The Earth has a definite boundary between rocky/ watery surface and gaseous atmosphere. The same cannot be said of the sun. Even though the photosphere gives an apparent "edge" to the sun via the human eye, the matter of the sun continues on significantly further. I have even heard a claim that from a certain perspective, all of the planets out to the KBOs are orbiting "inside" of the sun.
My question concerns what happens when we graph the density of the sun versus distance from the center. I suspect the result will resemble exponential decay; is this correct? Does the graph have any unusual characteristics (such as a lack of smoothness) at any point along the distance axis, in particular at the photosphere?