Astronomy Principles and Practice Fourth Edition.pdf

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234 The radiation laws radiation is likely to be polarized, although the polarization may not be complete or perfect. This type of radiation is said to be partially polarized. A beam of partially polarized radiation may be thought as being made up of two combined beams, one beam being perfectly polarized and the other being unpolarized. On a highly-resolved timescale, a partially polarized beam of light would show variations of the ‘instantaneous’ polarization form but, on average, one form, perhaps with a particular azimuth, would predominate. The degree of predominance would depend on how near to perfect the partially polarized radiation is. The ratio of the strength of the polarized component to the total strength of the beam defines the degree of polarization, p,ofthe beam. The most frequently met case in astrophysics is the measurement of partially linearly polarized light. If a polarimetric analyser is rotated in such a beam, the transmitted intensity will change according to I (1 + p cos 2 (α − β)) where α is the angle of the analyser’s axis in the instrument and β is the vibration azimuth of the polarization relative to the instrumental frame. On a complete rotation of the polarizer, the recorded signal will oscillate between a maximum and minimum value. If these levels are recorded as I max and I min , it is readily shown that p can be determined from p = I max − I min I max + I min . (15.31) The degree of polarization, together with the parameters which describe the ellipse associated with the polarized component, summarize the polarizational properties of a partially polarized beam. This polarizational information, together with the brightness, gives a complete description of any beam of radiation. All the parameters which are needed to describe a general beam of radiation are capable of carrying information about the condition of the radiating atoms which give rise to the energy, the nature of the matter which scatters the radiation in the direction of the observer or the nature of the matter which is in a direct line between the radiating atoms and the observer. If the observer wishes to gain as much knowledge as possible of the outside universe, all the properties associated with the electromagnetic radiation must be measured. Various scattering phenomena such as that associated with free electrons or dust in extended stellar atmospheres are important means of generating polarization. It also turns out that aligned dust grains in the interstellar medium give rise to linear polarization by differential extinction for the radiation’s components resolved orthogonally to the axis of the grains. Generation of polarization by the synchrotron process is revealed in the supernova remnant known as the Crab nebula (see figure 15.13). 15.10 The Zeeman effect Although it is not the only mechanism that gives rise to a particular spectral line behaviour accompanied by polarizational phenomena, the Zeeman effect serves as a classical example for the rationale of undertaking spectropolarimetric measurements. In the middle of the 19th century, Faraday examined the emission spectrum of sodium vapour which had been placed in a magnetic field. His apparatus, however, was insufficiently sensitive to detect any effect caused by the field. By repeating these experiments with more sensitive equipment, Zeeman, in 1896, demonstrated that the emission lines were broadened. Lorentz, shortly afterwards, proposed a theory, based on the electron theory of matter, which suggested that if the broadening were to be looked at closely, a splitting of the lines should be observed. His theory also predicted that the light of the split lines should be polarized. When the magnetic field is in a direction along the line of sight (a longitudinal field), two lines should be observed at wavelength positions on either side of the position for the emission line when there is no field. These lines should be circularly polarized but with opposite handednesses. When the field is across the line of sight (a transverse field) three lines
The Zeeman effect 235 Figure 15.13. Evidence of strong optical polarization in the Crab nebula; four photographs taken at marked rotational settings of a polarizer. Polarized light is produced as synchrotron radiation by spiralling fast-moving electrons in a magnetic field (photographs from the Mt Wilson and Palomar Observatories).
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Chapter 1 Naked eye observations 1.
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A month 5 seen to rise above the ea
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A year 7 between south and west. An
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Chapter 2 Ancient world models Firs
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Ancient world models 11 Figure 2.1.
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Chapter 3 Observations made by inst
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Instrumentation in astronomy 15 Fig
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The role of the observer 17 Earth a
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Electromagnetic radiation 19 meteor
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Electromagnetic radiation 21 If, fo
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Electromagnetic radiation 23 device
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Direction of arrival of the radiati
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Brightness 27 Figure 5.3. The windo
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Brightness 29 physical conditions w
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Time 31 to house radio transmitters
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Chapter 6 The night sky 6.1 Star ma
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Simple observations 35 Figure 6.1.
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Chapter 7 The geometry of the spher
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Position on the Earth’s surface 4
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Position on the Earth’s surface 4
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Spherical trigonometry 51 determine
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Spherical trigonometry 53 Figure 7.
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The small spherical triangle 55 7.4
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Problems—Chapter 7 57 Although th
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Chapter 8 The celestial sphere: coo
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The equatorial system 61 Figure 8.2
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Circumpolar stars 63 Figure 8.4. A
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Also Hence, we have or The measurem
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The geocentric celestial sphere 67
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Transformation of one coordinate sy
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Right ascension 71 or cos 47 ◦ 39
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The Sun’s geocentric behaviour 73
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Sunset and sunrise 75 Figure 8.15.
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Megalithic man and the Sun 77 Figur
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The ecliptic system of coordinates
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Galactic coordinates 81 Table 8.1.
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Galactic coordinates 83 Figure 8.22
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Galactic coordinates 85 Figure 8.25
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Problems—Chapter 8 87 where ε is
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Sidereal time 89 Figure 9.1. The ti
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Sidereal time 91 Figure 9.3. An equ
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Mean solar time 93 Figure 9.4. Posi
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The relationship between mean solar
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The civil day and timekeeping 97 It
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The tropical year and the calendar
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The Earth’s geographical zones 10
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Hence, the period of the year durin
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Twilight 105 Figure 9.10. The heati
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Twilight 107 For this to happen, ZB
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h m s Date Approximate ZT 16 30 0 J
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Problems—Chapter 9 111 Date (00 h
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Atmospheric refraction 113 Figure 1
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where ZOL = r. But ZOL = ζ .AlsoAB
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so that we have But Hence, Similarl
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Now But θ is a small angle so we m
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Geocentric parallax 121 Figure 10.6
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The semi-diameter of a celestial ob
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Measuring distance in the Solar Sys
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Stellar parallax 127 Figure 10.10.
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Stellar parallax 129 after. The val
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Problems—Chapter 10 131 Recent ob
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Chapter 11 The reduction of positio
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The velocity of light 135 Table 11.
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The constant of aberration 137 Figu
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Diurnal and planetary aberration 13
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Precession of the equinoxes 141 Fig
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Effect of precession on a star’s
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Nutation 145 Figure 11.10. The grav
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The tropical and sidereal years 147
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Chapter 12 Geocentric planetary phe
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The Copernican System 151 Figure 12
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Planetary configurations 153 (a) V
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The synodic period 155 Figure 12.5.
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Measurement of planetary distances
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Stationary points 159 Figure 12.8.
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Stationary points 161 Using equatio
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The phase of a planet 163 Figure 12
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Problems—Chapter 12 165 with an o
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Planetary orbits 167 Figure 13.1. M
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Planetary orbits 169 If P 1 SP 2 is
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Newton’s law of gravitation 171 a
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The Principia of Isaac Newton 173 N
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The two-body problem 175 Figure 13.
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The two-body problem 177 Figure 13.
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The two-body problem 179 13.6.5 The
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284 Detectors for optical telescope
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306 Astronomical optical measuremen
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Chapter 20 Modern telescopes and ot
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332 Modern telescopes and other opt
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Chapter 21 Radio telescopes 21.1 In
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354 Radio telescopes Figure 21.2. A
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358 Radio telescopes Figure 21.6. T
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362 Radio telescopes (a) Paraboloid
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364 Radio telescopes Figure 21.12.
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366 Radio telescopes The record fro
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368 Radio telescopes 2 N N Figure 2
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Chapter 22 Telescope mountings 22.1
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376 Telescope mountings arc and thi
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378 Telescope mountings Figure 22.4
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380 Telescope mountings The design
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382 High energy instruments and oth
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404 Practical projects to give the
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406 Practical projects Figure 24.2.
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408 Practical projects measurement
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416 Practical projects Summer Time
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418 Practical projects Figure 24.12
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422 Practical projects point was ch
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426 Practical projects N φ Earth 1
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428 Practical projects 24.5 Solar d
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430 Practical projects allows the S
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432 Practical projects 24.5.4 The e
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438 Practical projects Now in t hou
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440 Practical projects Table 24.2.
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442 Practical projects 24.7.2 The i
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448 Practical projects right ascens
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450 Practical projects amenable to
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452 Web sites • W 20.5—www.mrao
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Appendix: Astronomical and related
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456 Appendix: Astronomical and rela
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Bibliography 1 Source books The Ast
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Answers to problems Chapter 7 1. 32
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462 Answers to problems Figure A8.2
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464 Answers to problems Figure A10.
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466 Answers to problems Figure A13.
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468 Answers to problems 5. 1·64 6.
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470 Index black body radiation, 216
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472 Index atom, 221 line, 353 illum
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474 Index potential energy, 177 pow
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