I got a question at Wikipedia regarding the geometric albedo of Enceladus. Verbiscer et al. 2005 reported that Enceladus geometric albedo at 555 nm was 1.41, greater than unity. This is much greater than the 0.99 reported in Verbiscer and Veverka 1994. The 0.99 figure was listed in Wikipedia until the release of the Porco et al. paper on Enceladus, which cited the Verbiscer et al. 2005 paper when mentioning the visual geometric albedo (1.4 in the Porco et al. paper).

So someone on Enceladus' wikipedia talk page has asked how can Enceladus have a visual geomtric albedo greater than 1. I thought I would direct the question here.

Opposition surge plus a very high albedo. Unity is the case of a lambertian surface.

Isn't 0.99 a better number then, since the opposition surge is a rather special case?

Well, visual geometric albedo is supposed to be at a phase angle of 0, so opposition surge is supposed to be included. It is included in the values for every other body, so to remain consistent, it should be included for Enceladus.

Maybe I said it ambiguously before:

VGA is the luminosity at a phase angle of zero (which includes the opposition surge) divided by the brightness of a Lambertian white body the same size at a phase angle of zero (which would have no opposition surge).

A dark body like Mars still has opposition surge, but is far below the brightness of a Lambertian white. Enceladus is close enough to white that the opposition surge puts it over unity.

We have a confusion here between types of albedo which depend on both how much is being reflected and in which direction it's being reflected and BOLOMETRIC Albedo. That's the fraction of energy incident on a surface that's being reflected. If you need to get really fussy, that fraction can vary with incidence angle of the illumination. Imagine a dusting of white snow on black paint... at very low incidence angles, most of the light would hit the snowflakes and a good fraction would be scattered, not absorbed.

Radiometry/Photometry/Polarimetry takes up entire textbooks and will drive most to drink and distraction. But you can get good science out of it.

It's also useful to keep in mind that a Lambert sphere exhibits more pronounced limb darkening than e.g. Enceladus.

EDIT: This is a highly misleading comment by me since the geometric albedo is the brightness at zero phase divided by the brightness of a Lambertian disk, not sphere - see Anne Verbiscer's comment below. I didn't read the preceding discussion properly before hitting reply in a hurry - Bjorn

During Saturn's most direct opposition surge (July 2005(?)) there was considerable discussion about how bright the opposition surge of the entire Saturn system was. I don't know whether to write this off as over-enthusiastic hype by astronomers; or was this truly a puzzling event? At the time, we discussed whether or not atmospheric Fressnel lensing and/or the very slight predicted contribution of GR were players in this 'amazing surge'.

Just to clarify, the VGA is the brightness at a phase angle of zero divided by the brightness of a Lambertian disk, not a
sphere, at a phase angle of zero. (So comparisons of limb-darkening on Enceladus to limb darkening on a Lambert sphere
are irrelevant when considering the geometric albedo since a disk does not have a limb.) Enceladus, like many icy satellites
(and unlike terrestrial snow and frost), is extremely back-scattering. Most of it's incident sunlight is reflected right back in
the direction from which it came.

As for the other saturnian satellites observed at "true" opposition in January 2005, Tethys also has a geometric
albedo well in excess of unity: 1.23. The geometric albedos of Mimas, Dione, and Rhea are all about 0.95.

Anne

I really should read threads like this one more carefully before hitting reply in a hurry - my previous reply was misleading to say the least.

Why the geometric albedo can be >1 is obvious when one considers that at any point on a Lambertian surface the incident light gets evenly scattered in all directions whereas for a strongly backscattering surface like Enceladus' there is a 'spike' of reflected light towards the lightsource.


There was absolutely nothing magical about this event (January 2005). What happened was simply that Saturn's phase angle dropped to almost exactly zero (not exactly zero since the Sun's angular size isn't zero ) at opposition since the Earth transited the Sun as seen from Saturn. Usually the phase angle isn't this close to zero when Saturn is at opposition as seen from Earth. Even a very small decrease in phase angle results in significant brightening of things like the rings. This is nicely illustrated in some of the Cassini images, e.g. this one.

Well, I for one thought the event was quite "magical"... when will you be able to look through a telescope and see the rings of Saturn look like this again? I received many emails during and after that night from amateur observers who were awestruck by just how startlingly bright the rings were. While Cassini can give us an "Opposition View" of a bright spot on the rings, from our vantage point 8.5 AU away, only Earth-bound telescopes can capture the entire ring system at true opposition. The image credit belongs to the Calar Alto Observatory and NASA.

(The answer to the question above is 2049, when the next central transit of the Earth across the solar disk (seen from Saturn) will occur. If you can't wait that long, there will be another transit in 2020, though it will not be a central one.)