Stellar Spectroscopy

(NB. Blue links are links within the current page. Purple links are external links to other web sites.)

Types of Spectra
                      Continuous Spectra
                      Emission Spectra
                      Absorption Spectra
                      Links

The Spectrum of the Sun
Links

The Spectra of Other Stars
Molecular Spectra
Links

The Shape of a Spectral Line
                      Collisional Broadening
                      Doppler Broadening
                      Rotational Broadening
                      The Zeeman Effect
                      Links

Classifying Stellar Spectra
                      Spectral Type
                      Luminosity Classes
                      Links

Chemical Composition
Links

Radial Velocities

More than 300 years ago Sir Issac Newton (1642-1727) showed that sunlight can be split into different colours using a prism. He found that the shorter the wavelength the greater the angle of refraction so that a spectrum of light is produced from red through to violet.
Stellar Spectroscopy is the study of the spectra of starlight. It is a very powerful tool that enables astrophysicists to infer many physical and chemical properties of stars and classify them into a logical sequence.
In order to understand how spectroscopy can be a useful tool to astrophysicist we need to describe the different kinds of spectra that are observed and explain how they arise.

A German physicist Gustav Kirchoff (1824-1857) investigated the properties of a spectra in the laboratory and discovered that there are three kinds which are produced under different physical conditions. He formulated three empirical rules of spectral analysis:

Rule 1
A hot opaque solid, liquid or gas which is under high pressure will emit a continuous spectrum.

Rule 2
A hot gas under low pressure (i.e. much less than atmospheric) will emit a series of bright lines on a dark background. Such a spectrum is called a bright line or emission spectrum.

Rule 3
When light from a source that has a continuous spectrum is shone through a gas at a lower temperature and pressure, the continuous spectrum will be observed to have a series of dark lines superimposed on it. This kind of spectrum is known as a dark line or absorption spectrum.

The Bohr model of the atom can be used to understand how these different types of spectra are produced. Emission or absorption of light only takes place when a photon has an energy equal to the difference in quantised energy states that an electron can occupy in its orbit around the nucleus.

Continuous Spectra

In a very hot gas, the atoms have high kinetic energies and collisions between them are very frequent. Their electrons are raised to excited states and then drop down producing emission lines. However, if the gas is at very high pressure and density, then an electron in its excited state may not have enough time to drop down to its ground state before it undergoes another collision from a neighbouring atom. This has the effect of blurring the sharpness of each emission line into a broad band of wavelengths. The same thing happens to neighbouring lines so that by the time the light emerges from the gas it has 'smeared out' into a continuous spectrum at all wavelengths.

Emission Spectra

In a gas containing only atoms of one kind, the electrons will all be in their ground state if the temperature is low. As the gas is heated, its atoms gain kinetic energy and collide with their neighbours causing their electrons to be raised to excited states. As the electrons drop down, photons will be emitted with many different energies and wavelengths corresponding to the particular electron energy level scheme for the gas. The emission of these lines will cause the gas to glow with a light composed of wavelengths that correspond to the electron energy transitions. For moderate temperatures we might find that only the first excited state of the atom is attained and so the emission light will consist of a single bright emission line corresponding to the difference in energies between the first excited and ground states. As the temperature is increased, more emission lines will start to appear until at higher temperatures many lines will be visible corresponding to all the allowed energy transitions of electrons in the gas. In this way an emission line spectrum is formed that is related to the elemental composition of the gas.

Absorption Spectra

To explain Kirchoff's third rule we need to consider what happens when we place a gas of unknown composition in front of a source of light that emits a continuous spectrum. Light from the continuous source contains photons of all energies and wavelengths. Now if it is the case that the energy of some of these photons is exactly equal to the difference between the ground state and an excited state of an atom in the unknown gas, then that photon will be removed from the incident light. The excited electron will quickly return to the ground state emitting a photon however, the emitted photon need not be emitting along the same direction as the absorbed photon but is usually emitted in a different direction. The re-emitted photons are not therefore, generally observed through a spectroscope at the source, and the continuous spectrum is observed when looking to have dark lines at the wavelengths corresponding to excited states of the atoms in the unknown gas. It follows that it is precisely these wavelengths at which light would be emitted in an emission spectrum if the unknown gas was heated to a high temperature.
Both the dark lines superimposed on the continuous spectrum and the bright lines in the emission spectrum provide a 'spectral fingerprint' that identifies the elements present in a hot gas.

SIR ISSAC NEWTON
Links to Issac Newton sites
STARBASE People Page

SPECTROSCOPY
Some interesting slides
http://www.physics.fsu.edu/courses/spring98/ast1002/chap5/sld001.htm

The first star to be studied spectroscopically was the sun. A British astronomer William Hyde Woollaston (1766-1828), using a prism, observed that the sun emitted a continuous spectrum that had 784 dark lines which are now known as Fraunhofer lines. Fraunhofer realised that some of these dark lines were at the same position in wavelength as bright emission lines of spectra of various elements which were studied in the laboratory.
Astrophysicists have now observed thousands of dark absorption lines in the sun's spectrum. Using Kirchoff's rules they have been able to detect the presence of 67 elements in the sun.
As an interesting footnote, the element helium was first discovered in the sun before it was found on earth. An unknown line in the sun's spectrum was observed which could not be related to lines of elements then known in the laboratory. It was named helium after the Greek word for the sun helios, and was subsequently discovered on earth forty years later!

Fraunhofer Lines

SPECTRUM OF THE SUN
Information about the Sun's spectrum and other areas
http://www.physics.gmu.edu/classinfo/astr103/CourseNotes/ECText/ch12_txt.htm

When we observe the spectra of other stars we find that some are like the sun and others are very different. Vega for example, is a very hot star in the constellation Lyre and a pair of binoculars will easily show it glowing with a bluish tinge.
The sun's spectrum shows two lines of hydrogen 410.1 and 434.0 nm plus many other spectral lines. The spectrum of Vega, however, has the same two lines but they are much thicker and more intense. At first sight one might think that the thicker hydrogen lines mean that there is a greater abundance of hydrogen in Vega than in the sun. Actually, this is not the case and the composition of most stars are broadly similar in their chemical mixtures. It turns out in fact, that the thickness of the lines are related to the star's temperature.
The 410.1 nm line is produced when a photon of energy 3.02 eV is absorbed and an electron jumps from n = 2 to n = 4 quantum levels. The 434.0 nm line is caused by a photon of energy 2.85 eV being absorbed when an electron jumps from n = 2 to n = 5. For cool stars whose surface temperatures are low to moderate, most of the hydrogen atoms will be in the ground state. As a result the Lyman series which consist only of lines involving transitions from the ground state will figure prominently in the spectrum. Lines corresponding to the Balmer series will be weak since the hydrogen atoms will have less electrons populating the n = 2 state. At higher surface temperatures, though, there are a greater number of electrons populating the first excited state and the frequency of transitions from n = 2 to higher states will be greater. As a result, these stars will show the 410.1 and the 434.0 lines more strongly.

Molecular Spectra

Some stars display banded spectral features of many finely spaced lines. These are caused by molecules in the outer layers of a star. While a molecule consists of atoms with excited electronic states, it also has collective rotational and vibrational motion which is also quantised. If an electron undergoes a transition within an atom in a molecule to an excited energy then the rotational and vibrational energies also change although by a smaller amount. This has the effect of separating the energy of the electron's transition into many closely spaced energies and corresponding wavelengths.

SPECTRUM OF STARS
Information about spectra from other stars is also included in this site
http://www.physics.gmu.edu/classinfo/astr103/CourseNotes/ECText/ch12_txt.htm

The appearance of a spectral line in a star's spectrum is influenced by a number of physical processes occuring in the stellar atmosphere. A line's shape or profile is described as being weak, strong or very strong according to its intensity.
The three main processes that affect the shape of a spectral line are known as collisional broadening, Doppler broadening and rotational broadening. In addition a lesser effect called the Zeeman effect can also cause splitting of the spectral lines.

Collisional Broadening

If two atoms collide, then the electrons on each atom will repel each other and distort their respective energy levels. If a collision happens when one of the electrons is absorbing a photon, then the absorbed photon energy will be altered from the value it would have had if the atom was in an undisturbed state. In a gas that is at a moderate temperature and density, collisions between atoms are infrequent and so absorption is likely to happen when the atom is undisturbed. At higher temperatures and pressures the absorbed photon energies vary over a considerable range and hence the spectral line is widened or collision broadened.

Doppler Broadening

In the atmosphere of a star, the atoms have random velocities due to their thermal energy. At any instant some of the atoms travel towards us and others away when they emit photons. The effect of this is to produce a Doppler shift in the absorption lines of the spectrum. This Doppler broadening is a lesser effect than collisional broadening.

Rotational Broadening

A star that is rotating will produce a Doppler shift in each line of the star's spectrum. The amount of broadening depends on rotation rate and the angle of inclination of the axis of rotation to the line of sight. Astrophysicists can use this effect to calculate the stellar rotation rate. For simplicity lets assume that the axis of rotation is perpendicular to the line of sight of the observer. If the change in wavelength of a line at wavelength is ^, then the velocity v of atoms on the limb of a rotating star is given by...

If we know the radius R of the star then the period T of rotation can be calculated from...

Astrophysicists have found that, in general, the hottest stars (type O and B) rotate the fastest with periods as fast as 4 hours. G-type stars like the sun rotate fairly slowly at about once every 27 days.

The Zeeman Effect

Electrons in atoms are moving charges that constitute rings of electric current. This produces a magnetic field similar to that of a bar magnet. This causes the spectral lines to become split and is called the Zeeman Effect.
It is possible to relate the degree of splitting to the strength of the external magnetic field and astrophysicists can obtain information about a star's magnetic field distribution. Zeeman splitting is particularly useful in the study of sunspots which have very intense magnetic fields and produce pronounced splitting in the absorption spectrum of the sun.

DOPPLER BROADENING
Nice site about Doppler broadening
http://rugby.phys.uidaho.edu/~pbickers/Courses/310/Notes/book/node99.html

ZEEMAN EFFECT
Good, but quite advanced site on the Zeeman effect
http://csep10.phys.utk.edu/astr162/lect/light/zeeman-split.html

The changes in intensity of the hydrogen lines with temperature enables us to devise a spectral classification system. The first person to attempt to do this was the Italian astronomer P.A. Secchi who in 1860 classified stars into four distinct groups based on their spectral features. The modern scheme is called the MK system (devised by W.W. Morgan, and P.C. Keenan).
To be classified, a star is assigned a Spectral Type and a Luminosity Class.

Spectral Type

The spectral type of a star is designated by one of seven letters O, B, A, F, G, K, M, starting with the hottest type (O type) to the coolest type (M-type). The table below shows the temperatures and characteristic features in the star's spectrum that distinguish spectral types.

**The MK of Spectral Types**
Type	Surface Temperature/K	Spectral Type
O	>20 000	ionised helium (He II)
B	20 - 10 000	neutral helium, hydrogen lines start to appear
A	10 - 7000	strong neutral hydrogen (Balmer lines) visible
F	7 - 6000	ionised calcium (Ca II) visible, hydrogen lines weaker
G	6 - 5000	ionised Ca II very prominent, much weaker neutral H lines, also other metallic lines such as Iron (the sun is a G-type star)
K	5000 - 3500	neutral metals such as Ca and Fe prominent, molecular bands visible
M	3500 - 2000	molecular bands very visible, particularly those of Titanium Oxide (TiO)

In practise the classification of stars into spectral types is more complex than this. Each type can be subdivided into at least 10 subdivisions so that one might refer to a star of type A5 lying halfway between type A0 and F0. The spectral type order is commonly remembered by the mnemonic 'Oh Be a Fine Girl (Guy) Kiss Me'!

Luminosity Classes

For a given temperature, some stars are more luminous than others. This is usually because the star is larger and its outer atmosphere more tenuous and at a lower pressure than a fainter star. The spectral lines of very luminous stars are much narrower since the effects of line broadening due to collisions is much less and the line profile is sharper. We can therefore further classify stars for each spectral type in terms of luminosity on the basis of the 'sharpness' of their spectral lines. These luminosity classes are denoted by roman numerals and are divided into seven principal star-types:

I     Supergiant Stars
II    Bright Giant Stars
III   Giant Stars
IV   Subgiant Stars
V    Main Sequence Dwarf Stars
VI   Sub Dwarf Stars
VII White Dwarf Stars

In practise some luminosity classes, particularly those of the supergiants, are subdivided into suffixes a, ab and b and a class written as III-IV means a star with characteristics midway between the two classes.
The full spectral classification thus consists of [Spectral type] [number] [Luminosity Class] [suffix (if any)].
For example, the sun is classified as a G2V star and Betelgeuse, a red giant as M2Iab.

LUMINOSITY OF STARS
Numerical data for luminosity
http://scruffy.phast.umass.edu/a114/lectures/lec02/node3.html

Slides on luminosity and related areas
http://www.physics.gmu.edu/classinfo/astr103/CourseNotes/Ppt/Lec04_pt4_starRadiation/sld018.htm

It is clear that the spectral lines observed in a star's spectrum arise from the chemical elements present in the stellar material. Each element leaves its 'signature' in the form of a pattern of spectral lines corresponding to its electron shell structure.
At first sight you may think that the more intense the spectral line pattern is, then the more of that particular element the star contains. However, we have seen that a faint set of absorption lines can be due to the fact that the high temperature of a star means that not all the electrons of a particular element are in the correct initial energy levels in order to produce a particular line.
In order to calculate the relative abundances of the chemical elements in the stars, the astrophysicist needs to know, for a particular element, what fraction of atoms are in the first excited state, what fraction in the second and so on.
It is found that for the majority of stars, the chemical composition is very nearly the same. By mass, most stars contain about 72% hydrogen, 25% helium and the remaining 3% is made up of other elements (notably iron) in roughly equal abundances.

CHEMICAL COMPOSITION OF STARS
Information on the exact chemical composition of stars and a variety of links to other recommended sites
http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/961112a.html

The wavelength of a spectral line is affected by the relative motion of the star and the observer. Due to the Doppler effect, light from a star will be shifted to the blue end of the visible spectrum if it is approaching the observer and shifted to the red end if it is receding. Here is the Doppler equation...

where V is the radial velocity (the velocity of the star as measured along the line of sight of the observer in the manner of a 'radius' drawn from the earth to the star). If v is -ve then the star is approaching the observer. If it is +ve then it is moving away from the observer. ₀ is the wavelength of a particular spectral line in the laboratory, and is the difference between the wavelength of the spectral line as quoted in laboratory reference books and the wavelength that you actually observe in the star's spectrum as measured through a spectroscope connected to a telescope.
There is of course a component of velocity at right angles to the observer's line of sight. This transverse velocity called the proper motion, does not affect the wavelengths of the spectral lines and can be disregarded when measuring radial velocities.