At approximately what core temperature, supported by degeneracy pressure, does helium fusion ignite explosively in a Sun-like star?
Answer
About 100 million Kelvin
The initiation of helium fusion marks a highly specific, critical threshold in the evolution of a Sun-like star. While the core is supported by electron degeneracy pressure, it continues to contract and heat up dramatically under gravity, even though it cannot expand to self-regulate the temperature. When the core finally attains a temperature of approximately 100 million Kelvin, the kinetic energy of the helium nuclei is sufficient to overcome the repulsive barrier, leading to the sudden ignition of helium into carbon and oxygen. This temperature landmark is precisely what dictates the timing of the dramatic event known as the Helium Flash.

Related Questions
What primary nuclear reaction defines the main sequence phase for a star like our Sun?What event acts as the key trigger initiating the transition from the main sequence to the red giant phase for a Sun-like star?Despite a significant drop in surface temperature, why does a star become substantially brighter overall upon becoming a red giant?What specific type of pressure eventually supports the contracting helium core of a Sun-like star before helium fusion ignites?At approximately what core temperature, supported by degeneracy pressure, does helium fusion ignite explosively in a Sun-like star?Why does the Helium Flash occur suddenly and explosively rather than gradually in a degenerate core?What is the composition of the innermost structure of a Sun-like star immediately after the core helium burning phase is complete?What initial mass threshold roughly determines whether a star avoids the red giant path described and instead faces a supernova explosion?What fate awaits stars below the minimum mass required to expand into a red giant phase, such as those around $0.5$ solar masses?Where might the outer layers of our Sun swell during its red giant phase relative to the current orbits of the terrestrial planets?