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Exoplanets Roche Tidal Disruption Ratio versus Surface Acceleration Ratio
A diagram showing the tendency of an exoplanet to breakup due to tidal disruption (by its host star), versus the tendency to lose mass from its surface layers. Exoplanets are more likely to be tidally disrupted the higher they are on the diagram in the vertical direction, and they are more likely to lose mass from their surface layers the further to the left they are on the diagram. Therefore exoplanets located at the top left of the diagram are the most unstable and those located at the bottom right of the diagram are the most stable. What is actually plotted on the vertical axis is the ratio of a measure of the “Roche limit distance” from the host star, to the maximum orbital radius. This ratio approaches 1 as the orbital size approaches the critical threshold distance from the host star for tidal disruption to set in. The calculated values of the tidal disruption parameters are actually upper limits because the exoplanet masses are lower limits. On the horizontal axis a quantity called the “surface acceleration ratio,” is plotted, and it is a measure of the tendency of the surface of the planet to be tugged away by the host star, due to the star-planet gravity becoming comparable to the planet's self-gravity at its surface. The calculated values of the surface acceleration ratio are actually lower limits because the exoplanet masses are lower limits. The diagram is constructed from a subset of a snapshot of the confirmed exoplanets sample (on 5 August 2012) for which the necessary measurements existed for the relevant quantities to be calculated. Data are from the Extrasolar Planets Encyclopedia. For comparison, the planets in our solar system are marked as Me, V, E, Ma, J, S, U, N, corresponding to Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune respectively. As expected, the close-in hot Jupiters occupy the top left (most unstable region) of the diagram, and they have no counterparts in our solar system. A more detailed discussion can be found in the book Exoplanets and Alien Solar Systems.
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Note: There are 216 exoplanets shown in the plot, taken from a snapshot
(on 5 August, 2012) when there were 777 confirmed exoplanets in total
(residing in 623 alien solar systems, 105 of which harbored more than
one exoplanet).
File under: How close are exoplanets to tidal breakup? Which exoplanets
are undergoing tidal disruption? Are any of the exoplanets near the
Roche limit?
© Tahir Yaqoob 2011-2012.
