Rotation of the eclipsing object

Objects in motion will continue on their course and direction unless influenced by an external source. The leading edge is being pulled back, or is colliding with some source. Maybe this is what is causing the center of the eclipse being brighter?

Hi! Anyway, I wonder what the shape of the theorized disk would be accoring to the dynamics that you'd expect in the eps Aur system. If you see artists' illustrations or schematic diagrams of eps Aur then the secondary is always (a far as I've seen) a nice, circular, rotation-symmetrical disk with a hole in the middle. But come on, with the disk extending so far into the system, the gravitational pull from the primary at the near side rim (as seen from the primary) must be like 3 times higher than on the far side rim if it were circular, if my math is right ==> tidal forces and tidal friction must be considerable, right? There would also be a gradient of radiation pressure and solar wind, friction with whatever material there might be in the orbital plane .... so what would the disk really look like if all those forces are taken into account? Still a circular disk ?? CS Heinz

Hi Heinz, I think the problem with your idea is you are not considering a couple of important points. First, the mass of the eclipsing body is very close to that of the F star (14 solar mass/15 solar mass). This means the eclipsing body will have significant gravitation effects itself that will tend to make it round. Consider the distance from the F star. Some 26 AU. While there may be distortions I think they would be minimal. Consider Jupiter. Jupiter is a giant gas planet with very very small mass compared to the eclipsing body and yet at its distance from the Sun is pretty round. There is also the fact that the disk is rotating. Smarter astronomers than me have described the eclipsing body as a round paving stone with a hole in the middle. Jeff Hopkins Phoenix Observatory Phoenix,Arizona USA phxjeff@hposoft.com

I get your point, but I don't think the analogy with Jupiter is a good one. The diameter of Jupiter is about 1.4E8 m The distance from the sun is about 7.8E11 m So basically, locally at Jupiter the Sun's gravitational field can be considered flat for all practical purposes. It's just a big fat sphere of gas free-falling to a distant sun. But for the Eps Aur secondary disk, the diamter is more like perhaps 17 AU the distance from the primary is 26 AU so in contrast to the Jupiter analogy, you can no longer assume the gravitational field from the primary as flat, there are gradients which I think should cause some tidal bulges that the disk is rotating thru... With this small (EDIT: well... big rather) ratio of disk size and distance from the primary, I think a simple shape like a circular disk will not do to make Mr. Newton and Mr Kepler happy, and I think this was also part of the scepticism that the disk theory met when it was proposed first (would the disk be stable at all??). But of course somebody must have made a simulation (all the basic masses and velocities are known IIRC), I just couldn't find a reference to such a simulation yet. Anyone? CS Heinz

Hi Heinz, These are good questions. Except for the eclipse campaign times, there is really little literature on the epsilon Aurigae system. The one paper that comes close to answering your queries is Lissaur et al. (1996ApJ...465..371L): "The epsilon Aurigae Secondary: A Hydrostatically Supported Disk". They consider the increased heating on the side of the disk that is closest to the primary, and include discussion on why the disk can't be far out of the orbital plane, but don't directly answer the question about tidal effects. Perhaps Dr. Bob knows of an appropriate reference? If not, I bet that this will be one of the tasks of his graduate student... Arne

Bikeman, As Arne alluded to above, Dr. Bob's graduate student (me), does have a few additional references that might be worth reading. For a nealry complete list of literature on Epsilon Aurgae, I suggest looking at ADS(http://adsabs.harvard.edu/abstract_service.html) and typing "eps aur" into the title search field. At the moment over 200 items are listed.

The paper Arne mentions above (http://adsabs.harvard.edu/abs/1996ApJ...465..371L) does address the heating of material along the primary-facing edge of the disk and is well worth a read. But to address your question directly: the model of the secondary object is often thought to be a nice smooth disk as a first-order approximation. Our schematic representations of the system are an effort to quickly convey the important information like the tilt of the disk or the aspect ratio of the disk so that others can quickly visualize the system. For more detailed representations we turn to artists. Our artists have been attempting to render the disk with as much scientific accuracy as possible and therefore are very limited in the embellishments they can employ. I talk with at least one artists per week as to what they can do to improve their interpretation while maintaining the accuracy of their work.

I'll openly acknowledge that the disk probably is not smooth, flat, perfectly circular, and with a nice round hole in the middle, but when you scientifically model (i.e. simulate) an object, you need somewhere to start for which the “ideal disk” depicted so often is well-suited.

Let's first talk about how much tidal distortion the disk experiences and see if a perfectly circular disk is appropriate. I'll start by saying that the gravity that holds the disk in-place is dominated by the object(s) inside of the disk instead of the primary star and provide some clarification below:

If we adopt the high-mass “best model” of the system, the primary is about 15 solar masses and the object(s) inside of the disk is nearly the same (I'll assume it's 14 solar masses). At this point because the two masses are so close to being equal, the primary factor in gravitational effects are distance but we'll include mass in the calculation just for fun. Let's do a quick estimation on the gravitational acceleration (http://en.wikipedia.org/wiki/Gravitational_acceleration) experienced on the edge of the disk that is closest to the F-supergiant:

From the F-supergiant, we have a distance of ~20 AU to the edge of the disk. Doing the math, we find the acceleration due to gravity is ~0.0375 * G (where I have suppressed the units because I'll be taking a ratio in a moment in which case the units cancel). As for the distance to the edge of the disk from the center, we have ~7 AU. In this case, we have an acceleration due to gravity of 0.287 * G. Taking the ratio of Disk_Acceleration/Primary_Acceleration we find the acceleration due to the disk center object is 7.61 times more than the acceleration from the primary. So even at its strongest, the acceleration due to gravity of the primary star is dwarfed by the gravity from the object(s) inside of the disk (not to mention the gravity of the disk itself, but that would require more mathematics than can be easily represented on this forum. If we take these numbers at face value (I.e. without considering the self-gravitation of the disk), the amount of distortion would be less than 8% of one disk radii on the primary-facing side of the disk. Given that the distortion would ideally smoothly increase it would be difficult to depict an 8% distortion in artwork and have it be noticeable.

As for the disk being smooth and flat, I did read somewhere that the disk is likely to be warped. I don't remember the full argument, but the artist in Sky and Telescope (from which our banner is derived) did an excellent job showing that the disk isn't going to be smooth.

You are quite right to point out that there will be a difference in radiation pressure across the disk; however the effects should be more-or-less symmetric because we have no evidence to indicate that the primary has non-radially-symmetric wind. Because we don't know the exact composition of the disk, we can't comment on the cross-sectional area of the particles that make up the disk and therefore cannot comment on how much the disk will be distorted by radiation pressure. One thing we can say is that the ultraviolet radiation from the primary star may be the cause of Carbon Monoxide (CO) being seen in the spectrum. I suspect that the primary-facing side of the disk has a wider CO-based flared edge that gradually tapers downward as you move away from the primary-facing side. There is also evidence that this CO cloud trails behind the disk a little, but most artwork tends not to emphasize the trailing edge of the disk. I hope that helped answer some of your questions.

Actually that helps clarify some of what I have been reading from other ereferences. The papers that you guys are linking to do need to be clarified for those of us unused to the lingo the pros use. I have understood enough of what was written therin but there is much I did not fully understand, still don't for some of it, but I think I have enough to get the general idea. Thank you for explaining in lay terms. :) Can we get a single document that explains the situation in brief but still fully enough to get us up to speed? Then we can ease our way into the more technical parts as we learn. This learning curve is a bit daunting for many of us, as much of the terminology is quite confusing. Thank you for your time.

Thanks very much, I guess my mistake was to forget that the secondary is really massive. Well, there's nothing like actually doing the math, so with your parameters I had octave make a contour-plot of the acceleration in the system (the primary is on the coordinate origin) and the scale is by AUs. So if the iso-contours of the acceleration near 20 AU is any good to approximate the disk shape .... it's really quite circular ! Thanks again Heinz

Richard, I too agree that the jargon that we use can often be confusing and it is one of my tasks to help clarify the language and process used in astrophysics. The learning curve, as you mention, can be quite steep and fairly discouraging for most, but I really do admire those who dive into the subject and are willing to learn.

My talk that I gave at Adler (once it makes it online) might clarify a majority of the question as to why we think there is a disk in the system. Now that we have NSF funding, I suspect things will progress much more quickly than it has in the last six or so weeks and the videos might make it online soon.

I do plan to write a document that describes the Epsilon Aurigae system. More than likely it will come out in several parts each focusing on a particular observational technique. I'll reference historical data and even include some state-of-the art items in there too. Unfortunately, I have my Ph.D. qualification exam coming up in a few weeks and therefore need to dedicate my time to studying. After that is done, I'll be posting content to the main portion of Citizen Sky's website.

Brian

Hi Brian, To get back to the original question ;-) Do the observed asymetries in the KI line RV and EW at ingresscompared toegress tell us anything about the eclipsing body or are they considered to be just related to the orbital parametersand geometry of the system relative to us? Thanks Robin

Heintz, I am quite pleased to see another gnuPlot user and I have to say that you did a very good job. Although my acceleration argument demonstrates that the mass of the disk will dominate, the real diagnostic tool is using a potential diagram. I have been wanting to generate a gnuPlot of the Eps Aur system for a while for the user in presentations. Perhaps you might want to take on this task and share it with the Citizen Sky community? There is already a script that could generate a majority of the plot. What is actually being done is the generation of an equipotential surface diagram much like you created above (think of it as a topographic map in which the sinks are the massive objects). http://commons.wikimedia.org/wiki/File:Lagrange_points.svg I'm not sure how much effort this would entail, but I bet with a few functions you could add in a disk-like object to the model as well. Best of luck, Brian

Robin, I must start my reply with a disclaimer: I have not studied spectroscopy in detail so my interpretations may be incorrect and subject to revision down the road. Just so others who may not be as experienced as Robin can follow our conversation, we mention "RV" we mean radial velocity and "EW" is equivalent width. I could not find a ready-made introduction to radial velocity (aside from Wikipedia) that I thought was worth posting, but I did find an introduction to equivalent widths can be found here(http://astrosurf.com/buil/us/spe2/hresol7.htm) that might be well-worth reading. Now, on to Robin's question. The radial velocity you measured clearly provides us information about the dynamics of the system. A few papers feature spectra on Epislon Aurigae (sorry, I don't have the references handy) and helped us determine the direction that the object (at the time) was rotating. What we have determined from spectra is that as the eclipse begins the object is rotating away from us, and as the eclipse ends the object is rotating towards us. Speaking generically now, if the spectra is normalized and we can account for the Doppler shift of the object in question, the equivalent width can tell us about the relative abundance of a given molecule. For example if we were to find that He was half as abundant than H, if we can somehow figure out the amount of H, we can then infer the amount of He present (the numbers are of course made up). I'll have to think for a while about what your spectra (http://www.threehillsobservatory.co.uk/astro/spectra_40.htm) could be telling us. If we can find some historical data (say in the Ferluga paper that you link to or elsewhere) that provides spectra during egress and we can ratio those (accounting for the phase of the eclipse), we might be able to infer some form of evolution of the system. Now please take my last sentence with a grain of salt. There are a lot of assumptions that have to be made and tested before this idea could create anything meaningful (or perhaps it won't work at all), but again one needs to start somewhere. Perhaps someone with more experience in spectra could comment? Keep up the good work, Brian

Sounds like a nice little exercise, I'm not using gnuplut "natively" but just as the default graphics - backend of Octave (the open source Matlab clone, for those who don't know Octave), but even Octave allows a lot of customizing the graphics. Maybe a potential surface plot like this one en.wikipedia.org/wiki/File:GravityPotential.jpg would also be intuitive as some people find it difficult to get an idea of a field using equipotential / contour plots. So I'll experiment with this and will let you know when I have someting to show. Heinz

Hi Brian! So here are my first crude results. Let me check if I got it right... what we are looking for is a plot of the effective potential exactly as the one in the wikipedia article on the Lagrange Points of the Earth-Sun system. That means it's the sum of a) the gravitational potential phi(x) = sum(-G m_i/|x_i-x|) (outside of the bodies) plus b) the potential you get by choosing a rotating frame of reference, rotating around the barycenter of the system with the angular velocity matching that of the system, so that in this frame of reference the bodies of a 2-body system are at rest. That is phiRF(x) = -1/2 * r^2 * w^2 r is distance from center and w is angular velocity (radians / s). Hmm...ok, I tried to put this into octave, and as a sanity check I plotted the area around L1 and L2 for the Earth and it seems ok to me: So modelling EpsAur system as a system of 2 point masses (no disk yet) separated by 27 AU and masses 15 Ms and 14 Ms respectively, rotating around their barycenter once every 27.1 yr, I get this : If this looks about right I can go on to make it a bit prettier :-) (labels, nicer color choice, scale in AU instead of m ... ) As for the disk....ok you could add some more masses in a ring around the secondary, maybe? But what is the distribution of mass in the disk and the ratio of mass in the disk and in the central object(s) at the center of the disk???? CU Heinz

Heinz, Awesome! You can really see the system's symmetry. As for modeling the disk let's start with something simple: A uniform density disk of infinitesimal height. We can extend it to have some height later on so just assume h = 1 for now. The equation for mass distribution as a function of (r, h) would be: M(r, h) = rho * pi * r^2 * h where rho is the density of the object ~ (1 / (pi * 1500^2) in units of Solar Masses / (Solar Radii)^2 which will need to be converted to solar masses / au^2). R goes from zero to r_disk (which you could do using a step function that is on from disk_center to r_disk). Eventually we'll have to do some other tweaking to the model, but you have an excellent start.