Recapping the event, 2

     Now that the eclipse of 2009-2011 has ended, we can begin to reflect on the discoveries and realizations made possible by the new data.  To see where we are going, let's reflect on some more of the story leading up to the present.

     Struve’s student, Shu-Shu Huang in 1965 published the disk model [1] that corresponds to the interferometric images obtained first in 2009: a long thin dark object crossing the face fo the F star during eclipse.  Huang cited the idea originating with Zdenek Kopal [2] who in 1954 published a model featuring a semi-transparent flat ring consisting of large solid particles in orbit around a secondary star, which resolves many of the observational issues.  Huang then developed his model for a transiting opaque gaseous ring, based on the success of a similar model with beta Lyrae, which preserves the spectrum of the primary, adds rotationally-varying spectral features, plus can account for H-alpha and light variations.  Several authors seized on Huang's idea and resulted in a back and forth exchange, sometimes less than friendly, over the physics of such of a disk.  Recall that stellar disk theory was far less developed then, compared to today. 
      Huang's final paper on the subject [3] states that  "the observed light curve and opacity distribution are related by an integral equation - and that - once the thickness is given, fitting of the light curve is basically a question of assigning the opacity distribution to the disk, and vice versa."   Now that we know at least the angular thickness of the infrared (dust) disk - modelled as an ellipse with a semi-minor axis of 0.61 +/- 0.01 milli-arcsec [4] - we can in principle address Huang's claim.  Distance remains imprecisely determined, but the range of 650 +/- 50 pc seems plausible.  At that distance, the semi-thickness of the disk is 0.4 AU.  We'll be working on coding Huang's math and report back during 2012 on this.
     Another interesting paper that appeared about this same time was that based on a dissertation, by Handbury and Williams [5].   Among other things, they note early infrared work by Mitchell [6] that found an IR excess suggestive of a 500K cooler source in the system.   Comparing the ratio of total eclipse to overall eclipse length gives the ratio of radii of the two objects.  Handbury then derived a condition for eclipse that is dependent on the dust size, mass and disk parameters, including central star mass, and deduced that disk thickness is 86% of the F star radius - quite close to the interferometric imaging result.  Their equation 26 and a 550 pc distance leads to an F star radius of 0.54AU, mass of 10.4 suns, a disk-center star mass of 11.4 suns and opaque disk radius x thickness values 5.2 x 0.46AU (with a 25AU binary separation).  Handbury also predicts the extend of a semi-transparent disk to extend another 2AU beyond the opaque core - all constrained by eclipse light curve durations.  These papers illustrate the problems of deducing the real values without having a more precise distance with which to work.
      Next time, we'll look at efforts to address this distance ambiguity and other results emerging from the recent eclipse.

Papers cited:
[1] Huang 1965 - http://adsabs.harvard.edu/abs/1965ApJ...141..976H
[2] Kopal 1954 - http://adsabs.harvard.edu/abs/1954Obs....74...14K
[3] Huang 1974 - http://adsabs.harvard.edu/abs/1974ApJ...189..485H
[4] Kloppenborg et al. 2010 - http://arxiv.org/pdf/1004.2464v1
[5] Handbury & Williams 1976 - http://adsabs.harvard.edu/abs/1976Ap%26SS..45..439H
[6] Mitchell 1964 - http://adsabs.harvard.edu/abs/1964ApJ...140.1607M