5.3 Spectroscopy in Astronomy

Properties and Types of Spectra in Astronomy

Light is the primary tool astronomers use to study the universe. Since we can't visit stars or galaxies in person, we rely on analyzing the light they emit, absorb, or reflect. Spectroscopy, the study of how light interacts with matter, lets astronomers figure out what distant objects are made of, how hot they are, and how fast they're moving.

Properties of Light in Astronomy

Light has a dual nature: it behaves as both a wave and a particle. As a wave, it's described by wavelength (the distance between wave crests), frequency (how many crests pass a point per second), and amplitude (the wave's height, related to brightness). As a particle, light travels in discrete energy packets called photons.

The electromagnetic spectrum covers all wavelengths of light, not just what your eyes can see. From longest to shortest wavelength:

• Radio waves → microwaves → infrared → visible light (ROYGBIV) → ultraviolet → X-rays → gamma rays

Visible light is only a tiny sliver of this full spectrum. Most of the information in astronomy comes from wavelengths we can't see at all.

Three key relationships tie these properties together:

• The speed of light in a vacuum is constant: $c \approx 3 \times 10^8 \text{ m/s}$
• Wavelength, frequency, and the speed of light are related by: $c = \lambda f$
• Photon energy is inversely proportional to wavelength: $E = \frac{hc}{\lambda}$, where $h$ is Planck's constant

This means shorter wavelengths (like X-rays and ultraviolet) carry more energy per photon, while longer wavelengths (like infrared and radio) carry less.

Composition from Spectral Lines

Every element has electrons that can only occupy specific energy levels. When an electron jumps between levels, the atom either absorbs or emits a photon with a wavelength that corresponds exactly to the energy difference between those levels. Because each element has a unique set of energy levels, each element produces a unique pattern of spectral lines, like a fingerprint.

How astronomers identify elements:

• Hydrogen, the most abundant element in the universe, has a well-known set of visible spectral lines called the Balmer series (including a red line at 656 nm and a blue-green line at 486 nm).
• Sodium produces a distinctive pair of bright yellow lines called the Sodium D lines.
• Calcium has prominent H and K absorption lines in the violet part of the spectrum, commonly seen in stellar spectra.

What spectral lines reveal beyond composition:

• Line intensity reflects how much of an element is present. Stronger lines generally mean a higher concentration of that element. For example, hydrogen lines dominate most stellar spectra because hydrogen is so abundant.
• Line width gives clues about temperature and pressure. Broader lines point to higher temperatures or denser environments (like deep in a stellar atmosphere), while narrower lines suggest cooler, more diffuse conditions (like a thin nebula).
• Doppler shifts reveal motion. If an object moves toward you, its spectral lines shift to shorter (bluer) wavelengths. If it moves away, lines shift to longer (redder) wavelengths. The Andromeda galaxy is blueshifted because it's approaching us, while most distant galaxies are redshifted because the universe is expanding.
• Spectral resolution refers to how well an instrument can distinguish two closely spaced lines. Higher resolution means finer detail in the spectrum.

Types of Astronomical Spectra

There are three fundamental types of spectra, and understanding when each one appears is essential.

Continuous spectrum: A hot, dense object (like the glowing surface of a star) emits light across a broad, smooth range of wavelengths with no distinct lines. Stars like the Sun and Sirius approximate this as blackbody radiators, meaning their spectrum follows a smooth curve whose shape depends on temperature.

Emission spectrum: A hot, low-density gas emits light only at specific wavelengths, producing bright lines against a dark background. You see this in nebulae that are energized by nearby stars, such as the Orion Nebula.

Absorption spectrum: When light from a continuous source passes through a cooler gas, that gas absorbs photons at specific wavelengths, leaving dark lines in the otherwise continuous spectrum. The Sun's spectrum is a classic example: the hot interior produces a continuous spectrum, and the cooler outer atmosphere absorbs specific wavelengths, creating dark Fraunhofer lines.

In many real objects, emission and absorption features coexist. Light from a quasar, for instance, may show emission lines from hot gas near a supermassive black hole along with absorption lines from cooler gas clouds between the quasar and Earth.

Spectroscopic Instruments and Laws

A spectrograph is the instrument that splits incoming light into its component wavelengths so astronomers can analyze the spectrum. Most modern spectrographs use a diffraction grating, a surface with many finely spaced grooves that separates light by wavelength through interference.

Two important laws connect a blackbody's spectrum to its temperature:

• Wien's displacement law: The peak wavelength of a blackbody's emission is inversely proportional to its temperature ($\lambda_{\text{max}} = \frac{b}{T}$, where $b \approx 2.898 \times 10^{-3} \text{ m·K}$). Hotter objects peak at shorter wavelengths, which is why hot stars look blue and cooler stars look red.
• Stefan-Boltzmann law: The total energy radiated per unit area by a blackbody is proportional to the fourth power of its temperature ($F = \sigma T^4$). Even a small increase in temperature means a large increase in energy output.

Together, these laws let astronomers determine a star's surface temperature and luminosity from its spectrum alone.