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An Alternative Disk Model from Budaj (2011)

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Dr Jan Budaj, an astronomer at the Astronomical Institute of the Slovak Academy of Sciences, recently published a paper titled "Effects of dust on light-curves of epsilon Aur type stars". The paper uses data from Citizen Sky and the AAVSO. Dr Budaj was gratious enough to send us the following explanation of the paper and allow us to share it here:


An alternative model for epsilon Aurigae has been proposed by Jan Budaj. It consists of two geometrically thick flared disks: an internal optically thick disk and an external optically thin disk, which absorbs and scatters radiation (see top-left portion of figure below). Disks are in the orbital plane and are almost edge-on. The model is based on optical properties of dust grains. It takes into account the extinction due to the Mie scattering and absorption as well as thermal and scattering emission.

Striking property of dust grains is that they do not scatter the light isotropically (see top-right figure) but show a strong forward scattering. Let us assume a hypothetical 'eclipsing binary star' that consists of a star (source of light) and a distant ball of optically thin dust. Both objects revolve around their center of mass. The dusty ball will scatter the light in the forward direction, creating a beam of light analogous to the light-house effect. Whenever the beam hits the observer, which happens mainly during the eclipse, a pulse will be detected. The dusty ball may also cause attenuation of the light from the source during the eclipse. These two effects will compete. If the main source of light disappears, e.g. during the total eclipse by some optically thick object, then scattering by the optically thin dust may completely dominate the observed radiation. Consequently, such a 'naked' light-house effect might be a natural explanation of the MEB observed in some eclipsing binary stars.

Apart from the above mentioned effect we propose that the shallow MEB may also result from edge-on flared disks. Suppose that the disk is flared, homogeneous and optically thin (or at least partially transparent). Then the edges of the disk may have a larger effective cross-section and optical depth along the line of sight than the central part of the disk and consequently might attenuate the stellar light more effectively before and after the mid-eclipse. This effect relies mainly on the shape of the disk and opacity and is independent of the source of opacity, which is why it could work for both dusty and gaseous disks.

(Click on image for a larger version)

The illustration at bottom-left shows eclipse of epsilon Aur by a dark, geometrically thick, flared disk of dust. The disk consists of two parts: (1) The flared optically thick part that causes most of the eclipse, and (2) a flared optically thin part that causes additional absorption, scattering and mid-eclipse brightening.

Model (A): Disk has only one part (1).
Model (B): disk has both parts part (1) and part (2).

Mid-eclipse brightening arises mainly because the edges of the flared disk are more effective in the attenuation of the stellar light than the central parts of the disk. Thin dotted line is a best-fit quadratic function to the eclipse bed. Crosses - observations from AAVSO.

Thus there is no need for a highly inclined disk with a hole to explain the current eclipse of epsilon Aur even if there is a possible shallow mid-eclipse brightening.

 

The illustration at the bottom-right of the figure depicts a theoretical 2D image of epsilon Aurigae based on this model.


We thank Dr. Budaj for this explanation!

You can use the epsilon Aurigae simulator (java) to see what effect various aspects of the system (such as thickness, orientation, etc.) have on the light curve. However, it doesn't have an option for flaring the edge of the disks yet. But it can be used to help visualize the models that involve inclined disks with holes and then imagine what flaring would do in certain circumstances.

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robin_astro
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The detection of a mid eclipse brightening during this eclipse appeared to be observer dependent with observers falling into two groups, those who saw it and those who did not. It would be an interesting exercise to look into what these two groups did differently. (Mid eclipse coincided with the difficult period around solar conjunction where the low elevation for many observers would have made accurate extinction corrections critical) Theeclipsing objectcertainly has a semitransparent region which produces an absorption spectrum. The region generating thisspectrum(in particular the potassium line at 7699A which I have been following at Three Hills) extends in radius well beyond the opaque region and shows a clear thinning near mid eclipse which may be consistent with the proposed model. Attached ismy latest trend of the K I 7699A absorption line (The points marked L&S were measured by Lambert and Sawyer during theprevious eclipse.) Robin

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epsaur_7699line_EW.png 13.33 KB
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