Spectral Types & Composition — Interpret emission/absorption/continuous spectra and what they reveal about composition.

For most of human history, the chemical composition of celestial objects seemed permanently unknowable. In 1835, the philosopher Auguste Comte famously declared that humanity would never determine what the stars are made of—yet within two decades, a new scientific tool proved him spectacularly wrong. The systematic study of spectroscopy—the decomposition of light into its constituent wavelengths—opened a window into the physical and chemical nature of distant objects. By analyzing how matter emits, absorbs, and transmits electromagnetic radiation, astronomers gained the ability to identify elements, measure temperatures, and infer densities without ever touching a sample. This section traces the key discoveries that transformed spectroscopy from a laboratory curiosity into one of the most powerful diagnostic tools in all of astrophysics.

The central question that drove all of this work remains the organizing principle of stellar spectroscopy today: How does the pattern of light emitted or absorbed by matter encode information about its composition, temperature, and physical state? Answering this question requires a firm grasp of the three fundamental spectral types and the physical mechanisms that produce them.

The behavior of light as it interacts with matter can be distilled into three foundational scenarios, codified by Kirchhoff's laws of spectroscopy. These laws are empirical—they describe what is observed under controlled conditions—and they apply universally, from laboratory flame tests to the photospheres of distant stars. Each law corresponds to a distinct type of spectrum: continuous, emission (bright-line), and absorption (dark-line). Understanding the physical conditions that generate each type is essential before we can use spectra as diagnostic tools.

A crucial complementarity connects the second and third laws: the dark lines in an absorption spectrum occur at exactly the same wavelengths as the bright lines in the emission spectrum of the same element. This correspondence was the first strong evidence that absorption and emission are inverse manifestations of the same atomic transitions. In a stellar context, the hot, dense interior of a star produces a continuous spectrum, while the cooler, more tenuous outer atmosphere imposes absorption lines upon it. The pattern of those dark lines directly encodes the chemical makeup of the stellar atmosphere.

The following diagram illustrates the three physical setups that produce each spectral type according to Kirchhoff's laws. On the left, a hot dense source emits radiation. Depending on whether an observer views the source directly, or views through an intervening cloud of cooler gas, or views only the gas itself from the side, a different type of spectrum results. Study how the geometry of source, gas cloud, and observer determines the spectral outcome.

This geometric picture maps directly onto stellar structure. The stellar core and photosphere act as the hot, dense source, producing a near-perfect blackbody continuum whose peak wavelength encodes the surface temperature via Wien's displacement law. The cooler stellar atmosphere—composed of various atoms and ions—acts as the intervening gas cloud, carving out absorption lines whose positions reveal the elements present. Meanwhile, hot nebulae (such as H II regions) glow with emission lines because the diffuse ionized gas is viewed directly against the dark sky, with no continuum source behind it.

The discrete nature of spectral lines is a direct consequence of quantized energy levels within atoms. When an electron transitions between two energy levels, it either absorbs a photon (jumping to a higher level) or emits one (falling to a lower level). The wavelength of that photon is determined precisely by the energy difference between the two levels. We now formalize this relationship and connect it to the observable spectral line patterns.

For a transition between an upper level n₂ and a lower level n₁, energy conservation requires that the photon energy equals the difference in level energies: ΔE = E_n₂ − E_n₁. For hydrogen-like atoms, the Bohr model gives exact energy levels, leading to the Rydberg formula.

While the Rydberg formula applies exactly only to hydrogen (and hydrogen-like ions), the underlying principle generalizes: every element has its own unique set of energy levels, and therefore its own unique set of spectral line wavelengths. Multi-electron atoms produce far more complex spectra because electron–electron interactions split and shift energy levels, but the fundamental mechanism—photon energies matching energy-level differences—remains identical. This is why the pattern of lines serves as an unambiguous chemical fingerprint, regardless of whether the atom is in a laboratory flame or in the atmosphere of a star 10 kiloparsecs away.

Astronomers classify stars by their spectral type using a system refined at Harvard Observatory in the late 19th and early 20th centuries, primarily through the work of Annie Jump Cannon. The classification sequence—O B A F G K M—ranks stars from hottest (O, surface temperatures above 30,000 K) to coolest (M, below about 3,500 K). Critically, the spectral type is determined not by which elements are present (most stars share a similar hydrogen-dominated composition) but by which ionization and excitation states are populated at a given temperature. A star's surface temperature controls which absorption lines are strong, which are weak, and which are absent.

Suppose you observe the absorption spectrum of a distant star and identify dark lines at the following wavelengths: 393.4 nm, 396.8 nm, 410.2 nm, 434.0 nm, 486.1 nm, and 656.3 nm. Determine which elements are responsible for these lines, estimate the star's spectral type, and calculate the energy of the photon absorbed at 656.3 nm.

Spectroscopy is arguably the most information-rich observational technique in astronomy, but it is not without constraints. The following table summarizes what spectral analysis can and cannot do, highlighting both its remarkable diagnostic power and the situations where additional techniques or assumptions are required.

The framework of Kirchhoff's laws and the Rydberg formula provides a solid foundation, but modern astrophysical spectroscopy extends far beyond simple line identification. Advanced techniques incorporate quantum-mechanical selection rules, the Saha ionization equation (which quantitatively predicts ionization fractions as a function of temperature and electron density), and the Boltzmann excitation equation (which determines the population of different energy levels within a single ionization state). Together, these tools enable astronomers to derive precise chemical abundances, not merely detect the presence or absence of an element.

In recent decades, high-resolution spectrographs such as HARPS, ESPRESSO, and the James Webb Space Telescope's NIRSpec have pushed spectroscopy into new frontiers: detecting atmospheric compositions of exoplanets via transmission spectroscopy, measuring the chemical evolution of galaxies across cosmic time through stellar archaeology, and probing the intergalactic medium using quasar absorption-line systems. The foundational principles remain exactly those described in this lesson—only the scale and precision have grown.