A star's entire life story is written in its birth mass. This single property dictates the core pressure, temperature, and ultimately, how violently it fuses hydrogen into helium. While all main-sequence stars are in a state of hydrostatic equilibrium, where gravity's inward pull is balanced by the outward push of fusion, the sheer scale of that balance changes dramatically with mass.

A more massive star has a much stronger gravitational force trying to crush it. To counteract this, its core must generate far more outward pressure. This is achieved through a hotter, denser core, which in turn drives the rate of nuclear fusion to astonishing levels. The result isn't just a slightly brighter star, but a profoundly more luminous one. This fundamental connection is one of the most important scaling laws in astrophysics.

The relationship between a star's mass and its energy output isn't linear; it's exponential. A small increase in mass results in a huge leap in luminosity. For stars on the main sequence, this connection can be quantified.

This steep relationship has a profound consequence: high-mass stars burn through their available hydrogen fuel at a ferocious rate. They live fast and die young. A star ten times the mass of our Sun is a thousand times more luminous, but its main-sequence lifetime is a hundred times shorter. While it has more fuel, its consumption rate is disproportionately higher.

Mass also determines how a star transports energy from its core to its surface. Energy moves through two main processes: radiation, where photons carry energy outward, and convection, where hot plasma physically rises, cools, and sinks, like boiling water. The dominant process in different regions depends on the star's mass.

In stars like our Sun, the core is so hot that energy travels efficiently as radiation. Further out, the gas becomes cooler and more opaque, trapping heat and forcing it to churn in large convective cells. In very massive stars, the core fusion is so intense that radiation can't escape fast enough, triggering violent convection right at the center. This churning efficiently brings fresh hydrogen fuel into the core, a key factor in their evolution. The outer layers, in contrast, are stable and transport energy via radiation.

There is, however, an upper limit to how massive a star can be. If a star is too massive, its own luminosity—the sheer outward force of its photons—will be powerful enough to overcome gravity and blow the star's outer layers into space. This theoretical maximum mass is governed by the Eddington limit and is estimated to be around 150-200 times the mass of our Sun.

We can estimate a star's main-sequence lifetime with a simple principle: it's the total fuel available divided by the rate at which that fuel is consumed. The fuel is proportional to the star's mass ($M$), and the consumption rate is its luminosity ($L$).

By combining this with the mass-luminosity relationship ($L \propto M^{3.5}$), we can express the lifetime in terms of mass alone.

This powerful result confirms our intuition: the most massive stars, though containing the most fuel, are the first to exhaust their core hydrogen and evolve off the main sequence. Their immense gravity forces a life of brilliance and brevity, setting the stage for the dramatic and explosive end states that seed the cosmos with heavy elements.