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A Hertzsprung-Russell diagram plots stellar luminosity against effective temperature or a calibrated spectral classification. Conventionally, high luminosity is upward and high temperature is to the left. The Stefan–Boltzmann law, $L=4\pi R_{\star }^2\sigma T_{\mathrm{eff}}^4$, explains why stars of equal temperature but different luminosities must have different stellar radii.

The main sequence crosses the diagram, giant stars occupy a luminous region, and white dwarfs lie at low luminosity despite their high temperatures. An evolutionary track follows one model star through this space; a population diagram instead combines many stars at once. A colour-magnitude diagram is the observational counterpart, requiring distance, extinction and spectral calibration for the conversion.

Sirius is a nearby binary star containing a luminous main-sequence star and a much fainter white dwarf. Their coexistence makes a useful lesson in stellar appearance: a hot object can be faint because its radiating area is small. The resolved Hubble Space Telescope image separates the compact companion from the bright primary's surrounding light.^[ref]

The common orbit provides dynamical information, whereas spectral classification and luminosity constrain the two bodies' physical states. The white dwarf records prior stellar evolution; its current faintness does not mean it was always the less massive or less luminous member. Sirius therefore connects binary star measurements with white-dwarf cooling and the interpretation of the Hertzsprung-Russell diagram.

Spectral classification groups stars by the patterns of absorption lines, emission lines and molecular bands in their spectra. The Harvard spectral classification orders the familiar O, B, A, F, G, K and M types mainly by effective temperature. Changes in ionization and excitation make a given element's lines strongest over only part of that sequence; weak hydrogen lines do not directly imply little hydrogen.

Surface gravity also affects line shapes and ratios, supplying a separate luminosity class. Together the temperature type and luminosity class help distinguish a cool red giant from a cool main-sequence star. Composition, stellar activity, rotation and unresolved companions complicate the inference, so classification is an observational guide to a physical model rather than a complete measurement of the stellar structure.

The UBV photometric system measures stellar brightness in three broad photometric passbands: ultraviolet $U$, blue $B$ and visual $V$. Each measurement is an apparent magnitude defined relative to its calibration. Each of $U-B$ and $B-V$ is a color index: a difference in magnitudes that constrains spectral shape.

The measurement includes the filter, detector response and calibration convention, not merely a nominal wavelength. Effective temperature, composition, surface gravity and interstellar extinction can all affect the colours. Combining both indices with spectral classification therefore provides more information than interpreting one colour as a unique thermometer.