Chandrasekhar's conditions for stellar equilibrium set limits on how much radiation pressure a star can sustain before becoming unstable. The derivation assumes the gas particles follow a Maxwell-Boltzmann distribution — the equilibrium distribution for an ideal gas. Under this assumption, the ratio of radiation pressure to total pressure has a well-defined maximum that depends on the star's mass and composition. Stars exceeding this ratio cannot maintain hydrostatic equilibrium.
Hu and Du extend these conditions to a universal three-parameter non-Maxwell distribution that encompasses the Maxwellian as a special case. The three parameters control the distribution's shape — its power-law tails, its peak width, and its high-energy cutoff. The Maxwellian corresponds to specific parameter values; real stellar interiors, with their turbulence, magnetic fields, and non-equilibrium processes, may deviate.
The result is not what naive intuition might suggest. Relaxing the Maxwellian assumption — allowing the particle distribution to be more general — does not expand the range of stable stellar configurations. It contracts it. The maximum radiation pressure ratio under the non-Maxwell distribution is generically lower than Chandrasekhar's classical limit. The classical result, derived under the simplest possible distributional assumption, was the most permissive bound.
The mechanism is that non-Maxwellian tails redistribute the particle energies in ways that make the gas less effective at supporting itself against radiation. A broader high-energy tail means more particles contribute to radiation pressure relative to gas pressure, pushing the effective ratio closer to the instability threshold at lower total pressures.
Relaxing an idealization doesn't expand the possibility space — it contracts it. The simple assumption was the permissive one. The classical ceiling was not a floor waiting to be raised; it was already the highest the ceiling could be.