Re: What is the surface density of the sun?

The density of the sun decreases continuously outward from the center. The visible surface of the sun (i.e. the region of the sun from where we get most of the light is called the photosphere. This layer is very thin, only about 500 km thick as compared to the radius of the sun of 700,000 km. The density of the photosphere is very, very low, about 0.1% of the density of air at sea level on earth. We would call that kind of density a good vacuum and is much less than the density of wood. [The density of air at sea level is 0.0013 gm per cubic cm]. The average density of the sun is 1.4 gm per cubic cm showing the density in the center of the sun is very high, about 160 gm per cubic cm, much higher than any material that we know. There are gases above the photosphere of the sun. These gases in the chromosphere and corona are visible during a solar eclipse when the glare of the photosphere is covered up by the moon.

One way of studying the interior structure of the sun, meaning how the density and temperature vary throughout the sun is called "helioseismology." This is the study of the vibrations of the sun. (You can think of these vibrations as like the vibrations of a drum). Because it is a plasma instead of a solid, it can maintain these vibrations for fairly long periods of time, and by studying how the sun vibrates, astronomers can determine the densities inside the sun and determine the thickness of the photosphere as well as other layers. A good website for that is:
http://www.gong.noao.edu/helioseismology.html

Reference: any introductory astronomy textbook as for example "Foundations of Astronomy" by M. Seeds, 4th ed, p148