Main-sequence stars fuse hydrogen to helium in their cores via the proton-proton chain (low mass) or CNO cycle (high mass), generating the energy that maintains hydrostatic equilibrium. The hydrogen-burning lifetime scales as ~M/L ∝ M^(-2.5), varying from >10 billion years for low-mass stars to millions of years for massive stars. The main sequence represents the longest phase of stellar evolution and contains ~90% of all observable stars. The mass-luminosity relation emerges from this physics.
From your study of stellar interior structure, you know that a star maintains hydrostatic equilibrium — gravity pulling inward is balanced by pressure pushing outward. The energy source sustaining that outward pressure during the longest phase of a star's life is core hydrogen burning: the fusion of hydrogen nuclei into helium in the star's center, where temperatures and densities are extreme enough for nuclear reactions to occur.
The specific fusion pathway depends on stellar mass. In stars up to about 1.3 solar masses (including our Sun), the proton-proton (pp) chain dominates. Four hydrogen nuclei (protons) are converted into one helium-4 nucleus through a sequence of intermediate reactions, releasing energy as gamma rays and neutrinos. The process is relatively slow because it begins with two protons colliding and one converting to a neutron via the weak nuclear force — a very low-probability event that acts as a bottleneck. In more massive stars, core temperatures exceed about 15 million K and the CNO cycle takes over. Here, carbon, nitrogen, and oxygen nuclei act as catalysts: they are not consumed but facilitate the same net conversion of four hydrogens to one helium. The CNO cycle's rate depends on temperature far more steeply (roughly T¹⁶ compared to T⁴ for the pp chain), which is why massive stars are so dramatically more luminous.
This temperature sensitivity creates the mass-luminosity relation: luminosity scales roughly as L ∝ M^3.5 for main-sequence stars. A star ten times the Sun's mass is not ten times as luminous — it is roughly 3,000 times as luminous. This has a profound consequence for stellar lifetimes. A star's fuel supply is proportional to its mass, but it burns through that fuel at a rate proportional to its luminosity. The main-sequence lifetime therefore scales as M/L ∝ M/M^3.5 = M^(-2.5). A star with 10 solar masses lives only about 20 million years on the main sequence, while a star with 0.5 solar masses can burn hydrogen for over 50 billion years — longer than the current age of the universe.
The main sequence itself is the diagonal band on the Hertzsprung-Russell diagram where roughly 90% of all observed stars reside. This is not because stars preferentially form there, but because hydrogen burning is by far the longest phase of stellar evolution — stars spend the vast majority of their lives here before exhausting their core hydrogen and evolving off the main sequence. When you look at the night sky, almost every star you see is in this phase: steadily converting hydrogen to helium, maintaining the delicate equilibrium between gravity and radiation pressure that defines a stable star.