Spectra are wonderful for telling about the Sun's atmosphere, but nobody yet has directly observed light from the center of the Sun. Why is that?

Luckily, there are important tests to tell us about the internal structure (Temperature, Density, etc. as a function of Radius) of the Sun.

HELIO (Solar) Seismology
Sound bounces around the inside of the Sun, just like is seen in earthquakes on the Earth.

The bouncing 'rays' of sound create a ringing, which is seen as waves on the surface of the Sun.

Scientists study time-lapse photography of the Sun to measure these waves.

Measuring the surface waves seen can be used with models to obtain measurements of the density, pressure, composition and temperature of the Sun's interior--Provided we can simultaneously solve for 10 million different ringing patterns at once!