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Saturn Ring-Plane Crossing, May 1995: Pole Precession and Ring Thickness
ICARUS
129, 555–561 (1997) IS975767
ARTICLE NO.
NOTE Saturn Ring-Plane Crossing, May 1995: Pole Precession and Ring Thickness1 Amanda S. Bosh Lowell Observatory, Flagstaff, Arizona 86001-4499 E-mail: [email protected]
Andrew S. Rivkin Lowell Observatory, Flagstaff, Arizona 86001 and University of Arizona/Lunar and Planetary Lab, Tucson, AZ
Jeffrey W. Percival Space Astronomy Laboratory, University of Wisconsin, Madison, Wisconsin 53706
MaryJane Taylor Department of Physics and Engineering, Loras College, Dubuque, Iowa 52004
and G. Wayne van Citters Division of Astronomical Sciences, National Science Foundation, Arlington, Virginia 22230 Received October 9, 1995; revised May 15, 1997
On 22 May 1995, as the Earth crossed through Saturn’s ringplane, we used the Wide Field Planetary Camera 2 on the Hubble Space Telescope to image Saturn and its rings for 10 hr centered near the predicted time of ring-plane crossing. By performing photometry on the rings, we find that the time of ring-plane crossing is later than the nominal predicted time, suggesting that Saturn’s pole is precessing at a rate somewhat slower than is predicted for a rigid body under the influence of torques from the Sun and Saturn’s satellites and/or that Saturn’s pole position is different from the nominal position. We determine the equivalent thickness of the rings to be 1.4 6 0.1 km, and find that the measured value corresponds to the amplitude of perturbations from the Laplace plane warp and satellite-induced bending waves. 1997 Academic Press
1
Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA Contract NAS5-26555.
Ring-plane crossings occur when a planet’s ring-plane sweeps over the Earth or Sun. For Saturn these crossings occur roughly every 15 years, twice per Saturn orbit around the Sun. Observations made during a ringplane crossing have the advantage of reduced scattered light from the rings, allowing study of material normally obscured by Saturn’s bright rings: faint inner satellites and the tenuous other E ring, for example. During the two most recent ring-plane crossings in 1966 and 1980, five satellites were discovered (Janus, Epimetheus, Telesto, Calypso, and Helene), as was Saturn’s tenuous outer E ring. During the 1995–1996 ringplane crossing season, Saturn’s ring plane swept across the Earth on three dates: 22 May 1996, 10 August 1995, and 11 February 1996; it crossed the Sun once on 17–21 November 1995. The Earth crosses Saturn’s ringplane three times due to the differing inclinations of the Earth’s and Saturn’s orbits and the alignment of their ascending nodes. In other ring-plane crossing seasons (such as the next two), there is only one Earth crossing. At the moment of ring-plane crossing, we view the thin edge of the rings (Fig. 1). Even then, the rings still reflect light from the edge and so are visible from Earth; they never disappear completely. In previous observations of ring-plane crossing, ground-based observers imaged Saturn for several days before and after the crossing (Dollfus 1979, Brahic and Sicardy 1981, Sicardy et al. 1982). The time of minimum light from the rings and thus the time of ring-plane crossing was determined from analyses of these images. The residual flux at this time was used to calculate the thickness of the rings. During the passage of 1966, the
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FIG. 1. View of Saturn and its rings near minimum ring brightness. The signal in the boxes on the right (west) of this image have been multiplied by a factor of 25 to make the faint ring more visible. From top to bottom, the boxes are from HST orbits 3, 4, and 5, and were taken approximately ˚ methane band. In the top panel to the west, Janus is faintly visible; Enceladus is 96 min apart. These images are 7-sec exposures in the 8900-A seen in the middle panel. Rhea is easily visible, east of Saturn.
crossing time was determined with an accuracy of 2 hr, and the ring thickness was estimated to be 2.4 6 1.3 km (Dollfus 1979). During the ring-plane crossing of 1980, the ring thickness was determined to be 1.1120.9 0.5 km (Sicardy et al. 1982); due to sparse data in 1980, the crossing time was not determined.
I. WFPC2 DATA During the May 1995 ring-plane crossing event, we used the Wide Field Planetary Camera 2 (Burrows 1995) aboard the Hubble Space Telescope (HST) to observe Saturn and its rings near crossing time. The goals of this set of observations were (1) to refine the time of ring-plane crossing and therefore determine the pole precession rate, (2) to find the residual flux at the time of ring-plane crossing to be used to determine the thickness of the rings, and (3) to study Saturn’s small inner satellites. We discuss results on the timing and ring thickness here; satellite results are presented in a separate paper (Bosh and Rivkin 1996). To accomplish these goals, we required data with sufficient signal-tonoise ratio (S/N) to be able to confidently detect the rings even at their minimum light. The improved image quality of WFPC2 would provide both high spatial resolution (approximately 725 km per pixel at Saturn and a point-spread function that includes 50% of the enclosed light in a circle of radius 1 pixel) and high S/N as a result. With a surface brightness of about 7 mag per square arcsec in the visible, Saturn is not a faint ˚ methane filter—FQCH4N-D in target. Therefore we used the 8915-A Table 3.2 of Burrows (1995)—which provided better contrast between Saturn and its rings because Saturn’s reflectance at this wavelength is reduced. Observing parameters were chosen to maximize S/N in the ring at minimum brightness. The wide-field mode was chosen over the planetary mode because the increased pixel scale would provide higher S/N, and the wider field of view would hedge against possible centering difficulties; this was at the expense of undersampling the point-spread
function. The gain was chosen to be 7 electrons per data number (e2 /DN) for the lower read noise, which meant that the detector would saturate at lower light levels than with a gain of 14 e2 /DN. To reduce the amount of expected blooming of saturated charge along columns, the serial transfer registers of the CCD were kept running throughout the exposures (CLOCKS 5 YES). It was determined that all bright-object artifacts— blooming, spider diffraction spikes, ghost images, horizontal smear— would not fall on or near the rings. The integration time used was 400 sec: long enough to develop adequate signal over any read noise but still short enough to include three to four exposures per HST orbit (approximately 96 min). Multiple images per orbit allowed identification and removal of cosmic ray events and tracking of saturnian satellites. At least a few satellites were always superimposed on the rings, complicating the photometry. We required the observations to straddle the crossing time. The uncertainty in the time of ring-plane crossing (1s) was approximately 2 hr. This was due to a combination of uncertainty in the position of Saturn’s pole at the Voyager reference epoch (Bosh 1994) and uncertainty in the value of the pole precession (French et al. 1993). The predicted time of 5:14 UTC on 22 May 1995 was calculated for pole precession equal to its predicted rate. If precession were twice its predicted rate, the crossing time would move early by 82 min to 3:52 UTC; if precession were 0, the crossing time would move later by 82 min to 6:36 UTC. To compensate for this uncertainty in crossing time, we planned to image for 7 orbits of the HST (a total of 10 hr), centered on the predicted time of crossing. In this way, even if the crossing time changed by 1 hr, we would still have at least 2 orbits on either side of crossing. This was necessary to establish the rate of change of brightness of the rings and to determine the crossing time. In practice, we centered the observations at one full orbit later than the predicted time to avoid a conflict with HST scheduling activities—data for all these analyses were obtained between 1:49 and 11:55 UTC on 22 May 1995.
NOTE We began each observing window (defined by the HST orbit around the Earth) with 2 short 7-sec exposures intended for photometric and astrometric calibration and cosmic ray removal. These images were taken with Saturn and its rings centered in the flat region of wide-field chip 3 (WF3), using the methane filter set; this is near the WF3–FIX standard location for extended objects, but offset to move Saturn and its rings into the region where the response of the methane flat field is most constant. The WF3 images included the region out to 5 Saturn radii. Because all 4 of the WFPC2 chips were read out, the region from 5 to ˚ filter. These short 15 Saturn radii was included on WF2, with the 5462-A exposures were followed by 3 or 4 longer 400-sec exposures. This sequence of exposures achieved optimal orbit packing—along with overheads for the exposures, they filled the available time in each HST orbit. In the 7 orbits geared toward the science data, we obtained 14 short exposures and 27 long exposures. The data used in this analysis were the calibrated data frames provided by the Space Telescope Science Institute. These data were processed in the standard pipeline calibration (Burrows, 1995), including subtraction of bias level and dark counts, corrections for flat-field effects and analogto-digital conversion scaling, and marking known bad pixels. The photometry was not corrected for known small problems such as the pixellation effect (2%), optical distortion over the field (2% effect), or a charge transfer efficiency problem (at the intermediate background levels present here, this amounted to 1% across the rings) (Holtzman et al. 1995).
II. TIME OF RING-PLANE CROSSING We performed photometry on the rings by adding the signal in the calibrated data frames within an area 2 pixels (0.2 arcsec) wide and 8 pixels (0.8 arcsec) high, with the long direction of the box centered vertically on the rings. This box was rotated to be perpendicular to the ring plane; the angle for this rotation was determined by fitting to the known satellites visible on each frame for center, scale, and orientation. The value determined in this manner agreed well with the orientation information given in the data headers. This ‘‘rotated-box’’ photometry method accounted for fractional pixel area when a box boundary dissected a pixel. From this value was subtracted a ‘‘sky’’ value, determined by adding the signal in a 2 3 2 pixel area above and below the first box and scaled by pixel area. These boxes were moved down the rings at a 1pixel increment from F ring ansa, through the planet, to F ring ansa. We did not use an automatic routine to remove cosmic rays because these routines also had a tendency to remove portions of satellites and neighboring ring signal. Retaining cosmic rays did not introduce much spurious signal and the remainder of the data would work to cancel the effects of the cosmic rays. All pixels associated with saturated charge blooming near Saturn and with known satellites were not used in the analysis; the extent of these regions were determined by eye, with knowledge of the number of pixels covered by trailed satellites. No attempt was made to correct the signal levels in these pixels because satellites were often extended over more than 10 pixels, and ring brightness was not constant over that range. From this photometry method, we derived signal per linear pixel (along the rings) as a function of distance from Saturn and time (Fig. 2). To determine the time of ring-plane crossing, we averaged all the ring signal in each data frame (Fig. 3). We performed a weighted fit to these data with two simple linear functions, the negative slope corresponding to precrossing and the positive slope to postcrossing. The photometric errors were used in the weighting function. The intersection of these two lines gives the time of ring-plane crossing: 05:34 6 00:07 (3s) UTC on 22 May 1995. Thus the crossing occurred shortly after the last long exposure of HST orbit 3, while the HST was occulted by the Earth and not collecting data. As expected, the precrossing slope is negative and large because the brightness is decreasing rapidly as the lit side of Saturn’s rings becomes less visible. The postcrossing slope is positive and much
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shallower than precrossing as the brightness increases more slowly when we are looking at the unlit face of the rings. The minimum brightness of the rings was 304 6 25 (1s) DN per linear pixel in 400 sec, where the uncertainty is propagated from the fitted uncertainties in the parameters of the linear functions. The approximate magnitude is 16 per linear arcsec ˚ passband, uncorrected for distance or phase effects. The in the 8900-A minimum signal value includes contributions from both sunlight and Saturn-shine reflected off the thin edge of the rings and off bending waves or other vertical excursion of the rings. If the rings are warped (i.e., Laplace plane), then this value will also include signal from sunlight transmitted through the optically thin regions of the rings. The Saturnshine component of the minimum signal is expected to be small, due to the deep methane absorption feature at the wavelength used in this observation; we estimate that it contributes no more than 4% of the signal. If transmitted light were a significant part of the signal, we would expect its contribution to vary with ring location due to the dependence of projected area of the Cassini Division (for example) on distance from Saturn. However, the values of minimum signal show no clear trend with distance from Saturn, and the scatter in the values is only 7%. Therefore we can assume that the minimum signal values found here correspond almost entirely to sunlight reflected off the edge of the rings, to within the 1s errors quoted. As seen in Figs. 2 and 3, the rings did not darken and brighten uniformly. Precrossing, the B ring is brighter on the west ansa than on the east. Postcrossing, the C and A rings brighten more quickly on the east ansa than on the west. This asymmetry affects the derived crossing time slightly: for the B-ring region on the west ansa the time is 5:36, for the east ansa it is 5:32. Both times are within the quoted 3s error bar (7 min) of the derived time for all ring regions on both ansa. Brightness asymmetries were noticed by both Sicardy et al. (1982) during the 1980–1981 ringplane crossing and Nicholson et al. (1996) during the August 1995 crossing. Figure 2 represents a complicated situation because each ring region actually includes light from all rings exterior to the named ring due to their nearly edge-on configuration. Thus ‘‘C’’ includes light from the C, B, A, and F rings, ‘‘A’’ from the A and F rings, and ‘‘F’’ from just the F ring. We do not believe that the E or G rings contribute significantly to the residual flux because the signal level of the E ring away from the main rings is only 3% that of the minimum ring flux. The F ring is too thin to contribute a significant signal when away from ring-plane crossing, but near a crossing it dominates the signal. Ring signal extends out to the F ring region (Fig. 2). In addition, when photometry of just the F ring (the portion beyond the A ring) is performed, the equivalent thickness is 1.1 to 1.7 km. Clearly the F ring dominates the residual signal at minimum light. Therefore to achieve maximum S/N results, we adopt the timing and thickness results obtained by including all ring data from both ansae. What does a crossing time of 05:34 UTC mean for Saturn’s pole position and precession rate? With this one measurement of ring-plane crossing time, 20 min later than the predicted time, we cannot decouple the relative contributions of change in pole positions and change in precession rate from the predicted values for these quantities. To account for the entire difference in timing with a change in pole position would require an increase in its right ascension and/or declination by 2.0 6 0.7 arcsec. This is within the formal errors of the right ascension of the pole, but a factor of 3 larger than the formal error in the declination of the pole. To achieve the measured crossing time by changing only the precession rate, it would need to be 71% 6 10% of its predicted value. This agrees with work by Bosh (1994), who found from fitting several occultation chords spanning 13 years that the best fit value for pole precession was 55% 6 26% of the predicted value. As discussed in French et al. (1993), Saturn’s pole precession is expected to be a result of direct solar torque on the oblate figure of Saturn (and thus depends on the planet’s gravitational harmonics, J2n , which describe its departure from sphericity) and of solar torque on Saturn’s satellites (mainly Titan) transferred to Saturn through its oblate figure. Thus any
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FIG. 2. Evolution of ring brightness with time and ring location. Brightness as a function of projected distance from Saturn is plotted for both ring extensions, then folded back to align ring areas in the east and west ansae. Therefore, the top half of the plot depicts the east ansa with time increasing downward and the bottom half of the plot depicts the west ansa with time increasing upward. In this way we compare the postcrossing brightness evolution. Areas in black are earth occultations (when Saturn was blocked from the HST’s view by the Earth), or known satellites or cosmic ray hits removed from the rings. The color bar at the bottom of the figure shows the colors that correspond to intensity levels: black for no
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NOTE
III. EQUIVALENT THICKNESS OF THE RINGS The geometric albedo p of an extended body can be computed as the ratio of reflected (I ) to incident specific intensities at the body, at zero phase angle a (Rybicki and Lightman 1979) p5
I(a 5 0) . Fs /D2
(1)
The incident solar flux at the body is fFs /D2, where D is the heliocentric distance of the body in AU. The geometric albedo is also known as I/F (Hanel et al. 1992), and we will use this designation here. In terms of C, measured counts per pixel on the image, the reflected intensity is given by
FIG. 3. The residual ring signal per linear pixel (expressed as equivalent thickness for geometric albedo of unity) is plotted against time, for several different ring areas. Circular symbols represent values from the west ansa; squares, the east ansa. Filled symbols represent photometry from all visible rings (C, B, A, and F), open symbols indicate values for signal from the B ring region. Error bars (1s) are included but in most cases are smaller than the symbols used to represent data points. These data are fit with two lines, and the intersection of these lines is the time of ring-plane crossing. The steep slope on the left represents the dimming of the rings as the reflecting area becomes less visible as seen from Earth. After the Earth crosses the ring-plane, we are seeing the unlit face of the rings. This face is not illuminated directly by sunlight but instead light is transmitted through the ring plane from the lit face after multiple scatterings. This is the brightening on the right, with its much shallower slope. In this figure, asymmetry is visible in the B ring region: before crossing, the west ansa of the B ring is much brighter than the east. This assymetry disappears within 2 hr of crossing. The brightness evolution of the sum of all rings is more symmetric because the A ring compensates for the differences by being brighter in the east than the west, exactly out of phase with the B ring.
differences between measured and calculated precession rates would be caused by either a different value of one of the input parameters, or an incomplete application of the precession theory. The current uncertainty in the value of J2 changes the precession rate by only 0.04% (Bosh 1994). Theoretical problems may include the departure of Saturn from the rigid body that was assumed in the calculations. In Table I we list revised times for the ring-plane crossing events in 1995–1996. These times are insensitive to the difference between changing the reference pole position or the pole precession rate; either leads to the same determination of event time for all events. Therefore, data from later events this season will not help to decouple the errors in pole position and precession rate. As noted by Nicholson et al. (1996), the observed crossing times in August differed significantly between east and west ansae (Table I), straddling the time predicted here. Additional study of all data sets from the 1995–1996 crossing season is required to understand ring behavior close to a crossing.
I(a 5 0) 5
Cb , VDt
(2)
where V is the angle subtended by one pixel (ster), Dt is the exposure time for the frame (sec), and b is the conversion factor between counts ˚ 21. We adopt a value for b of 1.953 3 10216 for WF3, and erg cm22 A from Nicholson et al. (1996). To calculate the incident solar intensity, we first set Sl ; fFs to avoid confusion over factors of f. Then, the incident solar intensity Fs /D2 is Sl /(fD2). Combining Eqs. (1) and (2), we achieve an expression for geometric albedo I CbfD2 5 . F V Dt Sl
(3)
˚ (the mean wavelength of the The solar flux (Sl) at 1 AU and 8896.5 A ˚ 21 (Wehrli 1986). Equation (3) gives filter used) is 94.11 erg sec21 cm22 A the relation for geometric albedo of an area unit of 1 WF3 pixel at Saturn. However, we are interested in deriving the equivalent thickness of the rings from the photometric measurements of these data. To do this, we note that the angle subtended by the rings within one pixel, V, is equal to hl, where h is the thickness of the ring (in radians) and l is the length of a pixel (0.09968 arcsec 5 4.8278 3 1027 radians). Because the photometry was performed with the rotated-box method, we do not need to take into account the angle between the ring-plane projection and pixel axes. If we then assume a geometric albedo of unity for the ring material (feasible for Saturn’s high-albedo, water–ice rings), the equation for ring thickness (in km) becomes h5
CbfD2R , l Dt Sl
(4)
for a given geocentric distance R. We use the minimum ring signal per linear pixel to produce an estimate of the ring thickness and thus find a photometric thickness of 1.43 6 0.09 km (3s). This is the equivalent thickness of the rings, or the projection of the rings onto a plane perpendicular to our line of sight and to the ring plane. The equivalent thickness is not necessarily the same as the physical thickness of the rings (the local thickness of a ring region). Effects that cause the equivalent thickness to be greater than the physical
signal, red for intermediate signal, and light yellow to white for high signal. Several features are clearly evident: the C ring becomes bright shortly after ring-plane crossing (between HST orbits 3 and 4, marked ‘‘RPX’’) on both the east and west ansae, although the east ansa is much brighter at the end of the data acquisition interval (orbit 7). The Cassini Division also stands out clearly; the brightening is greatest at the inner edge of the Cassini Division because this is the location of maximum projected area in the gap. The postcrossing B ring is brighter on the west ansa, while the postcrossing A ring is brighter on the east. 1995 S 3 (Bosh and Rivkin 1996) is visible here, in orbit 5 on the east ansa in the B ring, moving closer to Saturn with increasing time. Although not evident in this graph, the precrossing B ring is considerably brighter on the east. The darker F ring region on the west corresponds to the F ring’s pericenter.
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TABLE I Revised Times of Ring-Plane Crossing Events
thickness include the 400-m warp of the Laplace plane due to torques from the Sun and Saturn’s satellites (Burns et al. 1979), the 1.4-km full amplitude of the Mimas 5:3 bending wave (Shu et al. 1983), and the possible presence of 1-km sized bodies in the rings (He´non 1981) or embedded satellites. Note that the Mimas 5:3 bending wave cannot account for the observed thickness for all ring regions because the equivalent thickness of the outer A ring and F ring remains approximately constant although it includes no contribution from this wave. Perhaps the most convincing argument for the equivalent thickness not representing the actual physical thickness of the rings is the evidence from a Voyager occultation that the ring is no more than 200 m thick (Lane et al. 1982). The stellar signal decreases very rapidly at the sharp edges of ring features, as would be the case only for a very thin ring. Of course, this is the thickness only at ring edges. However, Borderies et al. (1982) have noted a ring is likely to be thicker at a ring edge than interior to this edge due to an enhanced velocity dispersion caused by the confinement mechanism. Based on these observations, it is likely that the observed edge-on brightness and derived equivalent thickness are caused by the global warping of the rings and the presence of bending waves in the rings. Embedded satellites would not be the cause of this thickness because their effect would be localized and satellites larger than p10 km would be detected in this data set (Bosh and Rivkin 1996). A swarm of smaller satellites may account for the additional brightness, but they would be no greater than 1–2 km in radius; we would probably call them ‘‘large ring particles’’ rather than ‘‘satellites.’’
ACKNOWLEDGMENTS We thank A. Lubenow and A. Storrs of the Space Telescope Science Institute for their invaluable assistance in planning and scheduling these observations. P. Nicholson provided numerous sanity checks of the observation parameters. A. Watson was frequently called upon to explain the workings of the WFPC2. We thank the High Speed Photometer Instrument Team for allowing 10 orbits of the remaining GTO time to be used for this project; W. Baum and P. K. Seidelmann for helpful discussions about previous ring-plane crossings; and D. Hamilton and an anonymous referee for critical review of this paper. This work was supported by HSP GTO Grant NASG5-1613. A.S.R. was supported by NASA Grant NAGW-1912.
REFERENCES Borderies, N., P. Goldreich, and S. Tremaine 1982. Sharp edges of planetary rings. Nature 299, 209–211. Bosh, A. S. 1994. Stellar Occultation Studies of Saturn’s Rings with the Hubble Space Telescope. Ph.D. thesis, Massachusetts Institute of Technology. Bosh, A. S., and A. S. Rivkin 1996. Observations of Saturn’s inner satellites during the May 1995 ring-plane crossing. Science 272, 518– 521. Brahic, A., and B. Sicardy 1981. Apparent thickness of Saturn’s rings. Nature 289, 447–450. Burns, J. A., P. Hamill, J. N. Cuzzi, and R. H. Durisen 1979. On the ‘‘thickness’’ of Saturn’s rings caused by satellite and solar perturbations and by planetary precession. Astron. J. 84, 1783–1801. Burrows, C. J. 1995. Wide Field and Planetary Camera 2 Instrument Handbook. Dollfus, A. 1979. Photometric determination of the Saturn rings’ thickness. Astron. Astrophys. 75, 204–206. French, R. G., P. D. Nicholson, M. L. Cooke, J. L. Elliot, K. Matthews, O. Perkovic, E. Tollestrup, P. Harvey, N. J. Chanover, M. A. Clark, E. W. Dunham, W. Forrest, J. Harrington, J. Pipher, A. Barucci, A. Brahic, C. Ferrari, I. Grenier, F. Roques, B. Sicardy, and M. Arndt 1993. Geometry of the Saturn system from the 3 July 1989 occultation of 28 Sgr and Voyager observations. Icarus 103, 163–214. Hanel, R. A., B. J. Conrath, D. E. Jennings, and R. E. Samuelson 1992. Exploration of the Solar System by Infrared Remote Sensing. Cambridge Univ. Press, Cambridge. He´non, M. 1981. A simple model of Saturn’s rings. Nature 293, 33–35. Holtzman, J., J. J. Hester, S. Casertano, J. T. Trauger, A. M. Watson, G. E. Ballester, C. J. Burrows, J. T. Clarke, D. Crisp, R. W. Evans, J. S. Gallagher III, R. E. Griffiths, J. G. Hoessel, L. D. Matthews, J. R. Mould, P. A. Scowen, K. R. Stapelfeldt, and J. A. Westphal 1995. The performance and calibration of WFPC2 on the Hubble Space Telescope. Publ. Astron. Soc. Pacific 107, 156–178. Lane, A. L., C. W. Hord, R. A. West, L. W. Esposito, D. L. Coffeen, M. Sato, K. E. Simmons, R. B. Pomphrey, and R. B. Morris 1982.
NOTE Photopolarimetry from Voyager 2: Preliminary results on Saturn, Titan, and the rings. Science 215, 537–543. Nicholson, P. D., M. R. Showalter, L. Dones, R. G. French, S. M. Larson, J. J. Lissauer, C. A. McGhee, P. Seitzer, B. Sicardy, and G. E. Danielson 1996. Observations of Saturn’s ring-plane crossings in August and November 1995. Science 272, 509–515. Rybicki, G. B., and A. P. Lightman 1979. Radiative Processes in Astrophysics. Wiley, New York.
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Shu, F. H., J. N. Cuzzi, and J. J. Lissauer 1983. Bending waves in Saturn’s rings. Icarus 53, 185–206. Sicardy, B., J. Lecacheux, P. Laques, R. Despiau, and A. Auge 1982. Apparent thickness and scattering properties of Saturn’s rings from March 1980 observations. Astron. Astrophys. 108, 296–305. Wehrli, C. 1986. World Climate Research Programme Publication Series No. 7, WMO ITD-No. 149, pp 119–126.
129, 555–561 (1997) IS975767
ARTICLE NO.
NOTE Saturn Ring-Plane Crossing, May 1995: Pole Precession and Ring Thickness1 Amanda S. Bosh Lowell Observatory, Flagstaff, Arizona 86001-4499 E-mail: [email protected]
Andrew S. Rivkin Lowell Observatory, Flagstaff, Arizona 86001 and University of Arizona/Lunar and Planetary Lab, Tucson, AZ
Jeffrey W. Percival Space Astronomy Laboratory, University of Wisconsin, Madison, Wisconsin 53706
MaryJane Taylor Department of Physics and Engineering, Loras College, Dubuque, Iowa 52004
and G. Wayne van Citters Division of Astronomical Sciences, National Science Foundation, Arlington, Virginia 22230 Received October 9, 1995; revised May 15, 1997
On 22 May 1995, as the Earth crossed through Saturn’s ringplane, we used the Wide Field Planetary Camera 2 on the Hubble Space Telescope to image Saturn and its rings for 10 hr centered near the predicted time of ring-plane crossing. By performing photometry on the rings, we find that the time of ring-plane crossing is later than the nominal predicted time, suggesting that Saturn’s pole is precessing at a rate somewhat slower than is predicted for a rigid body under the influence of torques from the Sun and Saturn’s satellites and/or that Saturn’s pole position is different from the nominal position. We determine the equivalent thickness of the rings to be 1.4 6 0.1 km, and find that the measured value corresponds to the amplitude of perturbations from the Laplace plane warp and satellite-induced bending waves. 1997 Academic Press
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Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA Contract NAS5-26555.
Ring-plane crossings occur when a planet’s ring-plane sweeps over the Earth or Sun. For Saturn these crossings occur roughly every 15 years, twice per Saturn orbit around the Sun. Observations made during a ringplane crossing have the advantage of reduced scattered light from the rings, allowing study of material normally obscured by Saturn’s bright rings: faint inner satellites and the tenuous other E ring, for example. During the two most recent ring-plane crossings in 1966 and 1980, five satellites were discovered (Janus, Epimetheus, Telesto, Calypso, and Helene), as was Saturn’s tenuous outer E ring. During the 1995–1996 ringplane crossing season, Saturn’s ring plane swept across the Earth on three dates: 22 May 1996, 10 August 1995, and 11 February 1996; it crossed the Sun once on 17–21 November 1995. The Earth crosses Saturn’s ringplane three times due to the differing inclinations of the Earth’s and Saturn’s orbits and the alignment of their ascending nodes. In other ring-plane crossing seasons (such as the next two), there is only one Earth crossing. At the moment of ring-plane crossing, we view the thin edge of the rings (Fig. 1). Even then, the rings still reflect light from the edge and so are visible from Earth; they never disappear completely. In previous observations of ring-plane crossing, ground-based observers imaged Saturn for several days before and after the crossing (Dollfus 1979, Brahic and Sicardy 1981, Sicardy et al. 1982). The time of minimum light from the rings and thus the time of ring-plane crossing was determined from analyses of these images. The residual flux at this time was used to calculate the thickness of the rings. During the passage of 1966, the
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FIG. 1. View of Saturn and its rings near minimum ring brightness. The signal in the boxes on the right (west) of this image have been multiplied by a factor of 25 to make the faint ring more visible. From top to bottom, the boxes are from HST orbits 3, 4, and 5, and were taken approximately ˚ methane band. In the top panel to the west, Janus is faintly visible; Enceladus is 96 min apart. These images are 7-sec exposures in the 8900-A seen in the middle panel. Rhea is easily visible, east of Saturn.
crossing time was determined with an accuracy of 2 hr, and the ring thickness was estimated to be 2.4 6 1.3 km (Dollfus 1979). During the ring-plane crossing of 1980, the ring thickness was determined to be 1.1120.9 0.5 km (Sicardy et al. 1982); due to sparse data in 1980, the crossing time was not determined.
I. WFPC2 DATA During the May 1995 ring-plane crossing event, we used the Wide Field Planetary Camera 2 (Burrows 1995) aboard the Hubble Space Telescope (HST) to observe Saturn and its rings near crossing time. The goals of this set of observations were (1) to refine the time of ring-plane crossing and therefore determine the pole precession rate, (2) to find the residual flux at the time of ring-plane crossing to be used to determine the thickness of the rings, and (3) to study Saturn’s small inner satellites. We discuss results on the timing and ring thickness here; satellite results are presented in a separate paper (Bosh and Rivkin 1996). To accomplish these goals, we required data with sufficient signal-tonoise ratio (S/N) to be able to confidently detect the rings even at their minimum light. The improved image quality of WFPC2 would provide both high spatial resolution (approximately 725 km per pixel at Saturn and a point-spread function that includes 50% of the enclosed light in a circle of radius 1 pixel) and high S/N as a result. With a surface brightness of about 7 mag per square arcsec in the visible, Saturn is not a faint ˚ methane filter—FQCH4N-D in target. Therefore we used the 8915-A Table 3.2 of Burrows (1995)—which provided better contrast between Saturn and its rings because Saturn’s reflectance at this wavelength is reduced. Observing parameters were chosen to maximize S/N in the ring at minimum brightness. The wide-field mode was chosen over the planetary mode because the increased pixel scale would provide higher S/N, and the wider field of view would hedge against possible centering difficulties; this was at the expense of undersampling the point-spread
function. The gain was chosen to be 7 electrons per data number (e2 /DN) for the lower read noise, which meant that the detector would saturate at lower light levels than with a gain of 14 e2 /DN. To reduce the amount of expected blooming of saturated charge along columns, the serial transfer registers of the CCD were kept running throughout the exposures (CLOCKS 5 YES). It was determined that all bright-object artifacts— blooming, spider diffraction spikes, ghost images, horizontal smear— would not fall on or near the rings. The integration time used was 400 sec: long enough to develop adequate signal over any read noise but still short enough to include three to four exposures per HST orbit (approximately 96 min). Multiple images per orbit allowed identification and removal of cosmic ray events and tracking of saturnian satellites. At least a few satellites were always superimposed on the rings, complicating the photometry. We required the observations to straddle the crossing time. The uncertainty in the time of ring-plane crossing (1s) was approximately 2 hr. This was due to a combination of uncertainty in the position of Saturn’s pole at the Voyager reference epoch (Bosh 1994) and uncertainty in the value of the pole precession (French et al. 1993). The predicted time of 5:14 UTC on 22 May 1995 was calculated for pole precession equal to its predicted rate. If precession were twice its predicted rate, the crossing time would move early by 82 min to 3:52 UTC; if precession were 0, the crossing time would move later by 82 min to 6:36 UTC. To compensate for this uncertainty in crossing time, we planned to image for 7 orbits of the HST (a total of 10 hr), centered on the predicted time of crossing. In this way, even if the crossing time changed by 1 hr, we would still have at least 2 orbits on either side of crossing. This was necessary to establish the rate of change of brightness of the rings and to determine the crossing time. In practice, we centered the observations at one full orbit later than the predicted time to avoid a conflict with HST scheduling activities—data for all these analyses were obtained between 1:49 and 11:55 UTC on 22 May 1995.
NOTE We began each observing window (defined by the HST orbit around the Earth) with 2 short 7-sec exposures intended for photometric and astrometric calibration and cosmic ray removal. These images were taken with Saturn and its rings centered in the flat region of wide-field chip 3 (WF3), using the methane filter set; this is near the WF3–FIX standard location for extended objects, but offset to move Saturn and its rings into the region where the response of the methane flat field is most constant. The WF3 images included the region out to 5 Saturn radii. Because all 4 of the WFPC2 chips were read out, the region from 5 to ˚ filter. These short 15 Saturn radii was included on WF2, with the 5462-A exposures were followed by 3 or 4 longer 400-sec exposures. This sequence of exposures achieved optimal orbit packing—along with overheads for the exposures, they filled the available time in each HST orbit. In the 7 orbits geared toward the science data, we obtained 14 short exposures and 27 long exposures. The data used in this analysis were the calibrated data frames provided by the Space Telescope Science Institute. These data were processed in the standard pipeline calibration (Burrows, 1995), including subtraction of bias level and dark counts, corrections for flat-field effects and analogto-digital conversion scaling, and marking known bad pixels. The photometry was not corrected for known small problems such as the pixellation effect (2%), optical distortion over the field (2% effect), or a charge transfer efficiency problem (at the intermediate background levels present here, this amounted to 1% across the rings) (Holtzman et al. 1995).
II. TIME OF RING-PLANE CROSSING We performed photometry on the rings by adding the signal in the calibrated data frames within an area 2 pixels (0.2 arcsec) wide and 8 pixels (0.8 arcsec) high, with the long direction of the box centered vertically on the rings. This box was rotated to be perpendicular to the ring plane; the angle for this rotation was determined by fitting to the known satellites visible on each frame for center, scale, and orientation. The value determined in this manner agreed well with the orientation information given in the data headers. This ‘‘rotated-box’’ photometry method accounted for fractional pixel area when a box boundary dissected a pixel. From this value was subtracted a ‘‘sky’’ value, determined by adding the signal in a 2 3 2 pixel area above and below the first box and scaled by pixel area. These boxes were moved down the rings at a 1pixel increment from F ring ansa, through the planet, to F ring ansa. We did not use an automatic routine to remove cosmic rays because these routines also had a tendency to remove portions of satellites and neighboring ring signal. Retaining cosmic rays did not introduce much spurious signal and the remainder of the data would work to cancel the effects of the cosmic rays. All pixels associated with saturated charge blooming near Saturn and with known satellites were not used in the analysis; the extent of these regions were determined by eye, with knowledge of the number of pixels covered by trailed satellites. No attempt was made to correct the signal levels in these pixels because satellites were often extended over more than 10 pixels, and ring brightness was not constant over that range. From this photometry method, we derived signal per linear pixel (along the rings) as a function of distance from Saturn and time (Fig. 2). To determine the time of ring-plane crossing, we averaged all the ring signal in each data frame (Fig. 3). We performed a weighted fit to these data with two simple linear functions, the negative slope corresponding to precrossing and the positive slope to postcrossing. The photometric errors were used in the weighting function. The intersection of these two lines gives the time of ring-plane crossing: 05:34 6 00:07 (3s) UTC on 22 May 1995. Thus the crossing occurred shortly after the last long exposure of HST orbit 3, while the HST was occulted by the Earth and not collecting data. As expected, the precrossing slope is negative and large because the brightness is decreasing rapidly as the lit side of Saturn’s rings becomes less visible. The postcrossing slope is positive and much
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shallower than precrossing as the brightness increases more slowly when we are looking at the unlit face of the rings. The minimum brightness of the rings was 304 6 25 (1s) DN per linear pixel in 400 sec, where the uncertainty is propagated from the fitted uncertainties in the parameters of the linear functions. The approximate magnitude is 16 per linear arcsec ˚ passband, uncorrected for distance or phase effects. The in the 8900-A minimum signal value includes contributions from both sunlight and Saturn-shine reflected off the thin edge of the rings and off bending waves or other vertical excursion of the rings. If the rings are warped (i.e., Laplace plane), then this value will also include signal from sunlight transmitted through the optically thin regions of the rings. The Saturnshine component of the minimum signal is expected to be small, due to the deep methane absorption feature at the wavelength used in this observation; we estimate that it contributes no more than 4% of the signal. If transmitted light were a significant part of the signal, we would expect its contribution to vary with ring location due to the dependence of projected area of the Cassini Division (for example) on distance from Saturn. However, the values of minimum signal show no clear trend with distance from Saturn, and the scatter in the values is only 7%. Therefore we can assume that the minimum signal values found here correspond almost entirely to sunlight reflected off the edge of the rings, to within the 1s errors quoted. As seen in Figs. 2 and 3, the rings did not darken and brighten uniformly. Precrossing, the B ring is brighter on the west ansa than on the east. Postcrossing, the C and A rings brighten more quickly on the east ansa than on the west. This asymmetry affects the derived crossing time slightly: for the B-ring region on the west ansa the time is 5:36, for the east ansa it is 5:32. Both times are within the quoted 3s error bar (7 min) of the derived time for all ring regions on both ansa. Brightness asymmetries were noticed by both Sicardy et al. (1982) during the 1980–1981 ringplane crossing and Nicholson et al. (1996) during the August 1995 crossing. Figure 2 represents a complicated situation because each ring region actually includes light from all rings exterior to the named ring due to their nearly edge-on configuration. Thus ‘‘C’’ includes light from the C, B, A, and F rings, ‘‘A’’ from the A and F rings, and ‘‘F’’ from just the F ring. We do not believe that the E or G rings contribute significantly to the residual flux because the signal level of the E ring away from the main rings is only 3% that of the minimum ring flux. The F ring is too thin to contribute a significant signal when away from ring-plane crossing, but near a crossing it dominates the signal. Ring signal extends out to the F ring region (Fig. 2). In addition, when photometry of just the F ring (the portion beyond the A ring) is performed, the equivalent thickness is 1.1 to 1.7 km. Clearly the F ring dominates the residual signal at minimum light. Therefore to achieve maximum S/N results, we adopt the timing and thickness results obtained by including all ring data from both ansae. What does a crossing time of 05:34 UTC mean for Saturn’s pole position and precession rate? With this one measurement of ring-plane crossing time, 20 min later than the predicted time, we cannot decouple the relative contributions of change in pole positions and change in precession rate from the predicted values for these quantities. To account for the entire difference in timing with a change in pole position would require an increase in its right ascension and/or declination by 2.0 6 0.7 arcsec. This is within the formal errors of the right ascension of the pole, but a factor of 3 larger than the formal error in the declination of the pole. To achieve the measured crossing time by changing only the precession rate, it would need to be 71% 6 10% of its predicted value. This agrees with work by Bosh (1994), who found from fitting several occultation chords spanning 13 years that the best fit value for pole precession was 55% 6 26% of the predicted value. As discussed in French et al. (1993), Saturn’s pole precession is expected to be a result of direct solar torque on the oblate figure of Saturn (and thus depends on the planet’s gravitational harmonics, J2n , which describe its departure from sphericity) and of solar torque on Saturn’s satellites (mainly Titan) transferred to Saturn through its oblate figure. Thus any
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FIG. 2. Evolution of ring brightness with time and ring location. Brightness as a function of projected distance from Saturn is plotted for both ring extensions, then folded back to align ring areas in the east and west ansae. Therefore, the top half of the plot depicts the east ansa with time increasing downward and the bottom half of the plot depicts the west ansa with time increasing upward. In this way we compare the postcrossing brightness evolution. Areas in black are earth occultations (when Saturn was blocked from the HST’s view by the Earth), or known satellites or cosmic ray hits removed from the rings. The color bar at the bottom of the figure shows the colors that correspond to intensity levels: black for no
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NOTE
III. EQUIVALENT THICKNESS OF THE RINGS The geometric albedo p of an extended body can be computed as the ratio of reflected (I ) to incident specific intensities at the body, at zero phase angle a (Rybicki and Lightman 1979) p5
I(a 5 0) . Fs /D2
(1)
The incident solar flux at the body is fFs /D2, where D is the heliocentric distance of the body in AU. The geometric albedo is also known as I/F (Hanel et al. 1992), and we will use this designation here. In terms of C, measured counts per pixel on the image, the reflected intensity is given by
FIG. 3. The residual ring signal per linear pixel (expressed as equivalent thickness for geometric albedo of unity) is plotted against time, for several different ring areas. Circular symbols represent values from the west ansa; squares, the east ansa. Filled symbols represent photometry from all visible rings (C, B, A, and F), open symbols indicate values for signal from the B ring region. Error bars (1s) are included but in most cases are smaller than the symbols used to represent data points. These data are fit with two lines, and the intersection of these lines is the time of ring-plane crossing. The steep slope on the left represents the dimming of the rings as the reflecting area becomes less visible as seen from Earth. After the Earth crosses the ring-plane, we are seeing the unlit face of the rings. This face is not illuminated directly by sunlight but instead light is transmitted through the ring plane from the lit face after multiple scatterings. This is the brightening on the right, with its much shallower slope. In this figure, asymmetry is visible in the B ring region: before crossing, the west ansa of the B ring is much brighter than the east. This assymetry disappears within 2 hr of crossing. The brightness evolution of the sum of all rings is more symmetric because the A ring compensates for the differences by being brighter in the east than the west, exactly out of phase with the B ring.
differences between measured and calculated precession rates would be caused by either a different value of one of the input parameters, or an incomplete application of the precession theory. The current uncertainty in the value of J2 changes the precession rate by only 0.04% (Bosh 1994). Theoretical problems may include the departure of Saturn from the rigid body that was assumed in the calculations. In Table I we list revised times for the ring-plane crossing events in 1995–1996. These times are insensitive to the difference between changing the reference pole position or the pole precession rate; either leads to the same determination of event time for all events. Therefore, data from later events this season will not help to decouple the errors in pole position and precession rate. As noted by Nicholson et al. (1996), the observed crossing times in August differed significantly between east and west ansae (Table I), straddling the time predicted here. Additional study of all data sets from the 1995–1996 crossing season is required to understand ring behavior close to a crossing.
I(a 5 0) 5
Cb , VDt
(2)
where V is the angle subtended by one pixel (ster), Dt is the exposure time for the frame (sec), and b is the conversion factor between counts ˚ 21. We adopt a value for b of 1.953 3 10216 for WF3, and erg cm22 A from Nicholson et al. (1996). To calculate the incident solar intensity, we first set Sl ; fFs to avoid confusion over factors of f. Then, the incident solar intensity Fs /D2 is Sl /(fD2). Combining Eqs. (1) and (2), we achieve an expression for geometric albedo I CbfD2 5 . F V Dt Sl
(3)
˚ (the mean wavelength of the The solar flux (Sl) at 1 AU and 8896.5 A ˚ 21 (Wehrli 1986). Equation (3) gives filter used) is 94.11 erg sec21 cm22 A the relation for geometric albedo of an area unit of 1 WF3 pixel at Saturn. However, we are interested in deriving the equivalent thickness of the rings from the photometric measurements of these data. To do this, we note that the angle subtended by the rings within one pixel, V, is equal to hl, where h is the thickness of the ring (in radians) and l is the length of a pixel (0.09968 arcsec 5 4.8278 3 1027 radians). Because the photometry was performed with the rotated-box method, we do not need to take into account the angle between the ring-plane projection and pixel axes. If we then assume a geometric albedo of unity for the ring material (feasible for Saturn’s high-albedo, water–ice rings), the equation for ring thickness (in km) becomes h5
CbfD2R , l Dt Sl
(4)
for a given geocentric distance R. We use the minimum ring signal per linear pixel to produce an estimate of the ring thickness and thus find a photometric thickness of 1.43 6 0.09 km (3s). This is the equivalent thickness of the rings, or the projection of the rings onto a plane perpendicular to our line of sight and to the ring plane. The equivalent thickness is not necessarily the same as the physical thickness of the rings (the local thickness of a ring region). Effects that cause the equivalent thickness to be greater than the physical
signal, red for intermediate signal, and light yellow to white for high signal. Several features are clearly evident: the C ring becomes bright shortly after ring-plane crossing (between HST orbits 3 and 4, marked ‘‘RPX’’) on both the east and west ansae, although the east ansa is much brighter at the end of the data acquisition interval (orbit 7). The Cassini Division also stands out clearly; the brightening is greatest at the inner edge of the Cassini Division because this is the location of maximum projected area in the gap. The postcrossing B ring is brighter on the west ansa, while the postcrossing A ring is brighter on the east. 1995 S 3 (Bosh and Rivkin 1996) is visible here, in orbit 5 on the east ansa in the B ring, moving closer to Saturn with increasing time. Although not evident in this graph, the precrossing B ring is considerably brighter on the east. The darker F ring region on the west corresponds to the F ring’s pericenter.
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TABLE I Revised Times of Ring-Plane Crossing Events
thickness include the 400-m warp of the Laplace plane due to torques from the Sun and Saturn’s satellites (Burns et al. 1979), the 1.4-km full amplitude of the Mimas 5:3 bending wave (Shu et al. 1983), and the possible presence of 1-km sized bodies in the rings (He´non 1981) or embedded satellites. Note that the Mimas 5:3 bending wave cannot account for the observed thickness for all ring regions because the equivalent thickness of the outer A ring and F ring remains approximately constant although it includes no contribution from this wave. Perhaps the most convincing argument for the equivalent thickness not representing the actual physical thickness of the rings is the evidence from a Voyager occultation that the ring is no more than 200 m thick (Lane et al. 1982). The stellar signal decreases very rapidly at the sharp edges of ring features, as would be the case only for a very thin ring. Of course, this is the thickness only at ring edges. However, Borderies et al. (1982) have noted a ring is likely to be thicker at a ring edge than interior to this edge due to an enhanced velocity dispersion caused by the confinement mechanism. Based on these observations, it is likely that the observed edge-on brightness and derived equivalent thickness are caused by the global warping of the rings and the presence of bending waves in the rings. Embedded satellites would not be the cause of this thickness because their effect would be localized and satellites larger than p10 km would be detected in this data set (Bosh and Rivkin 1996). A swarm of smaller satellites may account for the additional brightness, but they would be no greater than 1–2 km in radius; we would probably call them ‘‘large ring particles’’ rather than ‘‘satellites.’’
ACKNOWLEDGMENTS We thank A. Lubenow and A. Storrs of the Space Telescope Science Institute for their invaluable assistance in planning and scheduling these observations. P. Nicholson provided numerous sanity checks of the observation parameters. A. Watson was frequently called upon to explain the workings of the WFPC2. We thank the High Speed Photometer Instrument Team for allowing 10 orbits of the remaining GTO time to be used for this project; W. Baum and P. K. Seidelmann for helpful discussions about previous ring-plane crossings; and D. Hamilton and an anonymous referee for critical review of this paper. This work was supported by HSP GTO Grant NASG5-1613. A.S.R. was supported by NASA Grant NAGW-1912.
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