The random walk area is called the radiation zone . Energy is transported by photons. When the temperature of the gas has dropped to about 2 million K, photons can start being absorbed by ions rather than bounced by electrons heat is built up by photon absorption. Very efficient method of energy transport. The Sun's surface Hard to define since the Sun is a gas.
Photosphere is where photons can escape more easily without further interaction.
Peak energy comes out about 510 nanometers, green light. Convection creates the granules we see on the surface. Bright center where hot gas is rising, dark edges where cool gas descends again. Go to Big Bear Solar Observatory page and see a movie of it. Sunspots show the rotation of the Sun, and show that rotation varies from about 25 days around equator to 36 days near the poles.