To what factor is the reaction rate of the CNO cycle fiercely sensitive?
Answer
Temperature
The Carbon-nitrogen-oxygen (CNO) cycle is inherently linked to extremely high temperatures found deep within the cores of massive stars, typically those above 18 million Kelvin. The physics governing this cycle dictate that its reaction rate escalates fiercely in response to even small increases in heat. This extreme temperature dependence is the fundamental reason why a star just a few times the Sun's mass can be thousands of times more luminous; it is utilizing a reaction pathway whose efficiency scales dramatically with thermal energy.
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