# . Trouble on the Upper Main Sequence Until it was understood that the CNO cycle operated in stars more massive than the Sun,

3. Trouble on the Upper Main Sequence Until it was understood that the CNO cycle operated in stars more massive than the Sun, there was a long standing mystery about the upper main sequence. Let’s find out just how bad things looked when only the pp cycle was known. (a) Use the luminosity derived for stars with M> Mo, L= M³ (in solar units), to find the central temperature, radius and effective temperature for stars powered by the pp cycle between 1 and 20 Mo Presume the central values are those of an n=3 polytrope. You can solve the resulting equations either numerically, or by expanding the nuclear burning luminosity as a power law and forging ahead by hand.
(b) Compare these properties to the observations of the main sequence for M> M. Are things different? If so, in what way? (c) The first stars born in the Universe have no CNO elements present and so this calculation is relevant. Is the temperature you reached in the above calculation high enough so that helium can ignite?