Edge darkening

The sun in June 1992. The edge darkening is clearly visible. The sunspot at the bottom left is about 5 times the size of the earth.

In astronomy, edge darkening is the phenomenon that the apparent disk of a star near the edge emits a noticeably lower flow of radiation in the direction of the observer. The effect can be observed directly on the basis of the sun's disk ; the darkening of the edges of other stars can be detected using the light spectrum .

As Karl Schwarzschild showed at the beginning of the 20th century, the edge darkening occurs because stars consist of gas, the temperature of which decreases towards the surface: in the middle of the disk, deeper, hotter regions can be seen that radiate more strongly; at the edge, on the other hand, the view only falls on higher, less hot and therefore less bright layers. If stars were solids , no darkening of the edges would be noticeable. The exact course of the marginal darkening provides information about the pressure and temperature course in the upper regions of the stellar atmosphere .

Geometric and physical basics

If light propagates in a medium , it comes to extinction : only some of the light particles manage to cross the medium; the others are absorbed or scattered .

For a homogeneous medium, the number of light particles remaining when passing through a medium of the same thickness depends exponentially on and on the material properties : ${\displaystyle l}$ ${\displaystyle l}$

${\displaystyle n=n_{0}\cdot {\frac {1}{e^{l/L}}}}$

The characteristic length , called penetration depth , is a material-specific measure of how deep an observer can look into the medium from outside. From a layer that is just the distance from the surface, only the emitted light particles reach the observer . e is Euler's number . ${\displaystyle L}$ ${\displaystyle l=L}$ ${\displaystyle 1/e}$

The figure on the right shows a cross-section of a star sphere, which consists of layers of gas with different densities and temperatures lying on top of each other like onion skin. Due to the geometry, an observer who is at a great distance beyond the right edge of the image can look deep into the star, namely up to layer A, if he is looking directly at center O; for the observer this corresponds to the center of the disc as which he perceives the star in the sky. In the edge regions of the star disc, point B is shown as an example, the same characteristic length L corresponds to a star layer further out; accordingly, the observer can look less deeply into the stellar atmosphere.

The effective temperature of those layers of star gas that generate visible light increases further and further towards deeper layers. The layers in question behave approximately like a black body whose radiation intensity , following the Stefan-Boltzmann law , increases with increasing temperature. The deeper layers visible in the middle of the disc are therefore lighter than the higher layers visible at the edge of the disc: the edge of the star disc is darkened.

Edge darkening in the sun

see photosphere # center-edge-darkening , with further formula.

Edge darkening of planets

Edge darkening can also be seen , for example, when observing Uranus .

literature

• Karl Schwarzschild : About the balance of the solar atmosphere . In: News from the Society of Sciences in Göttingen. (1906), pp. 41-53.
• Otto Zimmermann: Astronomical internship. 6th newly revised edition. Spectrum Akademischer Verlag, Heidelberg et al. 2003, ISBN 3-8274-1336-2 , Section 11: “Edge darkening of the sun”.