As far as Joe's work is concerned, let's look at the sources he's used:

1) Albedo maps of Enceladus based on officially released PDS Voyager data (created by Steve Albers). No problems there, though, of course, Albers would have to be cited for his contribution.

2) The existence of ice-particle plumes. Details of the plumes' origins and trajectories are not "officially" available, but their existence is official. So, distribution of plumes observed emanating from the south polar region will have to wait for official PDS release.

3) The existence and location of the tiger stripes. These features were hinted at in Voyager imaging, but are not well enough defined in the Voyager data to locate them well. Correlations between plume sources and tiger stripes will have to wait for the PDS release.

4) The simulator used to predict the trajectories of plume particles. Any peer review will require enough detail on the constraints and limitations of the simulation techniques to provide any kind of confidence in the validity of Joe's findings. This might require more information about the simulation programming than Joe has proprietary rights to provide.

So, it would seem like Joe could write up his paper, leaving blanks for the identifiers he will get from the PDS release, but assuming that the PDS data will not vary significantly from the data he already has at his disposal. As soon as the data is released to the PDS, he can verify it as it relates to his paper, insert the appropriate identifications in the placeholders he's left, and submit it.

However, he's going to have to deal with 4) above, regardless. If the calculations performed by the simulation software are proprietary and he can't demonstrate their validity (and state error margins), then no matter how valid his conclusions are, it'll be hard to get them published...

-the other Doug

The albedo map is by Anne Verbiscer, photometrically calibrated using Voyager and HST data. I used the Albers map to get the stripe locations. The Verbiscer map was published in 1994. More recently (Jan. 2005) she has published another Icarus paper The opposition surge of Enceladus: HST observations 338–1022 nm which concludes that the albedos need to be increased about 20% from previous values.



I guess we were posting at the same time & you didn't see my post about the prediction program being suspect, but you hit the nail on the head! I reran the sim overnight with the latest "fix" and while the results are quite a bit different, maybe it's not a total washout.

Here's the new distribution map I get:



So there's still a pattern, just not as distinct. I suppose that this result is suspect too, as there may be other problems with the sim. It would be nice if someone could independently try to replicate this simulation, to compare results.

I'm not sure what you're getting at about proprietary rights to the software though. I just programmed the thing from scratch in C--using the SPICE library which is also open source. I could post the source files if anyone's interested.

As for correlation with the Verbiscer albedo map, with the new distribution it's not nearly so clear. Amazing how a program bug matched so well by coincidence! However there may still be a correlation. Here's the result:




It's maybe hard to see the colored dots above, so here's the map with all dots bright yellow:



Anyway, that's where it stands. Again, I'd love to see someone else try this approach & see how it matches up.

I for one would be interested in the source, if you're really willing to provide it openly. Is it a very complex piece of work or is it "manageable"? You could send it to me via e-mail if it'd be more convenient that way.
And no, I wouldn't rip you off by changing the code a bit and saying it was all my work. Just in case you're wondering

Okay, Joe -- I wasn't sure whether you were using your own trajectory simulator or whether you were using some third-party software. If it's your own code, you're fine to publish -- but you will, indeed, need to provide enough detail about the code to generate confidence in its trajectory predictions.

I guess I was becoming somewhat confused between your trajectory sims and those run by some others using the freeware Orbiter program. Sorry 'bout that.

-the other Doug

This is extremely interesting and I for one would be interested in seeing the source, especially since I have also been using the SPICE library.

BTW wouldn't it be fairly easy to use this program with some modifications to simulate the appearance (or at least the density distribution) of the plumes as seen from Cassini when it imaged the plumes ? I once wrote a program to simulate the appearance of Io's plumes with somewhat interesting results - it was far more simple than this one (I didn't need to take Jupiter's gravity into account for instance) but visually the output was interesting (parts of the attached image are 'overexposed'):

Joe, its just a guess but it looks like you might not be allowing for the oblateness of Saturn. You have to modify the Newtonian equation of gravity using (at least) the first two zonal gravitational harmonics, J2 and J4. I know people who also use J6 and C22 (at least I think its C22, it could be one of the other C's).

Essentially the effect of a planet,s oblateness (non sphericity) is to increase the mean motion of orbiting objects (compared to a point mass model) and adds precession to elliptical orbits e.g. at the F ring the pericentre precesses by ~2.7 deg day.

sorry that should be "first two even zonal gravitational harmonics, J2 and J4."

Thanks--I'll look into doing that as with a super accurate simulation maybe even the development of the E-ring could be modeled. If I had a supercomputer cluster that is!

As it is though I modified the existing code to integrate both the particle set and Enceladus using the same (point mass) method so that each would be treated the same way & cleaned up the code since several people here have expressed interest in seeing it. And guess what--the original result stands & is perhaps even strengthened! It was my test program, casting doubt on the results, that was in error. The code now passes any test I have thought of and clearly shows the correlation between the predicted particle distribution and the Verbiscer albedo map.

I guess with all the attention here and mini-controversy about using Cassini data, I was a bit too hasty in reviewing the code. In any case, the bottom line is that I stand by the original result, and offer the code here for anyone to review:

Plume simulation code, 340K zip file

Here's the correlation with the Verbiscer map, plotting the impact locations of 200,000 simulated particles coming from the three tiger stripes (coded red, green, blue):





The match is quite remarkable in some areas.

Here's the south polar view on the Albers map:



I'm currently trying a sim such as Jason suggested, using random plume locations in the south polar region rather than the specific locations of the tiger stripes. I guess that would be of general interest, and not rely on Cassini-derived data so much. So far it looks like the general pattern is more or less the same. If so, a remarkable coincidence that the tiger stripes themselves are lined up the the two northward streams of particles.

Wonderful! Peer review at this level. It looks as though your observations and the model are holding up well.

One idea: Using the albedo features and the muting of the landscape I wonder if you could model a reverse-trajectory from the supposed impact points back to their source and "predict" the linear plume sources (tiger stripes)? There are a lot of variables and it might not work.

--Bill

The "backtesting" tack may also be useful in finding the sources for the Albedo features in the Northern hemisphere.

Frankly, I don't see how you could backtrace the impacts to their origin. There's no information "preserved" when the particle impacts: you'd need azimuth and elevation angles and particle speed for starters.
Otherwise you have no idea whether the particle came along a short trajectory from the immediate neighborhood or was kicked up from the opposite side of the moon.

You're right, without knowing anything about the particle trajectory there is no way to trace it back.

--Bill

I suppose a conclusion might be reached if the overall pattern changed based on whether the plumes were coming from defined stripes vs. from generally all over the south pole region. However, I ran the sim that Jason suggested--with particles coming from the south pole generally--and there is not much difference to the impact map. Here's the result of 200,000 particles from the area between 75S and 90S latitude:



For comparison here is the map based on the tiger stripes, this time with all points colored red:



Not much difference there.

That is a good datapoint. It seems that the Size and shape of the impact zone is more a function of the "gravitational harmonics" and is not strongly influenced by the number and characteristics of the plumes. This is good because it means that the plumes can change over time without changing the impact area. It is better that it works with generic plumes in a general area without referring to specific fracture systems.

You have done some impressive work on this.

--Bill

Very nice. Still, interesting that it predicts particle fallout along 30 and 210.