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Introduction to Stellar Spectroscopy
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Introduction to Stellar Spectroscopy
It has been known since antiquity that light passing through glass can produce "colors". For a long time it was thought that the glass itself produced the colors. It was not until the late 1600's that Newton developed the concept of refraction. He produced a spectrum with a glass prism then, by using several mirrors, recombined different colors back into white light. This proved that the spectrum was not created by the prism, but was a property of the light itself.
In 1802 English chemist and physicist William Hyde Wollaston noted several dark regions in the spectrum of sunlight, which he thought represented natural "boundaries" between different colors.
In 1814 Bavarian optician Joseph Fraunhofer invented the modern slit spectroscope. He demonstrated bright emission lines when burning various elements, as well as numerous dark absorption lines in the spectrum of sunlight which are in his honor still called Fraunhofer lines. In 1821 he improved the diffraction grating first invented in 1785 by American astronomer David Rittenhouse. Fraunhofer then founded stellar spectroscopy by showing that spectra of several bright stars differed from each other and from the spectrum of the Sun.
Fraunhofer demonstrating his slit spectroscope
Kirchoff and Bunsen in 1859, and William Huggins in 1864, proved that Fraunhofer lines represented atomic absorption lines, confirming that the same elements present on Earth were also present in the Sun and other stars. A preliminary explanation of spectral analysis was offered by Kerchoff in the form of three laws:
FIRST LAW: A luminous (hot) solid or liquid emits light of all wavelengths, producing a continuous spectrum. It was later discovered that hot, opaque gasses under high pressure also emit light in all wavelengths. A common example of the continuous spectrum, with no dark or bright lines, is an incandescent light bulb
Continuous Spectrum (GRISM Slit Spectrograph, Canon 600D unmodified camera, incandescent light bulb)
SECOND LAW: A rarefied luminous (hot) gas emits light whose spectrum shows bright lines. In fact, the atoms of the gas "excited" by heat re-emit that energy in the form of specific wavelengths of visible light, producing an emission spectrum.
Emission Spectrum (GRISM Slit Spectrograph, Canon 600D modified camera, plasma lamp)
THIRD LAW: If white light from a luminous source is passed through a (cold) gas, the gas may abstract (absorb) certain wavelengths from the continuous spectrum so that these wavelengths will be missing or diminished in the spectrum, thus producing dark lines. Such a spectrum, called an absorption spectrum, is typical of the Sun and other stars. Atoms of elements in the cooler, upper layers of the stellar photosphere, as well as atoms and molecules in Earth's atmosphere, absorb certain wavelengths, achieving an "excited state" in the process.
Absorption Spectrum (GRISM Slit Spectrograph, Canon 600D modified camera, sunlight)
Absorption Spectrum (GRISM Star Spectroscope, Celestron 5, Canon 600D modified camera, Delta 2 Lyrae, mag 4.2, class M4)
It was soon discovered that hot gases emit the same wavelengths which they absorb when they are cold, leading to spectral identification of elements and molecules and, eventually, to the theory of quantum physics. Of the thousands of Fraunhofer lines in the solar spectrum most have been associated with more than 60 known chemical elements. However, a large percentage of these lines remains unidentified to this day.
Further understanding of stellar spectroscopy was revealed by experimental and theoretical work on black body radiators, or perfect radiators, at the end of the 18th century. These are non-reflective objects, in thermal equilibrium with the environment, which emit electromagnetic radiation at wavelengths related to their temperature. At room temperature these objects emit invisible infra-red light and, since they are non-reflective, they appear black. At very high temperatures they begin to emit visible light, which shifts in color from red toward the violet as the temperature increases.
Commissioned by electric companies to maximize light output from light bulbs, German physicist Max Planck found a theoretical interpretation for black body radiation presented in his famous equation which relates temperature of an object to the intensity and wavelength of radiation. In the process he correctly hypothesized that light energy occurs only in discrete "packets", or photons, thereby laying the foundation for the quantum theory, for which he won the Nobel Prize in physics in 1918.
Three principles, in particular, become evident from Planck's formula:
1) A black body at any temperature emits some radiation at all wavelengths, but not in equal amounts.
2) A hotter black body emits more radiation per square centimeter at all wavelengths than does a cooler black body.
3) A hotter black body emits the largest proportion of its energy at shorter (blue) wavelengths than a cooler black body which emits at longer wavelengths (red).
It turns out that stars closely approximate perfect radiators, and the same three principles apply. If two stars are of equal size, the hotter star will appear bluer and brighter than the cooler star which will appear redder and fainter. These principles can also be illustrated in the form of diagrams:
Color-Temperature diagram ignores brightness, but correlates temperature to the apparent color of a black body radiator.
Fig. 1 Color-Temperature diagram
Black Body Radiation Graph clearly shows how in hotter bodies the overall brightness increases at all wavelengths, while the wavelength of maximum radiation shifts from the infrared toward the higher energy blue.
Fig. 2 Black Body Radiation graph
At the same time, as the result of advances in optics and photography in the late 19th century, astronomers became able to routinely analyze stellar spectra in large numbers. Work was begun by Henry Draper who first photographed the spectrum of Vega in 1872. It soon became obvious that stellar spectra could be divided into groups according to their general appearance, but the reason for the differences was poorly understood. As late as the 1930's it was assumed that stellar spectra look different due to differences in their chemical composition. Various classification schemes were proposed, of which the Harvard classification, carried out by astronomers Williamina Fleming, Annie Jump Cannon, and Antonia Maury, prevailed. Between 1918 and 1924 they carried out classification of 225,300 stars down to 9th magnitude, published in the Henry Draper Catalog, named after the benefactor who financed the study.
The Harvard classification was based on a steady change in the strengths of representative spectral lines. After several revisions, spectral classes were named O, B, A, F, G, K, M, which can be remembered by the mnemonic "Oh Be A Fine Girl Kiss Me". For better accuracy, each spectral class was divided into tenths to produce a series like ...A8, A9, F0, F1, F2... In this scheme, the Sun was classified as a G2 star. O and B are often referred to as early, and K and M late spectral types The nomenclature originated from now obsolete ideas about stellar evolution, but the terminology remains.
The most important lines in the Harvard classification scheme are the prominent Hydrogen Balmer lines, lines of ionized and neutral Helium, Iron lines, H and K doublet of ionized Calcium at 397 and 393 nm, neutral Calcium line at 423 nm, G band of the CH molecule, metal lines around 431 nm, and lines of the TiO molecule. Numerous lines of other elements and compounds are also present in stellar spectra, but are too delicate to be useful.
It was intuitive to initially assume that differences in stellar spectra were due to differences in chemical composition. Decades had to pass before it was recognized that, with minor variations and some exceptions, stars have very similar surface composition: Hydrogen 75%, Helium 23%, and metals 2%. Note that in astronomy all elements other than Hydrogen and Helium are regarded as "metals".
In 1925, British-American astronomer Cecilia Payne showed that the variability in stellar spectra is due to various degrees of ionization at different temperatures, and not to differences in chemical composition. She also showed that relative abundances of "metals" in the solar atmosphere (excluding Hydrogen and Helium) were identical to those present on Earth. Her PhD thesis is still considered one of the most brilliant ever written in the field of astronomy.
In the diagram below the Roman number following the chemical symbol represents the state of ionization. Thus, He I is neutral Helium, He II is a Helium atom which has lost one electron, and Si III is a Silicon atom with two missing electrons.
Surface composition of stars, where stellar spectra originate, is regarded as "primitive" because it reflects the makeup of the gas clouds from which the stars originally formed. Metals in a gas cloud come from previous generations of stars in that region which infused the cloud with heavier elements during supernova explosions. The concentration of metals in a gas cloud and local stars is referred to as metallicity. Stars of low metallicity are presumed to be first generation stars which have arisen from pure Hydrogen and Helium clouds. Such stars are most frequently found in globular clusters and galactic halos.
While fusion at the core results in fundamental chemical change, the core material does not generally mix with the visible surface of the star, and there is no appreciable nuclear processing in the outer gaseous envelope. Consequently, the main factor which determines the spectral type of a star is its surface temperature. It took a relatively long time to integrate black body radiation laws into stellar spectroscopy.
On the atomic scale, heat is manifested as movement, vibration and rotation of atomic particles, which imparts on the particles kinetic energy. The higher the temperature, the more rapid the motion, and the more frequent the collisions between particles. At extremely high temperatures of class O stars, atomic particle collisions are very frequent and violent. Molecules cannot exist because they are immediately dissociated (broken apart) into atoms, and electrons are "knocked out" of atoms turning them into charged ions. Therefore, such stars only show spectral lines of highly ionized elements. Meanwhile, in much cooler M type stars atomic particle collisions are much weaker and less frequent. Lower temperatures allow the presence of unionized, neutral atoms and even simple molecules such as Titanium Oxide, which produce dark absorption bands.
Fig. 4 below is a more symbolic representation of Fig. 3, but it is much easier to remember.
It is important to repeat that the elements and compounds in Fig. 3 and Fig. 4 are those which produce the most prominent absorption lines used in classification. Many other elements are also present in various forms, but produce less distinctive lines.
The following chart correlates spectral type with star color, surface temperature, and main spectral features
Note that the Harvard scheme correlates spectral type of a star only with its surface temperature. For example, there is no provision to differentiate between the tiny, medium, and giant G type stars. Since G type supergiants are millions of times brighter than G type white dwarfs, the Harvard scheme offers no information regarding star size, brightness or luminosity.
Luminosity is defined as the total amount of electromagnetic radiation emitted by a star per unit time. It is frequently referenced to the Sun which is ascribed the luminosity value of 1. Meanwhile, brightness is defined as luminosity of a star within a defined spectral region, such as the visible light. Large stars have greater surface area and, therefore, greater luminosity and brightness.
A star's apparent brightness as seen from Earth depends on its actual, intrinsic brightness and its distance from the observer. Thus, a faint star which is near the solar system may appear much brighter than a bright star which is very distant. Apparent Visual Magnitude of a star is its apparent brightness in the visible spectrum as seen from Earth. Absolute Visual Magnitude is the star's brightness as it would appear from the distance of 10 parsecs, or 32.6 light years. At the same distance, apparent magnitude of different stars would reflect their actual brightness.
In the second century BC Greek astronomer Hipparchus divided stars by brightness into 6 magnitudes. First magnitude stars were the brightest, while 6th magnitude stars were the faintest the human eye could see. In 1856, based on photometric measurements, Norman Pogson created a logarithmic scale in which the interval of 1 magnitude is equal to a difference in brightness of 2.512 times. Thus, a first magnitude star is 2.512 times brighter than a second magnitude star, and 100 times brighter than a sixth magnitude star. The same convention is used for absolute magnitudes, so that brighter stars are assigned lower magnitude values. Very bright celestial objects have negative magnitudes.
The difference in magnitude, M, between two stars is related to the difference in brightness, B, by the following relations:
M2 - M1 = -2.512 log (B2 / B1)
B2 / B1 = 2.512^ (M1 - M2)
In 1943 astronomers Morgan, Keenan, and Kellman introduced the Yerkes Spectral Classification which was based on the effect stellar surface gravity has on spectral absorption lines. Higher surface gravity produces higher pressure on the surface of a star, which results in measurable broadening of spectral lines. Now, if a small star and a giant star are of similar mass, the small star will be denser, and will have higher surface gravity and pressure because its surface is closer to the star's center of gravity. Therefore, small, dense stars will manifest a higher degree of spectral line broadening. At the same time, the small star has a smaller surface area, and will have less luminosity (or fainter absolute magnitude) than the giant star.
After some revisions and refinements this scheme was reintroduced in 1953 as the MK (Morgan-Keenan) Classification, which remains in use to this day.
The MK scheme distinguishes the following luminosity classes, which actually reflect star size within each spectral class:
|0 or Ia+||Hypergiants of extreme luminosity (or size)|
|Ia||Supergiants of high luminosity, Eta Canis Majoris (B5Ia)|
|Iab||Supergiants of intermediate luminosity, Gamma Cygni (F8Iab)|
|Ib||Supergiants of lower luminosity (or size), Zeta Persei (B1Ib)|
|III||"normal" Giants, Arcturus (K0III)|
|V||Main Sequence stars or Dwarfs, the Sun (G2V)|
|D prefix||White Dwarfs|
Spectral peculiarities are described in the form of lower case letters following the spectral type, however the subject is beyond the scope of this introductory article.
Note that Harvard and MK schemes provide information on the temperature, color, and luminosity (absolute magnitude) of a star. These properties, together with data from other sources, can then be used to determine distance, mass, past history, and the surrounding environment of the star.
In 1905, Danish astronomer Einar Hertzsprung and American astronomer Henry Russell separately noticed that the luminosity of stars decreased from spectral types O (hot) to M (cool). They used data from nearby stars whose distance could be determined by parallax. Once the distance and apparent magnitude were known, absolute magnitude or luminosity could be accurately calculated. When plotting luminosity against the surface temperature (spectral class), families of stellar types immediately began to emerge.
Fig. 6 Original Hertzsprung-Russell (H-R) Diagram for stars in the solar neighborhood
Take note that the scales are not linear, and that luminosity describes the actual brightness of a star (absolute magnitude), not its apparent magnitude. Bright stars in the upper portion of the diagram are therefore thousands of times brighter, larger, and more massive than the Sun, while the dim stars on the bottom are fainter, smaller and much less massive. The majority of stars lie along the S shaped curve called the Main Sequence, and the majority of these are smaller and fainter than the Sun.
Stars may occupy any position on the H-R diagram, but are more frequently found in specific regions which have been given names. Supergiants lie above the Main Sequence, Red Giants to the right of it, while White Dwarfs lie below it. Main Sequence stars are also called Dwarfs. The largest group of stars by far are the Red Dwarfs which are the cool, dim stars at the bottom of the Main Sequence.
The H-R diagram clearly demonstrates that temperature, luminosity, size (radius), and mass of a star are all related. Based on the Stefan-Boltzmann's law of thermodynamics, the relationship can be expressed in terms of solar units as follows:
L/Ls = (R / Rs)^2 x (T/Ts)^4
Where L is luminosity, R is radius, and T is temperature in Kelvin of an unknown star, while subscript "s" pertains to the Sun.
The equation basically quantifies our intuitive knowledge that a star is intrinsically brighter if it is bigger and hotter.
It seemed obvious at the beginning of the 20th century that the H-R diagram contains some type of information regarding the changes stars undergo during their lifetimes. But, the nature of that information could not be correctly interpreted because it was thought at the time that stars derive their energy entirely from gravitational contraction. It was believed that stars begin their life at the top of the Main Sequence as large (less dense), hot, bright objects then, as they age, move down the Main Sequence to become small (dense), cool, and dim objects. It was not till decades later that the H-R diagram and stellar evolution were better understood with the discovery that the main source of energy in stars during their early and middle age is thermonuclear fusion of Hydrogen to Helium to heavier elements (metals).
The current theory of stellar evolution is that stars begin their life on the Main Sequence, and spend their young life there while fusing Hydrogen to Helium in their cores. Their position on the Main Sequence, spectral type, temperature, and luminosity are determined by their mass. More massive stars are located higher on the Main Sequence. They have higher pressures in their cores, fuse Hydrogen more rapidly, appear hotter and brighter, and have much shorter life spans than less massive stars. Once Hydrogen in their cores is depleted, stars begin to fuse Helium into heavier elements (metals), and move away from the Main Sequence toward the right into the Red Giant or Supergiant phase. Once they have fused Iron, thermonuclear fusion stops, internal pressures decrease, and stars begin to shrink by gravitational contraction which now becomes the main source of energy. Most stars will end their life very gradually in the White Dwarf stage. But, a few very massive stars will die in spectacular supernova explosions, outshining the entire galaxy for a brief period of time. In the process, they rapidly fuse elements heavier than iron, and disperse these elements into new clouds of gas and dust from which a new generation of stars will be formed. We all owe chemical elements in our bodies to supernova explosions which occurred billions of years ago.
The following is an updated version of the H-R diagram which includes the MK spectral classification. It displays data from the general population of stars selected with no regard to the distance from the Sun.
Fig. 7 Hertzsprung-Russell (H-R) Diagram of the general star population regardless of the distance from the Sun
Notice that the Main Sequence is "top heavy" in Fig. 7, and "bottom heavy" in Fig. 6. The reason for this is that the Red Dwarfs are very small and dim, and are only visible when located nearby. Of all Main Sequence stars, 76% are class K and M Red Dwarfs. Their numbers predominate in the population of nearby stars because they are locally visible. Fig. 6 is then much more representative of the true distribution of star types. However, the vast majority of Red Dwarfs is not visible (and can not be counted) at large distances, and Fig. 7 greatly underestimates their actual number. When distance is disregarded, the majority of measurable stars includes the large, bright Main Sequence stars and the Giants.
Notice also that the H-R diagram in Fig. 7 includes on the vertical scale absolute magnitudes in addition to luminosities. From the knowledge of the absolute magnitude, M, and the apparent magnitude, m, distance in parsecs, D, can be found from the following relations:
m - M = ( 5 x log D ) - 5
D = antilog ((m - M + 5) / 5) = 10^((m - M + 5) / 5)
With some practice, most amateurs can learn to estimate the Harvard spectral class fairly accurately. With the spectral class of an unknown star, the H-R diagram, and the Stefan-Boltzmann's equation above it is possible to guesstimate the star's surface temperature, color index, luminosity, radius (size), absolute magnitude, and the distance. I use the word "guesstimate" because the determination of the MK spectral class is probably beyond the skill level and instruments available to the amateur, who will not be able to distinguish between the giants, main sequence stars, and white dwarfs. However, some reasonable statistical assumptions can be made. On the H-R diagram, two regions of highest star concentration are the Main Sequence stars and the class III Giants. For spectral types O, B, A, and F, the vast majority of stars are Main Sequence. We can therefore assume with fairly high confidence that an unknown star in that spectral region is not a giant or a white dwarf. For spectral types G, K, and M there is less certainty. In a general population of visible stars about half are Giants, and half lie on the Main Sequence. Confidence drops down to 50%, but we could make separate calculations for each group, knowing that one of the two answers will be approximately correct. Or, we could "cheat" by finding the star's MK classification in a star catalog.
Take as an example an unknown A3 type star of apparent magnitude 4.3. Looking at the distribution of stars on the HR diagram, such a star could be a giant or a white dwarf, but is most likely a main sequence star. On the HR diagram we read that the luminosity of the star (L) is 10 compared to the luminosity of the Sun (Ls).
Absolute magnitude of the star (M) is related to the absolute magnitude of the Sun (Ms = 4.83) by the following relation:
M - Ms = -2.512 log (L / Ls)
M - 4.83 = -2.512 log (10 / 1)
M = 4.83 - 2.512
M = 2.318 (Note that brighter stars have lower magnitude)
Distance (D) in parsecs can be calculated from the absolute magnitude (M) and the apparent magnitude (m = 4.3) as follows:
m - M = (5 x log D) - 5
D = antilog ((m - M +5) / 5)
D = antilog ((4.3 - 2.318 +5) / 5)
D = antilog ( 1.4 ) = 10^1.4
D = 25.12 parsecs
Luminosity (L), radius ®, and temperature (T) in Kelvin, where subscript "s" pertains to the Sun, are related as follows:
L / Ls = (R / Rs)^2 x (T / Ts)^4
Approximate temperature of the solar photosphere, Ts = 5800 K, and that of an A3 star T = 8500 K.
10 / 1 = (R / Rs)^2 x (8500 / 5800)^4
10 = (R / Rs)^2 x (1.47)^4
10 = (R / Rs)^2 x 4.6
(R / Rs)^2 = 10 / 4.6 = 2.2
R / Rs = (2.2)^0.5 = 1.5
R = 1.5 x Rs
The star is approximately 1.5 times larger than the Sun.
All values are approximate, but are actually much more reliable than those made by professional astronomers not so long ago.
Precisely classifying stellar spectra by the Harvard spectral type is not an easy task, and takes years of experience. However, approximate classification is not too difficult, and can initially be done by simple comparison with reference spectrograms. Later on, accuracy can be improved by learning the variation in the critical spectral lines of Hydrogen, Helium, Fe, and the CH, MgH and TiO molecules. Or, we may employ computer software, such as RSpec, to further refine our results.
Fig. 8 Harvard spectral classification reference spectrograms
Note that the reference spectrograms above were taken with a modified camera in which the internal IR blocking filter has been removed. Such cameras can show deep red wavelengths well beyond 700nm. Unmodified cameras will usually block above 655nm, and may not show the Hydrogen alpha line.
The following list of prominent Fraunhofer lines in the solar spectrum can further assist in identifying unmarked absorption lines in Fig.8
FRAUNHOFER LINES + BALMER SERIES
|D3 or d||He||587.5618|
The following is a list of spectral classes and associated stellar photosphere temperatures in Kelvin:
- Philip Levine, okiestarman56, Ohan Smit and 22 others like this