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9.7 Option – Astrophysics: 3. Spectroscopy

Syllabus reference (October 2002 version)
3. Spectroscopy is a vital tool for astronomers and provides a wealth of information	Students learn to: account for the production of emission and absorption spectra and compare these with a continuous blackbody spectrum describe the technology needed to measure astronomical spectra identify the general types of spectra produced by stars, emission nebulae, galaxies and quasars describe the key features of stellar spectra and describe how these are used to classify stars describe how spectra can provide information on surface temperature, rotational and translati onal velocity, density and chemical composition of stars	Students: perform a first-hand investigation to examine a variety of spectra produced by discharge tubes, reflected sunlight, or incandescent filaments analyse information to predict the surface temperature of a star from its intensity/wavelength graph

Extract from Physics Stage 6 Syllabus (Amended October 2002). © Board of Studies, NSW.
[Edit: 12 Aug 08]

Prior learning:
Preliminary module 8.2 The World Communicates
Preliminary module 8.5 The Cosmic Engine

Background:
Spectroscopy is the analysis of spectra. There are three types of spectra – continuous, emission (bright lines) or absorption (black lines.) This website covers the history of spectroscopy and what it has revealed: Spectroscopy: Information concealed in starlight Brian von Konsky, Curtin University of Technology, WA.

perform a first-hand investigation to examine a variety of spectra produced by discharge tubes, reflected sunlight, or incandescent filaments

• Your teacher may have planned a first hand investigation for you, or you could follow the sample procedure below. Ensure that the plan you use includes consideration of any safety aspects such as dangers from high voltage or X-radiation from discharge tubes or power supplies, and the brightness of the Sun. You should include details of any safe work practices you adopt as you perform this investigation in any report you write.
  
  
• Draw each spectrum you examine, noting any observable features. As a result of your investigation you should be able to group spectra into a small number of distinct types, based on similarity of identifiable features. You will find examples of what you would expect to see in astronomy texts or by searching the Internet.

account for the production of emission and absorption spectra and compare these with a continuous blackbody spectrum

• An emission spectrum consists only of radiation at a number of discrete wavelengths, appearing as bright lines against a dark background. This type of spectrum is produced by hot diffuse gases, such as in a gas discharge tube or in clouds of interstellar gas heated by hot young stars nearby. Electrical energy or heat supplied to the gas is absorbed by atoms or ions in the gas, raising the energy level of electrons. As the electrons fall back to their normal energy state, they give up a quantum of energy as a photon corresponding to one of the observed wavelengths. The emission spectrum is made up of lines corresponding to all the possible electron transitions. The relative intensity of each line depends on the composition of the gas.
  
  
• An absorption spectrum consists of a continuous range of wavelengths with discrete gaps at particular wavelengths, appearing as dark lines against a continuous background of colours. Absorption spectra are produced when a continuous spectrum of light passes through a cloud of cool gas. Atoms and ions in the gas absorb photons of wavelengths corresponding to the quanta of energy involved in possible transitions of electrons to higher energy levels. The electrons quickly fall back to their original energy level, re-emitting the absorbed wavelength in all directions, thus reducing the intensity of light transmitted at the corresponding wavelengths. These wavelengths correspond to the dark lines of the absorption spectrum. The relative darkness of each line depends on the composition of the gas. The darkness of the lines against the background spectrum depends on the size and density of the cloud of gas.
  
  
• A continuous black body spectrum has no lines, either dark or bright, but instead shows a continuous range of frequencies. Continuous spectra are given off by hot solids, liquids and high pressure gases. The intensity of the spectrum varies smoothly with frequency, with a maximum that depends on the temperature of the body.

An alternative way of comparing the three types of spectrum is by using a table:

Continuous black body spectrum	Emission spectrum	Absorption spectrum
consists of a continuous range of frequencies without either bright or dark lines, appearing as a continuous range of colours	consists only of radiation at a number of discrete wavelengths, appearing as bright lines against a dark background	consists of a continuous range of wavelengths with discrete gaps at particular wavelengths, appearing as dark lines against a continuous background of colours
given off by hot solids, liquids and high pressure gases	produced by hot diffuse gases	produced when a continuous spectrum of light passes through a cloud of cool gas
all wavelengths are produced at some intensity	wavelengths produced depend on possible energy transitions within atoms of the gas	wavelengths absorbed depend on possible energy transitions within atoms of the gas
intensity varies smoothly with wavelength, with the maximum depending on the temperature of the hot	intensity of lines varies discretely with each wavelength, depending on the composition of the gas	darkness of lines varies discretely with each wavelength, depending on the composition and density of the gas

on blackbody emission, that allows you to specify different values of surface temperature, can be found at: Continuos Emission and Absorption Spectra Center for Astrophysics, Harvard Smithsonian, USA. (This web site last checked 12 August 2008)

describe the technology needed to measure astronomical spectra

• An astronomical spectrum consists of the range of wavelengths of light and other radiation emitted, reflected or transmitted by an astronomical object such as a star, a nebula, a galaxy or a quasar.
  
  
• Astronomical spectra can be viewed using a spectroscope, or recorded and measured with a spectrograph, mounted at the focus of a telescope. A spectrograph consists of 3 parts:
  
  
• The first part, known as a collimator, uses a narrow slit and one or more mirrors or lenses to form a parallel beam of light from a single light source such as a star.
  
  
• The second part is known as the dispersive element as it produces the spectrum by dispersing the beam into its component wavelengths. It consists of either a triangular prism or a diffraction grating. The grating consists of many closely spaced parallel slits (transmission grating) or ruled lines (reflection grating).
  
  
• The third part is a device to view or record the different wavelengths. It may be a viewing telescope, a focussing mirror with photographic plate or film, or an electronic imaging device such as a charge coupled device (CCD) detector. CCD detectors, like those used in video cameras, have the advantage of being able to record very faint light signals. Other modern enhancements include the use of computer controlled positioning equipment in conjunction with fibre optics, and multiple spectroscopes to obtain the spectra of many objects in the viewing field at once, or selectively examine various parts of a single object concurrently.

identify the general types of spectra produced by stars, emission nebulae, galaxies and quasars

• Stars are masses of hot dense gas undergoing thermonuclear fusion at their core. They behave as approximate black bodies and so their spectrum is therefore that of a black body corresponding to the temperature of the star’s surface. Generally however there will also be prominent dark absorption lines produced as a result of the continuous black body light passing through the star’s relatively cooler atmosphere that is above its surface. For this reason stars are observed to produce absorption spectra.
  
  
• Emission nebulae are regions of hot gas, mainly hydrogen, and dust heated by the radiation from nearby young stars. As excited electrons in the atoms and ions within the nebula drop to lower energy levels, line spectra are produced with emission lines in the ultraviolet, visible, infrared and radio bands, characteristic of the elements that make up the nebula.
  
  
• A galaxy is an aggregation of hundreds of thousands to billions of stars. The spectrum of a galaxy is essentially a composite of the various spectra from its components. This generally consists of a continuous background superimposed with absorption lines of type B and K stars, along with emission lines due to hydrogen in gaseous nebulae. As most galaxies are receding from our point of view, the lines of galaxies are often strongly red-shifted.
  
  
• Quasars, are very distant objects that produce vast quantities of continuous radiation at all wavelengths but with most of their energy in the longer radio wavelengths. Quasars have quite different spectra from those of close galaxies, because they have broad, high intensity emission lines superimposed on the continuous spectrum. These lines show an extremely large red shift, which indicates that they are moving at speeds up to 0.9 c. Some show absorption lines with red shift near or less than those shown by emission lines. It is thought that these absorption lines could be caused by dim galaxies and interstellar gas between Earth and the quasars.

describe the key features of stellar spectra and describe how these are used to classify stars

• A stellar spectrum is the spectrum of radiation emitted by a star.
  
  
• A stellar spectrum consists of an approximate black body radiation spectrum for the temperature of the stellar surface, superimposed with absorption lines characteristic of the elements present in the stellar atmosphere.
  
  
• The shape of the curve of intensity against wavelength across a star’s black-body spectrum, and particularly the position of the intensity maximum, identifies the surface temperature of the star. When stars of different surface temperature are compared, there is an increase in luminosity along with a gradual change from red, for the coolest stars, through orange, yellow, white and eventually to blue for the hottest stars.
  
  
• Thus the spectral quality of stellar radiation can be used to classify visible stars into several spectral class: O, B, A, F, G, K, and M, from hottest to coolest. Each spectral class has a characteristic colour and surface temperature range, and each is characterised by specific absorption line patterns, indicating the elements in the star’s atmosphere. Each class is further subdivided into ten sub classes, e.g. O1, O2, O3...O8, O9, B0, B1, B2 ... There are also stars that radiate predominantly in the ultra-violet (class W) and infra-red (classes R, N and S) regions of the spectrum.

Table of spectral classes of visible stars

Spectral Class	Colour	Surface temperature (K)	Elements evident in absorption lines
O	blue	over 30 000	ionised He, weak H
B	blue-white	30 000 – 15 000	neutral He, weak H
A	white	15 000 – 10 000	strong H
F	white-yellow	10 000 – 7 000	weak H, metals (Ca, Fe)
G	yellow	7000 - 5000	strong metals, esp. Ca
K	orange	5000 - 4000	strong metals; CH and CN
M	red	4000 - 3000	strong molecules (incl. TiO)

describe how spectra can provide information on surface temperature, rotational and translational velocity, density and chemical composition of stars

• Surface temperature: The continuous spectrum of a star is similar to that of a black body radiator at the same surface temperature. By plotting the intensity of a star’s radiation as a function of its wavelength, the wavelength at which intensity is a maximum can be found. Wien’s Law shows that this wavelength is inversely proportional to the surface temperature (K) of the star. This means that the redder a star appears, the lower is its surface temperature, while the bluer the star, the higher the surface temperature.
  
  

  Wien’s Displacement Law: (not required by the syllabus)

  
  
  
  
• Rotational velocity: If a star is rotating, then one side is travelling away from us while the other side is coming toward us. Light emitted from the receding side will be red-shifted, while light from the approaching side will be blue-shifted by the same amount. Light from other parts of the star will fall within these two limits. Thus the individual spectral lines will be broadened by an amount depending on the rotational velocity of the star. The faster a star rotates, the more broadening of spectral lines is observed.

  

• Translational velocity: The component of the translational velocity of a star parallel to the observer’s line of sight can be determined by observing the extent and direction of Doppler shift exhibited by the star’s absorption lines. If a star is approaching the observer, every absorption line in the spectrum of the star is shifted toward the blue end of the spectrum by the same amount. If the star is moving away, all the lines are shifted towards the red end. The amount by which all the lines are shifted depends on the component of the velocity of the star along the line of sight.

The component of the translational velocity of a star perpendicular to the observer’s line of sight cannot be determined from the star’s spectrum, but only photographically over a lengthy period of time.

• Density: Density, and therefore pressure, at the surface of a star can also broaden spectral lines, but the intensity varies across the line in different way from the effect of rotation. In high density (small and massive) stars the increased gas pressure produces more rapid collision between atoms during the emission or absorption of radiation. These collisions cause changes in the electron orbits and hence produce a broader spectral line. Rotational velocity and the density of a star can both be deduced from the width and shape of the spectral lines.
  
  
• Chemical composition: Each chemical element has a unique emission spectrum consisting of lines corresponding to the internal electronic transitions within the element. These lines are in the same places as the lines in an absorption spectrum for a cloud of the same element. Elements in the star’s outer layers absorb light from the continuous black-body spectrum of the star. A comparison of a star’s absorption spectrum with the spectra of known elements allows the chemical composition of the star’s outer layers to be deduced.

analyse information to predict the surface temperature of a star from its intensity/wavelength graph

• You may be provided with a graph of intensity against wavelength for the spectrum of a star. Analyse the information by first identifying the wavelength at which the black body curve is at its highest intensity. You will need to be able to justify your estimate of this wavelength. This can best be done by drawing a vertical line down from the peak of the curve so that it intercepts the horizontal (wavelength) axis. You may need to interpolate between divisions on the wavelength axis. Take care to ensure that your answer is given in the correct SI unit.
  
  
• In order to predict the surface temperature of the star from the wavelength of maximum intensity, you will probably be given the Wien’s Law equation:

where (W = 2.89 x 10-3 m.K). Rearrange the equation so that T is the subject of the equation, then substitute in the value of wavelength from the graph.