🪐Intro to Astronomy Unit 5 – Radiation and Spectra

What is Radiation?

• Radiation is the emission or transmission of energy in the form of waves or particles through space or a medium
• Includes both electromagnetic radiation (light, radio waves, X-rays) and particle radiation (alpha, beta, gamma)
• Electromagnetic radiation consists of oscillating electric and magnetic fields that propagate through space at the speed of light
  • Does not require a medium to travel through and can propagate through a vacuum
• Particle radiation involves the emission of subatomic particles such as electrons, protons, and neutrons
• Radiation can be characterized by its wavelength, frequency, and energy
  • Wavelength is the distance between two consecutive crests or troughs of a wave
  • Frequency is the number of wave cycles that pass a fixed point per unit time
  • Energy is directly proportional to frequency and inversely proportional to wavelength
• Radiation plays a crucial role in the study of astronomy, allowing us to gather information about distant objects and phenomena

Types of Electromagnetic Radiation

• Radio waves have the longest wavelengths and lowest frequencies in the electromagnetic spectrum
  • Used in radio astronomy to study objects such as pulsars, galaxies, and interstellar gas clouds
• Microwaves have shorter wavelengths than radio waves and are used in microwave astronomy
  • Can penetrate through dust and gas, making them useful for studying the early universe and star-forming regions
• Infrared radiation has wavelengths longer than visible light but shorter than microwaves
  • Emitted by objects with temperatures above absolute zero, such as stars, planets, and interstellar dust
• Visible light is the portion of the electromagnetic spectrum that human eyes can detect
  • Ranges from about 380 nm (violet) to 700 nm (red) in wavelength
  • Most astronomical observations have historically been made in the visible range
• Ultraviolet (UV) radiation has shorter wavelengths than visible light
  • Emitted by hot objects such as young, massive stars and accretion disks around black holes
  • Largely absorbed by Earth's atmosphere, requiring space-based telescopes for UV astronomy
• X-rays have even shorter wavelengths and higher energies than UV radiation
  • Produced by extremely hot and energetic objects such as neutron stars, black holes, and supernova remnants
• Gamma rays have the shortest wavelengths and highest energies in the electromagnetic spectrum
  • Associated with the most extreme and violent events in the universe, such as gamma-ray bursts and the decay of radioactive elements

The Electromagnetic Spectrum

• The electromagnetic spectrum is the range of all possible frequencies and wavelengths of electromagnetic radiation
• Arranged in order of decreasing wavelength and increasing frequency and energy
• The main regions of the electromagnetic spectrum, from longest to shortest wavelength, are:
  • Radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays
• The relationship between wavelength ($\lambda$), frequency ($f$), and the speed of light ($c$) is given by the equation: $c = \lambda f$
• Different regions of the electromagnetic spectrum are used to study various astronomical objects and phenomena
  • For example, radio astronomy is used to study cold, diffuse gas and dust, while X-ray astronomy focuses on hot, energetic objects
• Earth's atmosphere is transparent to visible light, some radio waves, and limited infrared radiation, but opaque to most other parts of the spectrum
  • Space-based observatories are necessary to study the universe in other wavelengths, such as UV, X-ray, and gamma-ray

Blackbody Radiation and Wien's Law

• A blackbody is an idealized object that absorbs all incoming electromagnetic radiation and emits radiation solely due to its temperature
  • The radiation emitted by a blackbody is called blackbody radiation
• The spectrum of a blackbody depends only on its temperature and follows a characteristic curve known as the Planck curve
• Wien's displacement law states that the wavelength of peak emission ($\lambda_{max}$) from a blackbody is inversely proportional to its temperature ($T$)
  • The equation for Wien's law is: $\lambda_{max} = \frac{b}{T}$, where $b$ is Wien's displacement constant ($2.898 \times 10^{-3}$ m·K)
  • Hotter objects emit most of their radiation at shorter wavelengths, while cooler objects emit at longer wavelengths
• The Stefan-Boltzmann law relates the total energy emitted by a blackbody per unit surface area per unit time ($E$) to its temperature: $E = \sigma T^4$
  • $\sigma$ is the Stefan-Boltzmann constant ($5.670 \times 10^{-8}$ W·m$^{-2}$·K$^{-4}$)
• Many astronomical objects, such as stars and planets, can be approximated as blackbodies
  • By measuring the spectrum of an object and comparing it to blackbody curves, astronomers can estimate its temperature and composition

Spectroscopy and Atomic Structure

• Spectroscopy is the study of the interaction between matter and electromagnetic radiation
• Atoms consist of a positively charged nucleus surrounded by negatively charged electrons
  • Electrons occupy discrete energy levels or orbitals around the nucleus
• When an electron transitions between energy levels, it absorbs or emits a photon with a specific wavelength
  • The energy of the photon ($E$) is related to its wavelength ($\lambda$) by the equation: $E = \frac{hc}{\lambda}$, where $h$ is Planck's constant and $c$ is the speed of light
• Each element has a unique set of energy levels, resulting in a characteristic spectrum
  • This allows astronomers to identify the composition of astronomical objects by analyzing their spectra
• The Bohr model of the atom explains the discrete energy levels and the resulting spectral lines
  • Electrons can only orbit the nucleus at specific distances, corresponding to distinct energy levels
  • Transitions between these levels result in the absorption or emission of photons with specific wavelengths

Emission and Absorption Spectra

• An emission spectrum is produced when an object emits light due to its own energy source
  • Consists of bright lines at specific wavelengths against a dark background
  • Examples include the spectra of stars, nebulae, and galaxies
• An absorption spectrum is produced when light from a continuous source passes through a cooler gas
  • The gas absorbs photons at specific wavelengths, creating dark lines in the spectrum
  • Examples include the solar spectrum and the spectra of distant stars observed through interstellar gas
• The presence of emission or absorption lines in a spectrum provides information about the composition, temperature, and density of the object or gas
• Kirchhoff's laws of spectroscopy describe the conditions under which emission and absorption spectra are produced
  • A hot, dense gas or a solid object produces a continuous spectrum
  • A hot, diffuse gas produces an emission line spectrum
  • A cool, diffuse gas in front of a source of continuous spectrum produces an absorption line spectrum
• Doppler shifts in spectral lines can be used to measure the radial velocity of astronomical objects
  • Blueshifted lines indicate motion towards the observer, while redshifted lines indicate motion away from the observer

Applications in Astronomy

• Spectroscopy is a fundamental tool in astronomy, allowing researchers to study the properties and composition of celestial objects
• Stellar classification is based on the analysis of stellar spectra
  • The Harvard classification scheme (OBAFGKM) is based on the strength of hydrogen absorption lines and the overall appearance of the spectrum
  • The temperature, mass, radius, and luminosity of a star can be estimated from its spectral type
• Spectroscopy is used to study the composition and evolution of galaxies
  • The spectra of galaxies contain information about their stellar populations, gas content, and chemical enrichment history
• Spectroscopic measurements of the cosmic microwave background (CMB) provide insight into the early universe and the formation of large-scale structures
• Spectroscopy is crucial in the search for exoplanets and the study of their atmospheres
  • The radial velocity method uses Doppler shifts in stellar spectra to detect the gravitational influence of orbiting planets
  • Transit spectroscopy can reveal the composition and structure of exoplanet atmospheres by measuring the wavelength-dependent changes in the star's light as the planet passes in front of it
• Spectroscopic observations of interstellar and intergalactic gas provide information about the distribution, composition, and evolution of matter in the universe
  • Absorption lines in the spectra of distant quasars are used to study the properties of intervening gas clouds and the large-scale structure of the universe

Key Equations and Concepts

• The speed of light ($c$) is approximately $3 \times 10^8$ m/s
• The relationship between wavelength ($\lambda$), frequency ($f$), and the speed of light: $c = \lambda f$
• The energy of a photon ($E$) is related to its wavelength ($\lambda$) by the equation: $E = \frac{hc}{\lambda}$, where $h$ is Planck's constant ($6.626 \times 10^{-34}$ J·s)
• Wien's displacement law: $\lambda_{max} = \frac{b}{T}$, where $b$ is Wien's displacement constant ($2.898 \times 10^{-3}$ m·K) and $T$ is the temperature of the blackbody
• The Stefan-Boltzmann law: $E = \sigma T^4$, where $E$ is the total energy emitted per unit surface area per unit time, $\sigma$ is the Stefan-Boltzmann constant ($5.670 \times 10^{-8}$ W·m$^{-2}$·K$^{-4}$), and $T$ is the temperature of the blackbody
• Kirchhoff's laws of spectroscopy:
  • A hot, dense gas or a solid object produces a continuous spectrum
  • A hot, diffuse gas produces an emission line spectrum
  • A cool, diffuse gas in front of a source of continuous spectrum produces an absorption line spectrum
• The Doppler shift formula for non-relativistic radial velocities: $\frac{\Delta \lambda}{\lambda} = \frac{v_r}{c}$, where $\Delta \lambda$ is the change in wavelength, $\lambda$ is the rest wavelength, $v_r$ is the radial velocity, and $c$ is the speed of light