Adjust stellar temperature and radius to see blackbody spectra—compute photometric colors through filter bands
Stars emit light across the entire electromagnetic spectrum. To first approximation, stellar spectra follow Planck's blackbody law—the same physics that governs hot iron, filament bulbs, and the cosmic microwave background. The temperature determines the spectral shape: hot stars are blue, cool stars are red.
The Planck function describes the energy emitted per unit wavelength by a blackbody at temperature T. It peaks at a wavelength λ_max given by Wien's displacement law: λ_max T = 2.898 × 10⁶ nm·K. The Sun (T ≈ 5778 K) peaks in green light (500 nm), though it appears yellow-white because our eyes integrate across wavelengths. Hotter stars like Vega (9600 K) peak in blue; cooler red giants like Betelgeuse (3500 K) peak in near-infrared.
Astronomers measure stellar brightness through filters that transmit specific wavelength bands. The Johnson-Cousins UBVRI system is standard: U (ultraviolet, 365 nm), B (blue, 445 nm), V (visual/green, 551 nm), R (red, 658 nm), I (near-infrared, 806 nm). By integrating the stellar SED through each filter's transmission curve, we compute synthetic magnitudes. The difference between two bands (e.g., B−V) is a color index that correlates with temperature.
Color indices quantify stellar temperature. B−V measures blue-to-visual color: hot O-stars have B−V ≈ −0.3 (blue excess), the Sun has B−V ≈ +0.65 (slightly yellow), M-dwarfs have B−V ≈ +1.5 (very red). These indices are observable—no need for spectroscopy. Combined with apparent magnitude, color indices place stars on the H-R diagram and enable photometric distance estimates via main-sequence fitting.
Integrating the Planck function over all wavelengths yields the Stefan-Boltzmann law: total luminosity L ∝ R² T⁴. A small increase in temperature produces a large increase in luminosity. This is why Rigel (T ≈ 12,000 K), despite being only twice as hot as the Sun, is 120,000 times more luminous—it's also much larger. Conversely, white dwarfs are hot but faint: high T, tiny R.
Real stellar spectra deviate from perfect blackbodies due to atomic absorption lines (Fraunhofer lines). Hydrogen Balmer lines dominate A-stars; metal lines (Fe, Ca) are strong in G-K stars; titanium oxide bands appear in M-stars. Spectral classification (O B A F G K M) is based on these line strengths. But the overall continuum shape—the SED—is still well-approximated by a Planck curve at the effective temperature T_eff.