## Part 3: Properties of Solar Features In this section, you will examine the size of solar prominences and determine the temperature of a sunspot using the Stephan-Boltzmann law.

You are given an H-Alpha image of the Sun containing a sunspot and a solar prominence  The images are located in the shared drive ( Labimage -> Solar) on the desktop of the lab computers. Use the images of the Sun to answer the questions below.

The Stephan-Boltzmann Law:

The Stephan-Boltzmann law relates the amount of light given off by an object to its temperature.  The equation for this law is:

L = AσT4

Where L is the luminosity, A is the area of the region, σ is the Stephan Boltzmann constant, and T is the temperatures of the region.

If we are simply comparing the temperature of two regions using the same image, we can simply the expression by taking the ratio:

Bspot/Bsun = (Tspot/Tsun)4

Assuming that we use the area and brightness of a single pixel.

Exercises

Load the H-alpha image of the Sun into MaxIm DL. Open the screen stretch tool and change the contrast on the image. You will have to change the contrast to highlight different features on the sun. Think about what features you want to examine and change the contrast accordingly.

1. Measure the pixel height of a solar prominence as well as the pixel radius of the Sun.  Divide these numbers to obtain the ratio, or the height of the prominence in units of solar radii.

2. Look up the radius of the sun, and convert the height of the prominence from units of solar radii to km.  Compare this to the size of Earth.

3. Using the provided image, determine the minimum pixel brightness of the observed sunspot as well as the average pixel brightness of the solar surface near the sunspot.  You can then plug this into the equation above to find the ratio of temperatures between the solar surface and the sunspot (Tspot/Tsun).

4. Look up the average temperature of the surface of the sun.  Use this and the ratio from exercise three to determine the temperature of the sunspot.