Ring Radial Characteristics

Neptune is thirty times as far from the Sun as the Earth is. That translates to sunlight that is a scant l/900th as bright as sunlight at Earth, or something akin to late twilight on Earth. Combine with that the fact that Neptune's rings are inherently dark (as well as being optically thin) and the problem of imaging Neptune's rings becomes something like trying to image pieces of coal when the sole illumination is a full Moon. Because of the dust content of the rings, they become somewhat easier to see when back-lighted, so some of the best images of Neptune's rings come from phase angles (the angle between the Sun and the observer as seen from the target) of about 135°. Most of the images of the Neptune rings were shuttered either during approach to the planet, where the phase angle was about l5°, or during departure, where the phase angle was about 135°. Only a few images obtained about 6.5 hr before closest approach (phase angle ~8°) and 37 to 77min after closest approach (phase angle ^155°) were appreciably different from the approach and departure phase angles.

A table of the radial structure of the rings of Neptune was given earlier in Chapter 5 (Table 5.3). There are three continuous narrow rings (Adams, Le Verrier, and Arago), one faint and possibly intermittent narrow ring (which shares it orbit with the satellite Galatea), and two broad rings (Lassell and Galle). A radial scan of the measured brightness of the rings at 134° phase angle is shown in Figure 8.1 [3].

The radio science occultation experiment, which had yielded such a rich store of data for the Saturn and Uranus ring systems (no radio occultation of the Jupiter ring was attempted), yielded very little for the Neptune ring system. Tyler et al. [4] reported detecting no Neptune ring material down to the noise level of the radio signal, which corresponded to about 1% of the received signal strength for a radial resolution of 2 km. The team had three caveats on their non-detection: (a) only the Adams ring was probed on both the immerging and the emerging sides of Neptune and the Galle ring was not probed at all, (b) neither side probed the longitudes in the Adams ring that contained the denser ring arcs (see Section 8.3), (c) the radio data were affected by passage through Neptune's ionosphere, thus perhaps masking a weak ring signature.

The stellar occultation measurements of sigma Sagittarii occurred as Voyager 2 was inbound toward the planet, about 5 hr from closest approach. The occultation covered a range of radial distances from Neptune of 42,414 to 76,056 km. The lower end of this range is unfortunately at the outer edge of the Galle ring, but the upper end of the range is well outside the Adams ring. The Adams ring was detected by both the

Radius (km)

Figure 8.1. This plot of relative brightness versus radial distance was produced by Mark Showalter by radially scanning a wide-angle image (FDS 11412.51) of the rings taken at a phase angle of 135°. The data are azimuthally averaged to reduce image noise. The six rings of Neptune are clearly seen in the plot, which appears as fig. 3 of Porco et al. [1].

Radius (km)

Figure 8.1. This plot of relative brightness versus radial distance was produced by Mark Showalter by radially scanning a wide-angle image (FDS 11412.51) of the rings taken at a phase angle of 135°. The data are azimuthally averaged to reduce image noise. The six rings of Neptune are clearly seen in the plot, which appears as fig. 3 of Porco et al. [1].

photopolarimeter (with an effective wavelength of 0.26 micrometers) [5] and the ultraviolet spectrometer (with an effective wavelength of 0.11 micrometers) [6]. Both wavelengths are well below the range of visible light wavelengths in the far ultraviolet. The value of the radial distance depends somewhat on the inclination of the Adams ring, which is not well determined, but is close to 62,900 km, in reasonable agreement with the value of 62,932 given in Table 5.3.

At this point, let us pause for a moment to remind our reader of the concept of equivalent depth introduced in Chapter 7 in the discussion of the variable-width Uranus rings. Equivalent depth is basically the optical depth (mathematically corrected to vertical viewing) times the physical width (in kilometers) and is a measure of the total material in a cross-section of a ring. Optical depth (= optical thickness) is a measure of the amount of light absorbed in passage through a ring and is indicated as the natural logarithm of the ratio of the intensity of the incident light to that of the emerging light. In simple terms, a ring (or other semi-transparent sheet of material) is said to have an optical depth of 1 if the incident light is reduced by a factor of e (= 2.718). The optical depth is 2 if the reduction is a factor of e2 (= 7.389), and so forth. Vertical (or normalized) optical depth is the measured optical depth multiplied by the trigonometric sine of the viewing angle. (The viewing angle is the angle between the observing direction and the perpendicular to the ring plane.) Normalized optical depth is therefore an approximation of the optical depth of the rings for vertical illumination and viewing. In mathematical terms,

I = I0 e~r [or alternatively expressed as r = ln(I0/I)], where I0 is the incident light intensity, I is the emerging light intensity, e is the base of natural logarithms, ln is the natural logarithm, and r is the optical depth, rn = r sin B, where B is the viewing angle just described and rn is the normalized optical depth, and

A = Wrm where A is the equivalent depth and W is the physical width. For the rings of Uranus, equivalent depth tends to be relatively constant around the narrow rings, even when their physical widths vary. Equivalent depth is, in a sense, a measure of the amount of ring material in a cross-section of the ring.

Now back to our discussion of the stellar occultation measurements of the Neptune rings by Voyager 2. To reduce the noise in the data, the photopolarimeter, with a sampling interval of 1.5 km, was smoothed to an effective resolution of 5 km. The equivalent depth of the Adams ring as measured by the Voyager photopolarimeter [7] was determined to be 0.77 ± 0.13 km. The ultraviolet spectrometer, with a radial resolution of 2.3 km, measured an Adams ring equivalent depth [8] of 0.66 ± 0.12 km. The two numbers are statistically identical, an indication that there are few ring particles in a size range near 0.1-micrometer radius in that part of the Adams ring, which fortuitously corresponds to the leading edge of the Liberte arc within the Adams ring. The Liberte arc is much brighter than those portions of the Adams ring sampled by the radio occultation experiment (60° and 90° from the arc region); therefore, no conclusions can be drawn about the relative numbers of larger ring particles in the Adams ring.

The ultraviolet spectrometer detected no Neptune ring features other than the Adams ring. A statistical analysis of the photopolarimeter data [9] indicated that the Adams ring occultation was the only unambiguous non-random event detected during the occultation experiment. However, there is a slight dip in the starlight intensity near the radial distance of the Le Verrier ring, which may indicate a near detection of that ring. Otherwise, the most useful data on the radial positions of the six Neptune rings listed in Table 5.3 are those from the Voyager imaging data.

Beyond the rings seen by the imaging system, Voyager detected dust particles near the ring plane both inbound and outbound. The detections were made by the plasma wave [10] and planetary radio astronomy [11] investigations. The inbound equatorial crossing of Neptune was at a radial distance of 85,290 km and the outbound was at a radial distance of 103,950 km [12]. On the inbound leg, both investigations found a maximum in the numbers of dust particles at a radial distance of 85,400 km and a vertical height above the ring plane of +146 to +160 km. The numbers of particles dropped off smoothly above and below that point, reaching half the maximum number density at a distance of about ±140 km. The two investigations differed slightly in their derived numbers for the outbound ring crossing. The plasma wave investigation found the maximum numbers near a radial distance of 104,000 km and near a vertical distance of —948 km below Neptune's equatorial plane; the vertical width of the dust distribution was more than ±500 km at half maximum. The planetary radio astronomy investigation found a maximum at a slightly larger radial distance of 105,500 km and a little closer to Neptune's equator (—700 km); they found a much narrower dust distribution with a thickness of about ±115 km.

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