Observing Solar Limb Darkening in the Classroom

The falling temperature of the photosphere with height is responsible for the effect known as limb darkening. The Sun is not equally bright all over the disc. When we observe the Sun towards the limbs, it appears to get darker. Light from the photosphere travels through an absorptive medium. Therefore, one can see only so far into the photosphere. This is the optical depth (Fig. 1). The line of sight at the center sees deeper into the Sun to an optical depth of about 2/3 into the photosphere. In other words, photons that escape from a smaller radius of the photosphere have originated in a hotter region; therefore, they will have a higher intensity. Photons that originate from a larger radius come from a cooler part of the photosphere; therefore, this results in lower intensity. This effect is known as solar limb darkening. In addition, the solar photosphere displays various phenomena that can easily be observed in images obtained with small telescopes, such as sunspots, faculae, and granulation. Limb darkening results from the fact that we are looking into hot gas when we look at the Sun and, as a consequence of this, the brightness of the Sun decreases as one looks from the center of the disc (where we see deeper inside the Sun) towards the limb (where we will not see as deeply into the solar atmosphere because we are looking at a slant through the photospheric material).