Spectral Classification of Stars
Historical Development. The analysis of stellar spectra begins with Joseph von Fraunhofer's observations (1817) of the solar spectrum and the spectra of several bright stars, published in 1823. Fraunhofer measured the wavelength position of over 500 solar absorption lines, the most prominent of which are still identified today with the letter labels he assigned to them.
After the laboratory observation by Gustav Kirchhoff and Robert Bunsen in 1860 of spectral emission lines in the light emitted by heated chemical elements, and of matching absorption lines when broadband light was transmitted through the elemental gas or vapor, the potential was recognized to identify the chemical elements present in stars by matching stellar absorption lines to laboratory emission spectra, and perhaps to measure stellar radial motion relative to the Earth by means of Doppler shifts in line wavelengths.
William Huggins (1864) identified several chemical elements in stellar spectra, discovered emission lines in planetary nebulae, and documented significant spectral differences among the spectra of bright stars. Instruments of greater sensitivity were developed, in particular the prism spectrographs made by Lewis Rutherfurd (1863) and the high dispersion diffraction grating spectrographs made by Henry Rowland (1887). Using a spectrograph of his own construction, Rowland photographed the first atlas of the solar spectrum (Photographic Map of the Normal Solar Spectrum, 1888): a series of plates that assembled into a 40 foot long image resolving over 20,000 solar absorption lines.
From the beginning, astronomers proposed schemes to classify the observed variety of stellar spectra. Among the first and most influential of these was a system of four categories (stars matching I Sirius, II the Sun, III Betelgeuse or IV carbon stars) developed by Father Angelo Secchi from 1863 to 1870 on the basis of star color and the relative strength and width of spectral absorption features (diagram, right).
Why did stars differ in color and spectral features? Some astronomers adopted the hypothesis proposed by Hermann von Helmholtz (1863) and James Homer Lane (1871) that the energy of stars was created by the gravitational contraction of gas nebulae. This was believed to produce a continuous rise in stellar temperature up to the maximum contraction, followed by a prolonged cooling of the compact body, in a red-white-blue-white-red color sequence. Two influential classification systems based on this idea were proposed by Hermann Carl Vogel (1874-1895) and by Norman Lockyer (1890). The discovery of terrestrial helium in 1895, which matched solar absorption lines noticed in the total solar eclipse of 1868, stimulated Vogel (1899) to revise his system so that stars with helium lines were on the "compact and cooling" side of the contraction process.
These evolutionary conjectures were superseded by an ambitious and purely empirical cataloguing project launched in 1885 at the Harvard College Observatory and based on a photographic survey comprising 10,351 stellar spectra compiled under the supervision of E.C. Pickering. The project was funded as a posthumous memorial to New York physician Henry Draper, an avid amateur astronomer and pioneer of photographic spectrography, by his widow Mary Anne. Classification of spectra for the first Henry Draper Catalogue (1890) was performed under the supervision of Williamina Fleming by a cadre of female "computers" (so called because similar astronomical teams were used to calculate ephemerides and binary star orbits). For this work, Pickering and Fleming adopted Draper's method of applying A to M letter labels over subdivisions of the four Secchi categories to represent decreasing absorption lines of hydrogen (most pronounced in A type stars such as Sirius); they added categories O, P and Q to designate objects that uniquely showed emission lines: Wolf-Rayet stars, planetary nebulae and novae.
A greatly expanded sample of stellar spectra, including stars in the southern celestial hemisphere and new high resolution spectra of the brightest stars, required additional categorization that was tackled in a division of labor among Antonia Maury (niece of Henry Draper), Annie Jump Cannon and Henrietta Swan Leavitt among others.
Maury developed a complex categorization, published in 1897, based partly on temperature (starting with the "Orion type" or B stars) and the width of spectral lines; this system was cited in Ejnar Hertzsprung's 1905 to 1909 papers on the differences in apparent magnitude (luminosity) and proper motion (distance) across the O, B, G and M spectral types that opened the way to the Hertzsprung-Russell diagram, a plot of the distribution of the luminosity and surface temperature of stars (image, left). By then Maury had left the Harvard group due to conflicts with Pickering and his refusal to adopt her novel classification scheme and its claimed basis in stellar evolution. (She returned to the Harvard observatory in 1922 to continue work under Harlow Shapley.)
Meanwhile Cannon produced a conservative classification that relied on the progressive appearance or disappearance of specific spectral features, including helium, and was the first to correctly order all spectra in a temperature sequence (starting with the O type stars). Her system retained much of the already published Draper letter system by combining several categories and dropping their letter labels while repurposing others to form the now familiar spectral type sequence [W] O B A F G K M [C P], kept forever in memory by the gender neutral mnemonic phrase Odd Boys And Funny Girls Kiss Me. (Henry Norris Russell endorsed this alphabetical disorder because it "helps to keep the novice from thinking that the system is based on some theory of evolution.") Cannon added the numerical division of categories into 10 subgroups to more precisely specify subtle spectral differences. This final Harvard System was published in 1912 (a year after Cannon embarked on the task of cataloguing and classifying new and high quality spectra of over 225,000 stars). The Draper system was formally adopted as a provisional standard despite some reluctance to abandon the "evolutionary" Vogel approach by the International Astronomical Union at its first (1922) General Assembly in Rome.
By that time fundamental advances had been made in astrophysics. These included Max Planck's equations for blackbody radiation using a quantum theory of energy (1901), Niels Bohr's electron shell theory of atomic structure (1913), elucidation of the mass/luminosity relationship by Ejnar Hertzsprung and H.N. Russell (1905-1913), and the description of atomic ionization states by Megh Nad Saha (1920). Thereafter Cecilia Payne-Gaposchkin (1925) identified the elemental ionization states produced by different surface temperatures and demonstrated that stars consist mostly of hydrogen; Sir Arthur Eddington applied Karl Schwarzchild's concept of radiative equilibrium to the The Internal Constitution of the Stars (1916-1925); and Hans Bethe (1939) described the nuclear fusion processes that generate stellar energy, which Subrahmanyan Chandrasekhar (1939) formalized as a theory of stellar evolution, including the gravitational collapse that produces supernovae and white dwarfs. Contributing to these theoretical advances, several decades of intensive observations of the Sun motivated the development of new observing techniques and basic insights into stellar structure and thermodynamics. These placed the theory of stellar evolution and the procedures of spectral classification on a firm empirical basis, and provided a detailed understanding of the relationship between stellar spectral features, elemental excitation and ionization states, surface temperature and surface gravity.
Building on this foundation, luminosity codes were combined with the Harvard spectral types to form a two dimensional classification scheme in the Atlas of Stellar Spectra by William Morgan, Philip Keenan and Edith Kellman (1943). This atlas comprised 55 plates, each plate presenting 4 or more ultraviolet spectra taken with the 40 inch Yerkes refractor, that illustrated differences both in spectral type and in the luminosity features emphasized by Maury. Subsequently revised and augmented, the MK system is the principal stellar classification system in use today. Even so, no spectral classification system has been accepted as definitive by the IAU: as Morgan said in 1979, "The MK system has no authority whatsoever; it has never been adopted as an official system by the International Astronomical Union or by any other astronomical organization. Its only authority lies in its usefulness; if it is not useful, it should be abandoned."
Temperature & Spectral Type. The fundamental property of a star is its mass in stellar astrophysics, mass is destiny. Mass determines the gravitational pressure in the stellar core, which determines the core temperature and the rate of nuclear fusion: more massive stars are hotter, consume their nuclear fuel more rapidly, and have shorter lifetimes on the Hertzsprung-Russell main sequence (diagram above). Energy from the core nuclear fusion slowly radiates outward through the body of the star, becoming smoothed out into the distribution of radio to xray photons observable from Earth as the star's flux profile. (Stars also "shine" through neutrino emittance and mass loss or "evaporation" at the surface, but these do not affect the spectral type.) Thus, the mass, temperature and luminosity of a star are fundamentally related.
Spectral classification examines only the light emitted by the relatively thin external layer or photosphere of a star. The thermodynamically stable stellar plasma below the photosphere creates a continuous blackbody spectrum that peaks at a specific temperature. This determines the overall shape of a star's flux profile from the high energy, leftward rising profile of "blue" Type O and B stars that peak in the ultraviolet, through the relatively flat profile of "white" Type F and G stars that peak in the visual, to the low energy, rightward rising profile of "red" Type K and M stars that peak in the far red or infrared (diagram, right). The spectral type corresponds to the effective temperature (Te) of a star, which is the blackbody temperature that matches its radiant flux per surface area equivalent to the calculated temperature of the blackbody profile that best fits the overall shape and peak emittance of the observed flux profile.
The photosphere decreases in temperature from the inside out: the outer surface of the photosphere is cooled by radiating energy into space, which allows it to absorb some of the light from the stellar interior. Absorption occurs when a photon of a specific energy (frequency) increases the orbital energy of a specific electron within an atom, which returns to its original orbit by emitting the same energy at lower frequencies. Quantum physics dictates the specific wavelengths at which each chemical element will absorb and emit light, which identifies the signature absorption lines for each element in a stellar spectrum. These appear as troughs and notches in a flux profile.
As the temperature of the exterior layer of the photosphere goes down, it is able to absorb more energy and display more absorption features. Increased absorption significantly "filters" or obscures the flux profile at low temperatures, especially in high luminosity stars and stars with metallic content. (In astrophysics, a "metal" is any element heavier than helium.) In these situations the ratio between the strength of specific absorption lines can be used to infer temperature.
This method is used to calculate the excitation temperature (Tx), measured as the ratio in the strength of absorption lines produced by atoms of the same element at two different electron energies, or the ionization temperature (Ti), measured as the ratio in the strength of absorption lines produced by atoms of the same element stripped of one or more electrons. Simple molecules such as cyanogen or titanium oxide also form in the photosphere of relatively "cool" stars (temperatures of a few thousand kelvins), and temperature can be estimated by their appearance and relative strength. Because the peak excitation or ionization of different elements occurs at different temperatures, as illustrated in the schematic (above), comparison of the line strength of different elements can be used to infer the photosphere effective temperature (spectral type).
Hydrogen (H) lines (including the closely spaced absorption features that disappear at the Balmer Jump) are strongest in Type A0 stars (hence the original place of the A stars at the head of the stellar sequence), and grow fainter at both higher and lower temperatures. Sodium (Na) and calcium (Ca) lines become significant in Type G stars and grow more prominent as stars become cooler. Diatomic molecules including titanium oxide (TiO), cyanogen (CN) and many organic molecules form when the photosphere temperatures fall below a few thousand kelvins. In the coolest brown dwarf objects, water vapor (H2O) and methane (CH4) can form in the atmosphere.
Radius & Luminosity Class. Differences in luminosity are caused not by a star's mass but by its age. After a main sequence star has burned (through nuclear fusion) enough hydrogen to accumulate a massive core of helium "ash" (which takes about 10 billion years for a solar mass star), this core collapses under its own weight, increasing the core temperature to the point where helium fusion can occur and the resulting thermal pressure counteracts the gravitational contraction. The star fuses helium into carbon inside a shell of still burning hydrogen. In the most massive stars, a similar collapse of carbon ash fuses to form oxygen, which combines to form heavier elements neon, sodium, magnesium, sulfur, silicon and finally metals up to iron, which cannot release energy through nuclear fusion. (Energy is not released through iron fusion but must be added to make it happen, which means chemical elements heavier than iron are only formed in the energetic collapse and explosion of a supernova, where the necessary energy is supplied by a catastrophic gravitational collapse.)
In the devolution of an aging star, the outward pressure of energy released by the fusion of heavier elements is able to balance the inward force of gravity. But at some point the mass of the core ash is insufficient to compress the core into the temperature necessary to fuse heavier elements, and gravity wins. In solar mass stars, this final collapse produces a nova that results in an inert and slowly cooling white dwarf inside a planetary nebula; in the most massive stars the gravitational collapse of the iron core produces a supernova that results in a neutron star or black hole.
Before that end stage collapse occurs, the increased energy outflow produced by the transition to helium fusion causes a dramatic increase in the radius of the star. Because the photosphere has expanded to a great distance from the nuclear core and also has a greatly increased surface area, its temperature goes down. In addition, because it is much farther from the center of mass, the gravitational pressure on the photosphere is reduced: it expands and becomes more rarefied. This cooler, larger and less dense photosphere causes a narrowing and strengthening of spectral lines and the appearance of many absorption lines from any "metals" that were part of the star's original composition (diagram right, bottom). The increased surface area of the star also increases the luminosity of the photosphere and the absolute magnitude of the star.
These larger, brighter stars are subgiant, giant or supergiant stars, which can be tens to hundreds of times the radius and emit hundreds to thousands of times the energy of main sequence stars of the same mass. These spectral changes are indicated as the luminosity class joined to the spectral type.
The extent of these changes indicates the relative increase in the stellar radius. This is illustrated in the diagram (above right) in the flux profiles of an F0 type star on the main sequence (V), an F0 mass star with a large helium ash core (subgiant, III) and an F0 star with a helium burning core and greatly expanded radius (supergiant, Ia). These profiles illustrate the spectral effects of the decrease in surface gravitational pressure (increase in photosphere depth) and the decrease in surface temperature that result from an increase in stellar radius.
Physical Equations. The astrophysics can be summarized in a handful of basic equations standardized on solar units. The effective temperature or color temperature can be derived from the peak wavelength (λmax, in meters) of a blackbody spectrum of temperature T (in kelvins) as:
λmax = 2.898x10-3/T[K] (Wien's displacement law)
If the peak is obscured by absorption features, the effective temperature can be approximately calculated from the color temperature, as described below.
Then the luminosity of a star on the main sequence is related to its mass approximately as:
L/L⊙ = (M/M⊙)3.5
where L⊙ and M⊙ denote the luminosity and mass of the Sun. Finally, the radius of a star is estimated from its luminosity and surface temperature approximately as:
R/R⊙ = √(L/L⊙)/(T/T⊙)4
where R⊙ is the radius of the Sun. In addition, the lifetime of a star on the main sequence is related to its mass and luminosity approximately as:
t/t⊙ = (M·L⊙)/(L·M⊙)
where t⊙ is roughly 15 billion years.
Classification Process. In summary, a star's spectrum presents information about its mass, temperature, luminosity, radius and chemical composition, and can also be used in some cases to identify and measure rotational velocity, surface expansion or contraction, the strength of magnetic fields, the presence and speed of stellar winds, and the composition of circumstellar clouds of gas or dust. Spectral classification is a method to organize this wealth of information around the fundamental properties of mass (temperature) and radius (luminosity).
Fifty-one of the spectral/luminosity categories in the MK system are defined by specific Anchor Point Standard stars with stable and unobscured spectra a classification procedure first applied by Secchi. These serve to document the defining category attributes in the same way that a holotype specimen is used to define a biological species. Among these are β Orionis (Rigel, B8 Ia), α Cygnis (Deneb, A2 Ia), α Persei (Mirfak, F5 Ib), the Sun (G2 V), β Geminorum (Pollux, K0 III) and α Orionis (Betelgeuse, M2 Ib). To these are added Primary Standard stars as exemplars of the remaining categories, and Secondary Standard stars that are visible at different times of the year and in the northern or southern hemispheres.
A classification is made by comparing the flux profile of a star with the flux profiles of the standard stars. The flux profile records the electromagnetic energy emitted within narrow wavelength bins (0.1 to 0.4 nm, 1 to 4 Å) measured across a limited section of the electromagnetic spectrum, most conveniently represented as a graph of energy across wavelength (as shown in the diagrams above, right), or as a tabulation for computer analysis. The 1943 Atlas was limited to the "blue" end of the spectrum necessary to expose the slow photographic emulsions of the era, and the MK codes are still primarily defined by "ultraviolet" spectral features in the 380 to 500 nm range (indicated by the vertical blue band in diagrams, above). However, revisions and ancillary classification systems have extended the system into the xray and infrared, and have created new categories such as the L and T brown dwarfs.
A star is classified by assigning to it the type category of the closest matching standard flux profile or of the blend between two profiles; gradiations in the match are signified by the numerical subtypes. The spectral matching is made using very specific absorption features the strength and width of spectral lines, separately or as ratios between pairs of lines and the lines used in these comparisons are different across the different spectral types. As explained above, hydrogen (H), helium (He), silicon (Si) and magnesium (Mg) are useful to classify the hot early type stars O, B, A; calcium (Ca), sodium (Na) and iron (Fe) in solar type F and G stars; titanium (Ti), oxygen (O), carbon molecules (CO, CH, CN, etc.) and water (H2O) are useful (approximately in that order) to classify the cooler late type K and M stars and the L and T brown dwarfs. Note that these elements characterize the composition of the original gas cloud that contracted to form the star, because (with few exceptions) the elements formed in the stellar core never rise to the photosphere of the star. Thus, while absorption features are useful to calculate the stellar temperature, they document the star formation.
Luminosity is evaluated as the bandwidth narrowing of the most prominent spectral lines, the increase or decrease in the strength of absorption lines, and the appearance of new absorption lines characteristic of lower temperature or gravitational pressure.
The spectral type (but not luminosity class) of a star can be estimated by photometric measures of its flux through specific filters or narrowband sensors. The color temperature (Tc) of a star is the blackbody temperature that matches the flux ratio measured within these two spectral bands, which is sufficient to uniquely define the shape of the blackbody profile. The Johnson-Cousins UBV system (1953) uses rather broad filter bandwidths (as shown by the colored bars at the top of the flux profile diagram, above right); the BV index measures the slope of the Paschen continuum and captures well the effective temperature of the star. The Strömgren uvby system (1966) uses much narrower filters that avoid some measurement ambiguities of the UBV. (Note that V stands for "visual" [green] in the Johnson-Cousins system but v for "violet" in the Strömgren system.) Neither system is equivalent to a spectral classification, because information about specific absorption features is excluded; they are alternate and less labor intensive ways to quantify the blackbody temperature of a flux profile.
Spectral classification was performed in the past by human coders using microscopes to examine grainy photographic emulsions. In the current age of digital photometry, humans are being replaced by computer coding systems that can cope with the enormous datasets generated by Hipparcos, SDSS, 2MASS and GAIA.
Whatever the method used, the two principles affirmed by spectrographic astronomers are that stars should be classified according to the most fundamental features of the stellar spectrum and in an empirical manner free of extraneous theory. These principles gives the system robustness as a purely descriptive framework and allow theories of stellar astrophysics and evolution to develop as separate research efforts.
Spectroscopic Atlas for Amateur Astronomers by Richard Walker A beautifully documented, detailed and invaluable intoduction to stellar spectroscopy and classification.
Astronomical Spectroscopy Aggregator page of informational links.
Spectral Type. The table below lists the main attributes of stars within each spectral type on the main sequence. The values for surface temperature, radius and luminosity do not describe stars off the main sequence (giant and supergiant stars).
|The Morgan-Keenan Spectral Types (Main Sequence, Extended)|
|W||Wolf-Rayet||≥ 25000 K||< 3.0||≥ 20 M⊙||1015 R⊙||≥ 105 L⊙||~0.25||W5 = 2.0x105||2x108%|
|O||super massive||≥ 30000 K||5.6 to 4.3||18~150 M⊙||≥ 6.6 R⊙||53,000~106 L⊙||0.33 to 0.31||O5 = 3.6x105||0.23%|
|B||massive||1000030000 K||4.1 to 0.7||2.918 M⊙||1.86.6 R⊙||5452,500 L⊙||0.30 to 0.08||B5 = 7.2x107||8.9%|
|A||large||730010000 K||1.4 to 2.5||1.62.9 M⊙||1.41.8 R⊙||6.554 L⊙||0.02 to 0.28||A5 = 1.1x109||16.0%|
|F||solar type||60007300 K||2.6 to 4.2||1.051.60 M⊙||1.151.4 R⊙||1.56.5 L⊙||0.30 to 0.56||F5 = 3.5x109||22.0%|
|G||solar type||53006000 K||4.4 to 5.7||0.81.05 M⊙||0.961.15 R⊙||0.41.5 L⊙||0.58 to 0.78||G5 = 1.5x1010||19.6%|
|K||solar type||38005300 K||5.9 to 9.0||0.50.8 M⊙||0.70.96 R⊙||0.080.4 L⊙||0.81 to 1.36||K5 = 5.3x1010||27.6%|
|M||sub solar||25003800 K||9.2 to 16.1||0.070.5 M⊙||≤ 0.7 R⊙||10-3.50.08 L⊙||1.40 to ~2.00||M5 = 1.9x1011||5.0%|
|C||carbon star||24003200 K||.||≤ 1.1 M⊙||220550 R⊙||≤ 10-3 L⊙||> ~3.0||.||.|
|S||sub carbon star||24003500 K||.||≤ 0.8 M⊙||≤ 0.7 R⊙||≤ 10-3 L⊙||> ~2.2||.||0.14%|
|L||hot brown dwarf||13002100 K||11.5 to 14.0||0.0750.45 M⊙||≤ 0.2 R⊙||10-4.410-3.7 L⊙||n/a||.||.|
|T||cool brown dwarf||6001300 K||> 14.0||0.0120.075 M⊙||≤ 0.2 R⊙||10-5.210-4.5 L⊙||n/a||.||.|
|Y||gas giant||< 600 K||.||.||≤ 0.012 M⊙||≤ 0.15 R⊙||< 10-5.2 L⊙||n/a||.||.|
|≤ 100,000+ K||10.0 to 15.0||0.171.3 M⊙||0.0080.02 R⊙||< 10-4102 L⊙||n/a||.||.|
|Q||recurring nova||.||.||white dwarf companion to mass donating star|
|P||planetary nebula||.||gas shell ejected by giant star prior to collapse to white dwarf|
*Source: Mitchell Charity, What Color is a Blackbody? - Note that Charity presents "color" as a chromaticity (hue and saturation), but saturation is a function of brightness, which causes stars to appear much less saturated (closer to white) than web page color samples.
Luminosity Class. Luminosity refers to the total light output of the star. Given a constant temperature, an object with a larger surface area (radius) will radiate a larger amount of energy, and therefore appear more luminous.
Spectral Features. In addition to the general shift in the spectral profile produced by changes in the blackbody continuum, the different spectral categories are differentiated by examining absorption or emission features of specific elements and ionization states. The "neutral" or least energetic atomic state is indicated by the Roman numeral I, and incrementally more energetic ionization states by Roman numerals II and above. These are described in the table below (wavelengths given in angstroms) with a few bright stars characteristic of each type. Note that the spectral types K and M, because they are so faint, are mostly known in their most luminous (giant or supergiant) forms.
Absolute Magnitude & Temperature. Absolute magnitude is the apparent magnitude that the star would have if it were placed at a standard distance of 10 parsecs (32.6 light years) from Earth. The apparent magnitude of a star differs from its absolute magnitude because the star is either nearer to or farther from Earth than this standard distance. However this means that the difference between the apparent and absolute magnitudes can be used to calculate the approximate distance of the star in cases where the star is too far away to be measured by astrometric parallax. The table (below) summarizes the current best estimates for the average absolute magnitude of stars by spectral type and luminosity class.