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Eclipse Events in Binary Asteroid 1991 VH
ICARUS
133, 79–88 (1998) IS985890
ARTICLE NO.
Occultation/Eclipse Events in Binary Asteroid 1991 VH Petr Pravec Astronomical Institute, Academy of Sciences of the Czech Republic, CZ-25165 Ondrˇejov, Czech Republic E-mail: [email protected]
Marek Wolf Astronomical Institute, Charles University Prague, V Holesˇovicˇka´ch 2, CZ-18000 Prague, Czech Republic
and Lenka Sˇarounova´ Astronomical Institute, Academy of Sciences of the Czech Republic, CZ-25165 Ondrˇejov, Czech Republic Received August 4, 1997; revised December 1, 1997
planetary scientists. Some indirect evidence in support to the existence of such objects has been found over the few past tens of years: a binary nature was suggested for several asteroids with unusual lightcurves; radar observations revealed that (4769) Castalia consists of two bodies of similar size in touch, and a few other asteroids’ echoes were also bifurcated; several doublet craters were found on the Earth surface; and the presence of slowly rotating objects among small, and especially near-Earth, asteroids was proposed to be one of the end-states of evolution of binary asteroids (Weidenschilling et al. 1989, also Bottke and Melosh 1996, Chauvineau et al. 1995). No direct detection of an asteroid’s satellite was made, however, before the Galileo spacecraft flyby of (243) Ida, where a satellite (named Dactyl) was found (Chapman et al. 1995). Nevertheless, Dactyl is too small in comparison to Ida and the system cannot be considered as a true binary system consisting of bodies of comparable sizes (and mutual influences). Recently a lightcurve of a new, previously unobserved kind has been found for the near-Earth asteroid 1994 AW1 . Pravec and Hahn (1997)—hereafter PH 1997—analyzed the observations by Mottola et al. (1995) and Pravec et al. (1995) and found that its lightcurve, consisting of two components with periods 0.10497 and 0.9332 days, can be explained by the model of an eclipsing/occulting binary asteroid with the secondary-to-primary diameter ratio of 0.5 and nearly circular orbit. In this model, the primary rotation period is the shorter one, while the orbital period of the system the longer one. Although the authors felt that confirmation by other methods was necessary, the consistency of the model with the observations was good and no point contradicting it was found, bringing confidence to the hypothesis of the binarity of 1994 AW1 .
We present the results of photometric observations of the Apollo asteroid 1991 VH. Its lightcurve consists of two components: the first is the rotational lightcurve with period Ps 5 (0.109327 6 0.000003) d and amplitude 0.09 mag, while the second, with period Pl 5 (1.362 6 0.001) d, shows two minima with depth 0.16–0.19 mag, each with a duration of about 0.10 d, and little or no variation at phases between them. We present a model of the occulting/eclipsing binary asteroid with the secondary-to-primary diameter ratio ds /dp 5 0.40 that explains the observed lightcurve. In this model, the primary’s rotation is not synchronized with the orbital motion and produces the short-period lightcurve component (Ps). The orbital period is Pl . The mutual orbit’s semimajor axis is estimated to be a 5 (2.7 6 0.3) dp ; the eccentricity is 0.07 6 0.02. The similarity between the lightcurve of 1991 VH and those of 1994 AW1 (Pravec and Hahn, Icarus 127, 431, 1997) and (3671) Dionysus (Mottola et al. 1997, IAU Circular 6680) suggests that binary asteroids may be common among near-Earth asteroids. Based on the three known cases, we tentatively derive some typical characteristics of this new class of asteroids. They are mostly consistent with the hypothesis that binary asteroids are generated by tidal disruptions of weak, gravitationally bound aggregates (so-called ‘‘rubble piles’’) during encounters with the Earth (Bottke and Melosh, Nature 281, 51, 1996). A possible relationship between the population of binary asteroids and the belt of small near-Earth asteroids is discussed. 1998 Academic Press Key Words: minor planets; multiple period lightcurves; binary asteroids.
1. INTRODUCTION
The question of the existence of binary minor planets in the Solar System is a long-lasting controversy among 79
0019-1035/98 $25.00 Copyright 1998 by Academic Press All rights of reproduction in any form reserved.
´ PRAVEC, WOLF, AND SˇAROUNOVA
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TABLE I Observational Circumstances l UT 1997 Feb. 27.0 28.1 28.9 Mar. 2.0 3.0 3.9 4.9 11.0 12.0 12.9 Apr. 1.0 3.0 4.9 9.0 9.9
b
lhel
(2000.0)
bhel (2000.0)
[8]
[8]
[8]
[8]
r [AU]
171.1 170.4 169.9 169.2 168.5 167.8 167.1 162.8 162.1 161.5 151.3 150.7 150.2 149.4 149.2
21.2 21.9 22.4 23.0 23.6 24.1 24.6 27.6 28.0 28.3 32.3 32.4 32.4 32.4 32.4
161.5 162.1 162.6 163.3 163.9 164.4 165.0 168.7 169.3 169.9 181.6 182.8 184.0 186.6 187.2
5.3 5.5 5.6 5.7 5.8 6.0 6.1 6.9 7.0 7.1 9.4 9.6 9.9 10.3 10.4
1.299 1.300 1.300 1.300 1.300 1.300 1.300 1.300 1.300 1.299 1.292 1.290 1.289 1.286 1.285
D [AU]
a [deg]
Errors [mag]
0.332 0.331 0.331 0.331 0.331 0.331 0.331 0.337 0.339 0.341 0.397 0.404 0.412 0.428 0.432
18.5 18.3 18.2 18.2 18.3 18.4 18.7 21.4 22.0 22.6 36.1 37.4 38.5 40.8 41.3
0.025 0.015–0.02 0.017 0.015–0.02 0.03 –0.035 0.02 –0.025 0.02 0.02 0.02 –0.025 0.02 –0.025 0.03 0.035 0.02 –0.025 0.02 0.04
Prim./Sec. minimum detected
S P P S S P
P
We present here our observations of 1991 VH. We show that its lightcurve is similar to that of 1994 AW1 and interpret it as a detection of another, the second known, binary asteroid.
still apparent there. Typical behavior of lightcurves on these nights is shown in Figs. 1 and 2. In these figures, the best fit Fourier series expansion of the fast variation curve (see below for its derivation) is also plotted.
2. OBSERVATIONS
3. ANALYSIS OF THE OBSERVATIONS—DECOMPOSITION OF THE LIGHTCURVE
The Apollo asteroid 1991 VH was observed at Ondrˇejov Observatory on 18 nights during February 27.0–April 13.9, 1997. Three lightcurves obtained on April 7.1, 11.9, and 13.9 were poor in quality and coverage; we did not include them in the analysis and just discuss them below. Observational circumstances for observations on 15 nights used in the analysis are given in Table I. The table gives the UT midtime of the lightcurve coverage to the nearest tenth of a day, the geocentric and heliocentric ecliptic longitudes and latitudes of the asteroid (for equinox J2000), its heliocentric and geocentric distances, the phase angle, the mean error of the lightcurve points, and the indication of whether a primary or secondary minimum was detected on the given night (see below). The lightcurves were obtained in the R band, and all but last three lightcurves were calibrated using Landolt (1992) standard stars. The calibrations are consistent on the level 0.01–0.02 mag. On March 12.9 several additional measurements were made in the V and I bands and the color indices V 2 R 5 0.38 6 0.04 and R 2 I 5 0.36 6 0.04 were determined in the Johnson– Cousins system. On about half of the nights only a fast variation with period of 0.109 days and amplitude about 0.09 mag was apparent in the lightcurve. On several nights, however, deeper attenuations of brightness by nearly 0.2 mag lasting for 2–3 h were detected, in addition to the fast variation
The attenuations of the 1991 VH brightness from the normal 0.109-d lightcurve were detected during nine nights; see Table I for the dates for seven of them. (The other
FIG. 1. Secondary minimum of the long-period component detected on 1997 March 2.0. The fast variation rotation curve adds to the longperiod component minimum.
BINARY ASTEROID 1991 VH
FIG. 2. Primary minimum of the long-period component detected on 1997 March 11.0. The fast variation rotation curve adds to the longperiod component minimum.
two detections of the primary minima were made on April 7.1 and 13.9, but they were of poor quality.) We divide the detected attenuations into two subsets, one called ‘‘primary minima,’’ and the other called ‘‘secondary minima’’ (marked with ‘‘P’’ and ‘‘S,’’ respectively, in Table I). Within each subset, the intervals between minima are close to integer multiples of a period near 1.36 days, but the two subsets are mutually shifted by an amount different from 0.68 d. Thus, there are two different minima (P and S) occurring during one 1.36-d cycle rather than a single minimum occurring once per 0.68 d. The secondary minima are mostly better covered than the primary ones, although the latter were observed twice as often. During the lightcurve minima the fast variation was continuously present there. There are actually two components of the lightcurve that add together. This is the same behaviour as that found in the 1994 AW1 lightcurve (PH 1997). In the analysis of the 1991 VH lightcurve we used a somewhat different method for its decomposition, because of the presence of changes in the long-period component observed during the more-than-month-long observational coverage of the lightcurve.
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absolute magnitude HR 5 16.64 6 0.04 and the slope parameter GR 5 0.30 6 0.04 correspond to the obtained phase dependence. Because V 2 R 5 0.38 6 0.04, the mean V absolute magnitude is H 5 17.02 6 0.06. Then, to refine the obtained period and to define the shape of the short-period lightcurve component, we fixed the linear phase coefficient to 0.0254 mag/deg, included the last three non-calibrated lightcurves, adjusting their magnitude scales, and allowed the calibrated single-night lightcurves’ magnitude scales to be shifted by up to 60.03 mag. There were two reasons to shift the single-night magnitude scales of the small amounts: first, the calibration errors were 0.01–0.02 mag, so the magnitude scales of the single-night lightcurves can be shifted by corresponding amounts; second, the long-period lightcurve component may be actually not quite constant at phases outside the minima (as was assumed). The best fit of the sixth order Fourier series of all the lightcurve data (simultaneously adjusting the shifts of the single-night lightcurves’ magnitude scales in an iterative way) gives the period of the short period component Ps 5 (0.109327 6 0.000003) d. The composite lightcurve is presented in Fig. 3. Although there is a significant scatter of points (errors are only 3–4 times less than the amplitude), two maxima and two minima are apparent in the lightcurve, and all harmonics up to the sixth are detected significantly and contain some information about the lightcurve shape. The lightcurve does not change significantly during the observational interval. In Table II, the Fourier fit coefficients of the data of the first half of the observational interval (up to March 15), which were more accurate than the rest (April points) are presented. This Fourier fit of the short-period component is used in all subsequent computations. The short-
3.1. Short-Period Component For the derivation of the short-period lightcurve component we used observations obtained during 15 nights (see Table I) excluding parts taken at the times of occurrence of the long-period component’s minima. The Fourier analysis method described in Harris et al. (1989) and Pravec et al. (1996) was used and the period 0.109325 d and linear phase dependence coefficient (0.0254 6 0.0007) mag/deg were derived from the calibrated data (of 12 nights). The mean
FIG. 3. Short-period lightcurve component. The best fit 6th-order Fourier series to the February–March points is also plotted. The epoch (time of the zero phase) is JD 2450508.5.
´ PRAVEC, WOLF, AND SˇAROUNOVA
82
TABLE II Coefficients of the Best Fit Fourier Series to the Fast Variation R Lightcurve Component of 1991 VH Observed between February and Mid-March 1997 i
Ci
Si
Ampl.
0 1 2 3 4 5 6
17.4130 20.0003 20.0139 10.0112 20.0034 10.0022 10.0050
20.0078 20.0287 10.0022 10.0008 10.0042 10.0006
0.0078 0.0318 0.0114 0.0035 0.0047 0.0050
Note. The period is 0.1093267 d, epoch is JD 2450508.5, data were reduced to the solar phase 18.58. The formal error of each of the Fourier coefficients is 0.0012.
period component of the 1991 VH lightcurve has amplitude As 5 0.09 mag and looks like a normal asteroidal rotation lightcurve. 3.2. Long-Period Component We assumed that the long-period component added linearly (in irradiance, not in magnitude) to the short-period component derived in the previous subsection. Thus, we subtracted the short-period component from the data points. In Fig. 4 a sample lightcurve showing the primary minimum after the subtraction of the short-period component is presented. (Compare this with Fig. 2 showing the lightcurve before the subtraction.) We analyzed the long-period lightcurve component, at-
FIG. 4. Primary minimum of 1997 March 11.0 after subtraction of the fast variation component. Compare it with Fig. 2.
tempting to compose its fragments from individual nights into a single composite lightcurve. We found that the shape of the lightcurve minima (both primary and secondary) changed during the (more than one month long) observational interval. This fact makes the derivation of the long period somewhat uncertain, since we cannot be sure in what way the lightcurve minima’s branches shifted. The best fit was obtained for the (synodic) period Pl 5 (1.362 6 0.001) d; the error accounts for the uncertainties due to the changes of the minima’s shapes. We have, however, a good reason to believe that the real error is several times less than 0.001 d given above and that Pl is close to 1.3620 d. For this value, the steep decreasing branches in both the primary and the secondary minima agree well when folded into a composite lightcurve (see below) and the variation of the shape of the minima is confined to the increasing branches only. No other period can give similarly good fit for at least some parts of the long-period minima from different nights. In Fig. 5, the long-period lightcurve component composited with the period 1.3620 d is shown. All data from 1997 Feb. 27.0 to Apr. 4.9 are plotted in the figure. The three poorly covered primary minima detected on April 7.1, 9.9, and 13.9 are not plotted there, but they agree with the derived lightcurve. In Figs. 6 and 7, the secondary and primary minima, respectively, of the long-period lightcurve component are shown in detail. In each of the two figures just three singlenight lightcurves that cover the minimum are plotted (i.e., the points from other single-night lightcurves plotted in Fig. 5 that fall close to the minima but do not cover them are not replotted in the two more detailed figures.) From the figures, it is apparent that the decreasing branches are steeper than the increasing ones for both the primary and secondary minima. During the observational interval the secondary minimum increasing branch shifted progressively to greater phases, i.e., the duration of the secondary minima increased from 0.09 d on March 2.0 to 0.12 d on April 1.0. The primary minimum’s increasing branch has shifted by similar amount but in the opposite sense (decreasing the minimum’s duration) from March 11.0 to April 3.0. The shift of the times of the primary and secondary minima from symmetry (already mentioned in the first paragraph of Section 3) can be measured using the decreasing branches, which are the best defined parts of the minima and usable for the timing. Using them we found that the secondary minima occur at times shifted by (20.05 6 0.01) d with respect to those predicted for a symmetric long-period lightcurve component with the same times of occurrences of the primary minima. The depth of the secondary minimum is (0.16 6 0.01) mag, measured with respect to the mean level outside the minima (represented by the zeroth order of the Fourier fit of the short-period component). A possible decrease of
BINARY ASTEROID 1991 VH
83
FIG. 5. Long-period lightcurve component. The epoch is JD 2450508.5.
the level of the deepest part of the lightcurve minimum (i.e., increase of the depth) during the observational interval is apparent in Fig. 6. A part of nearly constant brightness (plateau) at the bottom of the secondary minimum is also apparent. Its duration varies with the shift of the increasing branch; on March 12.9 it lasted for about 0.05 days. The depth of the primary minimum is (0.19 6 0.01) mag. The existence of plateau in its deepest part is less certain than in the case of the secondary minima, but it could be of similar duration (0.05 d) on March 11.0 and, again, varies with the shift of the primary minimum increasing branch.
The long-period lightcurve component brightness at phases outside the minima appears to be constant to within a few hundredths of magnitude. There is an indication, however, that the constancy is not held exactly. For example, the part of the long-period lightcurve components at phases around 0.8 (just after the secondary minimum) appears brighter by 0.01–0.02 mag than the part around the phase 0.65 (just before the minimum). A similar effect, though less certain, is marginally apparent around the primary minimum. This apparent inconstancy may be at least partly due to an unknown (and unconstrained) rotation of the secondary in the model presented below.
FIG. 6. Secondary minima are shown in detail. This plot shows a zoomed part of Fig. 5.
FIG. 7. Primary minima are shown in detail. This plot shows a zoomed part of Fig. 5.
´ PRAVEC, WOLF, AND SˇAROUNOVA
84 4. INTERPRETATION
The characteristics of the lightcurve of 1991 VH are very similar to those of 1994 AW1 (PH 1997). We use the same model of an occulting/eclipsing binary asteroid for the interpretation of the 1991 VH lightcurve. Basic assumptions of the model are: 1. The asteroid consists of two bodies gravitationally bound and orbiting with period Pl . 2. Rotation of the primary is nonsynchronous and produces the short-period lightcurve component with period Ps . 3. The mutual occultations (or eclipses) of the bodies produce the long-period lightcurve component minima. The secondary occultations/eclipses are total. 4. The primary and the secondary have the same albedo and phase effect. 5. The occultation diameters corresponding to the crosssections of the bodies seen at the time of the occultation and the mean diameters of the bodies related to their volumes are the same. Since the effects caused in the lightcurve by occultations are very similar and largely undistinguishable from effects of eclipses, we do not resolve between these two modes below and discuss them jointly. The ratio of the occultation diameters of the bodies can be derived from the depth of the lightcurve minima. During the total secondary occultations (point 3 above), the depth of the secondary minima corresponds to the reduction of the irradiance by an amount corresponding to the elimination of the light from the secondary during the occultation. This assumption seems to be verified by the presence of the plateaus in the deepest parts of the minima. (The different depths of the primary and secondary minima will be discussed in the next section.) Assuming also that the primary and the secondary have the same albedo and phase effect (point 4), the secondary minimum depth (0.16 6 0.01) mag implies the secondary-to-primary occultation diameter ratio ds /dp 5 0.40 with formal error ,0.02. The semimajor axis a of the mutual orbit can be estimated from the period Pl using Kepler’s third law in the form a 5 d9p
! 3
Gr(1 1 q)P 2l 3 5 1.88d9p Ïr(1 1 q)P 2l , 24f
(1)
where d9p is the mean diameter of the primary that is related 3 to its volume Vp , d9p 5 Ï6Vp /f, G is the gravitational constant, r is the bulk density of the primary, and q is the secondary-to-primary mass ratio. The numerical constant 1.88 is computed for Pl in days and r in g/cm3. For a range of r(1 1 q) from 1.0 to 3.5 g/cm3 (plausible for minor
planets), the value of a spans from 2.3d9p to 3.5d9p . (Note: For spherical bodies, the mean diameters are equal to the occultation diameters; d9p 5 dp , d9s 5 ds . For more realistic figures, the equality is not held and the mean diameters can be greater or less than the occultation ones, depending on the shapes and their orientations. For the first-order estimate presented here we assume that the diameters are the same (point 5 above).) The semi-major axis a can be estimated more tightly from the duration of the long-period component minima. Considering dp 1 ds 5 1.40dp , we can compute the maximum duration of the minima (DTmax) using the formula DTmax 5
S
D
dp 1 ds Pl . arcsin 1808 2a
(2)
(The inequality DTobs # DTmax holds exactly only if the cross-sections of the bodies at the time of occultation are circular and the mutual orbit eccentricity is zero. Effects of the deviations from these conditions are discussed in the next section). A semimajor axis greater than 3.0dp seems to be ruled out, as in such a case an occultation (or eclipse) as long as 0.10 d cannot occur. A lower limit on the semimajor axis is not formally constrained, but, considering that the plateau of nearly constant brightness occurs in the secondary (and probably also in the primary) minimum deepest part, lasting for about half of the total duration of the minimum, the occultation (or eclipse) cannot be too far from central and a cannot be too low. For a 5 2.4dp , we get DTmax 5 0.128 d, and this also seems to be about the minimum value of a consistent with the shape of the minima. Thus, the semi-major axis is probably in the range 2.4–3.0dp , or a 5 (2.7 6 0.3)dp . This range is in agreement with that obtained from Eq. (1). If we take q 5 (dp /ds)3 5 0.06 (this is also equivalent to an assumption of the same bulk densities of the bodies, but moderate deviations can cause only small error), then the derived semimajor axis corresponds to the bulk density of the primary r 5 (1.6 6 0.5) g/cm3. The systematic error, however, can be greater if dp ? d9p . From the observed interval between the primary and the secondary minima decreasing branches different from Pl /2 (see the previous section) we can estimate the eccentricity of the orbit. The observed time shift corresponds to the difference between the mean anomalies of the secondary and the primary minima Ms 2 Mp 5 1678 6 28, while their true anomalies differ by 1808. In Fig. 8, the relation between the eccentricity and the true anomaly of the primary minimum decreasing branch leading to the observed difference in the mean anomalies is shown. Although it formally supplies only a lower limit on the eccentricity (0.05), we can constrain its upper limit using also the fact that the observed durations of the primary and
BINARY ASTEROID 1991 VH
FIG. 8. Relation between the eccentricity and the true anomaly of the primary minimum decreasing branch for the binary system. The values of these two parameters are probably in the area between the two dashed curves (1-s).
the secondary minima are the same within 10–20%. This rules out an eccentricity greater than p0.10, as in such a case the (primary and secondary) minima would occur at true anomalies within about 308 of 08 and 1808 (see Fig. 8) and there would occur an observable difference in their durations due to different pericenter and apocenter rates of motion of the bodies. No such effect is seen and we estimate that the eccentricity is 0.07 6 0.02 and the primary minimum decreasing branch occurred at true anomaly in the range 2208–3208. We conclude that the observed characteristics of the lightcurve are consistent with the model of occulting/ eclipsing binary asteroid. 5. DISCUSSION
In addition to the points used above for the estimation of the model’s parameters, there are three kinds of phenomena that can occur in the lightcurve of an occulting/ eclipsing binary asteroid but that we cannot use for setting further exact constraints to the model. They are (i) possible occurrence of both the occultations and eclipses in a lightcurve, (ii) effects related to nonspherical shapes of the bodies, and (iii) inhomogeneous illumination and scattering of their surfaces at nonzero phase angles. When the binary asteroid is observed at nonzero phase angle, the shadow of the occulting body is displaced from the body’s profile projection from the Earth at the distance of the secondary and, depending on the geometric conditions, we can see effects related both to occultations and eclipses. (At zero phase angle, no shadow is visible from
85
the Earth.) When the phase angle is large enough, the displacement between the shadow and the projection of the occulting body at the distance of the occulted one is so large that it is even possible to see only one of these two phenomena; when the shadow misses the occulted body, only occultations occur, and vice versa. We may see both phenomena during one period only if both the Earth and the Sun are close enough to the orbital plane of the system. In the case of 1991 VH, the maximum angular distance of the Earth (or the Sun) from the orbital plane of the system at which (at least partial) occultations (or eclipses) occur is 178 to 138 for a 5 2.4dp to 3.0dp . Since the phase angle was always greater than 188 (see Table I), the fact that we did not see any effect in the lightcurve attributable to a combination of occultations and eclipses is fully compatible with the derived model parameters. Although we cannot distinguish whether we saw occultations or eclipses, the Earth or the Sun only (but not both) was close to the orbital plane of the system during the period 1997 March 2.0–April 13.9. Since the shapes of the minima suggest that the occultations (or eclipses) were total at least during March 2.0–Apr. 1.0, while the geocentric (or heliocentric) position of the asteroid changed by 188 (or 198), the relevant body (Earth or Sun) probably moved along the plane of the system rather than perpendicularly to it. Effects caused by nonspherical shapes of the bodies may be complex and we cannot account for them exactly. Only the main effect—the fast variation due to the rotation of the primary with the period Ps —was removed from the occultation/eclipse lightcurve. Its low amplitude (0.09 mag) suggests that the primary shape is probably not too far from a spheroid, but we cannot evaluate how oblate the spheroid is. If the primary is a rubble pile (see below), the b/c ratio is significantly greater than 1.0 due to the fast rotation, but a value of the polar flattening depends on the actual density of the primary. In any case, the actual ‘‘diameters’’ traversed by the primary and the secondary during the primary and secondary occultation/eclipse events can be somewhat greater or smaller than dp derived from the brightness attenuation in the minimum and used in the computations presented in the previous section. The shape of the secondary is not constrained at all. These uncertainties may lead to certain difficult to judge systematic errors in the above derived parameters of the system. The basic conclusions, however, remain unchanged. Both the shapes and inhomogeneous illumination/scattering of the light may be responsible for some subtle details in the shapes of the lightcurve minima. For example, the very steep decrease of brightness after the beginning of the (both primary and secondary) occultation events may be caused by a transit of the occulting body over a bright limb of the occulted body. The more gradual increase of brightness before the end of the event may be
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86
TABLE III Heliocentric Orbits and Physical Parameters of the Binary Systems 1991 VH, 1994 AW1 , and (3671) Dionysus qhel [AU]
ahel [AU]
ihel [deg]
H [mag]
G
Object 1991 VH 1994 AW1 (3671) Mean sn21
0.973 1.022 1.003 1.00 0.03
1.137 1.105 2.195
13.9 24.1 13.6
17.0 17.5 16.7 17.1 0.4
0.30 (0.25) 0.21
Ps [day]
Pl [day]
As [mag]
ds /dp
0.1093 0.1050 0.1127 0.109 0.004
1.362 0.933 1.155 1.15 0.2
0.09 0.13 0.14 0.12 0.03
0.40 0.53 .0.28 (0.4)
V2R [mag]
R2I [mag]
B2V [mag]
Ref.
0.38 0.42 0.39 0.40 0.02
0.36 — 0.39 0.38 0.02
— — 0.68
(1) (2) (3)
Note. Symbols not used in text: qhel , ahel , and ihel are the perihelion distance, semimajor axis, and inclination, respectively, of the asteroid heliocentric orbit; H and G are the absolute V magnitude and the slope parameter, respectively, derived from the photometry; (1) orbital data from MPC 30091/ photometric data from this paper; (2) MPC 26191/Pravec and Hahn 1997; (3) MPC 29889/Mottola et al. (1997) 1 unpublished data from Pravec et al.
due to a transit of the occulting body over a terminator (possibly not perpendicular to it). Moves of the terminators on the bodies, change of the Earth position with respect to the system orbital plane, and a change of the distribution of the scattered light over the visible illuminated surfaces may be responsible for the observed evolution (shifts) of the increasing branches of both the primary and secondary minima during the observational interval. The decreasing branches might stay virtually unchanged since the bright limbs remained at the same sides of the bodies during the whole interval. It is clear, however, that an unambiguous solution for parameters describing the system orientation cannot be found from the available observation, so we only discuss the situation and do not attempt to derive the orientation of the system here. The primary minima are slightly deeper than the secondary ones (0.19 vs 0.16 mag). Although this may be caused by slightly different albedos of the bodies, it is also possible that the albedos are equal (which we assumed) and the greater depth of the primary minima is due to the transit of the secondary in front of an inhomogeneously illuminated or scattering surface of the primary (at the nonzero phase angles). Also, the fact that the area occulted on the surface of the primary during the central transit of the secondary—assumed to cause the primary minimum—is somewhat greater than the area actually occulted on the secondary during its total occultation by the primary (as a part between the terminator and the dark limb of the secondary is not illuminated at all) support the idea that the different depths of the minima are due to geometric effects, not different albedos. 6. POPULATION OF BINARY NEAR-EARTH ASTEROIDS
At present, there are three asteroids known to exhibit occultation/eclipse marks in their lightcurves: 1991 VH, 1994 AW1 , and (3671) Dionysus. In Table III we summarize some of their orbital and photometric characteristics.
It is apparent that these three asteroids are similar in many aspects; this indicates that they probably are members of a new, previously unknown group of asteroids of binary nature. Although their number is too low for any conclusions about the population of the binary asteroids group, the similarities between them lead us to estimate some typical characteristics of the population. They can be used for the identification of a process leading to formation of binary asteroids. Some of them, however, may be due only to selection effects. We estimate that the following characteristics are typical for the population of the binary near-Earth asteroids: • Perihelion distance qhel 5 1.00 AU (rms dispersion 0.03 AU). • Absolute magnitude H 5 17.1 (0.4), corresponding to diameter of 1.1 km, assuming geometric albedo p 5 0.20 (see below). This may be, however, only an upper limit of the actual population, due to the bias against fainter objects in the current photometric programmes. • Primary’s rotation is fast, with mean period 0.109 d (0.004 d). • Amplitude of primary’s rotation lightcurve is small, 0.12 mag (0.03 mag). This means that the figure of the primary is probably not far from a spheroid. • Orbital period is 1.15 d (0.2 d). For bulk density of the primary about r 5 1.7 g/cm3 (mean of the estimates for 1991 VH and 1994 AW1), this corresponds to a mean radius of the system’s orbit of 2.5 mean diameters of the primary. However, this value may be biased and there may actually exist some more distant binary systems, since the probability of the detection of the occultation events varies approximately with the inverse square of the system’s semimajor axis, i.e., approximately with the 24/3 power of the orbital period. • Diameter of the secondary is about 0.4 (0.1) times that of the primary. This may be clearly only a biased value, as it is difficult or almost impossible to detect a satellite smaller than 0.2dp by ground-based photometric tech-
87
BINARY ASTEROID 1991 VH
niques, since it produces too small change of brightness during an occultation to be clearly recognized as an occultation event. • Surface colors are slightly red: V 2 R 5 0.40 (0.02), R 2 I 5 0.38 (0.02). (For Dionysus, we obtained also B 2 V 5 0.68 6 0.07.) Although any classification from these three colors is uncertain, the infrared measurements of (3671) Dionysus in both the 10 and 1–3 em regions by Alan Harris and John Davies (personal communication) with the U.K. Infrared Telescope (Hawaii) reveal that it has a high geometric albedo of about 0.4 and near infared colors suggesting the E taxonomic type. The colors in the visual range are consistent with this classification for Dionysus. The taxonomic classes of the other two binary NEAs are uncertain, as we do not have available any direct information on their albedos. The G-value found for 1991 VH, however, suggests that its albedo is also relatively high, thus, considering its colors, consistent with the E or M classes. In summary, the three known binary NEAs are so similar in some of their orbital and physical parameters that we consider these properties as possibly connected to the formation and evolution processes of the population of binary NEAs. The processes are discussed in PH 1997. Most of the characteristics are consistent with the theory of Bottke and Melosh (1996) that binary asteroids are formed by tidal disruptions of weak, gravitationally bound aggregates (‘‘rubble piles’’) during encounters with the Earth. Only the last point of those given above, concerning similar colors of the three known systems, is not supported by the Bottke and Melosh theory; that point is, however, weak and the color similarity may be not too significant, since only one color index (V 2 R) was obtained for all the three NEAs and it does not allow us to judge how similar their colors really are over a wider spectral range. Another possible mechanism of creation of binaries during catastrophic fragmentations of asteroids was discussed in PH 1997. Whether the scenario of anisotropic ejection of the fragments (Martelli et al. 1993) leading to creation of the binaries is consistent with the similarity of the parameters of the three known binary systems remains to be seen from further investigation. An interesting point is that two of the three known binary NEAs—1991 VH and 1994 AW1 —have orbits that are characteristic of the belt of small NEAs suggested by Rabinowitz et al. (1993, 1994).1 The binary asteroids are much larger than small (,50 m), Rabinowitz objects, so any link between these two groups of asteroids is questionable. Nevertheless, if binary asteroids are tidally disrupted 1
1991 CS, the third of the three known 1-km-sized bodies found in orbits of this kind (in addition to the two above mentioned binary objects) also has a short rotation period of 0.0996 days (Pravec et al., unpublished)—a candidate for another binary object?
‘‘rubble piles’’ as suggested by Bottke and Melosh (1996), we speculate that the formation and evolution process may lead also to the creation of a large number of small fragments that are subsequently observed as small Earthapproachers. If these fragments correspond to the ‘‘building blocks’’ of the original rubble pile, these blocks would be only a few tens of meters large. This scenario, however, is not supported by the modeling of stochastic disruptions of near-Earth asteroids (Bottke et al. 1996), as they provide a poor fit to the dynamical constraints of the objects in the small near-Earth asteroid belt.
7. CONCLUSIONS
The peculiar lightcurve of the Apollo object 1991 VH, showing both fast (0.1093-day period) rotational variation and a longer-period (1.362-day) occultation-like component is interpreted as a product of occultations or eclipses in a binary asteroid system with a secondary-to-primary diameter ratio 0.40 and a mutual orbit with semimajor axis (2.7 6 0.3) primary diameters. It may be, together with 1994 AW1 and (3671) Dionysus, a member of the population of binary near-Earth asteroids. The three known binary systems may have been formed by similar mechanisms; this is suggested by the similarity in some of their orbital and physical parameters. They are mostly consistent with the hypothesis of the formation of binaries as result of tidal disruptions of ‘‘rubble piles’’ during encounters with the Earth, as suggested by Bottke and Melosh (1996).
ACKNOWLEDGMENTS This work has been supported by the Grant Agency of the Academy of Sciences of the Czech Republic, Grant A3003708, and by the Grant Agency of the Czech Republic, Grant 205-95-1498.
REFERENCES Bottke, W. F., and H. J. Melosh 1996. Formation of asteroid satellites and doublet craters by planetary tidal forces. Nature 281, 51–53. Bottke, W. F., M. C. Nolan, H. J. Melosh, A. M. Vickery, and R. Greenberg, 1996. Origin of Spacewatch small Earth-approaching asteroids. Icarus 122, 406–427. Chapman, C. R., J. Veverka, P. C. Thomas, K. Klaasen, M. J. S. Belton, A. Harch, A. McEwen, T. V. Johnson, P. Helfenstein, M. E. Davies, W. J. Merline, and T. Denk 1995. Discovery and physical properties of Dactyl, a satellite of asteroid 243 Ida. Nature 374, 783–785. Chauvineau, B., P. Farinella, and A. W. Harris 1995. The evolution of Earth-approaching binary asteroids: A Monte Carlo dynamical model. Icarus 115, 36–46. Harris, A. W., J. W. Young, E. Bowell, L. J. Martin, R. L. Millis, M. Poutanen, F. Scaltriti, V. Zappala`, H. J. Schober, H. Debehogne, and K. W. Zeigler 1989. Photoelectric observations of Asteroids 3, 24, 60, 261, and 863. Icarus 77, 171–186.
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Landolt, A. U. 1992. UBVRI photometric standard stars in the magnitude range 11.5 , V , 16.0 around the celestial equator. Astron. J. 104, 340–371. Martelli, G., P. Rothwell, I. Giblin, P. N. Smith, M. Di Martino, and P. Farinella 1993. Fragment jets from catastrophic break-up events and the formation of asteroid binaries and families. Astron. Astrophys. 271, 315–318. Mottola, S., G. De Angelis, M. Di Martino, A. Erikson, G. Hahn, and G. Neukum 1995b. The Near-Earth Objects Follow-Up Program: First results. Icarus 117, 62–70. Mottola, S., G. Hahn, P. Pravec, and L. Sˇarounova´ 1997. S/1997 (3671) 1. IAU Circular 6680. Pravec, P., and G. Hahn 1997. Two-period lightcurve of 1994 AW1 : Indication of a binary asteroid? Icarus 127, 431–440.
Pravec, P., L. Sˇarounova´, and M. Wolf 1996. Lightcurves of 7 near-Earth asteroids. Icarus 124, 471–482. Pravec, P., M. Wolf, M. Varady, and P. Ba´rta 1995. CCD photometry of 6 near-Earth asteroids. Earth Moon Planets 71, 177–187. Rabinowitz, D. L. 1994. The size and shape of the near-Earth asteroid belt. Icarus 111, 364–377. Rabinowitz, D. L., T. Gehrels, J. V. Scotti, R. S. McMillan, M. L. Perry, W. Wisniewski, S. M. Larson, E. S. Howell, and B. E. A. Mueller 1993. Evidence for a near-Earth asteroid belt. Nature 363, 704–706. Weidenschilling, S. J., P. Paolicchi, and V. Zappala` 1989. Do asteroids have satellites? In Asteroids II (R. P. Binzel, T. Gehrels, and M. S. Matthews, Eds.), pp. 643–658. Univ. of Arizona Press, Tucson.
133, 79–88 (1998) IS985890
ARTICLE NO.
Occultation/Eclipse Events in Binary Asteroid 1991 VH Petr Pravec Astronomical Institute, Academy of Sciences of the Czech Republic, CZ-25165 Ondrˇejov, Czech Republic E-mail: [email protected]
Marek Wolf Astronomical Institute, Charles University Prague, V Holesˇovicˇka´ch 2, CZ-18000 Prague, Czech Republic
and Lenka Sˇarounova´ Astronomical Institute, Academy of Sciences of the Czech Republic, CZ-25165 Ondrˇejov, Czech Republic Received August 4, 1997; revised December 1, 1997
planetary scientists. Some indirect evidence in support to the existence of such objects has been found over the few past tens of years: a binary nature was suggested for several asteroids with unusual lightcurves; radar observations revealed that (4769) Castalia consists of two bodies of similar size in touch, and a few other asteroids’ echoes were also bifurcated; several doublet craters were found on the Earth surface; and the presence of slowly rotating objects among small, and especially near-Earth, asteroids was proposed to be one of the end-states of evolution of binary asteroids (Weidenschilling et al. 1989, also Bottke and Melosh 1996, Chauvineau et al. 1995). No direct detection of an asteroid’s satellite was made, however, before the Galileo spacecraft flyby of (243) Ida, where a satellite (named Dactyl) was found (Chapman et al. 1995). Nevertheless, Dactyl is too small in comparison to Ida and the system cannot be considered as a true binary system consisting of bodies of comparable sizes (and mutual influences). Recently a lightcurve of a new, previously unobserved kind has been found for the near-Earth asteroid 1994 AW1 . Pravec and Hahn (1997)—hereafter PH 1997—analyzed the observations by Mottola et al. (1995) and Pravec et al. (1995) and found that its lightcurve, consisting of two components with periods 0.10497 and 0.9332 days, can be explained by the model of an eclipsing/occulting binary asteroid with the secondary-to-primary diameter ratio of 0.5 and nearly circular orbit. In this model, the primary rotation period is the shorter one, while the orbital period of the system the longer one. Although the authors felt that confirmation by other methods was necessary, the consistency of the model with the observations was good and no point contradicting it was found, bringing confidence to the hypothesis of the binarity of 1994 AW1 .
We present the results of photometric observations of the Apollo asteroid 1991 VH. Its lightcurve consists of two components: the first is the rotational lightcurve with period Ps 5 (0.109327 6 0.000003) d and amplitude 0.09 mag, while the second, with period Pl 5 (1.362 6 0.001) d, shows two minima with depth 0.16–0.19 mag, each with a duration of about 0.10 d, and little or no variation at phases between them. We present a model of the occulting/eclipsing binary asteroid with the secondary-to-primary diameter ratio ds /dp 5 0.40 that explains the observed lightcurve. In this model, the primary’s rotation is not synchronized with the orbital motion and produces the short-period lightcurve component (Ps). The orbital period is Pl . The mutual orbit’s semimajor axis is estimated to be a 5 (2.7 6 0.3) dp ; the eccentricity is 0.07 6 0.02. The similarity between the lightcurve of 1991 VH and those of 1994 AW1 (Pravec and Hahn, Icarus 127, 431, 1997) and (3671) Dionysus (Mottola et al. 1997, IAU Circular 6680) suggests that binary asteroids may be common among near-Earth asteroids. Based on the three known cases, we tentatively derive some typical characteristics of this new class of asteroids. They are mostly consistent with the hypothesis that binary asteroids are generated by tidal disruptions of weak, gravitationally bound aggregates (so-called ‘‘rubble piles’’) during encounters with the Earth (Bottke and Melosh, Nature 281, 51, 1996). A possible relationship between the population of binary asteroids and the belt of small near-Earth asteroids is discussed. 1998 Academic Press Key Words: minor planets; multiple period lightcurves; binary asteroids.
1. INTRODUCTION
The question of the existence of binary minor planets in the Solar System is a long-lasting controversy among 79
0019-1035/98 $25.00 Copyright 1998 by Academic Press All rights of reproduction in any form reserved.
´ PRAVEC, WOLF, AND SˇAROUNOVA
80
TABLE I Observational Circumstances l UT 1997 Feb. 27.0 28.1 28.9 Mar. 2.0 3.0 3.9 4.9 11.0 12.0 12.9 Apr. 1.0 3.0 4.9 9.0 9.9
b
lhel
(2000.0)
bhel (2000.0)
[8]
[8]
[8]
[8]
r [AU]
171.1 170.4 169.9 169.2 168.5 167.8 167.1 162.8 162.1 161.5 151.3 150.7 150.2 149.4 149.2
21.2 21.9 22.4 23.0 23.6 24.1 24.6 27.6 28.0 28.3 32.3 32.4 32.4 32.4 32.4
161.5 162.1 162.6 163.3 163.9 164.4 165.0 168.7 169.3 169.9 181.6 182.8 184.0 186.6 187.2
5.3 5.5 5.6 5.7 5.8 6.0 6.1 6.9 7.0 7.1 9.4 9.6 9.9 10.3 10.4
1.299 1.300 1.300 1.300 1.300 1.300 1.300 1.300 1.300 1.299 1.292 1.290 1.289 1.286 1.285
D [AU]
a [deg]
Errors [mag]
0.332 0.331 0.331 0.331 0.331 0.331 0.331 0.337 0.339 0.341 0.397 0.404 0.412 0.428 0.432
18.5 18.3 18.2 18.2 18.3 18.4 18.7 21.4 22.0 22.6 36.1 37.4 38.5 40.8 41.3
0.025 0.015–0.02 0.017 0.015–0.02 0.03 –0.035 0.02 –0.025 0.02 0.02 0.02 –0.025 0.02 –0.025 0.03 0.035 0.02 –0.025 0.02 0.04
Prim./Sec. minimum detected
S P P S S P
P
We present here our observations of 1991 VH. We show that its lightcurve is similar to that of 1994 AW1 and interpret it as a detection of another, the second known, binary asteroid.
still apparent there. Typical behavior of lightcurves on these nights is shown in Figs. 1 and 2. In these figures, the best fit Fourier series expansion of the fast variation curve (see below for its derivation) is also plotted.
2. OBSERVATIONS
3. ANALYSIS OF THE OBSERVATIONS—DECOMPOSITION OF THE LIGHTCURVE
The Apollo asteroid 1991 VH was observed at Ondrˇejov Observatory on 18 nights during February 27.0–April 13.9, 1997. Three lightcurves obtained on April 7.1, 11.9, and 13.9 were poor in quality and coverage; we did not include them in the analysis and just discuss them below. Observational circumstances for observations on 15 nights used in the analysis are given in Table I. The table gives the UT midtime of the lightcurve coverage to the nearest tenth of a day, the geocentric and heliocentric ecliptic longitudes and latitudes of the asteroid (for equinox J2000), its heliocentric and geocentric distances, the phase angle, the mean error of the lightcurve points, and the indication of whether a primary or secondary minimum was detected on the given night (see below). The lightcurves were obtained in the R band, and all but last three lightcurves were calibrated using Landolt (1992) standard stars. The calibrations are consistent on the level 0.01–0.02 mag. On March 12.9 several additional measurements were made in the V and I bands and the color indices V 2 R 5 0.38 6 0.04 and R 2 I 5 0.36 6 0.04 were determined in the Johnson– Cousins system. On about half of the nights only a fast variation with period of 0.109 days and amplitude about 0.09 mag was apparent in the lightcurve. On several nights, however, deeper attenuations of brightness by nearly 0.2 mag lasting for 2–3 h were detected, in addition to the fast variation
The attenuations of the 1991 VH brightness from the normal 0.109-d lightcurve were detected during nine nights; see Table I for the dates for seven of them. (The other
FIG. 1. Secondary minimum of the long-period component detected on 1997 March 2.0. The fast variation rotation curve adds to the longperiod component minimum.
BINARY ASTEROID 1991 VH
FIG. 2. Primary minimum of the long-period component detected on 1997 March 11.0. The fast variation rotation curve adds to the longperiod component minimum.
two detections of the primary minima were made on April 7.1 and 13.9, but they were of poor quality.) We divide the detected attenuations into two subsets, one called ‘‘primary minima,’’ and the other called ‘‘secondary minima’’ (marked with ‘‘P’’ and ‘‘S,’’ respectively, in Table I). Within each subset, the intervals between minima are close to integer multiples of a period near 1.36 days, but the two subsets are mutually shifted by an amount different from 0.68 d. Thus, there are two different minima (P and S) occurring during one 1.36-d cycle rather than a single minimum occurring once per 0.68 d. The secondary minima are mostly better covered than the primary ones, although the latter were observed twice as often. During the lightcurve minima the fast variation was continuously present there. There are actually two components of the lightcurve that add together. This is the same behaviour as that found in the 1994 AW1 lightcurve (PH 1997). In the analysis of the 1991 VH lightcurve we used a somewhat different method for its decomposition, because of the presence of changes in the long-period component observed during the more-than-month-long observational coverage of the lightcurve.
81
absolute magnitude HR 5 16.64 6 0.04 and the slope parameter GR 5 0.30 6 0.04 correspond to the obtained phase dependence. Because V 2 R 5 0.38 6 0.04, the mean V absolute magnitude is H 5 17.02 6 0.06. Then, to refine the obtained period and to define the shape of the short-period lightcurve component, we fixed the linear phase coefficient to 0.0254 mag/deg, included the last three non-calibrated lightcurves, adjusting their magnitude scales, and allowed the calibrated single-night lightcurves’ magnitude scales to be shifted by up to 60.03 mag. There were two reasons to shift the single-night magnitude scales of the small amounts: first, the calibration errors were 0.01–0.02 mag, so the magnitude scales of the single-night lightcurves can be shifted by corresponding amounts; second, the long-period lightcurve component may be actually not quite constant at phases outside the minima (as was assumed). The best fit of the sixth order Fourier series of all the lightcurve data (simultaneously adjusting the shifts of the single-night lightcurves’ magnitude scales in an iterative way) gives the period of the short period component Ps 5 (0.109327 6 0.000003) d. The composite lightcurve is presented in Fig. 3. Although there is a significant scatter of points (errors are only 3–4 times less than the amplitude), two maxima and two minima are apparent in the lightcurve, and all harmonics up to the sixth are detected significantly and contain some information about the lightcurve shape. The lightcurve does not change significantly during the observational interval. In Table II, the Fourier fit coefficients of the data of the first half of the observational interval (up to March 15), which were more accurate than the rest (April points) are presented. This Fourier fit of the short-period component is used in all subsequent computations. The short-
3.1. Short-Period Component For the derivation of the short-period lightcurve component we used observations obtained during 15 nights (see Table I) excluding parts taken at the times of occurrence of the long-period component’s minima. The Fourier analysis method described in Harris et al. (1989) and Pravec et al. (1996) was used and the period 0.109325 d and linear phase dependence coefficient (0.0254 6 0.0007) mag/deg were derived from the calibrated data (of 12 nights). The mean
FIG. 3. Short-period lightcurve component. The best fit 6th-order Fourier series to the February–March points is also plotted. The epoch (time of the zero phase) is JD 2450508.5.
´ PRAVEC, WOLF, AND SˇAROUNOVA
82
TABLE II Coefficients of the Best Fit Fourier Series to the Fast Variation R Lightcurve Component of 1991 VH Observed between February and Mid-March 1997 i
Ci
Si
Ampl.
0 1 2 3 4 5 6
17.4130 20.0003 20.0139 10.0112 20.0034 10.0022 10.0050
20.0078 20.0287 10.0022 10.0008 10.0042 10.0006
0.0078 0.0318 0.0114 0.0035 0.0047 0.0050
Note. The period is 0.1093267 d, epoch is JD 2450508.5, data were reduced to the solar phase 18.58. The formal error of each of the Fourier coefficients is 0.0012.
period component of the 1991 VH lightcurve has amplitude As 5 0.09 mag and looks like a normal asteroidal rotation lightcurve. 3.2. Long-Period Component We assumed that the long-period component added linearly (in irradiance, not in magnitude) to the short-period component derived in the previous subsection. Thus, we subtracted the short-period component from the data points. In Fig. 4 a sample lightcurve showing the primary minimum after the subtraction of the short-period component is presented. (Compare this with Fig. 2 showing the lightcurve before the subtraction.) We analyzed the long-period lightcurve component, at-
FIG. 4. Primary minimum of 1997 March 11.0 after subtraction of the fast variation component. Compare it with Fig. 2.
tempting to compose its fragments from individual nights into a single composite lightcurve. We found that the shape of the lightcurve minima (both primary and secondary) changed during the (more than one month long) observational interval. This fact makes the derivation of the long period somewhat uncertain, since we cannot be sure in what way the lightcurve minima’s branches shifted. The best fit was obtained for the (synodic) period Pl 5 (1.362 6 0.001) d; the error accounts for the uncertainties due to the changes of the minima’s shapes. We have, however, a good reason to believe that the real error is several times less than 0.001 d given above and that Pl is close to 1.3620 d. For this value, the steep decreasing branches in both the primary and the secondary minima agree well when folded into a composite lightcurve (see below) and the variation of the shape of the minima is confined to the increasing branches only. No other period can give similarly good fit for at least some parts of the long-period minima from different nights. In Fig. 5, the long-period lightcurve component composited with the period 1.3620 d is shown. All data from 1997 Feb. 27.0 to Apr. 4.9 are plotted in the figure. The three poorly covered primary minima detected on April 7.1, 9.9, and 13.9 are not plotted there, but they agree with the derived lightcurve. In Figs. 6 and 7, the secondary and primary minima, respectively, of the long-period lightcurve component are shown in detail. In each of the two figures just three singlenight lightcurves that cover the minimum are plotted (i.e., the points from other single-night lightcurves plotted in Fig. 5 that fall close to the minima but do not cover them are not replotted in the two more detailed figures.) From the figures, it is apparent that the decreasing branches are steeper than the increasing ones for both the primary and secondary minima. During the observational interval the secondary minimum increasing branch shifted progressively to greater phases, i.e., the duration of the secondary minima increased from 0.09 d on March 2.0 to 0.12 d on April 1.0. The primary minimum’s increasing branch has shifted by similar amount but in the opposite sense (decreasing the minimum’s duration) from March 11.0 to April 3.0. The shift of the times of the primary and secondary minima from symmetry (already mentioned in the first paragraph of Section 3) can be measured using the decreasing branches, which are the best defined parts of the minima and usable for the timing. Using them we found that the secondary minima occur at times shifted by (20.05 6 0.01) d with respect to those predicted for a symmetric long-period lightcurve component with the same times of occurrences of the primary minima. The depth of the secondary minimum is (0.16 6 0.01) mag, measured with respect to the mean level outside the minima (represented by the zeroth order of the Fourier fit of the short-period component). A possible decrease of
BINARY ASTEROID 1991 VH
83
FIG. 5. Long-period lightcurve component. The epoch is JD 2450508.5.
the level of the deepest part of the lightcurve minimum (i.e., increase of the depth) during the observational interval is apparent in Fig. 6. A part of nearly constant brightness (plateau) at the bottom of the secondary minimum is also apparent. Its duration varies with the shift of the increasing branch; on March 12.9 it lasted for about 0.05 days. The depth of the primary minimum is (0.19 6 0.01) mag. The existence of plateau in its deepest part is less certain than in the case of the secondary minima, but it could be of similar duration (0.05 d) on March 11.0 and, again, varies with the shift of the primary minimum increasing branch.
The long-period lightcurve component brightness at phases outside the minima appears to be constant to within a few hundredths of magnitude. There is an indication, however, that the constancy is not held exactly. For example, the part of the long-period lightcurve components at phases around 0.8 (just after the secondary minimum) appears brighter by 0.01–0.02 mag than the part around the phase 0.65 (just before the minimum). A similar effect, though less certain, is marginally apparent around the primary minimum. This apparent inconstancy may be at least partly due to an unknown (and unconstrained) rotation of the secondary in the model presented below.
FIG. 6. Secondary minima are shown in detail. This plot shows a zoomed part of Fig. 5.
FIG. 7. Primary minima are shown in detail. This plot shows a zoomed part of Fig. 5.
´ PRAVEC, WOLF, AND SˇAROUNOVA
84 4. INTERPRETATION
The characteristics of the lightcurve of 1991 VH are very similar to those of 1994 AW1 (PH 1997). We use the same model of an occulting/eclipsing binary asteroid for the interpretation of the 1991 VH lightcurve. Basic assumptions of the model are: 1. The asteroid consists of two bodies gravitationally bound and orbiting with period Pl . 2. Rotation of the primary is nonsynchronous and produces the short-period lightcurve component with period Ps . 3. The mutual occultations (or eclipses) of the bodies produce the long-period lightcurve component minima. The secondary occultations/eclipses are total. 4. The primary and the secondary have the same albedo and phase effect. 5. The occultation diameters corresponding to the crosssections of the bodies seen at the time of the occultation and the mean diameters of the bodies related to their volumes are the same. Since the effects caused in the lightcurve by occultations are very similar and largely undistinguishable from effects of eclipses, we do not resolve between these two modes below and discuss them jointly. The ratio of the occultation diameters of the bodies can be derived from the depth of the lightcurve minima. During the total secondary occultations (point 3 above), the depth of the secondary minima corresponds to the reduction of the irradiance by an amount corresponding to the elimination of the light from the secondary during the occultation. This assumption seems to be verified by the presence of the plateaus in the deepest parts of the minima. (The different depths of the primary and secondary minima will be discussed in the next section.) Assuming also that the primary and the secondary have the same albedo and phase effect (point 4), the secondary minimum depth (0.16 6 0.01) mag implies the secondary-to-primary occultation diameter ratio ds /dp 5 0.40 with formal error ,0.02. The semimajor axis a of the mutual orbit can be estimated from the period Pl using Kepler’s third law in the form a 5 d9p
! 3
Gr(1 1 q)P 2l 3 5 1.88d9p Ïr(1 1 q)P 2l , 24f
(1)
where d9p is the mean diameter of the primary that is related 3 to its volume Vp , d9p 5 Ï6Vp /f, G is the gravitational constant, r is the bulk density of the primary, and q is the secondary-to-primary mass ratio. The numerical constant 1.88 is computed for Pl in days and r in g/cm3. For a range of r(1 1 q) from 1.0 to 3.5 g/cm3 (plausible for minor
planets), the value of a spans from 2.3d9p to 3.5d9p . (Note: For spherical bodies, the mean diameters are equal to the occultation diameters; d9p 5 dp , d9s 5 ds . For more realistic figures, the equality is not held and the mean diameters can be greater or less than the occultation ones, depending on the shapes and their orientations. For the first-order estimate presented here we assume that the diameters are the same (point 5 above).) The semi-major axis a can be estimated more tightly from the duration of the long-period component minima. Considering dp 1 ds 5 1.40dp , we can compute the maximum duration of the minima (DTmax) using the formula DTmax 5
S
D
dp 1 ds Pl . arcsin 1808 2a
(2)
(The inequality DTobs # DTmax holds exactly only if the cross-sections of the bodies at the time of occultation are circular and the mutual orbit eccentricity is zero. Effects of the deviations from these conditions are discussed in the next section). A semimajor axis greater than 3.0dp seems to be ruled out, as in such a case an occultation (or eclipse) as long as 0.10 d cannot occur. A lower limit on the semimajor axis is not formally constrained, but, considering that the plateau of nearly constant brightness occurs in the secondary (and probably also in the primary) minimum deepest part, lasting for about half of the total duration of the minimum, the occultation (or eclipse) cannot be too far from central and a cannot be too low. For a 5 2.4dp , we get DTmax 5 0.128 d, and this also seems to be about the minimum value of a consistent with the shape of the minima. Thus, the semi-major axis is probably in the range 2.4–3.0dp , or a 5 (2.7 6 0.3)dp . This range is in agreement with that obtained from Eq. (1). If we take q 5 (dp /ds)3 5 0.06 (this is also equivalent to an assumption of the same bulk densities of the bodies, but moderate deviations can cause only small error), then the derived semimajor axis corresponds to the bulk density of the primary r 5 (1.6 6 0.5) g/cm3. The systematic error, however, can be greater if dp ? d9p . From the observed interval between the primary and the secondary minima decreasing branches different from Pl /2 (see the previous section) we can estimate the eccentricity of the orbit. The observed time shift corresponds to the difference between the mean anomalies of the secondary and the primary minima Ms 2 Mp 5 1678 6 28, while their true anomalies differ by 1808. In Fig. 8, the relation between the eccentricity and the true anomaly of the primary minimum decreasing branch leading to the observed difference in the mean anomalies is shown. Although it formally supplies only a lower limit on the eccentricity (0.05), we can constrain its upper limit using also the fact that the observed durations of the primary and
BINARY ASTEROID 1991 VH
FIG. 8. Relation between the eccentricity and the true anomaly of the primary minimum decreasing branch for the binary system. The values of these two parameters are probably in the area between the two dashed curves (1-s).
the secondary minima are the same within 10–20%. This rules out an eccentricity greater than p0.10, as in such a case the (primary and secondary) minima would occur at true anomalies within about 308 of 08 and 1808 (see Fig. 8) and there would occur an observable difference in their durations due to different pericenter and apocenter rates of motion of the bodies. No such effect is seen and we estimate that the eccentricity is 0.07 6 0.02 and the primary minimum decreasing branch occurred at true anomaly in the range 2208–3208. We conclude that the observed characteristics of the lightcurve are consistent with the model of occulting/ eclipsing binary asteroid. 5. DISCUSSION
In addition to the points used above for the estimation of the model’s parameters, there are three kinds of phenomena that can occur in the lightcurve of an occulting/ eclipsing binary asteroid but that we cannot use for setting further exact constraints to the model. They are (i) possible occurrence of both the occultations and eclipses in a lightcurve, (ii) effects related to nonspherical shapes of the bodies, and (iii) inhomogeneous illumination and scattering of their surfaces at nonzero phase angles. When the binary asteroid is observed at nonzero phase angle, the shadow of the occulting body is displaced from the body’s profile projection from the Earth at the distance of the secondary and, depending on the geometric conditions, we can see effects related both to occultations and eclipses. (At zero phase angle, no shadow is visible from
85
the Earth.) When the phase angle is large enough, the displacement between the shadow and the projection of the occulting body at the distance of the occulted one is so large that it is even possible to see only one of these two phenomena; when the shadow misses the occulted body, only occultations occur, and vice versa. We may see both phenomena during one period only if both the Earth and the Sun are close enough to the orbital plane of the system. In the case of 1991 VH, the maximum angular distance of the Earth (or the Sun) from the orbital plane of the system at which (at least partial) occultations (or eclipses) occur is 178 to 138 for a 5 2.4dp to 3.0dp . Since the phase angle was always greater than 188 (see Table I), the fact that we did not see any effect in the lightcurve attributable to a combination of occultations and eclipses is fully compatible with the derived model parameters. Although we cannot distinguish whether we saw occultations or eclipses, the Earth or the Sun only (but not both) was close to the orbital plane of the system during the period 1997 March 2.0–April 13.9. Since the shapes of the minima suggest that the occultations (or eclipses) were total at least during March 2.0–Apr. 1.0, while the geocentric (or heliocentric) position of the asteroid changed by 188 (or 198), the relevant body (Earth or Sun) probably moved along the plane of the system rather than perpendicularly to it. Effects caused by nonspherical shapes of the bodies may be complex and we cannot account for them exactly. Only the main effect—the fast variation due to the rotation of the primary with the period Ps —was removed from the occultation/eclipse lightcurve. Its low amplitude (0.09 mag) suggests that the primary shape is probably not too far from a spheroid, but we cannot evaluate how oblate the spheroid is. If the primary is a rubble pile (see below), the b/c ratio is significantly greater than 1.0 due to the fast rotation, but a value of the polar flattening depends on the actual density of the primary. In any case, the actual ‘‘diameters’’ traversed by the primary and the secondary during the primary and secondary occultation/eclipse events can be somewhat greater or smaller than dp derived from the brightness attenuation in the minimum and used in the computations presented in the previous section. The shape of the secondary is not constrained at all. These uncertainties may lead to certain difficult to judge systematic errors in the above derived parameters of the system. The basic conclusions, however, remain unchanged. Both the shapes and inhomogeneous illumination/scattering of the light may be responsible for some subtle details in the shapes of the lightcurve minima. For example, the very steep decrease of brightness after the beginning of the (both primary and secondary) occultation events may be caused by a transit of the occulting body over a bright limb of the occulted body. The more gradual increase of brightness before the end of the event may be
´ PRAVEC, WOLF, AND SˇAROUNOVA
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TABLE III Heliocentric Orbits and Physical Parameters of the Binary Systems 1991 VH, 1994 AW1 , and (3671) Dionysus qhel [AU]
ahel [AU]
ihel [deg]
H [mag]
G
Object 1991 VH 1994 AW1 (3671) Mean sn21
0.973 1.022 1.003 1.00 0.03
1.137 1.105 2.195
13.9 24.1 13.6
17.0 17.5 16.7 17.1 0.4
0.30 (0.25) 0.21
Ps [day]
Pl [day]
As [mag]
ds /dp
0.1093 0.1050 0.1127 0.109 0.004
1.362 0.933 1.155 1.15 0.2
0.09 0.13 0.14 0.12 0.03
0.40 0.53 .0.28 (0.4)
V2R [mag]
R2I [mag]
B2V [mag]
Ref.
0.38 0.42 0.39 0.40 0.02
0.36 — 0.39 0.38 0.02
— — 0.68
(1) (2) (3)
Note. Symbols not used in text: qhel , ahel , and ihel are the perihelion distance, semimajor axis, and inclination, respectively, of the asteroid heliocentric orbit; H and G are the absolute V magnitude and the slope parameter, respectively, derived from the photometry; (1) orbital data from MPC 30091/ photometric data from this paper; (2) MPC 26191/Pravec and Hahn 1997; (3) MPC 29889/Mottola et al. (1997) 1 unpublished data from Pravec et al.
due to a transit of the occulting body over a terminator (possibly not perpendicular to it). Moves of the terminators on the bodies, change of the Earth position with respect to the system orbital plane, and a change of the distribution of the scattered light over the visible illuminated surfaces may be responsible for the observed evolution (shifts) of the increasing branches of both the primary and secondary minima during the observational interval. The decreasing branches might stay virtually unchanged since the bright limbs remained at the same sides of the bodies during the whole interval. It is clear, however, that an unambiguous solution for parameters describing the system orientation cannot be found from the available observation, so we only discuss the situation and do not attempt to derive the orientation of the system here. The primary minima are slightly deeper than the secondary ones (0.19 vs 0.16 mag). Although this may be caused by slightly different albedos of the bodies, it is also possible that the albedos are equal (which we assumed) and the greater depth of the primary minima is due to the transit of the secondary in front of an inhomogeneously illuminated or scattering surface of the primary (at the nonzero phase angles). Also, the fact that the area occulted on the surface of the primary during the central transit of the secondary—assumed to cause the primary minimum—is somewhat greater than the area actually occulted on the secondary during its total occultation by the primary (as a part between the terminator and the dark limb of the secondary is not illuminated at all) support the idea that the different depths of the minima are due to geometric effects, not different albedos. 6. POPULATION OF BINARY NEAR-EARTH ASTEROIDS
At present, there are three asteroids known to exhibit occultation/eclipse marks in their lightcurves: 1991 VH, 1994 AW1 , and (3671) Dionysus. In Table III we summarize some of their orbital and photometric characteristics.
It is apparent that these three asteroids are similar in many aspects; this indicates that they probably are members of a new, previously unknown group of asteroids of binary nature. Although their number is too low for any conclusions about the population of the binary asteroids group, the similarities between them lead us to estimate some typical characteristics of the population. They can be used for the identification of a process leading to formation of binary asteroids. Some of them, however, may be due only to selection effects. We estimate that the following characteristics are typical for the population of the binary near-Earth asteroids: • Perihelion distance qhel 5 1.00 AU (rms dispersion 0.03 AU). • Absolute magnitude H 5 17.1 (0.4), corresponding to diameter of 1.1 km, assuming geometric albedo p 5 0.20 (see below). This may be, however, only an upper limit of the actual population, due to the bias against fainter objects in the current photometric programmes. • Primary’s rotation is fast, with mean period 0.109 d (0.004 d). • Amplitude of primary’s rotation lightcurve is small, 0.12 mag (0.03 mag). This means that the figure of the primary is probably not far from a spheroid. • Orbital period is 1.15 d (0.2 d). For bulk density of the primary about r 5 1.7 g/cm3 (mean of the estimates for 1991 VH and 1994 AW1), this corresponds to a mean radius of the system’s orbit of 2.5 mean diameters of the primary. However, this value may be biased and there may actually exist some more distant binary systems, since the probability of the detection of the occultation events varies approximately with the inverse square of the system’s semimajor axis, i.e., approximately with the 24/3 power of the orbital period. • Diameter of the secondary is about 0.4 (0.1) times that of the primary. This may be clearly only a biased value, as it is difficult or almost impossible to detect a satellite smaller than 0.2dp by ground-based photometric tech-
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BINARY ASTEROID 1991 VH
niques, since it produces too small change of brightness during an occultation to be clearly recognized as an occultation event. • Surface colors are slightly red: V 2 R 5 0.40 (0.02), R 2 I 5 0.38 (0.02). (For Dionysus, we obtained also B 2 V 5 0.68 6 0.07.) Although any classification from these three colors is uncertain, the infrared measurements of (3671) Dionysus in both the 10 and 1–3 em regions by Alan Harris and John Davies (personal communication) with the U.K. Infrared Telescope (Hawaii) reveal that it has a high geometric albedo of about 0.4 and near infared colors suggesting the E taxonomic type. The colors in the visual range are consistent with this classification for Dionysus. The taxonomic classes of the other two binary NEAs are uncertain, as we do not have available any direct information on their albedos. The G-value found for 1991 VH, however, suggests that its albedo is also relatively high, thus, considering its colors, consistent with the E or M classes. In summary, the three known binary NEAs are so similar in some of their orbital and physical parameters that we consider these properties as possibly connected to the formation and evolution processes of the population of binary NEAs. The processes are discussed in PH 1997. Most of the characteristics are consistent with the theory of Bottke and Melosh (1996) that binary asteroids are formed by tidal disruptions of weak, gravitationally bound aggregates (‘‘rubble piles’’) during encounters with the Earth. Only the last point of those given above, concerning similar colors of the three known systems, is not supported by the Bottke and Melosh theory; that point is, however, weak and the color similarity may be not too significant, since only one color index (V 2 R) was obtained for all the three NEAs and it does not allow us to judge how similar their colors really are over a wider spectral range. Another possible mechanism of creation of binaries during catastrophic fragmentations of asteroids was discussed in PH 1997. Whether the scenario of anisotropic ejection of the fragments (Martelli et al. 1993) leading to creation of the binaries is consistent with the similarity of the parameters of the three known binary systems remains to be seen from further investigation. An interesting point is that two of the three known binary NEAs—1991 VH and 1994 AW1 —have orbits that are characteristic of the belt of small NEAs suggested by Rabinowitz et al. (1993, 1994).1 The binary asteroids are much larger than small (,50 m), Rabinowitz objects, so any link between these two groups of asteroids is questionable. Nevertheless, if binary asteroids are tidally disrupted 1
1991 CS, the third of the three known 1-km-sized bodies found in orbits of this kind (in addition to the two above mentioned binary objects) also has a short rotation period of 0.0996 days (Pravec et al., unpublished)—a candidate for another binary object?
‘‘rubble piles’’ as suggested by Bottke and Melosh (1996), we speculate that the formation and evolution process may lead also to the creation of a large number of small fragments that are subsequently observed as small Earthapproachers. If these fragments correspond to the ‘‘building blocks’’ of the original rubble pile, these blocks would be only a few tens of meters large. This scenario, however, is not supported by the modeling of stochastic disruptions of near-Earth asteroids (Bottke et al. 1996), as they provide a poor fit to the dynamical constraints of the objects in the small near-Earth asteroid belt.
7. CONCLUSIONS
The peculiar lightcurve of the Apollo object 1991 VH, showing both fast (0.1093-day period) rotational variation and a longer-period (1.362-day) occultation-like component is interpreted as a product of occultations or eclipses in a binary asteroid system with a secondary-to-primary diameter ratio 0.40 and a mutual orbit with semimajor axis (2.7 6 0.3) primary diameters. It may be, together with 1994 AW1 and (3671) Dionysus, a member of the population of binary near-Earth asteroids. The three known binary systems may have been formed by similar mechanisms; this is suggested by the similarity in some of their orbital and physical parameters. They are mostly consistent with the hypothesis of the formation of binaries as result of tidal disruptions of ‘‘rubble piles’’ during encounters with the Earth, as suggested by Bottke and Melosh (1996).
ACKNOWLEDGMENTS This work has been supported by the Grant Agency of the Academy of Sciences of the Czech Republic, Grant A3003708, and by the Grant Agency of the Czech Republic, Grant 205-95-1498.
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