By Chris Deziel
Updated Aug 30, 2022
While it may seem that a star’s size is beyond our reach, the Hubble Space Telescope has shattered many of those limitations. By operating above Earth’s turbulent atmosphere, Hubble can resolve stellar disks that were once only theoretical. Nonetheless, diffraction still imposes a limit, so this direct‑imaging approach is most effective for the largest stars.
Astrophysicists also use occultations—when a star disappears behind an intervening body such as the Moon—to gauge its angular diameter. Knowing the angular velocity of the occulting object (v) and measuring the disappearance time (Δt) gives the star’s angular size via θ = v × Δt. When combined with the star’s distance, this yields a physical radius.
Even so, the most common and reliable method for determining stellar radii remains the Stefan–Boltzmann law, which links a star’s luminosity (L) and surface temperature (T) to its radius (R).
Treating a star as a black‑body, the power per unit area emitted is governed by the Stefan–Boltzmann law:
P/A = σT⁴, where σ is the Stefan–Boltzmann constant. For a spherical star, the surface area is A = 4πR², and its total power output equals its luminosity (L = P). Substituting gives:
L = 4πR²σT⁴
This equation shows that a star’s luminosity scales with the square of its radius and the fourth power of its temperature.
Spectroscopy is the primary tool for determining a star’s temperature: the color of its light—blue for hot, red for cool—directly reflects surface temperature. Stars are grouped into the O, B, A, F, G, K, and M classes on the Hertzsprung–Russell diagram, which plots temperature against luminosity.
Luminosity is derived from a star’s absolute magnitude—the brightness it would have at a standard distance of 10 parsecs. Accurately measuring this requires knowledge of the star’s distance, obtained through parallax or standard‑candle comparisons with variable stars.
Rather than expressing radii in meters, astronomers typically quote them as multiples of the Sun’s radius (R☉). Rearranging the Stefan–Boltzmann equation yields:
R = k √L / T² where k = 1 / (2√πσ)
Taking the ratio to the Sun eliminates the constant:
R / R☉ = (T☉² √(L / L☉)) / T²
For example, a massive O‑type main‑sequence star might have a luminosity a million times that of the Sun (L/L☉ ≈ 10⁶) and a surface temperature of ~40,000 K. Plugging these values gives a radius roughly 20 R☉, illustrating how temperature and luminosity together constrain stellar size.
These methods, grounded in well‑tested physics and precise observations, give astronomers robust estimates of stellar radii across the cosmos.
