Spectral Classes and the H-R Diagram

We previously mentioned the development of spectral classification in our History posts, but now we can really understand the science behind it.

Edward Pickering and Williamina Fleming (you remember them, don’t you?) originally classified stars based on the strength of hydrogen spectral lines — stars with the strongest hydrogen lines were class A, the next strongest were class B, and so on through class N. Later, Antonia Maury started to rearrange Fleming’s spectral classes, and then Annie Jump Cannon further rearranged them into the modern order OBAFGKM, which orders stars by temperature. O-stars are the hottest, typically >30 000 K, while M-stars are the coolest at between 2000 K and 3500 K. These classes are each divided into ten subclasses 0-9; for example, the hottest F-stars are F0 and the coolest are F9.

Stellar Spectra

Credit: University of Arizona [click for full-size image]

Characteristic spectral lines:

  • O — relatively weak H; strong HeII, neutral He; Si IV; double-ionized N, O, and C.
  • B — stronger H; neutral He (max intensity around B2); ionized O, N , Ne, Mg, Si.
  • A — very strong H (strongest at A0); ionized metals (Fe II, Mg II, Si II, Ca II).
  • F — weak H; both ionized and neutral metals.
  • G — weaker H; neutral metals (Fe, Ca, Na, Mg, Ti), especially Ca II in hotter stars.
  • K — even weaker H; Ca II, neutral Ca; neutral metals; TiO in cooler stars.
  • M — very weak H, if visible at all; neutral Ca; molecules like TiO, VO, and CN.

As one can see in the image below, the relative strength of spectral lines depends heavily on a star’s temperature. Spectral line strength can be described by the combination of the Boltzmann and Saha equations (both rather complicated). Basically, as the temperature rises, more atoms will be able to elevate their electrons to higher energy levels and thus produce absorption lines. However, if temperatures are too high, the atoms will have absorbed enough energy to be ionized and will not have the necessary electrons to excite to produce absorption lines.

Temperature Dependence for Spectral Lines

Credit: KCVS at The King’s University College (Alberta, Canada)

It should be noted that there are more spectral classes than just OBAFGKM — here we present a brief survey of those you’re mostly likely to cross paths with in Astronomy. Classes L, T, and Y are reserved for stars/substellar objects with temperatures progressively cooler than 2000 K. Class W (or WR) indicates a Wolf-Rayet star, a supergiant whose powerful stellar winds have blown away most of the hydrogen in its atmosphere. Carbon stars, dying supergiants with a large amount of carbon in their atmospheres, are spectral class C. White dwarfs are classified as D, because they are made of degenerate matter. Objects like neutron stars and black holes aren’t given a spectral class, because they are stellar remnants rather than stars.

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However, our discussion of spectral classes merely serves as an introduction to the Hertzsprung-Russell diagram, which is perhaps the most single important graph-chart-diagram-thing that you’ll ever encounter in astronomy (a slightly idealized version is shown in the image below). The H-R diagram is named after Ejnar Hertzsprung and Henry Norris Russell; they discovered it independently after plotting the luminosity of stars against color or spectral type, both of which are proxies for the star’s temperature.

H-R Diagram

Credit: ESA

This H-R diagram has double axes, showing the link between temperature and spectral class, and between absolute magnitude and luminosity. The numbering on some of the axes does seem to be going the wrong direction, but by convention, high temperatures are on the LEFT and larger absolute magnitudes are towards the BOTTOM (this is partly due to the fact that the entire magnitude system is “backwards”). Alternately, the x-axis may be labeled in terms of the stars’ B-V index, but no matter, it’s still an H-R diagram.

The main sequence appears as a diagonal line across the H-R diagram, clearly showing the link between luminosity and temperature for these stars — actually, both are dependent on a third factor, but we’ll cover that later. Above the main sequence are giant stars, which are relatively cool but have swelled up enough to cause an increase in overall luminosity. Even further above that lie the supergiants, very large stars that are also extremely luminous. Below the main sequence lies white dwarf stars, which are dim but rather hot. They will eventually migrate to the lower right as they cool off.

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When Hertzsprung and Russell plotted their data, they found for classes G, K, and M, there were a wide range of stellar luminosities. Independently, they both decided to call the brighter stars “giants”, since for two stars of the same temperature, the more luminous one must also be larger.

This led to the development of the Morgan-Keenan spectral classification, which sorts stars by not only spectral class but also by luminosity class. Stars in luminosity classes I-V are progressively less luminous and smaller in size for their spectral class. The luminosity classes correspond to supergiants, bright giants, giants, subgiants, and dwarfs (NOT white dwarfs, just main sequence stars). Class 0 has been tacked on for incredibly luminous “hypergiants”, while on the other end of the luminosity spectrum, classes VI and VII used to designate subdwarfs and white dwarfs but have since fallen out of common usage.

To give a familiar example, the Sun is a G2V star — its spectral class is G2, so it is slightly cooler than the 6000 K of a G0 star, and it is a main sequence “dwarf” as indicated by luminosity class V.

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Perhaps most practically, H-R clusters can be used to determine the age of star clusters. Imagine that a cluster has just been formed, with stars of all masses. This forms a “perfect” main sequence (ZAMS, the Zero-Age Main Sequence) when the H-R diagram of that cluster is plotted. As the highest-mass stars end hydrogen core fusion, they migrate away from the ZAMS towards the red giant branch, and the H-R diagram for the cluster starts to form a hook shape. The point where the hook starts to diverge from the ZAMS is called the main-sequence turnoff point.

H-R Diagram Clusters

Credit: Mike Guidry, University of Tennessee (through Penn State University)

After pinpointing the main-sequence turnoff, we can now find the age of the cluster. The stars located right at the turnoff point have just reached the end of their main-sequence lifetime; therefore, by determining their ages, we can determine the age of the cluster as a whole. The main-sequence life expectancy of a star is approximately: T = 1/(M^2.5), where M is in solar masses and T is in solar lifetimes (1 solar lifetime ≈ 10 billion years).

As shown in the image above, young clusters like h + χ Persei have turnoff points towards the left of the main sequence, since only the most massive stars in the cluster have had time to evolve off the main sequence. Old clusters like M67 have turnoff points closer to the middle or right side of the ZAMS because less massive stars have also had time to evolve off the main sequence.

And thus concludes our explanation of spectral classes and the H-R diagram. We do hope it was…stellar.

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TL;DR — Stars are divided into spectral classes O, B, A, F, G, K,  and M (and several others that are less common), each of which is characterized by certain absorption lines. The absorption lines depend on temperature, so spectral class is also an indicator of temperature. The H-R diagram typically plots temperature against luminosity; the main sequence stretching across the diagram shows the correlation between greater luminosity and greater temperature. The Morgan-Keenan luminosity classes show how luminous a star is for its temperature. The age of a cluster can be determined through its H-R diagram, by seeing where the cluster stars are beginning to leave the main sequence.

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Sources and links for further reading:

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