Asteroid albedos deduced from stellar occultations

Icarus 184 (2006) 211–220 www.elsevier.com/locate/icarus

Asteroid albedos deduced from stellar occultations Vasilij G. Shevchenko a,∗ , Edward F. Tedesco b a Institute of Astronomy of Kharkiv National University, Sumska str. 35, Kharkiv 61022, Ukraine b Space Science Center, University of New Hampshire, Durham, NH 03824, USA

Received 10 January 2006; revised 3 April 2006 Available online 30 May 2006

Abstract Albedos for 57 asteroids were determined using diameters obtained from stellar occultations. For 18 objects, the occultation albedos were determined to accuracies better than 5%. The effect on the occultation albedo due to errors in the asteroid absolute magnitude is discussed and correlations between the occultation albedos and IRAS and polarimetric albedos are presented. The higher-quality occultation albedos presented here are suitable for calibrating albedos obtained by indirect methods. © 2006 Elsevier Inc. All rights reserved. Keywords: Asteroids; Occultations; Photometry

1. Introduction The geometric albedo and diameter are two fundamental physical parameters of asteroids. Because of their small angular sizes, asteroid diameters are difficult to measure using direct techniques such as imaging and radar. Thus, the diameters and albedos for most asteroids with such measurements have been determined using indirect methods using radiometric and polarimetric observations. Currently, the diameters and albedos obtained using data from the Infrared Astronomical Satellite (IRAS; Tedesco et al., 2002a) are widely used in asteroid physical studies because they constitute the largest dataset, outnumbering other datasets by at least one order of magnitude. Asteroid diameters obtained from direct measurements via occultations of stars are more accurate than those determined using indirect methods. From the occultation diameter and the absolute magnitude of an asteroid, we can calculate its occultation albedo, which, in principle, will also be more accurate than other albedo estimates. Such albedos have often been used for calibration of albedos obtained using other methods (Brown et al., 1982; Lebofsky et al., 1986; Lupishko and Mohamed, 1996; Lupishko, 1998). Although at present occultation diameters are known for more than a hundred asteroids, occultation albedos * Corresponding author. Fax: +38 057 7055349.

E-mail address: [email protected] (V.G. Shevchenko). 0019-1035/$ – see front matter © 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2006.04.006

are only available for about ten of them (Lupishko, 1998). This situation is due to a lack of knowledge of the asteroid’s absolute magnitude for the observing geometry at the time of the occultation. This, in turn, is a consequence of (in many cases) the absence of asteroid magnitude measurements at the time of the occultation, and/or to a lack of knowledge of the magnitude–phase dependence for the asteroid’s aspect at the time of the occultation. The aspect angle1 is unimportant for asteroids with nearly spherical shapes but quite important for irregularly shaped asteroids where knowledge of the asteroid’s lightcurve, and its variation with phase angle, is required. In this paper, occultation albedos of fifty-seven asteroids are determined. The occultation diameters are from the PDS asteroid occultation dataset (AOD)2 compiled by D. Dunham or from the original papers cited. Only asteroids with highquality diameter fits, i.e., those described as “good” or “excellent” in the AOD, were used in the present study. For some asteroids, the absolute magnitudes were calculated using their magnitude–phase relations. For others the magnitudes were taken from the Asteroid Photometric Catalogue (Lagerkvist et 1 The angle between the asteroid’s rotation axis and the observer’s line-of-

sight. 2 Millis and Dunham (1989), Dunham et al. (2002), and the PDS asteroid occultation dataset (AOD) are available from the NASA Planetary Data System’s Small Bodies Node—http://www.psi.edu/pds/archive/occ.html.

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al., 2002) and reduced to the epoch of the occultation using the asteroid photometric model developed by Shevchenko (1997b). The Shevchenko model assumes a three-axial ellipsoid shape for the asteroid and takes into account the viewing geometry and the changing asteroid area with aspect for the time of the occultation. This model has been successfully applied to determining asteroid pole coordinates (Shevchenko et al., 2003; Tungalag et al., 2002, 2003). The occultation albedos (pH ) were calculated using log(pH ) = 6.2472 − −2 log(Docc ) − 0.4H

(1)

(Fowler and Chillemi, 1992), where pH is the occultation albedo computed using the absolute magnitude (H ) and Docc is the occultation diameter in kilometers. In some cases, the absolute magnitude was calculated using an approximation function from Shevchenko (1997a), and the mean value of the opposition effect from Belskaya and Shevchenko (2000). The results are presented in Table 1 which gives: (1) the asteroid number and name, (2) the date and time of the occultation, (3) the phase angle and (4 and 5) ecliptic coordinates at the time of the occultation, (6) the taxonomic class (from Tedesco

Table 1 Aspect data of asteroids and results of calculations Asteroids

Date

α

λ2000

β2000

Class

Docc

DIRAS

pIRAS

ppol

1 Ceres 2 Pallas

1984 Nov 13.19653 1978 May 29.22569 1983 May 29.20674 1979 Dec 11.38229 1991 Jan 4.01097 2004 Oct 29.30389 1993 Oct 9.29132 1998 Mar 21.79271 1999 Jul 02.94722 1984 Sep 06.10063 1983 Sep 11.29298 2004 Jul 03.47156 1980 Sep 04.46792 1995 Dec 10.02653 2004 Dec 12.87882 2001 Oct 12.58072 1997 Dec 04.50479 1983 Jan 19.79146 2003 Mar 29.46400 2003 Jun 24.44155 2001 Sep 09.17918 1980 Nov 24.17826 1988 Apr 21.77319 2005 Jan 05.53504 2003 Dec 31.29307 2003 Apr 21.42907 1980 Oct 10.29167 1991 Jan 21.18634 2001 Mar 06.29785 2005 Feb 23.36314 – 1998 Jun 27.87822 – 2004 Jul 06.61733 2000 Jan 10.27867 2004 Nov 16.21978 1987 Dec 08.52500 2002 Dec 24.41554 2002 Sep 17.03134 2002 Nov 14.32657 1991 Jan 13.54160 1999 Oct 25.08023 2003 Feb 21.32219 2003 Aug 26.90530 2002 Nov 03.07558 – 1994 Jan 08.56111 1987 Jan 24.99720 2000 Nov 07.82539

3.4 14.3 15.4 18.6 19.1 30.1 5.0 20.6 20.5 1.9 1.8 19.3 19.4 10.1 7.1 17.6 15.0 2.2 27.5 24.0 3.3 13.1 7.0 7.5 11.0 4.0 12.7 20.1 3.8 19.3 – 9.7 – 14.7 13.7 17.0 11.7 5.8 25.2 10.6 4.5 17.5 11.1 5.9 7.0

46.781 254.929 293.711 117.719 44.771 117.245 5.224 91.625 241.742 348.158 352.425 38.130 41.658 52.218 94.287 134.018 107.487 122.991 79.148 177.176 345.140 35.035 196.934 91.518 132.627 223.160 351.951 180.833 177.342 85.182 – 298.406 – 255.536 152.624 177.610 96.921 116.557 64.019 76.821 98.082 271.703 164.784 313.795 61.806

−8.657 48.451 43.351 −20.458 −6.108 −3.047 −2.847 −7.887 26.729 −2.345 1.424 1.105 8.748 −11.490 −16.475 6.710 −30.933 5.899 7.327 0.695 −9.323 16.858 −7.028 13.113 2.247 −0.854 12.465 −12.455 −3.373 −14.842 – 4.603 – 10.627 −4.139 −1.383 17.004 −2.053 −1.365 −15.685 −6.743 15.336 22.682 8.867 −2.375

933 544 522 269 503 160.8 96.9 177.9 185.9 138.0 142.6 50.3 103.9 163.7 175.9 187.5 103.7 140.3 88.2 65.4 129.5 112.2 160.2 137.1 44.3 66.8 104.3 101.8 146.5 145.3 – 54.0

21.5 13.9 23.2

37.849 87.716 314.162

−8.893 7.022 9.227

G?,C m,B m,B S,Sk r,V S,S -,S S,S C,Ch C,B G,Ch E,Xe C,Ch C,B C,B C,C C,Ch G,Cgh C,Ch S,S –,X C,Ch –,X –,C S,Sk CF,Cb M,Xe S,Sl C,Ch C,Ch –,S – –,Cb S,S l,T l,T -,Cp C C,Ch C,Ch C,Cb C,C C,Ch P C,B –,S C,C S,S C,X

848 498 498 234 468 135.9 – 149.5 174.0 127.0 147.9 60.0 120.6 154.8 154.8 204.9 119.1 146.6 89.4 76.4 113.0 123.3 156.6 131.0 41.3 86.7 135 109 148.5 148.5 28.0 48.7 58.1 46.7 140.7 140.7 229.4 158.6 94.1 118.4 120.6 165. 97.7 141.3 95.0 23.6 163.1 134.2 116.8

0.11 0.16 0.16 0.24 0.42 0.24 – 0.29 0.083 0.098 0.093 0.43 0.071 0.067 0.067 0.040 0.047 0.089 0.070 0.17 0.16 0.036 0.056 0.054 0.27 0.044 0.12 0.17 0.043 0.043 0.24 0.062 0.044 0.21 0.048 0.048 0.063 0.062 0.065 0.057 0.061 0.069 0.046 0.042 0.064 0.206 0.049 0.20 0.049

0.076 3.34 0.087 4.04 0.087 4.13 0.22 5.29 0.35 3.19 0.21 6.35 0.22 7.0 0.25 5.89 0.059 7.31 0.085 7.98 0.066 7.38 0.66 7.92 – 8.20 0.091 7.71 0.091 7.65 – 7.63 – 8.86 – 7.66 – 8.96 – 8.09 0.16 6.90 – 8.89 0.075 8.10 0.063 8.20 – 9.07 – 9.33 0.10 7.45 0.15 7.37 – 8.12 – 8.15 – – – 10.21 – 8.96 – 8.17 – 8.17 0.083 7.00 0.095 7.95 0.070 8.81 – 8.55 – 8.25 – 7.49 – 9.01 – 8.31 – 8.72 0.24 – 8.00 0.26 6.73 – 8.55

3 Juno 4 Vesta 8 Flora 27 Euterpe 39 Laetitia 41 Daphne 47 Aglaja 51 Nemausa 64 Angelina 78 Diana 85 Io 94 Aurora 105 Artemis 106 Dione 109 Felicitas 124 Alkeste 129 Antigone 134 Sophrosyne 139 Juewa 141 Lumen 208 Lacrimosa 210 Isabella 216 Kleopatra 230 Athamantis 238 Hypatia 243 Idac 248 Lameia 253 Mathildec 306 Unitas 308 Polyxo 324 Bamberga 334 Chicago 345 Tercidina 350 Ornamenta 381 Myrrha 386 Siegena 404 Arsinoe 420 Bertholda 431 Nephele 433 Erosc 444 Gyptis 471 Papagena 476 Hedwig

51.6 144.4 117.1 235.5 174.1 99.0 99.5 129.1 174.0 98.7 144.0 68.6 172.4 128.3 98.6

H

pH

V (1, 4)a

pV (1,4)

0.0936 0.145 0.145 0.187 0370 0.197 0.298 0.246 0.0609 0.0596 0.0970 0.474 0.0859 0.0543 0.0497 0.0446 0.0470 0.0775 0.0592 0.240 0.183 0.0390 0.0396 0.0493 0.212 0.0733 0.170 0.192 0.0465 0.0460 0.21 0.0500 0.036 0.173 0.0457 0.0695 0.0505 0.0385 0.0540 0.0679 0.0531 0.0589 0.0451 0.0404 0.122 0.29 0.0375 0.218 0.0691

3.73 4.37 4.46 5.61 3.49 6.70 7.35 6.33 7.51 8.20 7.72 8.17 8.36 7.87 7.81 7.83 9.02 7.86 9.12 8.45 7.25 9.04 8.3 8.61 9.42 9.74 7.80 7.72 8.28 8.31

0.0653 0.1066 0.1067 0.139 0.280 0.143 0.216 0.164 0.0507 0.0487 0.0709 0.376 0.0742 0.0469 0.0429 0.0371 0.0406 0.0645 0.0511 0.172 0.132 0.0339 0.0330 0.0338 0.154 0.0503 0.123 0.139 0.0401 0.0397

Qualb

3e 3e 4e 4e 3e 3g 1e 3e 3g 4e 3e 2g 4g 3g 2g 2e 2e 3g 3g 1g 2g 4g 2g 1g 2g 1g 3g 2g 3g 2g 4e 10.62 0.0343 1g 4e 9.31 0.125 1g 8.58 0.0313 1g 8.58 0.0476 1g 7.16 0.0435 3g 8.11 0.0333 2g 9.16 0.0391 1e 8.71 0.0586 1e 8.66 0.0364 1e 7.65 0.0508 2g 9.42 0.0309 1g 8.72 0.0277 1e 9.13 0.0839 1g 4e 8.16 0.0324 2g 7.14 0.149 1e 8.96 0.0474 1g (continued on next page)

Refined occultation albedos

213

Table 1 (continued) Asteroids

Date

α

λ2000

β2000

Class

Docc

DIRAS

pIRAS

ppol

498 Tokio 522 Helga 566 Stereoskopia 568 Cheruskia 578 Happelia 704 Interamnia

2004 Feb 17.69126 2004 Jun 30.29658 2004 Mar 23.11582 1999 Oct 24.33005 2004 May 23.22406 1996 Dec 17.38097 2003 Mar 23.39208 2003 Dec 07.95868 2000 Apr 07.89192 1996 Jan 29.91528 2004 Sep 12.5 2003 Dec 22.91056 – 2003 Jul 19.36259 2003 Jul 18.25279 2003 Apr 28.21080 2002 May 07.57713

14.3 3.6 6.2 23.3 7.9 10.8 17.2 25.9 15.4 8.6 21.6 8.5

199.168 291.276 206.150 104.847 223.681 57.253 111.597 1.711 119.797 104.830 26.015 79.707

12.277 1.013 5.662 −4.691 −3.877 14.490 −9.906 0.938 1.630 13.378 39.032 20.207

77.9 83.7 134.0 75.8 69.1 332.8 326.1 36.7 82.5 51.5 91.2 59.2

81.8 101.2 168.2 87 69.3 316.6 316.6 32.1 103.5 76.1 76.6 54.3

0.069 0.039 0.038 0.054 0.077 0.074 0.074 0.14 0.033 0.050 0.094 0.28

7.9 19.9 10.4 4.3

271.868 201.382 185.349 239.714

6.273 28.053 2.035 −6.574

T CF C –,C Xc F,B F,B M,Xk C,Ch XF T S,S –,S – –,Xc – PD

65.0 44.2 29.9 65.0

80.5 49.3 27.6 82.7

0.056 0.046 0.15 0.037

– 8.95 – 9.12 – 8.03 – 9.10 – 9.20 0.084 6.11 0.084 6.06 – 9.96 – 9.25 – 10.33 – 8.76 – 8.41 – – 9.22 – 10.50 – 10.45 – 9.62

757 Portlandia 791 Ani 828 Lindemannia 914 Palisana 925 Alphonsina 951 Gasprac 976 Benjamina 1263 Varsavia 1366 Piccolo 1512 Oulu

H

pH 0.0765 0.0567 0.0604 0.0705 0.0774 0.0574 0.0626 0.136 0.0518 0.0492 0.0666 0.218 0.23 0.0857 0.0571 0.131 0.0594

V (1, 4)a

pV (1,4)

Qualb

9.36 9.53 8.44 9.51 9.61 6.27 6.22 10.12 9.66 10.74 9.27 8.76

0.0525 0.0388 0.0414 0.0483 0.0530 0.0495 0.0540 0.117 0.0355 0.0337 0.0416 0.158

9.63 10.91 10.80 10.03

0.0587 0.0392 0.0951 0.0407

1g 1g 1g 1g 1g 4e 2e 1g 1g 1g 1g 1g 4e 1g 1g 1g 1g

a For Qual = 1 G was assigned as follows: low albedo—0.07, moderate albedo—0.20 (from Shevchenko and Lupishko, 1998), for the remainder, V (1, 4) was calculated using individual phase curves. b 1. No lightcurve or phase curve observations are available, therefore the absolute magnitude was taken from Tedesco et al. (2002a). 2. No observations of lightcurve at the moment of occultation or phase curve is available but there exists a lightcurve for another aspect and the coordinates of the pole and axis ratios for a three-axis model of the asteroid are available, therefore the absolute magnitude was reduced using the photometric model developed by Shevchenko (1997b). 3. There is a lightcurve at (or near) the moment of occultation but no phase curve, therefore the absolute magnitude was calculated using the magnitude at the time of the occultation and an approximation function from Shevchenko (1997a) and the mean value of the opposition effect for the taxonomic class of the asteroid (Belskaya and Shevchenko, 2000) or using the H ,G magnitude system (Bowell et al., 1989) and mean slope parameter G taken from Shevchenko and Lupishko (1998). 4. There is a lightcurve at (or near) the time of the occultation and a phase curve, therefore the absolute magnitude was calculated using the phase curve for the aspect at the time of the occultation. c There are no useable occultation or IRAS observations for 951 Gaspra or 433 Eros. For Eros the D IRAS and pIRAS values are actually those obtainable from Harris (1998) and the pH is the NEAR result from Domingue et al. (2002). The pH for Gaspra is the Galileo value from Helfenstein et al. (1994). There are no useable occultation or polarimetric results for 243 Ida, 253 Mathilde, or 951 Gaspra. The pH for Ida is the Galileo result from Helfenstein et al. (1996) and that for Mathilde is the NEAR–Shoemaker result from Clark et al. (1999).

et al., 1989; Bus and Binzel, 2002), (7) the effective occultation diameter, (8, 9—Tedesco et al., 2002a) the IRAS-diameter and albedo, (10) the polarimetric albedo,3 (11) the absolute magnitude, H (for, where possible, the observing geometry at the time of the occultation), (12) the occultation albedo determined herein (those with uncertainties better than 5% are presented in bold), (13) the so-called four-degree absolute magnitude, V (1, 4)4 (also, where possible, the observing geometry at the time of the occultation), (14) the four-degree occultation albedo determined herein, and (15) the quality of the absolute magnitude adopted herein and the quality of the occultation diameter (g—“good,” e—“excellent”). We also include in this table results for four asteroids with diameters and albedos determined by spacecraft. 3 For determination of polarimetric albedos, we used the P min and h from Lupishko and Mohamed (1996) and the calibration coefficients, based upon the H ,G system, from Cellino et al. (1999). The Lupishko and Mohamed listing is the largest published asteroid polarimetric albedo dataset but is based upon absolute magnitudes on the V (1, 0) system (Gehrels and Tedesco, 1979) that was replaced by the H ,G system in 1990 (Tedesco, 1990). 4 Because the actual opposition effect is uncertain we also give the albedo for four-deg phase since we can determine the brightness at this phase angle more accurately than at 0-deg and because prior to about the mid-1980s this was how many asteroid albedos were reported.

2. Results Except where noted, all occultation diameters for the asteroids below are from the AOD. 1 Ceres An occultation of a star by this asteroid was observed by Millis et al. (1987) on 13 November, 1984. They used twelve chords to obtain a profile of Ceres. They also calculated an albedo for Ceres of 0.073 using V (1, 0) = 3.61 mag from Tedesco et al. (1983), i.e., without including the opposition effect. To determine the albedo in this paper the absolute magnitude H was calculated using lightcurves from Millis et al. (1987) and the magnitude–phase relation from Tedesco et al. (1983). All data are presented in Table 1. Thus, our albedo (0.094) is higher than that obtained by Millis et al. (1987) solely because it accounts for the opposition effect. This is true in all cases where an albedo is computed from a diameter using V (1, 0) rather than H . 2 Pallas There are two occultations involving this asteroid (Wasserman et al., 1979; Dunham et al., 1990), one in 1978 and another in 1983. The albedos determined by these authors are 0.103 and 0.101, respectively. In both cases, the absolute magnitudes

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without opposition effect (i.e., V (1, 0) rather than H ) were used. In our determinations of the absolute magnitudes, we computed the magnitudes for the times of the occultations using lightcurves from Wasserman et al. (1979) and Binzel (1984) and the magnitude–phase curve from Binzel (1984). We obtained absolute magnitudes of 4.04 and 4.13, respectively. 3 Juno Millis et al. (1981) measured the diameter of this asteroid from an occultation in 1979. They also determined an albedo equal to 0.164, but the absolute magnitude was obtained using a mean linear phase coefficient of 0.033 mag/deg and did not account for the opposition effect. We used the magnitude–phase curve from Harris and Young (1989) and the magnitudes at the time of the occultations using the light curves from Millis et al. (1981) for the determination of the absolute magnitude. Thus, our albedo is higher than that obtained by Millis et al. (1981). 4 Vesta We used the diameter determined from a 1991 occultation by this asteroid (AOD). Lagerkvist and Oja (1991) obtained a lightcurve near the time of the occultation in January 1991. The occultation occurred during the lightcurve minimum. We used this lightcurve, and the magnitude–phase curve from Gehrels (1967), to determine the absolute magnitude (3.19) resulting in an albedo of 0.37 for this cross section of asteroid. 8 Flora There are no lightcurves close to the time of the 2004 occultation, but Lagerkvist et al. (2002) present earlier lightcurves with amplitude <0.04 mag from close to the 2004 aspect. We used the function from Shevchenko (1997a) and the average amplitude of the opposition effect for moderate albedo asteroids (Belskaya and Shevchenko, 2000) to determine the absolute magnitude at the time of the occultation. 27 Euterpe No lightcurve is available near the date of the occultation. Therefore, to calculate the occultation albedo we used the absolute magnitude (7.0) from the Minor Planet Center’s orbital elements file. Euterpe’s rotation period and amplitude range (10.410 h, 0.15–0.21 mag; Harris and Warner, 2005) are typical for asteroids of this size. The albedo determined here (0.30) differs significantly from the polarimetric albedo (0.22). This is likely due to a poor determination of the absolute magnitude, and perhaps the occultation diameter as well, for this asteroid. In principle, the absolute magnitude for the observing geometry at the time of the occultation can be determined and used to resolve this discrepancy. 39 Laetitia Krugly (2003, personal communications) carried out photometric observations of Laetitia on the night of the occultation event and showed that the occultation occurred during the second lightcurve maximum. The absolute magnitude was calculated using the approximation function from Shevchenko (1997a) with mean parameters for S-asteroids (Shevchenko and Lupishko, 1998).

41 Daphne Scaltriti and Zappalà (1977) carried out photometric observation in April–March 1976 during which they observed the linear part of magnitude–phase curve for the aspect close to 1999. We used the sidereal period from De Angelis (1995) to determine the magnitude at the time of the occultation. The absolute magnitude was calculated using the approximation function from Shevchenko (1997a) with mean parameters for C-asteroids (Shevchenko and Lupishko, 1998). 47 Aglaja Millis et al. (1989a) obtained the diameter of this asteroid from an occultation in 1984. Using observations from this apparition and others from 1979, they determined the absolute magnitude H and obtained an albedo of 0.071. We used the magnitude at the time of the occultation from Millis et al. (1989a), but the magnitude–phase curve from Chernova et al. (1991). The absolute magnitude was calculated using the approximation function from Shevchenko (1997a), because, according to Belskaya and Shevchenko (2000) the H ,G function poorly describes the phase dependence of the brightness at low phase angles. The albedo in this case (0.060) is lower than that obtained by Millis et al. (1989a). 51 Nemausa There is a diameter determination for this asteroid from an occultation event in 1983 (Dunham et al., 1984). We used a lightcurve obtained by Kristensen and Gammelgaard (1985) at the time of the occultation together with the average amplitude of the opposition effect for C-class asteroids (Belskaya and Shevchenko, 2000) to determine the absolute magnitude of Nemausa from which we determined an albedo (0.097) somewhat higher than the albedo (0.062) obtained by Dunham et al. (1984). 64 Angelina No published lightcurve exists for the aspect of the occultation, but magnitude observations at other aspects are available (Lagerkvist et al., 2002). We applied the numerical model of Shevchenko (1997b) to determine the magnitude at the time of the occultation using the pole coordinates, semi-axis ratios, and sidereal period from Erikson (2000) and Shevchenko et al. (2003) and the magnitude–phase curve from Harris et al. (1989) to obtain H = 7.92 and pH = 0.47. This is the first high-albedo asteroid with an occultation albedo. Tedesco et al. (2002a, 2002b) have obtained albedos of 0.43 and 0.41 from IRAS and MSX-data, respectively, but the polarimetric albedo (0.66) is significantly higher. This may be connected with a polarimetric peculiarity in the polarimetric phase curve for this asteroid (polarimetric opposition effect, detected by Rosenbush et al., 2005). 78 Diana The occultation event of this asteroid was in September 1980 (Millis and Dunham, 1989). Harris and Young (1989) carried out photometric observations of 78 Diana during that same opposition. We used the function from Shevchenko (1997a) and the average amplitude of the opposition effect for low-albedo asteroids (Belskaya and Shevchenko, 2000) to determine the

Refined occultation albedos

215

absolute magnitude at the time of the occultation (8.20) from which we obtained an albedo of 0.086.

asteroids from Belskaya and Shevchenko (2000) for the determination of the absolute magnitude.

85 Io An occultation of a star by this asteroid occurred in December 1995 close in time to photometric observations made by Erikson et al. (1999) who, although they did not obtain a phase curve, modeled the asteroid’s shape and spin vector. We used their estimation of the magnitude at the moment of the occultation and the average amplitude of the opposition effect for C-class asteroids from Belskaya and Shevchenko (2000) to determine the absolute magnitude (7.71) and an albedo of 0.054. Another occultation by this asteroid occurred in December 2004 (AOD). This occultation event fell near the lightcurve maximum (Behrend, 2005) but there is no V magnitude at the time of occultation. As in the previous case, we used Erikson et al.’s (1999) magnitude estimate and the asteroid’s shape and spin vector to determine the absolute magnitude to obtain H = 7.65 and pH = 0.050.

124 Alkeste There is no lightcurve near the aspect of the occultation and so we used the absolute magnitude from Shevchenko et al. (2002).

94 Aurora No published lightcurve exists for the aspect of the occultation, but magnitude observations at other aspects are available (Lagerkvist et al., 2002). We applied the numerical model of Shevchenko (1997b) to determine the magnitude at the time of the occultation using pole coordinates, semi-axis ratios, and the sidereal period from Erikson (2000) and average parameters of the magnitude–phase curve for C-class asteroids from Shevchenko and Lupishko (1998) to obtain H = 7.63, pH = 0.045. 105 Artemis There is a diameter for this asteroid from a 1997 occultation (AOD), but no lightcurve near that aspect. Therefore, we did the same as for 94 Aurora but using pole coordinates, semi-axis ratios, and the sidereal period from Tungalag et al. (2002) and the magnitude–phase curve from Shevchenko et al. (2002) to obtain H = 8.86 and pH = 0.047. 106 Dione The diameter of this asteroid was determined by Kristensen (1984) using the results from a January 1983 occultation. Kristensen also calculated the albedo (0.064) using the magnitude V = 7.86 for the phase angle 2.4 deg at the time of the occultation, reduced to zero phase angle assuming a phase coefficient of 0.039 mag/deg, i.e., without taking into account the opposition effect. We used the average amplitude of the opposition effect for C-class asteroids from Belskaya and Shevchenko (2000) to determine H = 7.66 and pH = 0.078. 109 Felicitas There is no lightcurve for the epoch of the occultation, but Harris and Young (1989) obtained photometric observations of this asteroid in 1981 at a similar aspect (lightcurve amplitude 0.06 mag) and obtained the linear part of the magnitude–phase dependence. We used their magnitude–phase dependence and the average amplitude of the opposition effect for low-albedo

129 Antigone There was an occultation event for this asteroid in September 2001 (AOD) but no lightcurves were obtained during this opposition. However, there are observations for the same aspect in 1986 (Lagerkvist et al., 2002). Therefore, we used the magnitude from Lagerkvist et al. (2002) and the average amplitude of the opposition effect from Belskaya and Shevchenko (2000) to obtain an absolute magnitude of 6.90 and an albedo of 0.18. 134 Sophrosyne The occultation event for this asteroid was in November 1980 (Millis and Dunham, 1989). Harris and Young (1989) carried out photometric observations of Sophrosyne in November 1980 and obtained the linear part of the magnitude–phase curve. The occultation event occurred near the minimum of the lightcurve. We used these data to determine the absolute magnitude (8.89) at the moment of occultation. The corresponding albedo is 0.039. 139 Juewa The occultation diameter of this asteroid was taken from Millis and Dunham (1989). There are no published lightcurves near the aspect of the occultation, but there is a magnitude measurement from another aspect (Harris et al., 1999). We used the numerical model of Shevchenko (1997b) to determine the magnitude at the time of the occultation. The pole coordinates, semi-axis ratios, and sidereal period were taken from Michalowski (1993) and average parameters for the magnitude–phase curve for low-albedo asteroids from Shevchenko and Lupishko (1998) were used to obtain H = 8.10 and an occultation albedo of 0.040. 208 Lacrimosa There is no published lightcurve near the aspect of the occultation, but there is an estimate of the magnitude at other aspects close to that of the occultation event (Slivan and Binzel, 1996). We used the Shevchenko (1997b) model to determine the magnitude at the time of the occultation. The pole coordinates, semi-axis ratios, and sidereal period were taken from Tungalag et al. (2003) and the average parameters of the magnitude–phase curve for S-class asteroids from Shevchenko and Lupishko (1998). From these data we deduced that the occultation event occurred near lightcurve maximum. 216 Kleopatra There was an occultation in 1980 involving this asteroid (Millis and Dunham, 1989) and published lightcurves for the time of this event (Lagerkvist et al., 2002). The occultation occurred near lightcurve minimum. We used an estimate of the magnitude from Harris and Young (1989) and the phase func-

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tion from Shevchenko (1997a) to determine H (7.45) at the time of the occultation in 1980 to obtain an albedo of 0.17.

nitude to obtain an absolute magnitude of 7.00 and an albedo of 0.051.

230 Athamantis There was an occultation by this asteroid in 1991 (AOD) but no associated lightcurves. We used an estimate of the magnitude from Harris et al. (1992) for an aspect close to that of the occultation together with the Shevchenko (1997b) model to determine the absolute magnitude at the moment of occultation. The pole coordinates and semi-axis ratios were taken from Blanco and Riccioli (1998). The absolute magnitude for this event was difficult to determine because the sidereal period is unknown. Therefore, we used the average value of the absolute magnitude, taking into account the lightcurve amplitude (0.30 mag), to obtain H (7.37) and an albedo equal to 0.19.

334 Chicago There is no lightcurve at the moment of occultation, but there is an estimate of the magnitude at another aspect close to that of the occultation event (Erikson, 2000). We used the Erikson (2000) magnitude together with the Shevchenko (1997b) model to determine the magnitude at the time of the occultation. The pole coordinates, semi-axis ratios, and sidereal period were taken from Erikson (2000) and average parameters of the magnitude–phase curve for low-albedo asteroids were taken from Shevchenko and Lupishko (1998). In this way, we determined that the occultation event occurred near the minimum of the lightcurve.

238 Hypatia There are no published lightcurves during the oppositions of the occultation events in 2001 and 2005, but there are observations at similar aspects (Lagerkvist et al., 2002). We used the Shevchenko (1997b) model with pole coordinates, semi-axis ratios, and sidereal period from De Angelis (1995) to determine the absolute magnitudes (8.12, 8.15) for the times of the occultations, leading to albedos of 0.047 and 0.046. 243 Ida An occultation by this asteroid has not yet been observed. For comparison with the radiometrically determined albedo we used that determined from direct imaging with the Galileospacecraft (Helfenstein et al., 1996). 253 Mathilde A high-quality occultation by this asteroid has not yet been observed. For comparison with the radiometrically determined albedo we used that determined from direct imaging by the NEAR–Shoemaker spacecraft (Clark et al., 1999). 308 Polyxo There were two occultations by this asteroid in 2000 and 2004 (AOD). There are no lightcurves available near the time of either occultation event; the absolute magnitudes used to determine the occultation albedos are from Tedesco et al. (2002a). Dotto et al. (2002) obtained an albedo of 0.043 from ISO data using the same absolute magnitude as Tedesco et al. (2002a), about 26% lower than the occultation results (the mean of which, from the two occultations, is 0.058 ± 0.012) and 10% lower than the IRAS (0.048) results. 324 Bamberga Millis et al. (1989b) obtained the diameter of Bamberga from an occultation in December 1987. They measured the magnitude at the moment of occultation (9.16 mag) and, using G = 0.10, determined the absolute magnitude to be 6.81 mag which gave an albedo of 0.066. We used the magnitude from Millis et al. (1989b), the magnitude–phase curve from Scaltriti et al. (1980), and the average amplitude of the opposition effect for low-albedo asteroids from Belskaya and Shevchenko (2000) for the determination of the absolute mag-

345 Tercidina No V lightcurve near the date of occultation is available; we used the absolute magnitude from Harris and Young (1989) to determine the occultation albedo. 350 Ornamenta There is no V lightcurve near the date of the occultation, but Schober et al. (1993) carried out photometric observations of this asteroid in 1991 when it was at a similar aspect (lightcurve amplitude 0.20 mag). We used their estimate of the average magnitude per rotation period, the Shevchenko (1997a) phase function, and the average amplitude of the opposition effect for low-albedo asteroids from Belskaya and Shevchenko (2000) to determine the absolute magnitude. 381 Myrrha The diameter of this asteroid was determined from the occultation event in January 1991 (Sato et al., 1993). There is no V lightcurve near the date of the occultation and so we used the absolute magnitude from Tedesco et al. (2002a) for the determination of the occultation albedo. 386 Siegena There are no lightcurves for this occultation event. We used an estimate of the magnitude near the aspect of the occultation from Harris and Young (1989) and the Shevchenko (1997b) numerical model for the determination of the absolute magnitude at the moment of occultation. The pole coordinates and semi-axis rates were taken from Blanco and Riccioli (1998). We obtained the absolute magnitude equal to 7.49 and respectively albedo equal to 0.059. 433 Eros A high-quality occultation by this asteroid has not yet been observed. In Table 1 we present the albedo determined using the radiometric diameter from Harris (1998) for comparison with that determined using direct imaging by the NEAR–Shoemaker spacecraft (Domingue et al., 2002). 444 Gyptis No lightcurve is available from the epoch of the January 1994 occultation. The data from Harris et al. (1984) and Shevchenko et al. (2004) were used to obtain the absolute magnitude at the time of the occultation. Using the sidereal period

Refined occultation albedos

217

(6.2159776 h) we found that the occultation occurred near the second lightcurve maximum. We determined the absolute magnitude to be 8.00 mag from which we obtained an albedo of 0.036.

3. Discussion

704 Interamnia Buie et al. (1997) obtained the diameter of this asteroid from an occultation in December 1996. They obtained lightcurve observations before the occultation and found V = 6.76 mag (at phase angle 11◦ ) and that the occultation occurred near a broad secondary minimum in the lightcurve. Since the ecliptic position of Interamnia in 1969 was near that in 1996, we used the magnitude–phase curve obtained by Tempesti (1975) to determine the absolute magnitude. The absolute magnitude at the time of the occultation was calculated using the approximation function from Shevchenko (1997a) and the average amplitude of the opposition effect for low-albedo asteroids from Belskaya and Shevchenko (2000). The second occultation diameter of this asteroid (in March 2003) is from the AOD. No contemporaneous lightcurve observations are available. We used the Shevchenko (1997b) numerical model to determine the magnitude at the time of the occultation. Pole coordinates, semi-axis ratios, and the sidereal period are from Erikson (2000) and the magnitude–phase curve is from Tempesti (1975).

The accuracy of an occultation albedo depends on two factors: (a) the accuracy of the diameter determination, and (b) the accuracy of the absolute magnitude for the aspect of the diameter determination. For asteroids with well-determined occultation diameters, the largest source of error in the albedo is due to the uncertainty in the absolute magnitude. As can be seen from Eq. (1), a change in H of 0.1 mag leads to an error in the albedo of about 10%. If a lightcurve near the time of the occultation is available, and the magnitude–phase relation for the aspect of the occultation is known, then the absolute magnitude can be calculated to an accuracy of 0.01 to 0.02 mag, resulting in an albedo uncertainty of 2 to 3%. In cases where there is a lightcurve near the time of the occultation but the magnitude–phase relation is unknown, the absolute magnitude can be calculated using an approximation function from Shevchenko (1997a) and the mean value of the opposition effect estimated from the compositional class (Belskaya and Shevchenko, 2000) or using the H ,G magnitude system (Bowell et al., 1989) and a mean slope parameter (G) from Shevchenko and Lupishko (1998). In this case, the uncertainty in the absolute magnitude is between about 0.03 and 0.05 mag, leading to uncertainties in the albedo of between 5 and 6%. If there is no lightcurve near the time of the occultation but there are lightcurves for other aspects from which the coordinates of the pole and axis ratios of a triaxial-ellipsoid model were determined, then the photometric models above allow us to determine the absolute magnitude to an accuracy between 0.05 and 0.1 mag. In other cases, the error in the determination of the absolute magnitude exceeds 0.1 mag.

757 Portlandia No lightcurves near the time of the occultation are available but there is a determination of the linear part of the magnitude– phase curve for this asteroid in Lagerkvist et al. (1998) for other aspects. We determined the absolute magnitude for the lightcurve maximum (9.96) from their data. 914 Palisana There are no lightcurves for this occultation event; we used the absolute magnitude from Tedesco et al. (2002a). Dotto et al. (2002) estimated the albedo and diameter from ISO data, using the same absolute magnitude as Tedesco et al. (2002a), and obtained a diameter of 71 km in reasonable agreement with the IRAS diameter (76.6 km) but both are in poor agreement with the occultation diameter (91.2 km). 951 Gaspra An occultation by this asteroid has not yet been observed. The albedo given here is from direct imaging with the Galileospacecraft (Helfenstein et al., 1994) and is in good agreement with that obtained by Goldader et al. (1991) from ground-based radiometry. 141 Lumen, 210 Isabella, 248 Lameia, 306 Unitas, 404 Arsinoe, 420 Bertholda, 431 Nephele, 471 Papagena, 476 Hedwig, 498 Tokio, 522 Helga, 566 Stereoskopia, 568 Cheruskia, 578 Happelia, 791 Ani, 828 Lindemannia, 925 Alphonsina, 976 Benjamina, 1263 Varsavia, 1366 Piccolo, and 1512 Oulu No lightcurves near the time of the occultation are available for these events; we used the absolute magnitude from Tedesco et al. (2002a) to determine the occultation albedos.

3.1. Accuracy of albedos

3.2. Correlations with albedos obtained using other techniques Fig. 1 shows correlations of the occultation albedos with IRAS-albedos (solid dots, correlation coefficient 0.96, with coefficients of regression 0.0005 ± 0.0054 and 1.017 ± 0.041, respectively) and polarimetric albedos (open dots, correlation coefficient 0.93, with coefficients of regression −0.0021 ± 0.0165 and 1.124 ± 0.095, respectively) for the entire data set (excluding 27 Euterpe). The errors for the IRAS albedos are from Tedesco et al. (2002a); the errors for the polarimetric albedos were calculated using quality codes from Lupishko and Mohamed (1996) and a remark of Zellner et al. (1974) that the precision of albedos obtained using the slope parameter h is about 6%.5 The correlation coefficients are high for both the polarimetric and IRAS data sets with the latter formally slightly more accurate. The correlations of occultation albedos with IRAS-albedos and with polarimetric albedos for low-albedo asteroids only 5 We assumed the uncertainty was 6% for quality code = 3, 12% for 2, and 18% for 1.

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Fig. 1. Correlations of the occultation albedos with the IRAS-albedos and the polarimetric albedos (for all data).

Fig. 2. Correlations of the occultation albedos with the IRAS-albedos and the polarimetric albedos (for low-albedo asteroids only).

are given in Fig. 2. For this dataset, there is an inverse correlation of the occultation albedos with the polarimetric albedos. If real, this implies that the polarimetric method of albedo determination works poorly for at least some classes of dark asteroids. For example, Belskaya et al. (2005) have detected

small values for the inversion angle and Pmin for some Fclass asteroids and concluded from this that the texture of the surface regolith layer of the asteroid influences the polarization characteristics of the scattered light. However, the present sample, 13 asteroids with polarimetric albedos <0.12, nine of

Refined occultation albedos

which have Lupishko and Mohamed (1996) Quality codes less than 3, is too small and noisy to determine where, or even whether, the polarimetric method fails for low-albedo asteroids. 4. Summary We have determined albedos from occultation diameters, and accurate absolute magnitudes corresponding to the time of the occultation, for 57 asteroids of different taxonomic classes. For 18 objects, the occultation albedos were determined to an accuracy better than five percent. IRAS-albedos are in slightly better agreement than published polarimetric albedos with the occultation albedos presented here. In part, this may be due to the fact that the accuracy of albedos determined by the polarimetric method is probably poor in the case of low-albedo asteroids since, at least for laboratory samples, the polarimetric slope–albedo relation “saturates” for low-albedo asteroids, i.e., h and Pmin cease to change for albedos less than ∼0.05 (Zellner et al., 1977). However, because the minimum physically meaningful albedo is ∼0.03 (Zellner et al., 1977), any asteroid for which the polarimetric technique saturates has an albedo of 0.04 ± 0.01. The “occultation albedos” presented in bold in Table 1 and, of course, those directly determined by spacecraft imaging, are of sufficient accuracy to be used to calibrate indirect methods of obtaining asteroid diameters and/or albedos. Acknowledgments We thank the referees, A.W. Harris (USA) and Anonymous, for their constructive reviews. E.F.T.’s portion of the work presented here was supported by the National Aeronautics and Space Administration under Grants NNG04GF40G and NNG04GK46G, issued through the Office of Space Science Research and Analysis Programs. References Belskaya, I.N., Shevchenko, V.G., 2000. Opposition effect of asteroids. Icarus 146, 490–499. Belskaya, I.N., Shkuratov, Yu.G., Efimov, Yu.S., Shakhovskoy, N.M., GilHutton, R., Cellino, A., Zubko, E.S., Ovcharenko, A.A., Bondarenko, S.Yu., Shevchenko, V.G., Fornasier, S., Barbieri, C., 2005. The F-type asteroids with small inversion angles of polarization. Icarus 178, 213–221. Behrend, R., 2005. Observatoire de Geneve web site. http://obswww.unige.ch/~ behrend/page_cou.html. Binzel, R.P., 1984. The rotation of small asteroids. Icarus 57, 294–306. Blanco, C., Riccioli, D., 1998. Pole coordinates and shape of 30 asteroids. Astron. Astrophys. Suppl. Ser. 131, 385–394. Bowell, E., Hapke, B., Domingue, D., Lumme, K., Peltoniemi, J., Harris, A.W., 1989. Application of photometric models to asteroids. In: Binzel, R.P., Gehrels, T., Matthews, M.S. (Eds.), Asteroids II. Univ. of Arizona Press, Tucson, pp. 524–556. Brown, R.H., Morrison, D., Telesco, C.M., Brunk, N.E., 1982. Calibration of the radiometric asteroid scale using occultation diameters. Icarus 52, 188– 195. Buie, M.W., Wasserman, L.H., Millis, R.L., White, N.M., Nye, R., Dunham, E.W., Bosh, A.S., Stone, R., Hubbard, W.B., Hill, R., Dunham, D., Fried, R., Klinglesmith IV, D., Sanford, J., Schwaar, P., Maley, P., Owen, W., Benner,

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