If I glance at your passport, I am able to figure out — depending on where you are from — your age, your country of origin, your full name, your social security number, and your gender, among other things, and in order to retrieve these bits of information from your passport, I need first and foremost to be able to read the language in which the information is written.
By the same token, the light that reaches us from stars carries a goldmine of data about their individual characteristics, and it is stellar spectroscopy that allows us to uncover and read these properties from the emitted light.
Some of the physical quantities that can be extracted by studying starlight include the temperature of the outer layer of the star, the nature and the relative amount of the chemical substances present, the luminosity, the density, and the star’s motion with respect to our position. Other pieces of information that can be obtained either directly or indirectly are the mass and size of the star, its rotational speed, the presence of any magnetic fields, stellar winds, or orbiting partners, as well as the distribution of matter around the star.
This article embraces three aspects in particular: the nature of matter (the chemical composition), the temperature, and the relative motion.
Spectra and Spectral lines
Light is made of oscillating electromagnetic fields, which carry energy with them and are able to propagate through empty space — this is how we can feel the heat of the Sun. That is, light fundamentally consists of energy waves, whereby their frequency, i.e., the number of oscillations per second, stretches across an entire continuous spectrum from a very low (radio waves) to a very high value (gamma rays).
The wavelength of an electromagnetic wave is defined as the distance between two peaks or two troughs, and it is connected to the frequency in the following way: a lower (higher) frequency implies a longer (shorter) wavelength. Moreover, a shorter (longer) wavelength (or a higher (lower) frequency) means that this specific type of light carries a greater (lesser) amount of energy.
Based on the specific nature of the various regions within the electromagnetic spectrum of light as well as practical considerations, the spectrum is divided into seven types of radiation (in order of ascending frequency): radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays.
Fig. 1 — The electromagnetic spectrum of light [Hz = Hertz; eV = electronvolt; cm = centimeter (10-2 m); µm = micrometer (10-6 m); nm = nanometer (10-9 m); pm = picometer (10-12 m)]. (Source: own creation).
Stellar spectroscopy is the study of the light emitted by astronomical objects, whereby the light is split into a spectrum of individual wavelengths by means of an instrument called a diffraction grating. The produced spectra come in three types: a continuous spectrum, an emission spectrum, and an absorption spectrum.
A continuous spectrum is the spectrum generated by a gas, liquid, or solid (typically called a blackbody radiator) that lacks any gaps in its spectrum. In contrast, an emission spectrum is the result of a (hot) gas that emits light and is characterized by only a few coloured lines against a dark background, whereas an absorption spectrum is created when light first travels through a (cooler) gas cloud before being collected and consists of a continuous spectrum containing black lines. The lines of the emission and absorption spectra are referred to as spectral lines.
Fig. 2 — A schematic view of the three basic types of spectra. (Source: Swinburne University).
Keep in mind that the gaps in an absorption spectrum arise at exactly the same wavelength at which the coloured spectral lines appear in an emission spectrum. Also, instead of depicting the emission and absorption spectra as electromagnetic bands upon which the respective spectral lines are imprinted, the spectra can also be portrayed in a graph, whereby the flux is plotted against the wavelength — the flux is the luminosity or the intrinsic brightness of a star, i.e., the energy received per unit of time, measured across a certain area.
Fig. 3 — The continuous, absorption, and emission spectrum. (Source: own creation).
Shining Light on Matter
Atoms, Energy Levels, and Wavelengths
The spectral lines shown in Fig. 3 are the result of matter interacting with light. That is, the atoms of which matter is made are able to absorb and re-emit electromagnetic waves. However, this only occurs when a certain condition is fulfilled: the energy of the incoming light must match the difference in energy between two specific energy levels within the atom.
In a nutshell, an atom consists of a positively charged nucleus around which negatively charged electrons are whizzing around in certain bands of energy called orbits at a more or less fixed distance from the nucleus. The electrons can either switch to lower energy orbits closer to the nucleus or jump to higher energy bands farther away from the atomic centre. More accurately, the orbits, a.k.a. electron shells, each contain a well-defined number of more subtle energy levels, referred to as subshells.
When an electron falls down from a higher to a lower energy subshell, i.e., it moves closer to the nucleus, it releases energy, whose value is equal to the difference in energy between the two respective subshells. Moreover, the energy is emitted in the form of electromagnetic radiation, i.e., light. Conversely, an electron climbing to a higher energy subshell requires an intake of energy, which it gets from incoming electromagnetic waves. These two actions of an atom are designated as the emission and absorption of light, respectively.
An atom of one chemical element, such as iron (Fe) or magnesium (Mg), is distinguished from an atom of another element, say hydrogen (H) or copper (Cu), by the number of positive charges, called protons, residing within the nucleus. As every chemical element has a distinct number of protons, it follows that the strength of the electrostatic force, which draws protons in the nucleus and electrons in the surrounding subshells closer together, differs from subshell to subshell and from element to element.
In other words, the corresponding amount of energy of a subshell is uniquely defined for every chemical element as well as the energy difference between two subshells. Put differently, if the energy associated with a certain wavelength of electromagnetic radiation resonates with the energy difference of two subshells in a certain atom, it means that this specific wavelength is exclusively linked to that particular subshell transition. When considering all the possible energy transitions of the electrons in an atom of a certain element, it can be concluded that every element generates a unique set of wavelengths.
This is the reason, in the context of stellar spectroscopy, why a specific pattern of spectral lines is able to give away which chemical element is absorbing or emitting the respective wavelengths of light.
Fig. 4 provides an overview of the first fifteen subshells in ascending order in terms of energy (left-hand side) — every little square is called an orbital and can hold a maximum of two electrons — as well as the unique spectra for the elements hydrogen (H), helium (He), and oxygen (O), restricted to the electromagnetic region of visible light (right-hand side).
Fig. 4 — The atomic subshells ordered by increasing energy (left-hand side) and the spectra for hydrogen (H), helium (He), and oxygen (O). (Sources: own creation (subshells) and nagwa (spectra)).
Bear in mind that the spectral lines produced in the infrared, visible light, and the ultraviolet region of the electromagnetic spectrum (see Fig. 1) are mainly a manifestation of energy transitions carried out by the electrons in the outer electron shell, called valence electrons, not by the inner electrons closer to the nucleus.
As an example, Fig. 5 illustrates how the valence electron of the elements sodium (Na) and hydrogen (H) is able to engage in a wide range of possible energy transitions between various subshells, whereby the electron’s lowest energy state, i.e., the ground state, is represented by the subshells 3s and 1s, respectively.
Fig. 5 — Some energy transitions for the elements sodium (Na) and hydrogen (H). The indicated values for sodium are expressed in nm. (Source: adapted from David Harvey (sodium) and phys.libretexts (hydrogen)).
Also, the more protons present in a nucleus — thus the heavier the element — the more electrons surrounding the atom — in an electrically neutral atom, the number of protons and electrons is the same — and therefore the larger the number of spectral lines, since there is an increasing number of energy transitions possible between the subshells. At the same time, it becomes progressively more difficult to interpret their spectra, as the spacing between subsequent energy levels grows ever smaller.
Table 1 further demonstrates the unique connection between wavelengths and the specific chemical element, listing besides a selection of wavelengths also the width of the corresponding spectral line for the elements calcium (Ca), aluminum (Al), iron (Fe), strontium (Sr), hydrogen (H), magnesium (Mg), chromium (Cr), barium (Ba), and sodium (Na). The Roman numeral I after an element specifies that it concerns a neutral atom, whereas the numeral II indicates that one electron has been stripped away from the atom, i.e., the atom has been ionized once.
Table 1 — The wavelengths and spectral line widths for a number of chemical elements. (Source: adapted from Columbia University).
Starlight Spectra
After light is created within the core of a star as a result of hydrogen (H) and helium (He) atoms fusing together in a process called stellar nucleosynthesis, the rays of light travel towards the outer regions of the star — they follow a random path, not a straight line, since they are constantly being scattered around — where they only become detached from the star — and thus visible to the outside world — after crossing the innermost shell of the star’s atmosphere, i.e., the photosphere.
Nevertheless, the electromagnetic waves still have to pass through a couple of outer gaseous atmospheric layers before finally venturing into empty space. Therefore, some of the wavelengths are stopped in their tracks and absorbed by the atoms or ions that dwell in these outer layers, resulting in an absorption or emission spectrum — ions are atoms that have gained or lost electrons and are thus electrically charged particles.
With the assistance of stellar spectroscopy, it is then possible to identify upon reception of that starlight which chemical elements are present in the star’s atmosphere.
For instance, Fig. 6 portrays the absorption spectrum for electromagnetic radiation (light) captured from the star in our Solar System, i.e., the Sun, indicating the chemical elements associated with some of the more prominent spectral lines. Note, however, that the molecular oxygen (O₂) spectral lines towards the red end of the spectrum are due to the absorption of sunlight in the Earth’s atmosphere, not the Sun’s atmosphere.
Fig. 6 — The absorption spectrum of sunlight. (Source: adapted from Montana State University).
The width of a spectral line — or, alternatively, the strength of the line’s profile (shape) in a flux versus wavelength graph (see the jagged blue line in Fig. 6) — is impacted by the number of atoms involved in the corresponding energy transition. That is, the greater the number of atoms or ions of a certain chemical element absorbing this particular wavelength, the broader the spectral line — or, the stronger the line’s profile.
Having said that, however, it must be highlighted that the number of atoms is not the only factor affecting the spectral line width. Other dynamics at play are the temperature (more on that in the section “Heat Waves Exposed” further below) and the pressure of a star’s atmosphere, the nature of reality at the smallest of scales (i.e., quantum mechanical phenomena), the frequency of collisions between atoms or ions in the atmospheric gas (i.e., the gas density), and a star’s rotation rate (see subsection “Spinning Stars” further below).
Because of this plethora of factors influencing a line’s profile, the spectra of stars can exhibit various appearances, as illustrated below in Fig. 7, whereby the spectra of eleven stars are shown with respect to the electromagnetic region of visible light, a.k.a. the optical region.
Fig. 7 — The absorption spectra in the optical region of eleven different stars. (Source: Rochester Institute of Technology).
Despite the wide variety of stellar spectra, the astronomer Cecilia Payne discovered that the chemical composition of a star’s atmosphere is largely the same for most stars: in terms of mass, it consists of 71.0% hydrogen (H), 27.1% helium (He), and 1.9% oxygen (O), carbon (C), and other heavier elements, whereas in terms of number of atoms, stars are made of 91.2% hydrogen (H), 8.7% helium (He), and 0.1% other elements, including oxygen (O), carbon (C), nitrogen (N), silicon (Si), magnesium (Mg), neon (Ne), iron (Fe), and sulphur (S).
Based on her work, it is now established that it is the relative portion of atoms residing in each of the energy levels, i.e., the ground state, the first excited energy level, the second one, and so on, that must be calculated for every element — instead of considering the line width or the relative number of spectral lines — in order to correctly identify the star’s chemical composition.
Heat Waves Exposed
Appearing and Disappearing Profiles
As highlighted in the previous section, a wide range of factors determine the profile of a spectrum. In fact, when it comes to the absorption lines, it is predominately the temperature of the photosphere that is holding sway over their strength. In other words, the absorption spectrum of a star reveals in the first instance information about the star’s surface temperature, rather than its chemical composition.
A higher temperature, which is defined as the average energy of motion (kinetic energy) of a whole swarm of particles, means that the electrons within the atoms are thermally excited to higher energy levels. This, in turn, leads to the observation that the relative fraction of spectral lines associated with lower energy subshells is diminished — or, the intensity of their profile is weakened.
As a result, it is not because a particular spectral line is missing from the optical spectrum — or, that it is less pronounced — that the respective chemical element is not present in the star’s atmosphere — or, lesser in number. Similarly, a greater number of spectral lines coupled to a certain element — or, a more intense profile — does not necessarily imply that this element is relatively more abundant.
Fig. 8 demonstrates the impact of different photosphere temperatures on a line’s profile strength. Concerning the hottest stars (the upper two lines), most of the hydrogen (H) and metal atoms, such as magnesium (Mg), sodium (Na), and calcium (Ca), are ionized, leaving the atoms without any electrons to engage in energy transitions and thus without any possibility of emitting or absorbing electromagnetic waves. This translates into the appearance of a weak spectral profile, which is particularly conspicuous for the uppermost line T=40,000K — note that the corresponding energy level for a state of full ionization is the level n=∞ (see Fig. 5).
Fig. 8 — Seven stellar spectra in descending order in terms of surface temperature, from top to bottom, with temperatures expressed in Kelvin. (Source: adapted from ‘Astrophysics in a Nutshell’, Dan Maoz, 2nd ed., 2016, p.20).
In the case of hydrogen (H), this means that, relatively speaking, only a very small number of atoms are absorbing wavelengths associated with lower energy levels — after all, the temperature is an average measure, so some atoms will possess a lower temperature.
As illustrated in Fig. 5 (right-hand side), the only lower energy level in the hydrogen (H) atom that absorbs light in the optical region — we wish to focus on this region, as it the region zoomed in on in Fig. 8 — is the level n=2, with the respective wavelengths of 656 nm (n=3), 486 nm (n=4), and 434 nm (n=5), and, indeed, Fig. 8 shows that for these optical wavelengths the hydrogen (H) profiles of the hottest stars are only marginally pronounced.
When turning to medium temperature stars (the third, fourth, and fifth line from the top in Fig. 8), the surface temperature is just right for most of the hydrogen (H) atoms to reside in the second energy level (n=2), resulting in a stronger spectral profile in the optical-wavelength region, especially with respect to the line T=8,500K.
In cooler stars (the two bottommost lines), the line’s profile for the hydrogen (H) atoms is again weakened, as the lower temperature is arranging for the atoms to dwell mostly in their ground state (n=1), which absorbs wavelengths in the ultraviolet region of the spectrum (around 100 nm), not the optical region (see Fig. 5, right-hand side).
In contrast, the spectral profile of metal atoms grows stronger in cooler stars since their ground state energy level absorbs optical wavelengths (see Table 1). Not only that, the spectra become also sensitive to the presence of molecules, such as titanium oxide (TiO) in the line T=3,500K, whose absorption in the optical-infrared border region (700–900 nm) is the main reason for the line’s more prominent spectral profile.
Labelling Stars
Stars are categorized into the following seven classes according to their surface temperature (in ascending order): M, K, G, F, A, B, and O. Every capital letter of a certain class is furthermore followed by two indices: a number from 0 to 9, with 0 referring to the highest temperature, and a Roman number between I and VII, with I indicating the strongest luminosity.
Table 2 — The stellar spectral classification system based on the atmospheric temperature, mentioning some of the properties of the different classes, with M(𐍈), R(𐍈), and L(𐍈) the mass, radius, and luminosity of the Sun, respectively. (Source: adapted from University of California San Diego).
For example, the Sun is classified as a G2V star with a surface temperature of approximately 5,800K, Alnitak Aa (located in the Orion constellation) as a O9.5Iab star at 30,000K, Aldebaran (situated in the Taurus constellation) as a K5III star at 4,000K, and Sirius (positioned in the Canis Major constellation) as a A1Va star at 9,940K — note that the luminosity class is often further specified by three sublevels, i.e., a, ab, and b (in descending order).
In general, stars that belong to the same class exhibit similar physical properties, such as mass, radius, and luminosity. What is more, a number of trends exist between these physical parameters. For instance, brighter stars are usually larger within a given class, and more massive stars are typically hotter and more luminous. Taking also into account the age of stars, these relationships between the various physical quantities can be organized into one graph called the Hertzsprung-Russell Diagram, which shows that some stars can be very hot and small but faint (e.g., Sirius B), while others cold and large but very bright (e.g., Betelgeuse).
Fig. 9 — The Hertzsprung-Russel Diagram. (Source: New Jersey Institute of Technology).
Line Widths and Profile Shapes
Apart from a relative effect of the surface temperature on the line strength (as discussed in the above subsection “Appearing and Disappearing Profiles”), the temperature also exerts an absolute effect. That is, the spectral lines of hotter stars are more broadened relative to the lines of their cooler counterparts — or, alternatively, the line’s profile in a flux versus wavelength graph is less sharp and more spread out.
The underlying reason is what is known as thermal Doppler broadening and is based on the relative motion of the atoms or ions that are absorbing incoming light. The Doppler effect in the context of electromagnetic radiation tells us that waves emitted by an object moving towards (away from) an observer are perceived by the observer as more squeezed together (more stretched out), resulting in an apparent shorter (longer) wavelength, i.e., a shift towards the blue (red) end of the spectrum.
As all atoms or ions are moving in a gas, they all cause a Doppler shift to some extent. However, atoms or ions in a hotter (cooler) gas move at greater (lower) speeds, so the Doppler effect becomes more (less) pronounced. In other words, the wavelengths of the atoms or ions of a particular chemical element that are moving away from (towards) us are more red-shifted (blue-shifted) in a hotter gas with respect to a cooler gas.
The overall effect of the greater (lesser) motion of the atoms or ions in a star’s atmosphere — and thus, of a higher (lower) surface temperature — is that the respective spectral lines become more (less) broadened.
Fig. 10 — The effect of temperature on the spectral line width and line strength. (Source: own creation).
Besides the line width and strength, the surface temperature also affects the entire shape of a spectrum. That is, a higher (lower) temperature moves the peak of a line’s profile in a flux versus wavelength diagram towards shorter (longer) wavelengths.
Fig. 11 — The effect of temperature on the overall shape of a line’s profile. (Source: own creation).
The reason for this is that, as the temperature of an object rises, more energy is being radiated out, which not only pushes up the peak flux (and the luminosity) but shifts that peak towards the blue end of the optical spectrum, since electromagnetic waves with a shorter wavelength carry more energy with them. Note that in a flux versus wavelength graph, the total amount of radiated energy is equal to the surface below the curve.
In the context of the stellar spectral classification scheme (see subsection “Labelling Stars” above), the above-described relationship explains why a hotter B star exhibits a bluish white colour, whereas a cooler M star features a red colour.
Unscrambling Stellar Motion
Directional Cues
In the above subsection “Line widths and Profile Shapes”, the Doppler effect explains how the surface temperature of a star impacts the nature of spectral lines. However, this motion-related effect also provides insight into other physical quantities and astrophysical phenomena. For one, the Doppler effect equally accounts for the direction in which stars, or even entire (clusters of) galaxies, are headed.
That is, if a star is moving towards us, then the received starlight exposes a shift in the position of the spectral lines towards shorter wavelengths — the electromagnetic waves are perceived by us as more squeezed together. Conversely, a star receding from us emits light that features red-shifted spectral lines — the wavelengths appear longer to us.
Moreover, the difference in value between the observed wavelengths and those of a reference star, such as the Sun, which is stationary relative to our position, is used to calculate the velocity of the moving star along the line of sight of the observer — this velocity is called the radial velocity. The larger the wavelength gap, the greater the velocity of the moving star.
Apart from the radial velocity, there is another component to a star’s velocity, namely, the transverse velocity, a.k.a. the proper motion, which is oriented at a perpendicular angle with respect to the line of sight of the observer. However, the proper motion of stars leaves the position of the spectral lines unaffected and is therefore not further discussed here.
Fig. 12 — The impact of a star’s relative motion on the perceived position of its hydrogen (H) spectral lines within its absorption spectrum. (Source: own creation).
Fig. 12 illustrates this effect of the relative motion of a star on the position of the hydrogen (H) spectral lines within its absorption spectrum. Given that most stars, in terms of mass, contain 71.0% hydrogen (H) — see above subsection “Starlight Spectra” — it follows that most stars also feature hydrogen (H) lines in their optical spectra, assuming an adequate surface temperature — see above subsection “Appearing and Disappearing Profiles”. This fact allows for the comparison of the position of the hydrogen (H) lines between a stationary star and a star in motion with respect to the Earth.
Other than the Doppler redshift due to the receding motion of stars, there is another kind of wavelength stretching which is related to the distance of the moving star or galaxy and a consequence of the expansion of the Universe itself: the cosmological redshift.
Not only is the wavelength shift more pronounced as the star or galaxy is located farther away from the Earth — by crossing a larger distance, the light has been subjected to a greater amount of expansion of the fabric of spacetime itself and thus features a larger redshift — but a larger distance also implies that the star or galaxy is receding from us at a greater velocity — the latter relationship is referred to as Hubble’s Law.
Spinning Stars
Besides the relative motion of stars and galaxies, the Doppler effect can furthermore shed light on rotating stars. That is, in spinning stars, one side, say, the left side, is moving towards us, whereas the other (right) side is receding from us — for simplicity, we imagine the axis of rotation to be perpendicular to our line of sight — so that the light coming from the left (right) side is blue-shifted (red-shifted).
The net effect is that the spectrum of a rotating star shows broadened spectral lines — this phenomenon is known as rotational broadening — and the faster a star rotates around its axis, the thicker the spectral lines appear. From the wavelength shift, it is then possible to calculate the rotation rate of the star, i.e., the time it takes for the star to complete one rotation.
In addition, hotter stars generally tend to rotate faster than cooler stars. For example, the rotation rate of the Sun (a G2V star) measures on average 27 days, that of Alpha Caeli A (an F2V star) about 1.4 days, and that of Altair (an A7V star) merely 9.3 hours.
Fig. 13 — A schematic of spectral broadening in rotating stars. (Source: own creation).
Treasures in a Flickering Disguise
This article explored how the nature of matter in the outer layer of stars, the atmospheric temperature, and both the relative and rotational motion of stars can be inferred from the light they generously emit.
Nonetheless, the article just scratched the surface, as much more information can be retrieved or deduced from stellar spectra, including the presence of magnetic fields, the identification of binary star systems, information on the structure of galaxies and dark matter, as well as the size of the Universe (via the Hubble’s constant).
Unlike the information on your passport, the treasure troves of information embedded within starlight will never be up to date since the electromagnetic waves can only propagate through vacuum at a limited speed, i.e., the speed of light. In other words, if we look up at the stars in the sky, we are gazing into the past due to the vast distances that separate us.
Be that as it may, this restricting factor will never quench our eagerness to decrypt the flickering messages that the wider Universe imparts upon us.
Richie
Hi Olivier,
Another fascinating article, thank you.
Matters of the universe tend to blow my mind!
I know that when I look at a star I am seeing a historical representation of the star, because of the delay in receiving the visual information, but it still seems strange. And if we can calculate the size of the universe … what is there after the universe? I suspect that there is still a great deal for man to discover in space but until we learn how to travel much faster it will remain a mystery 🙂
Olivier Loose
Hi Richie, I’m glad you enjoyed the article! I might have been a bit sloppy with the terminology. When talking about the Universe, what is usually implied is the observable Universe. That is, due to restriction on the speed with which light travels, there is a limit to the distance at which we can observe astronomical phenomena around us. Although we typically think that distance is equal to 13.8 billion light years (due to the age of the Universe), it is actually calculated to be 46.1 billion light years as a result of the expansion of the Universe.
If you wish to read more about this, here are two links:
1/ https://www.forbes.com/sites/startswithabang/2020/01/21/how-far-is-it-to-the-edge-of-the-universe/?sh=6b27474f55a3
2/ https://lweb.cfa.harvard.edu/seuforum/faq.htm