Once again I’ve been doing more research than actual creative work. Don’t tell the boss. As usual, Cornell’s arxiv.org site dominated my research. Also, as usual, the scattered nature of my research mirrors the scattered nature of my brain. So it goes…
On the other hand, in my searches of the net I have found another reliable source for e-prints of useful scholarly articles within my, sometimes odd, fields of interest. The SAO/NASA Astrophysics Data System(aka ADS) is often a godsend.
At one point, I was looking for an article called, “The Internal Composition of the Planets,” written by D.S Kothari in 1936. This was a reference from the readme file of the ever-popular starform program(available here, available and somewhat explained here, improved version here. I’ve been stealing little bits of that program for years(I don’t seem to be alone in that…), so I was hoping to better understand the rationale behind some of the algorithms that program uses. While I like Burdick’s starform and particularly like Jim Burrow’s StarGen, I have a few issues that led me to try figuring out my own methodology. The first simply is I wanted a better understanding of the real science behind the planets I was generating. Secondly, the existing accretion algorithms fail altogether to generate certain kinds of extrasolar planetary systems that we have discovered to be common since the algorithm was created. Notably, the epistellar gas giant. Most importantly to me, I wanted to be able to pass in my own stellar and planetary parameters and have the remaining parameters generated(for instance, start with a particular stellar mass and generate a system or assume the presence of a planet of a particular mass in the habitable zone and generate the environment for that planet). If I didn’t have some issues with accrete and its progeny, this blog likely wouldn’t exist or would at least be considerably different. But I digress…
With my current work on Yaccatrice, I have been very interested in the nature of satellite systems, particularly those of large gas giants. I wanted to do some research into the feasibility of a moon of roughly Earth-like size orbiting a planet of roughly Jupiter-like size in the habitable region of a small red dwarf star. I figured it was unlikely that all of these issues would be covered by any one article, but it was worth a look.
First off I found, “Post-Capture Evolution of Potentially Habitable Exomoons,” by Simon Porter and William Grundy(2011). This article appears to suggest that a gas giant can successfully capture and retain a planet of roughly Earth-like mass. It also leads me to believe that my assumption of a captured satellite taking up a nearly circular low-inclination orbit of about a day in length is plausible. On simulations based on the satellite of a planet of an M0 star of 0.47 Solar masses(larger than, but similar to Cintilla), and a Jupiter-sized planet(smaller than Sky Moon, but also similar), the information in Table 1 and Table 2 on page 4 indicates a survival rate of 23%(not great, but reasonable), and an orbital period of about a day. Not looking too bad for Yaccatrice. Not surprisingly, survival rates are higher for planets orbiting larger stars, although with longer orbital periods for the satellite. More surprising, at least to me, the higher survival rates for captured satellites of smaller gas giants. I’m not at all sure why the Neptune-sized planet seems to show a slightly higher survival rate and, as far as I can tell, the article doesn’t discuss this issue. Maybe the reason is obvious to an experienced astrophysicist?
It looks like tidal heating is so great for a short period that the moon’s surface might even be liquified. This might have some effect on the morphology of the surface(though what that might be after a few billion years, I have no idea), and pretty much assures that any life on the planet would have arisen after the capture event. On the whole this doesn’t change much as I pretty much assumed the capture event would be so catastrophic as to assure total extinction of life on the captured body in any case.
“The 1/1 resonance in Extrasolar Systems: Migration from planetary to satellite orbits,” by John Hadjidemetriou and George Voyatzis(2011) appears to look more at capture. Ultimately, after looking at this a bit, I had to give up and look over the conclusions. It seems to give a fairly low probability of capture, but I really don’t quite understand what this article is saying beyond a rudimentary level. I’ll stick to an optimistic assumption. Anyway, this seems to be discussing a three-body transition for a near co-orbital pair to a planet/satellite system. In the case of the Sky Moon/Yaccatrice system orbiting Cintilla, I was assuming that Sky Moon had an existing system of one or more satellites that were expelled by a momentum transfer event that led to the capture of Yaccatrice. It seems like, depending on the configuration of Sky Moon’s original satellite system and the way in which Sky Moon approached the original orbit of Yaccatrice, this could be a much higher-probability event. For my level of education in the subject, this was a much less useful article than the Porter/Grundy one, but it was tantalizing. I felt like I was right on the verge of understanding something really interesting, but I just never quite made the connection. Too bad, that.
“Pathways Towards Habitable Moons,” by D.M Kipping et al(2009) is a good introduction to the existing literature on the care and feeding of extrasolar moons. In the introduction there is a discussion of the likelihood of Earth-sized moons forming around gas giants(not great), and the possibility of Earth-sized planets being captured as stable satellites by gas giants(better). It goes on to a lengthy discussion as to methods for detecting moons of extrasolar planets and what kind of information can be gleaned by those methods. Some of the details are a little sketchy if you aren’t pretty math-inclined, but it’s just interesting to learn just how much information can be gleaned with the tools we now have. Exciting.
“Massive Satellites of Close-In Gas Giant Exoplanets,” by Timothy Cassidy, Rolando Mendez et al(2009), was written for the purpose of discussing satellites of “Hot Jupiters.” Since the kinds of planets I’m really interested are the kinds where I can get out and take a walk without a spacesuit. Still, I’ve found a few tidbits in the section on tidal dissipation. Formulas 12 and 13 on page 3 give an estimate for the maximum mass of a body which can maintain a stable satellite orbit. For Sky Moon, assuming a Q, or tidal dissipation function, of about 2 x 105, like Jupiter, this comes to about 3.6 x 1021 kilograms, or about 0.0006 Earth masses. Disappointing, but in the text it mentions that gas giant Q could be as high as 1013. After messing about a bit with the formula, I worked out that a planet a little bigger than Yaccatrice could maintain a stable orbit with a Q as low as 2 x 108. Guess what the tidal dissipation function is for Sky Moon? Another useful formula is equation 21 on page 6 for the effective temperature due to tidal heating.
The Q in this case is for the satellite. Assuming the satellite is a, “solid body,” similar to the Earth in structure, a Qs of about 10 is reasonable. I’ve yet to use this(time constraints), but it could be of interest.
Perhaps the more interesting result of looking over Cassidy et al(2009) has been hunting down some of its references. One thing I found, rather indirectly, was, “Q in the Solar System,” P. Goldreich and S. Soter(1966). This was a reference from the starform README which I’ve been hunting unsuccessfully for quite some time. While trying to search for tidal dissipation Q, it just sorta showed up. Yay! Apparently, the day length calculations for starform were based on this. I see that there is stuff in here for the Earth-Moon system, so for future work, I’ll look into this to see if I can refine my rotation period calculations.
I’ve come across a few other nice articles, I’m looking forward to sitting down with. “Formation of the Earth,” by George W. Wetherill(1990). Yeah, that George Wetherill! Okay, maybe that ain’t the kind of name you really want to drop at a cocktail party. Depending on just what sort of nerds you’re making bolshoyeh praz’navoon’yeh with… “How common are Earth-Moon planetary systems?,” by S. Elser et al(2011). “Planetesimals and satellitesimals: formation of the satellite systems,” by Ignacio Mosqueira et al(2009). “Tidal Dissipation In Rotating Solar-type Stars,” by G. I. Ogilvie and D. N. C. Lin(2006). “Stable satellites around extrasolar giant planets,”R. C. Domingos, O. C. Winter and T. Yokoyama.