord and Chapman (1975a,b). Table 3-6 gives the colors for these faint objects, and the computed values of the reflectances are plotted in Fig. 3.2.

U B V R U 8 R I 1' 1 i 1 i i 11 i [' 1 1 i

: _ 2.0 4 1172 - - 52 1.2 1.6 - • • 1.0 / •. •.. " - QS 1.6 / / j U / yj 12 - - 1.6 1583/j 1,0 \.L " 4--*~ 1.0 A" __11867" V. h *-4- in _ 1.0 *--•- '' U37 1.0 1.0 1.0 "4-4- - 0.8 i 1 1 I 1 1 • i i 1 Q3 0.5 0.7 0.9 0.3 0,5 0.7 0.9 X urn

Fig.3.2 Spectral reflectance points for Trojan asteroids preceding (.) and following (A) Jupiter. The V-point is taken as unity and the measurements are referred to the spectra of 5 bright asteroids (including c-type asteroid 52 Europa) measured by Chapman et at. (1973), and McCord and Chapman (1975a,b). The error bars show the error in the mean of the measurements. The steep curve towards the red for 88t and 1172 was confirmed in a second night. 37

Table 3.6 Colors and Spectral Reflectances for Faint Trojans and Satellites j \eff *"" 0.38 0.45 0.55 0.83 0.90 I' Fi lterband V-V B-V V-R V-I u 9 V R I

617 Patroclus 0.90 0.68 0.95 0.96 0.94 1.0 1.34 f» 88it Pr iamus 0.94 0.70 1.13 0.93 0.92 1.0 1.58 fr 1172 Aeneas 0.98 0.72 1.38 0.90 0.90 1.0 2.00 S' i' 1867 Deiphobus 0 97 0.75 0.79 0.90 0 88 .0 1.16 & ' I 624 Hektor 1 03 0.75 0.94 1.22 0.86 0 88 1 .0 1.33 1 .32 t' 1437 Diomedes 0 95 0.70 0.81 1.06 0• 92 0 92 .0 1.18 1 .14 1583 Antilochus 1.03 r.°.76 1.06 0.86 0 87 1 .0 1.49 J 6 0.98 0.67 0.8J4 0• 90 0.95 1 .0 1.21 S 7 0.97 0.66 0.78 0• 90 0.96 1 .0 0.88 S 9 0.97 0.73 0.66 0.90 0.90 1 .0 1.03

A comparison between the reflection spectra of Trojan asteroids 624 and 911 (McCord and Chapman 1975b), 1173 (Chapman, pers. comm.) and UBV photometry, shows an inconsistency in the ultraviolet drop-off. If we assume the reflectance at 0.55 ym to be 1.0, then the reflectance at 0.38 urn, as obtained from the sources mentioned previously, is 0.65, 0.65, and 0.82. This is similar to the values 0.70 and 0.71 for the S-type asteroids 6 Hebe and 196 Philomela. The U-V colors differ, however, significantly. It is 1.24 for ths two S-type asteroids and 0.97 for the Trojans. If we assume that the UBV colors of

! I' | i i i—r~'1 1 ' ' F 1.8 - 0 0 O 1.6 0 1.4 o* o Oo 1.2

K)o0°0 0 - 1.0 - 0.8 Fig.3.3 Comparison between the - o - 0.6 spectral reflectance points o 624 Hektor . 0.4 of 624 Hektor (+), and the

i i i i i 1 i i data published by McCord and 0.3 0.5 0.7 0.9 1.1 Chapman (1975b). X urn 88

bright and faint asteroids and the reflection spectra of the bright asteroids are correct, then the ultraviolet drop-off for the 3 published reflection spectra of Trojans must be wrong. For 62*» Hektor this difference is indicated in Fig. 3-3. Chapman (pers. comm.) measured the Trojan spectra with a relatively small telescope, and in particular in the violet the signal was barely detectable with narrow band filters.

3.2.2 Variability and Body Shapes

The average diameter of Trojan 62*» Hektor is measured with infrared radiometry and is about 200 km (Cruikshank 1977). It has a very elongated body shape of 2.75:1 being the ratio of the longest to the shortest body axis (Dunlap and Gehrels 1969). Such a body shape is for such a large object without a prece- dent in the solar system. IR radiometric studies of Hektor (Hartmann and Cruikshank 1978) show a constant albedo (0.02-0.03; see also Table 3.1) during a revolution period. The model as used by Duniap and Gehrels is correct, but they assumed an albedo of 0.28, being 9-^k times too high. Therefore the scale of their model has to be multiplied with the root of this factor. If Hektor's elongated body shape is related to the typical environment of the Trojan clouds during their origin, then more Trojans are expected to show large lightcurve amplitudes. To check this hypothesis more lightcurve observations are needed. Because not enough observing time with large telescopes was available to do extensive lightcurve studies, the alternative was to obtain as many as possible magnitude points with a wide range of phase angles. The presence of large lightcurve amplitudes must then reveal itself by striking scatter in the resulting phase functions. I embarked on such a program, because even if such a scatter is absent and a smooth phase function is found, then a comparison with the phase function of asteroids of the same size in the main belt will be possible. This comparison might give an insight into the possible difference in surface texture between the objects in both locations. The measurements are given in Table 2.7 and the values of 7(1,a) are plotted in Fig. 3.*» against phase angle. The deviations from the average phase function for bright asteroids in the main belt (Gehrels 1967) hardly exceed those expected from the rms errors in the observations (0.05 mag, see Fig. 2.12). Exceptions are 1583 and 1*»37 for which a piece of a lightcurve was observed by Gehrels (Dunlap and Gehrels 1969) indicating an amplitude of 0.4 mag. Firm conclusions about body shapes from only 2 to 7 magnitude points per object are obviously im- 89

617 1208 " 92 16 9-t 8.6 96

68* 9-8 9.0 U37 64 92 8.6

1172 15*3 - 9-0 8* 92 as 9*

1173 1167 6-8

ac 90 9.2 92 9.4 i K 12 0 L 6 8 W 12 Solar Phase Angfto a Fig.3.4 F(l,o) of 6 Trojans following Jupiter and 2 (numbered 1437 and 1583) preceding. The data were obtained between Au- gust 1977 and June 1978 (Table 2.7). Observations made in De- cember 1975 (Zellner et at.1977) are depicted with o. The dashed line represents the average phase function for many bright asteroids in the main belt (Gehrels 1967b). Typical rms errors in the observations are <0.05 mag. possible. However, the conclusion appears warranted that the measurements of these 8 Trojans are not compatible with a lightcurve amplitude at the Hektor level of 1.2 mag. More data for the same 8 Trojans during an opposition 3 years later are desi- rable to examine if a different aspect yields more insight into the true body shape. The less elongated body shapes of the 8 Trojans, as compared with the shape of Hektor, indicate that very elongated shapes are not typical for bodies in the Trojan clouds. This implies that the origin of Hektor is different from the origin of a typical Trojan. Cooke (1970 suggested Hektor to be a co- orbiting binary pair of asteroids or a contact binary. Two spherical bodies in contact with each other give, however, for an aspect angle of 90 degrees an amplitude of 0.75 mag. It is not possible to get the required amplitude of 1.2 mag with such a model. Hartmann and Cruikshank (1978) proposed Hektor to be

\ 90

the result of partial coalescence of two primitive 70-km spher- oidal planetesimals in the Trojan clouds. Their arguments are mainly based upon the peculiar motion of the bodies in the Tro- jan clouds. The speed between two colliding bodies varies strongly with the position in the clouds. In such an environment partial coalescence without rebound after a low speed collision may occur.

3.2.3 The Phase Function

It is possible to derive an average phase function with the magnitude information given in Fig. 3.k . For that purpose the V{\,a) magnitudes of 5 Trojans (617, 88*, 1172, 1173, and 1208), with a sufficiently large range in observed phase angle, were fitted by least-squares (Fig. 3.5) to the average phase

mag

Fig.3.5 F(l,a) of 5 Trojans, with diameters between 100-200 km, from Fig.3.t fitted to the phase function of -.0.2 Gehrels (1967) by least- squares. Only the Tro- --0.4 jans with a large range in observed phase angle --0.6 (617, 884, 1172, 1173, and 1208) were used. 8 12 Solor Phase Angle a function of many bright asteroids in the main belt (Gehrels 1967b). In contradiction with the preliminary results of van Houten (1971), there appears to be no deviation from this ave rage curve, and this indicates that the surface texture does not differ from that of asteroids of comparable size in the main belt.

3.2.4 Radiometric Albedos and Diameters

I measured 10.6 ym fluxes of k Trojans (Table 3-J). A description of the instrumental system and the radiative model are given in Ch. •.6. The rms errors in albedo and diameter are derived from the rms errors in the observations both at 10.6 11m and 0.55 um. Radiometric albedos and diameters for Trojans are published by Cruikshank (1977). Cruikshank used the radiometric information of the 20 urn band which is for Trojans close to the maximum of the Planck curve at about 25 ym (120°K). He measured four Trojans but used visual estimates for the magnitudes. Morrison (1977) recomputed the albedos and diameters in a consistent system and used the absolute visual magnitudes from Gehrels and Gehrels (1977 version). His results are given in Table 3.7 column 4-6. It appears, however, from the results of the rather extensive visual photometry of Trojans reported in Table 2.7 that also the visual .nagnitudes adopted by Morrison are not correct. Therefore I recomputed the albedos for the better values of the magnitudes (Table 3*7, column 1). The effect on the diameter is negligible. These recomputed values are given in the columns 4-6 for objects 617, 1172, and 1173. Also my own albedo values given in Table 3.1 are readjusted for the better magnitude values and given in the columns 7 and 8.

Table 3-7 Trojans: Absolute Magnitudes, Albedos, and Diameters

Adopted Old New Adopted v(1.0 ) t B-V vi1,0 ) Pv D D 0 km ¥ km ¥ km (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Preceding Jupitei 588 Achilles 8• 93 a+b 0.74 624 Hektor 7.89 a 0.76 7.89 0.038 179 0.030 201 0.034 190: 911 Agamemnon 8.42 a+b 0.77 0.029 159 0.029 159 1143 Odysseus 8.70 a+b 0.78 1437 Diomedes 8.57 a+b 0.71 0.019 190 0.019 190 1583 Antilochus 8.98 a+b 0.76

Following Jupiter 617 Patroclus 8 61 b 0 68 8 34 0.037 147 0.021 172 0.025 160 8 61 0.028 147 884 Priamus 9.08 b 0.71 1172 Aeneas 8.62 b 0.73 8.42 0.044 130 0 036 130 8.62 0.036 130 1173 Anchises 9.17 b 0.74 9-47 0.034 92 0. 043 92 9.17 0.043 92 1208 Troilus 9.38 b 0.67 1867 Deiphobus 8.86 b 0.75 t Source of 7(1,0): a) Gehrels and Gehrels (1977 version), b) From Table 2.7. 92

It is of interest to look for a systematic difference in albedo for objects in the two clouds. The data in Table 3-7 show an average and error in the mean for the albedos of: 0.027 +_ 0.004 (n*3) for Trojans preceding and 0.035 +, 0.005 (n*3) for Trojans following Jupiter. The higher number of Trojans down to a certain magnitude limit in the cloud preceding Jupiter than the number following Jupiter (van Kouten, unpublished; see Gehrels 1970, 1977), cannot be explained by systematically different albedos for objects in each cloud, if the difference between the average albedos for the 3 objects in each cloud would be real, then it would even work in the wrong sense.

Refevenoes

Allen, C.W. 1973 Astrophysical quantities University of Lon- don The Athlone Press Chapman, C.R. 1976 interpretation of new asteroid spectro photometry (abstract) BAAS 8, 460 Chapman, C.R., McCord, T.B., and Johnson, T.V. 1973 Asteroid spectral reflectivities Astron. J. 78, 126 Cole, M., and Ryer, D. 1972 Electro Optical Design June 1972 18 Cook, A.F. 1971 624 Hektor: a binary asteroid? Physical studies of Minor Planets pi55 (Ed. T. Gehrels) NASA SP-267 Cruikshank, D.P. 1977 Radii and albedos of four Trojan asteroids and Jovian satellites 6 and 7 Icarus SO, 224 Dunlap, J.L., and Gehrels, T. 1969 Minor planets. Ill Light- curves of a Trojan asteroid Astron. Journ. 74, 796 Frecker, J., and Serkowski, K. 1976 Linear polarimeter with rapid modulation, achromatic in the 0-3-1.1 ym range Appl. Opt. 15, 605 Gehrels, T. 1967 Minor planets.11 Photographic magnitudes Astron. J. 72, 1288 Gehrels, T. 1970 Photometry of asteroids Surfaces and Interiors of Planets and Satellites p317 (Ed. A. Oollfus) Academic Press London Gehrels, T. 1977 Some interrelations of asteroids, Trojans and satellites Comets-Asteroids-Meteorites: interrelatimts, evolution and origin p323 (Ed. A.H. Delsemme) Univer- sity of Toledo Press Gehrels, T., and Genre's, N. 1978 Minor planets and related objects. XXVI magnitudes for the numbered asteroids A.J. submitted Golay, M. 1974 Introduction to astronomical photometry Dor- drecht Reidel 1974 Gradie, J.C. 1978 An astrophysical study of the minor planets in the Eos and Koronis asteroid families Ph.D. thesis University of Arizona 93

Hansen, O.L. 1976 Radii and albedos of Sk asteroids from visual and infrared photometry Astron. J. 81, Ik Hartmann, W.K., and Cruikshank, O.P. 1978 The nature of Trojan asteroid 624 Hektor Subm. tc laarus Houten, C.J. van, Houten-Groeneveld, I. van, and Gehrels, T. 1970 Minor planets and related objects. V The density of Trojans near the preceding Lagrangian point Astron. Journ. 75, 659 » Houten, C.J. van 1971 Descriptive survey of families, Trojans and jetstreams Physical studies of Minor Planets pi73 (Ed. T. Gehrels) NASA SP-267 Kron, G.E., White, H.5., and Cascoigne, S.C.B. 1953 Red and infrared magnitudes for 138 stars observed as photometric standards Ap. J. 118, 502 McCord, T.B., and Chapman, C.R. 1975a Asteroids: spectral reflectance and color characteristics Astrophys. J. 195, 553 McCord, T.B., and Chapman, C.R. 1975b Asteroids: spectral reflectance and color characteristics II Astrophys. J. 197, 78 J Morrison, D. 1977 Asteroid sizes and albedos Icarus 31, 185 Taylor, R.C. 1971 Photometric observations and reductions of lightcurves of asteroids Physical studies of Minor Pla- nets pi 17 (Ed. T. Gehrels) NASA SP-267 Taylor, R.C., Gehrels, T., and Capen, R.C. 1976 Minor planets and related objects. XXI Photometry of eight asteroids Astron. J. 81, 778 ? Zellner, B., Andersson, L., and Gradie, J. 1977 VBV photometry ; of small and distant asteroids Icarus 31, kWj CHAPTER IV FAINT SATELLITES

4.1 Outer Jovian Satellites

For eight outer satellites of Jupiter some orbital elements are listed in Table 4.1. These elements are obtained from Allen (1973), and Kowal et al. (1975). Two tight groupings with for each group remarkably similar orbital radii, inclinations, and eccentricities are apparent. The objects in the first group (J6, J7, J10, and J13) move prograde and the objects in the second group (J8, J9, J11, and J12) move retrograde. The orbital radii for the second group are two times larger than those for the first group.

Table 4.1 Outer Satellites of Jupiter and Saturn: Orbits and Diameters (1) (2) (3) I*) (5) (6) Orbital Rad i us i e V Diam 105 km opp km

J6 11-5 28 0.16 14.8 185 J7 11.7 26 0.21 16.7 75 J10 11.7 29 0.12 18.4 35 J13 11.1 27 0.15 20.2 15 J8 23-5 147 0.40 17.7 50 J9 23.6 156 0.28 18.3 35 J11 22.6 163 0.21 18.0 40 J12 21.2 147 0.17 18.9 30 S9 13.0 150 0.16 16.4 150

Opposition magnitudes fcolumn 5 of Table 4.1 ) for J6, and S9 are taken from Table 4.2 a.nd 4.3. Magnitudes for the other satellites are from estimates by Dr. E. Roemer on photographic plates (quoted by Anderssom 1974). A B-V color of 0.7 was adopted (Degewij et al. 1978) to obtain I'magnitudes. The albedo for J6 and J7 was measured in the infrared radiometry of Cruikshank (1977); he obtained for both objects an albedo of 0.03. The diameters (column 6 of Table 4.1) for all other satellites are derived from V by assuming the same albedo of 0.03.

Body shapes and Rotation Periods

The brightest satellite J6 has been monitored by Andersson (1974) for a rotational 1ightcurve. He found weak evidence for 95

a variation of possibly 0.2 mag on 16 June 1972. Photographic Iightcurves of the satellites J6 (0.1), J8 (0.4), J9 (0.4), J11 (0.3), and J12 (0.4) were obtained on 15 August 1974 from Schmidt plates (Ch. 2.1.1). The observing period was 6.4 hours. The number between parentheses is the standard deviation in magnitudes of the 1ightcurves of the nearby comparison stars. These high values of the standard deviation are caused by the combination of faintness of the object and a heavy background fog of the plates caused by the light of Jupiter scattered in the emulsion. In similar observing runs on 29 and 30 October 1975, the observing period was 2.5 and 2.9 hours resp. for the satellites J6 (0.1), J7 (0.2), J8 (0.2), J9 (0.2), J11 (0.2), and J13 (1.4). During these three observing dates only J6 showed some variability; the J amplitude was between 0.1 and 0.2 mag. I did photoelectric photometry of J6 on 28 November 1976 with the 154 cm telescope of the Lunar and Planetary Laboratory; it revealed a piece of a lightcurve with an asymmetric maximum. Dr. B. Zeliner was able to obtain another stretch of the lightcurve on the following night with the 228 cm Steward reflector. The two 1ightcurves overlap a little (Fig. 4.1 ), and it appears that J6 has an asteroid-like lightcurve with two maxima and two minima. The lightcurve period is 9.5 hours and its amplitude is 0.12 mag.

frOO 800 1000 UT NOV 29 1 ' 1 1 1 J6 -

:» 1 »* o i o 4 - o 8 • * ^ o ° 00 — o q, i °Vo« o • • • • •

1 i i i i , 1 600 1000

Fig.4.1 V-lightcurve of the Jovian satellite J6 (Himalia) obtained in 1976 by J.Degewij ( . ), and by Dr.B.Zellner ( o ). I plotted 26 points again, at the end. The measurements of the comparison star are depicted in the lower part of the figure. 96

The Phase Function for J6 Himalia

Table 4. gives single V measurements of J6, and the observational circumstances are given in Table 2.6. Only the measurement on 28 November 1976 is an average of the lightcurve. The phase angle and the distances are computed with formulae given by Bobone (1937a, b). He used a series expansion to obtain phase angles with a precision of 2 decimals and distances with a precision of 4 decimals.

Table 4.2 Photometry of Satellite J6

Year Date UT a 51og(pA) degrees

1976 Nov 28.4 14.55 2.22 6.46 8.09 1978 Feb 9.3 15.31 8.73 6.87 8.44 1978 Apr 5.2 15.63 10.81 7.19 8.44 1978 Apr 12.2 15.65 10.48 7-22 8.43

The F(1,o) points are plotted in Fig. 4.2 together with measurements from Andersson (1974) and Zeliner (Degewij et al. 1978). There is a close agreement with the average phase relation (dashed line) for many bright asteroids in ths main belt (Gehrels 1967b).

Fig.«K2 7(1,a) points for Jovian satellite J6 (Hiroalia). The data are from Table 4.2 , Andersson (1974), and Zellner (Degewij et al. - 85 1978). The dashed curve is the average phase function of many bright - 86 asteroids in the main 8 10 12 Solar Phase Angle a belt (Gehrels 1967). 97

UBVR Reflectances for J6 Hirnalia

UBV colors for J6 are given in Table 3-6 and are from Degewij et at. (1978). VR colors are also given in Table 3.6 and the reduction method to obtain reflectances and the observational circumstances were discussed in Ch. 3.2.1. The UBVR reflectances from Table 3.6 are plotted versus wavelength in Fig. 4.3. The spectrum of J6 shows a similarity with that of

I • ! • . - U B V R = _ 1 I1 1 • 1 i i i j I - 52 u Fig.«t. 3 Spectral reflectance # • ••• •• * 1.0 for three faint satellites - 0.8 beyond the main belt. The V point is taken as unity and - 1.2 the measurements are referred 1.0 to the spectra of five bright "*" S9 asteroids (including C-type 1.0 .-}— » 52 Europa) measured by Chapman - r 1.0 et al. (1973), and McCord and Chapman (1975a,b). The error - 0.8 Lars show the error in the mean j 06 of the measurements. • till 0.2 Qi 0.6 0.8 1.0

some Trojans (Fig. 3.2), For instance 1^37, which is an object of comparable size and albedo. Or. S. Zeilner measured in two nights UBV colors for J? and found 5-T/*0.66, and 5-S-0.31. These values are remarkably similar to those of J6 (B-F-0.67, 0-5*0.31).

Conclusions

The presently available data are still meager. An insight into some physical parameters exists only for J6, the brightest member of the prograde group. The satellite has a body shape, albedo, and reflectance spectrum similar to the Trojans \kyj and 1867. Some polarization points were obtained (Degewij et al. 1978) and the curve is similar to a curve for a C-type asteroid and Trojan (>2k Hektor. For the other satellites more observational work is needed to obtain physical parameters. The first step should be to obtain UBV colors and possibly a V-I color for J8, the brightest member of the retrograde group. 4.2 Saturns' Satellite S9 Phoebe

Table 4.1 gives some orbital elements for Phoebe. Its distance from Saturn is comparable to that between Jupiter and the first group of outer satellites, but it has a retrograde motion. An albedo of 0.05 is assumed to compute a diameter. Andersson (1974) did extensive photometry and obtained a phase function that differed not too much from the average phase function of bright asteroids (Gehrels 1967b). He was able to estimate a rotational period from pieces of Iightcurves obtained between 9 and 18 November 1971• The amplitude was about 0.3 mag, but a single solution for the period was not possible. Values of both 11.25 and 21.2 hours appeared to be acceptable solutions. Table 4.3 gives single V and VBV measurements that I obtained for Phoebe, and the observational circumstances are given in Table 2.6. The phase angle and the distances to Sun and Earth are computed with formulae given by Zadunaisky (1954). He used a series expansion to obtain sufficient precision in the values. The 7(1,a) magnitudes are plotted in Fig. 4.4, together with values from Andersson (1974) and Zellner (Degewij et al. 1978). There appears to be a deviation from Gehrels1 phase function (dashed line) for the larger phase angles. The discrepancy for the large phase angle was observed for two different nights. More observations are needed because the lightcurve amplitude may have contributed to this discrepancy. The reductions to derive UBVR reflectances were similar to those for J6 (p. 85). The reflectances are plotted as a function of wavelength in Fig. 4.3. This spectrum does not show similarities with J6, but looks like a C-type asteroid.

Table 4.3 UBV Photometry of Satellite S9

Year Date UT U-B B-V V 51og(pA) viu «) degrees

1977 Feb 20.3 0.77 16.24 2.05 9.35 6.89 1978 Feb 4.3 0.75 16.29 1.31 9.41 6.88 1978 Feb 4.5 0.36 0.72 16.18 1.29 9.41 6.77 1978 Mar 10.2 16.23 2.57 9.41 6.82 1978 Apr 12.2 16.68 5.35 9.49 7.19 99

Fig.4.4 7(1,a) points for Saturns1 satellite S9 Phoebe. The symbols indicate data from the apparitions in 1S70 (o),1971(.), 1972U), 1973(T), 1977(«), and 1978(O). The data are from Table 4.3, Andersson (1974), and Zellner (Degewij et al. 1978). The dashed curve is the average phase function of many bright asteroids in tiie main belt (Gehrels 1967 ).

6 8 Solar Phase Angita

References

Allen, C.W. 1973 Astrophysical quantities University of Lon- don The Athlone Press Andersson, L.E. 1974 A photometric study of Pluto and satellites of the outer planets Ph. D. thesis Indiana Univer- sity Bobone, J. 1937a Tab)as del VI satellite de Jupiter Astron. Naohr. 2623 321 Bobone, J. 1937b Tablas del VII satellite de Jupiter Astpon. Nachr. 26S3 401 r- Chapman, C.R., McCord, T.B., and Johnson,T.V. 1973 Asteroid spectral reflectivities Astron. J. 783 126 Cruikshank, O.P. 1977 Radii and albedos of four Trojan asteroids and Jovian satellites 6 and 7 Icarus S03 224 Degewij, J., Andersson, L.E., Gradie, J., and Zellner, B. Photometric properties of the satellites J6 (Hnnalia), J7 (Elara), S7 (Hyperion), S9 (Phoebe) and N1 (Triton) Icarus3 to be published Gehrels, T. 1967 Minor planets. II photographic magnitudes Astron. J. 723 1288 100

Kowai, C.T., Aksnes, K., Harsden, B.G., Roemer, E. 1975 Thir- teenth satellite of Jupiter Astron. J. 803 460 HcCord, T.B., and Chapman, C.R. 1975a Asteroids: spectral reflectance and color characteristics Astrophys. J. 19S3 553 McCord, T.B., and Chapman, C.R. 1975b Asteroids: spectral reflectance and color characteristics II Astrophys. J. 1973 781 Zadunaisky, P.E. 1954 A determination of new elements of the orbit of Phoebe, ninth satellite of Saturn Astron. J. S93 1

Addition: Some printing errors are present in Tabie 3.6 (page 87) for UBV colors and V and B reflectances of S7 and S9. Andersson (1971*) gives for S7 Hyperion: tf-7«1.11 and B-7=0.78. With formula 34 • find U and B reflectances of 0.79 and 0.86. Andersson gives for S9 Phoebe: U-V=0.99 and B-7-0.66 and the V and B reflectances are 0.89 and 0.95. Figure k.3 shows the correct reflectance spectra for both satellites. 101

CHAPTER V HISTORY OF SHALL BODIES IN THE SOLAR SYSTEM

Some important questions concerning the origin and history of small bodies in the solar system were raised in section 1.1 (page 6). These questions formed the leading theme of the work presented in this dissertation. In this chapter I will attempt to synthesize the observational results given in earlier chapters in order to arrive at possible answers to these questions. As a natural consequence of this discussion I also include some recommendations for new observing programs. Very briefly the results presented in this chapter are: a) all observational data are consistent with collisions between asteroids as a dominant process in determining their size distribution and individual properties (Ch. 5.1); b) mixing of compositional types in the main belt continues into the Hilda zone and Trojan clouds and the similarity of physical parameters for some Trojans and J6 makes dynamical interrelation possible (Ch. 5.2); and c) not yet enough information is known about the physical parameters of small asteroids with sizes between 1 and 10 km to recognize possible defunct cometary nuclei (Ch. 5-3). The text draws heavily on the work of many colleagues. Their work is cited in the previous chapters. Some papers had a strong influence on this chapter, they are by: Gehrels (1971 a,b), KresSk (1972), Kuiper (197*), Chapman (1976, 1978), Gehrels (1977), Whipple (1977), Zellner and Bowel I (1977), Boweli et al. (1978).

5.1 CollisFonal Processes

It is possible to estimate the chance that an asteroid in the main belt collides with another asteroid. Oohnanyi (1972) showed that the present dencity in the main belt is just high enough for some catastrophic collisions between asteroids during the history of the solar system. Chapman and Davis (1975) did numerical experiments and found a much higher density of bodies in the main belt during .he first billion years of the history of the solar system. These qualitative arguments show mat collisions might be important for the history of these bodies, but more evidence has to come from the studies of physical parameters. The results presented in this dissertation concern mainly small bodies in the main belt with sizes between 1 and 50 km. An important question is: are the asteroids in this size domain the fragments of collisions between the larger bodies. The information about physical parameters was partly obtained 102

with the purpose to get more observational evidence for coilisional processes in the main belt. I will synthesize in the following sections all results from this dissertation that may help to find the answer to this question. Results of colleagues that have a bearing on collisions are also included.

The Large Spread in Rotational Parameters Information about rotation periods is contained in the TRIAD 1ightcurve file maintained by E.Tedesco of the Univer- sity of Arizona (Bender et al. 1978). It shows a wide range of values for the rotation period. The extreme values are 2.2 hours for 1566 Icarus and probably 70 hours for 887 AUnda. The distribution of rotation frequency appears to have a max- well ian shape (Harris and Burns 1979). The results of the photographic lightcurve runs (Ch. 2.1, pages 43-45) show evidence that small asteroids in the main belt with sizes between 1 and 10 km rotate on the average faster than do the larger asteroids. However, the shape of the distribution of rotation periods for small asteroids looks like the distribution of rotation periods for the larger asteroids (Fig.2.10, p.43). The sense of rotation can be determined from the analysis of many lightcurves of one asteroid during several apparitions (Gehrels 1970) and by comparing the infrared flux before and after opposition (Morrison 1977). The first method applied to a sample of six asteroids yields four with prograde and two with retrograde rotation. Some of these results were confirmed with the radiometric method. The position of the pole can also be determined from the analysis of several lightcurves of one asteroid during many apparitions. Vesely (1971) reviews the literature and lists pole positions for 16 asteroids. These data together with those of Gehrels and Taylor (1977) and Taylor (1977) do not indicate a preference for these positions. A few lightcurve studies of the same objects showed that the rotation axes do not precess. Gehrels and Owings (1962) studied the lightcurves for 22 Kailiope during 20,000 rotations. Calculations by Prendergast (1958), Burns (1971), Burns and Safronov (1973) and HcAdoo and Burns (1974) predict a mean "alignment time" from considerable to negligible precession. McAdoo and Burns found 107 years for a spherical 100 km body and 109 years for an elongated 1 km body. This seems to be in contradiction with the observation that Earth approaching bodies with dynamical lifetimes of 107 years (Wetherill 1974) do not show beat frequencies (Sher 1971) in their lightcurves 103

caused by the precession of the rotation axis. All data in the previous paragraphs have been inferred from observing programs which are still in a reconnaissance phase. In any case a relatively large spread in these rotational parameters appears evident. Such a laige spread may indicate, that eotlisiona affecting these parameters in an irregular way were important during the history of the asteroids.

Body Shape and Orbital Eccentricity The arguments for a relation between the orbital eccentricity and the distribution of body shapes for small asteroids are given on page ^S-W]. I assumed a coilisional erosion process to be responsible for this relation.

UBV Colors of Large and Small Asteroids The study of UBV colors given in Ch. 2.2 refers mainly to faint asteroids whose sizes are roughly between 10 and 30 km. UBV colors for brighter objects with sizes between 50 and 200 km we re published by Zellner et al. (1975) and others. Figure 2.13 (page 57) shows the distribution of UBV colors for the smaller asteroids and it can be seen that a dozen objects have colors deviating from the regions where the colors of the larger bodies occur. The majority of the peculiar colors in this small sample was measured on more ttian one night and can be trusted. This fragmentary information might point towards collisional processes in which the pieces show unusual colors. Another explanation can be that these objects with unusual colors have nothing to do with the main belt and come from other locations in the solar system. More observations of bodies with such colors are needed. Also an extension to one or more bands at red wavelengths is necessary to obtain more information about the spectra of these bodies.

Size Distributions and Compositional Types Size distributions corrected for observational bias for different zones in the main belt and different compositional types are given on page 67. These figures give the best evidence for collisional processes in the main belt. A ronotonic relation between log number and log size in nature means nearly always a mechanism in which the smaller pieces are the products of collision or grinding processes. It had been known since the Yerkes-McDonald Survey that 104

different zones in the main belt have significantly different absolute magnitude distributions (Page 60, g<9). Figure 2.20 on page 67 shows that this difference is preserved if the absolute magnitude distributions are transformed into size distributions. The distribution of the outer zone has a steeper slope than that of the inner zone. The main belt also shows other changes progressing with increasing distance to the sun: a) The average value of asini, corresponding with the thickness of the belt, increases with increasing distance from the sun. The ratio between the values for inner zone (2.0

New and exciting work about size distributions became possible after the discovery of the two major asteroid (albedo) types C and S. With the assumption that the crushing strength 105

for a C-type asteroid was 103 times smaller than that of an S- type asteroid, Chapman and Davis (1975) managed to reproduce the observed distributions (Fig. 2.21, page 67) for C- and 3- type bodies. A recent paper by Chapman (1978) uses as initial distributions: a) for C-type asteroids a straight line with the same slope as given in the diagram for sizes larger than 150 km; and b) for S-type asteroids a Gaussian curve with a maximum near 100 km. The Gaussian curve was seen as the original distribution of strong stony-iron and iron cores of dif- ferentiated bodies (Chapman 1976). A crucial question in assessing such an interpretation is whether or not the classification of asteroids into a limited number of classes is too simplistic. The spread of data in the diagrams of Bowel 1 et al. (1978) is rather large and the bound- aries between the domains, although visible, are not convincing. It is also noted in the preceding section: "UBV Colors of Urge and Small Asteroids", that some of the smaller asteroids show peculiar UBV colors, that can not be classified. Some indications of the possible invalidity of the Bowel I et al. recipe are: a) The existence of asteroids in a color and albedo domain that is intermediate between the S- and C- domains. They were discovered by Gradie (1978) and are members of the 221 Eos family; and b) The need for more than five groups when detailed reflectance spectra between 0.3 and 1.1 vim are available (Chapman 1976; Gaffey and NcCord 1977a,b). Granting the correctness of the division into a limited number of types and the interpretation of Fig. 2.21 (page 67) as an indication that indeed the crushing strength of the two major types is vastly different, it becomes very important to measure separate size distributions for each type in each of the zones of Fig. 2.20 (page 67). At the moment the number of data is insufficient to do this with reasonable accuracy.

The Size Distribution for Trojan Asteroids

Van Houten et al. (1970a) published the results of a survey for Trojans preceding Jupiter in its orbit. The 122 cm Pa- lomar Schmidt telescope was used and an absolute magnitude distribution was obtained down to B(1,O)~14. This corresponds to an asteroid having a diameter of 15 km with the assumption of 3% reflectivity (page 92). It was found by van Houten et al. that the slope of the magnitude distribution is approximately the same as that of the common asteroids, and they concluded that both groups might have a similar origin or history. By comparing Fig. 3 of the van Hou- ten et al. paper with Fig. 2.17 (page 61), I find a good match with the absolute magnitude distribution of the outer zone of 106

the main belt. The distributions of the intermediate and inner zones, however, do not match that well with the Trojan distribution. A large difference in the distribution of collisional velocities in the Trojan clouds as compared with that of the main belt was postulated by Hartmann and Cruikshank (1978). | They require a low collision velocity between two 70-km bodies ! in order to make partial coalescence without rebound possible. \ Such a mechanism could explain the elongated body shape of Hektor. If indeed a difference in the distributions of collision velocities exists, then it is surprising that the size distributions are that similar.

Synops i s All arguments mentioned in the preceding sections are consistent with collisions between asteroids during the recent history of the solar system as a dominant process in determining their size distribution and individual properties. It is difficult to find any argument speaking against this conclusion.

New Observing Programs

Very little is known about the physical parameters of the smaller asteroids with sizes between 1 and 10 km. A productive approach might be the usage of a big Schmidt telescope for a UBWI program. At least five plates per color band are needed to obtain sufficient precision in the colors for classification purposes. VBVRI colors of some stars in the field have to be measured photoelectrica!?y to calibrate the system. Colors could be obtained for 100-200 faint asteroids in one plate field and the total measuring and reduction effort would be comparable to that of the 1973 lightcurve run (page 27-33). .' Such a program would be attractive because of its productivity during some observing nights. However, the orbits of the objects are not known. Photoelectric observing programs of faint numbered asteroids with narrow-band filters is a rather time consuming effort. An optimum approach is by Dr. B. Zellner of the University of ; Arizona who has started to use 8 filters of intermediate band- • • width (0.08 ym) equally spaced through the spectrum between 0.3 ; and 1.1 vm (Gradie et at. 1978). It is planned to obtain in three years the reflectance spectra for a thousand objects. i These observing programs will improve the quality of the r size distributions for several types of asteroids and for dif- \ ferent zones in the main belt. Also reliable size distributions ° for some orbital parameters such as e and i can be obtained. \ The recent history of asteroids could be greatly clarified by 107

the availability of such distribution functions.

i 5.2 Similarities between Distant Asteroids and Faint Satellites

: in this section I will synthesize the information about | physical parameters for asteroids with Hilda-type orbits, Tro- ts jan asteroids, outer Jovian satellites, and Saturns1 satellites • S7 (Hyperion) and S9 (Phoebe). This information is contained ; in the Chapters III and IV and in the work of colleagues. All ' bodies have sizes between 50 and 200 km, only the satellites J9 to J13 are smaller.

Physical Parameters There is a strong discrepancy between the size distributions of Trojan asteroids and the outer Jovian satellites. The size distribution for outer Jovian satellites has a maximum near 40 km. Extensive searches for smaller objects have been made to a limit of the photographic magnitude as faint as 21.2, and only one satellite has been found. It is J13 (Kowal et.oL. 1975), a member of the prograde group. A suspected faint 14th satellite has been lost again.With the magnitude distribution of the Trojans, -40 new satellites should have been discovered. Large outer satellites also are deficient. The topic is discussed by Gehrels (1976,1977). Phase functions of 5 Trojans (page 90) and of J6 (page 3&) agree well with the average phase function of many bright asteroids in the main belt (Gehrels 1967). This might indicate that the surface texture is comparable, presumably because of the comparable impact by cometary particles (Humes 1976, Gehrels 1977). The body shapes of these objects are only slightly elongated, except for 624 Hektor which might be a binary (Hartmann and Cruikshank 1978). The smaller outer Jovian satellites also have apparently nearly spherical body shapes, or they rotate slowly (page 95). Much more work about lightcurve studies for Trojans and faint satellites is needed to firm up this conclusion. My data about albedos for Trojans (page 90 confirm the pioneering work of Cruikshank (1977) who also obtained low albedos (-0.03) for J6 and J7. Reflectance spectra between 0.4 itm and 0.9 um for 7 Trojans (page 36) and three satellites (page 97) show a similarity of Trojan 1437 with J6. The Trojan spectra show a mixture of compositional types. Albedos are not yet known for the Trojans 1173 and 1867; they apparently have C-type spectra. 108

Synops i s The mixture of compositional types in the main belt, continues into the Hilda zone and apparently also into the Trojan clouds. It appears possible that this mixing continues into the satellite groupings of Jupiter and Saturn. More observational work is needed. The resemblance of spectrum, albedo, phase relation and body shape among the majority of the Tro- jans and J6 makes dynamical interrelation in the solar system possible (Bailey 1971,1972). It is, however, difficult to con- ceive why such a mechanism will transport from the distant asteroid zones preferentially bodies with sizes of about 40 km. Greenberg (1976) made an extensive discussion about recent calculations for the possibility that the outer Jovian satellites are captured asteroids. He showed that Bailey used too many restraints and that we are left with two possibilities for the origin of the outer Jovian satellites: a) capture and breakup of a comet-like object in a gaseous envelope (Kuiper 1956); and b) a collision between asteroids within Jupiter's sphere of influence (Colombo and Franklin 1971). My data argue in favor of the second mechanism, because of the similarity in physical parameters between J6 and Trojan 1437-

New Observing Programs The most important observing programs for the future, in order to obtain more detailed answers to the questions raised in this section, are: a) Detailed studies of the apparent minimum in the reflectance spectra of Trojans between U and V wavelengths (page 86). This minimum is caused by the unique location of Trojans in the UBV diagram, and by the assumption that the reflectance spectra are correct for the five bright asteroids that were used as standards; b) A need for albedos of S7 Hyperion and S9 Phoebe. Polarization studies at maximum phase angle are for faint objects very time consuming and would at best give only a preliminary answer. These distant and cold objects emit their infrared flux at wavelengths beyond 20 11m and could perhaps be observed with the IRAS satellite; c) Measurement of radiometric albedos of the apparently C-type Trojans 1173 and 1867; d) Measurement of radiometric albedos of some more Hildas; e) A program for a large telescope in the k meter domain with TV acquisition to measure UBVEI colors of J8 and possibly J9 to J13; and f) A photographic program with a big Schmidt telescope to obtain UBVRI colors for Trojan asteroids. Scattered light by Jupiter precludes such a program for the outer Jovian satellites. 109

5.3 Where are the Dead Comets? This last section brings us back to the plot of semi-major axis against eccentricity e on the cover showing asteroids in low-ecceotric'ty orbits without any gaseous activity and the comets in high-eccentricity orbits. Also asteroids in high- eccentricity orbits can be seen but they have all semi-major axes distinct from those of the comets. These asteroids cross the orbit of Mars end occasions!ly the orbit of the earth. The second class of bodies is called Apollos. All distant bodies have a strong gravitational interrelation with Jupiter. The process of outgassing results into a net force which may slightly affect the orbit (MarsJen 1976). A tantalizing gap separates the asteroids from the comets and there is no overlap between the orbital parameters of objects of both types, with the exception of 3kk Hidalgo. One has to bear in mind that cometary nuclei have sizes in the 1-10 km domain (Roemer 1966). This is a severe restriction for speculations about possible defunct comets in the Hilda- and Trojan-zones and even in the Jovian satellite zone because all these bodies with some knowledge about physical parameters are much too large. I wi11 discuss in the following sections the observing programs that are aimed to get evidence for: a) The possibility of interrelation between extinct cometary nuclei and Trojan-, Hilda-, and out main beit zones; and b) Are some Apollos extinct cometary nuclei or do they all come from the main belt? Question b) is of extreme importance because we know from meteorite studies a little about the processes to which these bodies were exposed during their history in the solar system. A recent review on this topic is by Wasson (1974). Unfortunately, we do not yet know from which parts of the solar system the Apollos came. In any case it is evident that meteorites are related to Apollos. A dispute about question b) exists between meteoriticists and astrophysicists and a recent review of the main arguments is given in the first chapter of Morrison and Wells (1978). The major problem causing the dispute is the small amount of physical information about Apollos and the problem of scale between a 10 km body in space and pieces in the laboratory of meter-sized objects entering the atmosphere.

Asteroids with Peculiar Physical Parameters 3hh Hidalgo is in a typical cometary orbit, while cometary activity has never been observed. A search for cometary spectral emission lines was made by Soderblom and Harlan (1976) at the Lick Observatory, but nothing was seen. Unfortunately very few observing programs were undertaken during its recent 110

1976 opposition. An important discovery by Tedesco and Bowel 1 (1979) was that UBV color studies showed a relatively strong change in color during a rotational lightcurve cycle (see Table 2.9 page 72). Chapman (pers. comm.) reported an M-like spectrum between 0.4 and ^.1 pm. No albedo was measured, however, and this makes a comparison with other objects very difficult. For small asteroids little has yet been done concerning the study of color changes during a rotational 'ightcurve cycle. 433 Eros has been studied extensively but did not show any variation (Mi 11 is et al. 1976). I observed a few other asteroids and none of these show variation. The results are given in Table 2.9 together with the discussion in Chapter 2.4. It was found that 12 asteroids extensively studied for color spots show in only four cases some effect close to the detection limit. Another peculiar asteroid is 1580 Betulia. It is a Mars- orbit crosser with a high orbital inclination of 52 degrees. Tedesco et al. (1978) report photoelectric and polarimetric studies and they found a mean diameter of 7 km. No color variation with rotation was detected, but the lightcurve shows three maxima and three minima during one rotational cycle, which are explained by a major topographic feature. Lebofsky et al. (1978) made radiometric studies and the comparison between observations at infrared wavelength, polarImetry and radar observations suggested that the surface of Betulia has the thermal characteristics of bare rock rather than those of the lunar regolith model used for the analysis of the radiometric studies of other asteroids.

Search for Outgassing Asteroids By looking at the cover picture the question rises if the tantalizing gap between the asteroids and comets is not an arbitrary one: do some of the asteroids close to this gap show perhaps a very weak cometary activity that has not yet been recorded by direct photography? Some experience concerning spectroscopy of faint comets was obtained together with Dr. W. G. Tifft at the 228 cm telescope of Steward Observatory with a low dispersion spectrograph at the cassegrain focus (Ch. 1.4 page 19). It was shown that Comet Arend-Rigaux was not yet dead during its recent approach to the earth and Sun (Degewij 1978). The sensitivity of the equipment for detecting weak gaseous activity did initiate a small program of observing asteroids close to the gap in the a, e domain. The objects studied were: a) Trojan 884 Priamus; b) Hildas 190 lsmene, 499 Venusia, 1162 Larissa, 1512 Oulu, and 1746 Brouwer; c) Satellites J6, 111

J7 and S7; and d) Asteroids in peculiar orbits: 3M» Desiderata, k$5 Bruchsalia, 664 Judith, 814 Tauris, 1006 Lagrangea, 1036 Ganymed, 1362 Griqua, 1607 Mavis, 1625 The NORC, 1916-1953RA, and 1977RA. Great care was taken to permit a proper subtraction of the spectroscopic features in the night sky. In most cases a spectrum of the sky near to the object was taken with the same exposure time. A study by eye did not reveal any gaseous activity. The night sky spectrum can be subtracted with image processing techniques. If some activity close to the detection limit is found, then new spectra are needed to confirm this result.

Synops i s No answer can be given yet on the question heading this section. It is plausible that Apollos are a mixture of defunct cometary nuclei and bodies perturbed out of the main belt. No criteria exist to assign an Apollo to one of these classes. Where are the dead comets? Some important steps that wi11 lead towards the answer of this question are: a) a higher productivity of searches for fast moving objects with a dedicated big Schmidt telescope; b) more intensive studies of the physical parameters of smaller asteroids and of the nuclei of faint comets.

References Anders, E. 1265 Fragmentation history of asteroids Icarus 4, 399 Bailey, J.H. 1971. Origin of the.outer satellites of Jupiter Journ. Geophys. Res, 76, 7827 Bailey, J.M, 1972 Studies on planetary satellites. Satellite capture in the three-body elliptical problem Astron. J. ??, 177 Bender, D., Bowel 1, E., Chapman, C, Gaffey, M., Gehrels, T., Zellner, B., Morrison, D., and Tedesco, E. 1978 The Tucson revised index of asteroid data (note) Icarus 333 630 Burns, J.A. 1971 The alinement of asteroid rotation Physical studies of Minor Planets p*»29 (Ed. T. Gehrels) NASA SP-267 Burns, J.A., Safronov, V.S. 1973 Asteroid nutation angles Monthly Notices Roy. Astron. Soa. 16S3 *»03 Bowel 1, E., Chapman, C.R., Gradie, J.C., Morrison, 0., and Zellner, B. 1978 Taxonomy of asteroids Icarus in press 112

Chapman, C.R. 1976 Asteroids as meteorite parent-bodies: the astronomical perspective Geodhim. Coamoohim. Acta 40, 701 Chapman, C.R. 1978 Asteroid collisions, craters, regoliths, and lifetimes Asteroids: An Exploration, Assesment pik5 (Eds. D. Morrison and W.C. Wells) NASA Conf. Pubi. 2053 Washington Chapman, C.R. and Davis, D.R. 1975 Asteroid collisional evolution: evidence for a much larger early population Science 190, 553 Colombo, G. and Franklin, F. 1£>71 On the formation of the outer satellite groups of Jupiter Icarus 15, 186 Cruikshank, D.P. 1977 Radii and albedos of four Trojan asteroids and Jovian satellites 6 and 7 Icarus 30, 224 Degewij, J. 1978 Comet Arend-Rigaux: not dead yet Sky and telescope 55, 14 Dohnanyi, J.S. 1972 Interplanetary objects in review: statistics of their masses and dynamics Icarus 17, 1 Gaffey, M.J. and HcCord, T.B. 1978 Asteroid surface materials: mineralogical characterizations from reflectance spectra Space Sai. Rev. 21, 555 Gehrels, T. 1967 Minor planets. II. Photographic magnitudes Astron. J. 72, 1288 Gehrels, T. 1970 Photometry of Astera><-i« Surfaces and Interi- ors of Planets and Satellites p3*7 (Ed. A. Dollfus) Academic Press London Gehrels, T. 1971a Physical parameters of asteroids and interrelations with comets From Plasma, to Planet Nobel Sym- posium 21 (Ed. A. Elvtus) Stockholm Gehrels, T., Roemer, E. and Harsden, B.G. 1971b Minor planets and related objects. Vl'l. Asteroid 1971 FA Astron. J. 76, 607 Gehrels, T. 1977 Some interrelations of asteroids, Trojans and satellites Comets, Asteroids, Meteorites p323 (Ed. A.H. Delsemme) University of Toledo Press Gehrels, T. and Taylor, R.C. 1977 Minor planets and related objects. XXII. Phase functions for (6) Hebe Astron. J. 82, 229 Gradie, J.C. 1978 An astrophysical study of the minor planets in the Eos and Koronis asteroid families Ph.D. thesis University of Arizona Gradie, J., Tedesco, E., and Zeilner, B. 1978 A photometric system for faint asteroids BAAS 10, 59*t Greenberg, R.J. 1976 The motions of satellites and asteroids: natural probes of Jovian Gravity Jupiter (Ed. T. Gehrels) University of Arizona Press Harris, A.W. and Burns J.A. 1978 Asteroid rotation: I. Tabu- 1 at ion and analysis of data; submitted to Icarus Hartmann, W.K. and Hartmann, A.C. 1968 Asteroid collisions and evolution of asteroidal mass distribution and meteoritic flux Icarus 8, 361 113

Hartmann, W.K. and Cruikshank, D.P. 1978 The nature of Trojan asteroid 624 Hektor; submitted to Icarus Houten, C.J. van and Houten-Groeneveld, I. van, Gehrels, T. j. 1970a Minor planets and related objects. V. The densi- i ty of Trojans near the preceding Lagrangian point Astron t. J- 75* 659 \. Houten, C.J. van and Houten-Groeneveld, I. van, Herget, P, and ;\ Gehrels, T. 1970b The Paiomar-Leiden survey of faint j minor planets Astron. Astrophys. Suppl. Ser. 23 339 :-- Houten, C.J. van 1971 The Palomar-Leiden survey Physical 1 studies of Minor Planets pi83 (Ed. T. Gehrels) NASA SP- ;. 267 Humes, D.H. 1976 The Jovian meteoroid environment Jupiter X p1052 (Ed. T. Gehrels) University of Arizona Press ;' Kowal, C.T., Aksnes, K., Marsden, B.G., Roemer, E. 1975 Thir- i' teenth satellite of Jupiter Astron. J. 80, 460 Kresak, L. 1972 On the dividing line between cometary and as- '.. teroidal orbits The ltotion3 Evolution of Orbits3 and Origin of Comets p503 (Eds. G.A. Chebotarev and E.I. •: Kazimirchak-Polonskaya) D. Reidel : Kuiper, G.P. 1956 On the origin of the satellites and the ; Trojans Vistas in Astronomy 2, 1631 )•• KuTper, G.P., Fujita, Y., Gehrels, T., Groeneveld, I., Kent, i J., Biesbroeck, G. van, and Houten, C.J. van, 1958 ; Survey of asteroids Astrophys. J. Suppl. Ser. 33 289 ; Kuiper, G.P. 197** On the origin of the Solar System. I. Ce- l lestial Mechanics 93 321 Lebofsky, L., Veeder, G.J., Lebofsky, N.J., and Matson, D.L. > 1978 Visual and radiometric photometry of 1580 Betulia \- Subm. to Icarus ' Marsden, B.G. 1976 Nongravitational forces on comets; a re- ;" view The study of comets I (Eds. B. Donn, M. Mumma, W. : Jackson, M. A'Hearn, and R. Harrington) NASA SP-393 {] McAdoo, D.C., Burns, J.A. 1974 Approximate axial alignment times for spinning bodies Icarus 21, 86 h Mill is, R.L., Bowell, E. and Thompson, O.T. 1976 UBV Photo- l±_ metry of asteroid 433 Eros Icarus 283 53 K Morrison, D. 1977 Asteroid Sizes and Albedos Icarus Sl3 185 I Morrison, 0. and Wells, W.C. 1978 Asteroids: an exploration ! assessment NASA Conf. Publ. 2053 Washington f Prendergast, K.H. 1958 The effects of imperfect elasticity in I problems of celestial mechanics Astron. J. 633 412 y- Roemer, E. 1966 The dimensions of cometary nuclei Mem. Soc. jr Roy. des Sai. de LiSge 123 23 |- Sher, D. 1971 On the variation in light of tumbling bodies I- Astrophys. Space Soi. 113 222 % Soderblom, D.R. and Harlan, E.A. 1976 IAU circular ZOO? j Taylor, R.C. 1977 Minor planets and related objects. XXIII. I Photometryof asteroid (7) Iris Astron. J. 823 441 l- Tedesco, E., Drummond, J., Candy, M., Birch, P., Nikoloff, I., I and Zellner, B. 1978 1580 Betulia: an unusual asteroid Ii with an extraordinary lightcurve; submitted to Icarus Tedesco, E. and Bowel 1, E. 1979 In preparation Vesely, CD. 1971 Summary on orientations of rotation axes Physioal Studies of Minor Planets pi 33 (ed. T. Gehrels) NASA SP-267 Wasson, J.T. 197*t Meteorites Springer, New York Wetherili, G.W. 197*4 Solar system sources of meteorites and large meteoroids Ann. Rev. of Earth and Planetary Sa. 2, 303 Whippie, F.L. 1977 The constitution of cometary nuclei Comets, Asteroids, Meteorites p25 (Ed. A.H. Delsemme) Universi- ty of Toledo Zellner, B., Wisniewski, W.Z., and Andersson, L. 1975 Minor planets and related objects. XVIII. UBV photometry and surface composition Astron. J. 80, 986 Zellner, B., and Bowel 1, E. 1977 Asteroid compositional types and their distributions Comets, Asteroids, Meteorites pi85 (Ed. A.H. Delsemme) University of Toledo 115

SAMENVATTING

Dit proefschrift geeft de resultaten van waarnemingspro- gramma's, die gericht zijn op het verkrijgen van fysische parameters van de kleinst waarneembare lichamen in het zonnestelsel. Het doel was iets meer inzicht te krijgen in de volgende vragen: a) zijn de kleine asteroTden de fragmenten van botsingen tussen de grotere objecten; b) hoe zijn de Trojanen en de kleine satellieten van Jupiter en Saturnus onstaan; hebben zij iets met elkaar te maken; kwamen zij van andere plaatsen in het zonnestelsel, of werden zij ter plekke gevormd; c) waar zijn de dode kometen, of, welke astero"den zijn uigedoofde komeetkernen. Dit werk werd in Leiden in 1974 begonnen met het meten van de 1ichtvariaties van kleine asteroTden als zij om hun as roteren. Vervolgens werden in de jaren 1376 tot 1978 waarne- mingen gedaan van kleine asteroTden, de satellieten van Jupi- ter en kernen van kometen met de grote telescopen van de Uni- versiteit van Arizona. Tezamen met mijn collega's in Arizona en Leiden verkregen wij de volgende algemene inzichten in fysische parameters; interrelaties en de ontstaanswijze van deze objecten. De kleine asteroTden met diameters van ongeveer 1 km blij- ken gemiddeld sneller om hun as te draaien dan de grotere as- teroTden met diameters van ongeveer 200 km. Het merendeel van deze kleine asteroTden is misschien bolvormig. Dit komt waar- schijnlijk door een erosie proces, veroorzaakt door botsingen met kleinere rotsblokken. Diameter verdelingen, gekorrïgeerd voor volledigheid, werden afgeleid voor de twee voornaamste asteroTden typen in de hoofd gordel, met een minimum diameter van ongeveer 25 km. Dit is het C type met lage albedo (3.5%) en het hoge S type met hoge albedo (15%). Er is een toename van S type asteroTden ten opzichte van C type asteroTden voor de kleinere diameters. Dit kan te wijten zijn aan een grotere fragmentatie sterkte voor botsingen van S type asteroTden. Dit zou dan betekenen, dat beide types asteroTden niet alleen verschillen in de laag aan de buitenste oppervlakte, maar ook inwendig in het lichaam. Polarizatie metingen met hoge precisie tijdens de omwen- telingsperiode van asteroTde Vesta toonden aan dat de helder- heidsvariatie wordt veroorzaakt door vlekken op haar opper- vlak. Deze vlekken kunnen te wijten zijn aan plaatselijke verschillen in samenstelling, of door het plaatselijk omhoog brengen van diepere lagen door de inslag van een meteoriet. In het algemeen zijn echter de oppervlakken van asteroTden zeer regelmatig. Vermoedelijk is de geringe zwaartekracht er oorzaak van dat na een niet-katastrofale botsing de asteroTde over zijn gehele oppervlakte bedekt wordt met zijn eigen gruis. 116

Kleurmetingen tussen O.*» en 0.8 mikron en infrarode radio- metrie van enige Hilda's, Trojanen en de zwakkere satellieten van Jupiter en Saturnus, alle met diameters tussen 100 en 200 km, toonden aan, dat een menging van typen voor kont. Echter de gelijkenis tussen de meerderheid van de Trojanen en Jupiter 6 met betrekking tot reflektiespektrum, albedo, fase funktie, de onwentelingsperiode en lichaamsvorm, maakt een dynamische interrelatie in de geschiedenis van het zonnestelsel aanneme- lijk. Als sommige astero"den de uitgedoofde kernen van kometen zijn, dan zouden er enige asteroTden moeten voorkomen met nog zeer zwakke kometaire aktiviteit. Een dozijn asteroTden met baanelementen, die gelijkenis vertonen met die van kort-perio- dieke kometen werd waargenomen met «jevoelïge spestroskopïsche apparatuur. Er werd geen aktivite'c gevonden. 117

STUDIE OVERZICHT

Tussen 1956 en 1965 bezocht ik respektievelijk een lagere technische school voor machin: bankwerken, een uitgebreid technische school voor vliegtuigmonteur en de hogere technische school in Haarlem, waar ik afstudeerde in vliegtuigbouwkunde. Van 1965 tot 19C7 vervulde ik de militaire dienstplicht als soldaat schrijver. Hierna werkte ik als project engineer voor één jaar op het Nationaal Laboratorium voor Ruimtevaart te Amsterdam waar ik verantwoordelijk was voor een vlot verloop van supersone windtunnel metingen aan een model van de Concorde en een goede kwaliteit van de meetresultaten. Gedurende deze tijd was ik als aktief amateur astronoom bijzonder geïnteres- seerd in de fysika en dynamika van heldere meteoren (Icarus 8, 404, 1968 en Sky and Telescope 35, 51», 1968). Ik begon de sterrekunde-studie in 1968 in Leiden, behaal- de mijn kandidaatsexamen in de sterrekunde in 1972 en werd student-assistent op de Leidse Sterrewacht. Tijdens de docto- raalfase volgde ik o.m. colleges bij Prof. H.C. van de Hulst, Prof. H. van der Laan, Prof. R.G. Conway, Prof. G. Zoutendijk, Prof. P. Hazur, Dr. J. Tinbergen, Dr. Th. Wal raven en Dr. A. Oiiongren. Ik deed doctoraal examen in mei 1976 met de bij- vsKken Natuurkunde en Wiskunde. Van juli 1976 tot juli 1978 vervolgde ik mijn onderzoek als Research Associate op het Lunar and Planetary Laboratory van de Universiteit van Arizona in het kader van het samen- werkingsprogramma tussen de universiteiten van Leiden en Arizona. In juli 1978 werd ik doctoraal-assïstent op de Leid- se Sterrewacht. De volgende konferenties werden door mij bezocht: a) Image Processing Techniques in Astronom (1975 in Utrecht, Hol- land); b) Lunar and Planetary Science Conferences (1976 en 1977 in Houston, USA); c) the Division of Planetary Sciences Con- ferences van de American Astronomical Society (1977 in Boston, USA en in 1978 in Pasadena, USA) and d) Protostars and Planets (1973 in Tucson, USA). 118

ACKNOWLEDGEMENT

The questions and ideas brought forward by Tom GehreJs, Ben Zeiiner, Clark Chapman, Kees van Houten, and Ingrid van Houten-Groeneveld in the course of many years of cooperation have become a very essential part of the work presented in this dissertation. Together with their interest and friend- ship S acknowledge the suggestions and help of many other people in the Netherlands and America.

Financial support from the Leids Kerkhoven-Bosscha Fonds is greatly acknowledged.

Coverpicture: adapted from Kresik (1972), see also page 2.