Surface Flux & Colors of Stars

Section 1 of 8

Two Stars with the Same Luminosity

After completing this reading, you should be able to:

Distinguish
received flux (what an observer measures) from surface flux (a stellar property).
Explain
why surface brightness is independent of distance using inverse-square scaling.
Apply
the Stefan-Boltzmann law $L = 4\pi R^2 \sigma T^4$ to connect luminosity, temperature, and radius.
Use
Wien’s displacement law to infer stellar surface temperature from observed color.
Calculate
stellar radius given measurements of luminosity and temperature.
Connect
the color sequence to the temperature sequence and preview the HR diagram’s organization.
Evaluate
the blackbody and spherical-symmetry assumptions and their impact on inferred properties.

What 'color' means here

When we say “color is temperature,” we do not mean only the color your eyes perceive. We mean electromagnetic color — the peak wavelength of a star’s Planck curve across the entire spectrum. Rigel’s “color” peaks in the ultraviolet (~240 nm); Betelgeuse’s in the near-infrared (~830 nm). Neither peak is visible, yet both encode temperature through Wien’s law.

Two complications matter in practice: interstellar dust scatters blue light preferentially, making stars look redder and cooler than they are; and astronomers rarely measure the exact peak — they compare flux through standardized filters and infer an effective temperature. “Color” here means “where the Planck curve peaks,” and the temperature we infer is always an effective temperature requiring dust corrections before it is reliable.

Part 1: Two Stars with the Same Luminosity

Look toward Orion. Blue-white Rigel at the foot and red Betelgeuse at the shoulder both radiate roughly 100,000 times the Sun’s power — yet one is a compact blue supergiant and the other an enormous red supergiant whose surface would reach past Mars’s orbit. How can two stars with the same luminosity differ so much in size?

A hot (blue) object radiates energy much more efficiently per square centimeter than a cool (red) object. So to produce the same total luminosity, a hot star can be smaller; a cool star must be huge. This lecture quantifies that intuition with the Stefan-Boltzmann law — the second major step in stellar inference.