Fundamental Astronomy

More documents

Recommendations

Info

$P 0.1 Stabilişti natura şsi suma seriilor: a) Σ 1 n\ ; b) Σ arctan 1 n# + n ...$

This is greater than the speed of light, if the radius is smaller than the critical radius RS = 2GM/c 2 . (14.3) The same value for the critical radius, the Schwarzschild radius, is obtained from the general theory of relativity. For example, for the Sun, RS is about 3 km; however, the Sun’s mass is so small that it cannot become a black hole by normal stellar evolution. Because the mass of a black hole formed by stellar collapse has to be larger than MOV the radius of the smallest black holes formed in this way is about 5–10 km. The properties of black holes have to be studied on the basis of the general theory of relativity, which is beyond the scope of this book. Thus only some basic properties are discussed qualitatively. An event horizon is a surface through which no information can be sent out, even in principle. A black hole is surrounded by an event horizon at the Schwarzschild radius (Fig. 14.10). In the theory of relativity each observer carries with him his own local measure of time. If two observers are at rest with respect to each other at the same point their clocks go at the same rate. Otherwise their clock rates are different, and the apparent course of events differs, too. Near the event horizon the different time definitions become significant. An observer falling into a black Fig. 14.10. A black hole is surrounded by a spherical event horizon. In addition to this a rotating black hole is surrounded by a flattened surface inside which no matter can remain stationary. This region is called the ergosphere 14.3 Black Holes hole reaches the centre in a finite time, according to his own clock, and does not notice anything special as he passes through the event horizon. However, to a distant observer he never seems to reach the event horizon; his velocity of fall seems to decrease towards zero as he approaches the horizon. The slowing down of time also appears as a decrease in the frequency of light signals. The formula for the gravitational redshift can be written in terms of the Schwarzschild radius as (Appendix B) ν∞ = ν 1 − 2GM = ν 1 − rc2 RS . (14.4) r Here, ν is the frequency of radiation emitted at a distance r from the black hole and ν∞ the frequency observed by an infinitely distant observer. It can be seen that the frequency at infinity approaches zero for radiation emitted near the event horizon. Since the gravitational force is directed towards the centre of the hole and depends on the distance, different parts of a falling body feel a gravitational pull that is different in magnitude and direction. The tidal forces become extremely large near a black hole so that any material falling into the hole will be torn apart. All atoms and elementary particles are destroyed near the central point, and the final state of matter is unknown to presentday physics. The observable properties of a black hole do not depend on how it was made. Not only all information on the material composition disappears as a star collapses into a black hole; any magnetic field, for example, also disappears behind the event horizon. A black hole can only have three observable properties: mass, angular momentum and electric charge. It is improbable that a black hole could have a significant net charge. Rotation, on the other hand, is typical to stars, and thus black holes, too, must rotate. Since the angular momentum is conserved, stars collapsed to black holes must rotate very fast. In 1963 Roy Kerr managed to find a solution of the field equations for a rotating black hole. In addition to the event horizon a rotating hole has another limiting surface, an ellipsoidal static limit (Fig. 14.10). Objects inside the static limit cannot be kept stationary by any force, but they must orbit the hole. However, it is possible to escape from the region between the static limit and the event horizon, called the ergosphere. In fact it is 299
300 14. Compact Stars Fig. 14.11. The arrow shows the variable star V1357 Cyg. Its companion is the suspected black hole Cygnus X-1. The bright star to the lower right of V1357 is η Cygni, one of the brightest stars in the constellation Cygnus possible to utilize the rotational energy of a black hole by dropping an object to the ergosphere in such a way that part of the object falls into the hole and another part is slung out. The outcoming part may then have considerably more kinetic energy than the original object. At present the only known way in which a black hole could be directly observed is by means of the radiation from gas falling into it. For example, if a black hole is part of a binary system, gas streaming from the companion will settle into a disc around the hole. Matter at
Page 2:
Fundamental Astronomy
Page 5 and 6:
Dr. Hannu Karttunen University of T
Page 7 and 8:
VI Preface to the First Edition The
Page 9 and 10:
VIII Contents 5.6 Continuous Spectr
Page 11 and 12:
X Contents 16. Star Clusters and As
Page 14 and 15:
1. Introduction 1.1 TheRoleofAstron
Page 16 and 17:
1.2 Astronomical Objects of Researc
Page 18 and 19:
theory of relativity must be used t
Page 20 and 21:
of the gas may be 10 −21 kg m −
Page 22 and 23:
12 2. Spherical Astronomy angles co
Page 24 and 25:
14 or 2. Spherical Astronomy sin B
Page 26 and 27:
16 2. Spherical Astronomy defined t
Page 28 and 29:
18 2. Spherical Astronomy the verna
Page 30 and 31:
20 2. Spherical Astronomy pole. The
Page 32 and 33:
22 2. Spherical Astronomy Fig. 2.16
Page 34 and 35:
Page 36 and 37:
26 2. Spherical Astronomy
Page 38 and 39:
Page 40 and 41:
30 2. Spherical Astronomy numbers,
Page 42 and 43:
32 2. Spherical Astronomy In the 19
Page 44 and 45:
34 2. Spherical Astronomy mid-Septe
Page 46 and 47:
36 2. Spherical Astronomy correspon
Page 48 and 49:
38 2. Spherical Astronomy second of
Page 50 and 51:
2. Spherical Astronomy 40 Since ∆
Page 52 and 53:
42 2. Spherical Astronomy For the s
Page 54 and 55:
44 2. Spherical Astronomy red. What
Page 56 and 57:
3. Observations and Instruments Up
Page 58 and 59:
the long, oblique path through the
Page 60 and 61:
Fig. 3.6a-e. Diffraction and resolv
Page 62 and 63:
3.2 Optical Telescopes Fig. 3.10. T
Page 64 and 65:
3.2 Optical Telescopes Fig. 3.13. T
Page 66 and 67:
so thin that it absorbs very little
Page 68 and 69:
3.2 Optical Telescopes 59
Page 70 and 71:
3.2 Optical Telescopes 61
Page 72 and 73:
3.2 Optical Telescopes ◭ Fig. 3.1
Page 74 and 75:
and CCD-cameras have largely replac
Page 76 and 77:
Fig. 3.22a-e. The principle of read
Page 78 and 79:
than a prism. The dispersion can be
Page 80 and 81:
3.4 Radio Telescopes Fig. 3.25. The
Page 82 and 83:
Fig. 3.27. The Atacama Large Millim
Page 84 and 85:
Fig. 3.30. The VLA at Socorro, New
Page 86 and 87:
Fig. 3.31. (a) X-rays are not refle
Page 88 and 89:
Fig. 3.33. Refractors are not suita
Page 90 and 91:
tored by laser interferometers. If
Page 92 and 93:
4. Photometric Concepts and Magnitu
Page 94 and 95:
If we are outside the source, where
Page 96 and 97:
magnitudes can be equal, the flux d
Page 98 and 99:
flux L will now decrease with incre
Page 100 and 101:
this line is extrapolated to X = 0,
Page 102 and 103:
since due to extinction, radiation
Page 104 and 105:
96 5. Radiation Mechanisms Fig. 5.1
Page 106 and 107:
98 5. Radiation Mechanisms From (5.
Page 108 and 109:
100 5. Radiation Mechanisms Fig. 5.
Page 110 and 111:
Page 112 and 113:
104 5. Radiation Mechanisms We now
Page 114 and 115:
5. Radiation Mechanisms 106 Again F
Page 116 and 117:
Page 118 and 119:
110 5. Radiation Mechanisms We can
Page 120 and 121:
112 5. Radiation Mechanisms differe
Page 122 and 123:
114 6. Celestial Mechanics The solu
Page 124 and 125:
116 6. Celestial Mechanics prove (6
Page 126 and 127:
118 6. Celestial Mechanics in the d
Page 128 and 129:
120 6. Celestial Mechanics But cons
Page 130 and 131:
122 6. Celestial Mechanics by the e
Page 132 and 133:
124 6. Celestial Mechanics Substitu
Page 134 and 135:
126 6. Celestial Mechanics a cloud
Page 136 and 137:
128 6. Celestial Mechanics Since th
Page 138 and 139:
130 6. Celestial Mechanics Exercise
Page 140 and 141:
132 7. The Solar System Fig. 7.1. (
Page 142 and 143:
134 7. The Solar System for each ob
Page 144 and 145:
136 7. The Solar System Fig. 7.5. L
Page 146 and 147:
138 7. The Solar System Inserting t
Page 148 and 149:
140 7. The Solar System Therefore o
Page 150 and 151:
142 7. The Solar System Fig. 7.10.
Page 152 and 153:
144 7. The Solar System behaves mor
Page 154 and 155:
146 7. The Solar System Table 7.1.
Page 156 and 157:
Page 158 and 159:
150 7. The Solar System of the plan
Page 160 and 161:
152 7. The Solar System If we denot
Page 162 and 163:
154 7. The Solar System where F⊥
Page 164 and 165:
Page 166 and 167:
158 7. The Solar System larized fea
Page 168 and 169:
Page 170 and 171:
162 7. The Solar System The outer c
Page 172 and 173:
Page 174 and 175:
Page 176 and 177:
168 7. The Solar System weak and co
Page 178 and 179:
170 7. The Solar System amount of w
Page 180 and 181:
Page 182 and 183:
Page 184 and 185:
176 7. The Solar System ter the rin
Page 186 and 187:
178 7. The Solar System face, most
Page 188 and 189:
180 7. The Solar System The F ring,
Page 190 and 191:
182 7. The Solar System Herschel hi
Page 192 and 193:
Page 194 and 195:
Page 196 and 197:
188 7. The Solar System liding, sin
Page 198 and 199:
Page 200 and 201:
Page 202 and 203:
Page 204 and 205:
196 7. The Solar System of this mat
Page 206 and 207:
Page 208 and 209:
Page 210 and 211:
202 7. The Solar System Near the po
Page 212 and 213:
204 7. The Solar System be solved f
Page 214 and 215:
8. Stellar Spectra All our informat
Page 216 and 217:
which appears as irregular fluctuat
Page 218 and 219:
8.2 The Harvard Spectral Classifica
Page 220 and 221:
ate of ionization is essentially de
Page 222 and 223:
lines of titanium, scandium and van
Page 224 and 225:
efore τ = 1, i. e. the radiation i
Page 226 and 227:
yielding Iν(0,θ)= Sν(τ ∗ ) +
Page 228 and 229:
222 9. Binary Stars and Stellar Mas
Page 230 and 231:
Page 232 and 233:
Page 234 and 235:
10. Stellar Structure The stars are
Page 236 and 237:
where a = 4σ/c = 7.564 × 10−16
Page 238 and 239:
where me is the electron mass and N
Page 240 and 241:
is produced by the proton-proton (p
Page 242 and 243:
oxygen, which in turn reacts to for
Page 244 and 245:
According to (4.7), (4.4) and (5.16
Page 246 and 247:
Example 10.6 The Radiation Pressure
Page 248 and 249:
11. Stellar Evolution In the preced
Page 250 and 251:
increases. The stellar surface temp
Page 252 and 253: Since stars are most likely to be f
Page 254 and 255: Fig. 11.4a-c. Energy transport in t
Page 256 and 257: Fig. 11.5. The structure of a massi
Page 258 and 259: tract to planetlike brown dwarfs. S
Page 260 and 261: Fig. 11.10a-f. Evolution of a low-m
Page 262 and 263: Fig. 11.12. The Wolf-Rayet star WR
Page 264 and 265: In a neutron capture, a nucleus wit
Page 266 and 267: This is several orders of magnitude
Page 268 and 269: 264 12.TheSun Fig. 12.2. (a) The ro
Page 270 and 271: 266 12.TheSun according to the heli
Page 272 and 273: 268 12.TheSun shines into view for
Page 274 and 275: 270 12.TheSun was established that
Page 276 and 277: 272 12.TheSun Fig. 12.11. In pairs
Page 278 and 279: 274 12.TheSun Fig. 12.15. (a) Quies
Page 280 and 281: 276 12.TheSun Fig. 12.17. An X-ray
Page 282 and 283: 13. Variable Stars Stars with chang
Page 284 and 285: Fig. 13.3. The variation of brightn
Page 286 and 287: Fig. 13.5. The lightcurve of a long
Page 288 and 289: duced when the carbon condenses int
Page 290 and 291: 13.3 Eruptive Variables Fig. 13.12.
Page 292 and 293: Fig. 13.15. Supernova 1987A in the
Page 294 and 295: 14. Compact Stars In astrophysics t
Page 296 and 297: about 1.4 M⊙, which is thus the u
Page 298 and 299: 1968. In the following year it was
Page 300 and 301: ditions required for hypernova expl
Page 304 and 305: Fig. 14.12. Scale drawings of 16 bl
Page 306 and 307: are (or, in the radio case, have on
Page 308 and 309: 14.6 Exercises Exercise 14.1 The ma
Page 310 and 311: 308 15. The Interstellar Medium Fig
Page 312 and 313: 310 15. The Interstellar Medium R d
Page 314 and 315: 312 15. The Interstellar Medium pol
Page 320 and 321: 318 15. The Interstellar Medium Tab
Page 324 and 325: 322 15. The Interstellar Medium met
Page 326 and 327: 324 15. The Interstellar Medium
Page 328 and 329: 326 15. The Interstellar Medium He
Page 332 and 333: 330 15. The Interstellar Medium up
Page 334 and 335: 332 15. The Interstellar Medium hav
Page 336 and 337: 334 15. The Interstellar Medium len
Page 338 and 339: 336 15. The Interstellar Medium dro
Page 340 and 341: 338 15. The Interstellar Medium the
Page 342 and 343: 340 16. Star Clusters and Associati
Page 348 and 349: 17. The Milky Way On clear, moonles
Page 350 and 351: Fig. 17.3. The directions to the ga
Page 352 and 353:
classes of stars are main sequence
Page 354 and 355:
Fig. 17.9. The size of the volume e
Page 356 and 357:
lar material similarly moves in the
Page 358 and 359:
Fig. 17.14. In order to derive Oort
Page 360 and 361:
Fig. 17.17. The radial velocity as
Page 362 and 363:
a suitable mass distribution, such
Page 364 and 365:
esting because it may be a small-sc
Page 366 and 367:
material constituting the galaxy. I
Page 368 and 369:
18. Galaxies The galaxies are the f
Page 370 and 371:
Fig. 18.3. The classification of no
Page 372 and 373:
18.1 The Classification of Galaxies
Page 374 and 375:
Fig. 18.7. Compound luminosity func
Page 376 and 377:
In order to measure the mass at eve
Page 378 and 379:
length r0 = 1-5 kpc. In Sc galaxies
Page 380 and 381:
18.4 Dynamics of Galaxies We have s
Page 382 and 383:
gas. Some normal spirals may have b
Page 384 and 385:
the Large and Small Magellanic Clou
Page 386 and 387:
stars are forming and evolving into
Page 388 and 389:
panion galaxy. The tail is interpre
Page 390 and 391:
een made at these wavelengths with
Page 392 and 393:
galaxies in our present neighbourho
Page 394 and 395:
394 19. Cosmology tographs form an
Page 396 and 397:
396 19. Cosmology Fig. 19.3. Hubble
Page 398 and 399:
398 19. Cosmology element after hyd
Page 400 and 401:
400 19. Cosmology 19.3 Homogeneous
Page 402 and 403:
402 19. Cosmology The potential ene
Page 404 and 405:
404 19. Cosmology In an expanding c
Page 406 and 407:
406 19. Cosmology about 40,000 degr
Page 408 and 409:
408 19. Cosmology rather slowly. In
Page 410 and 411:
410 19. Cosmology Fig. 19.15. Corre
Page 412 and 413:
412 19. Cosmology where Ω0 = ρ0/
Page 414 and 415:
414 19. Cosmology Example 19.2 Find
Page 416 and 417:
416 20. Astrobiology According to t
Page 418 and 419:
418 20. Astrobiology of spiral gala
Page 420 and 421:
420 20. Astrobiology Fig. 20.2. Bla
Page 422 and 423:
422 20. Astrobiology reached 10% of
Page 424 and 425:
424 20. Astrobiology Now panspermia
Page 426 and 427:
426 20. Astrobiology 20.9 Detecting
Page 428 and 429:
428 20. Astrobiology cles that we s
Page 430 and 431:
Appendices 431
Page 432 and 433:
Ellipse. Equation in rectangular co
Page 434 and 435:
A and B can be determined graphical
Page 436 and 437:
When using matrix formalism it is c
Page 438 and 439:
Similarly, a volume integral I = f
Page 440 and 441:
B. Theory of Relativity Albert Eins
Page 442 and 443:
time interval between the events is
Page 444 and 445:
C. Tables Table C.1. SI basic units
Page 446 and 447:
Table C.6. The Sun Property Symbol
Page 448 and 449:
Table C.11. Osculating elements of
Page 450 and 451:
Discoverer Year of a Psid e i r M
Page 452 and 453:
Table C.16. Periodic comets with se
Page 454 and 455:
Table C.17 (continued) C. Tables Na
Page 456 and 457:
C. Tables Table C.19. Some double s
Page 458 and 459:
Table C.22. Optically brightest gal
Page 460 and 461:
Table C.23 (continued) Abbreviation
Page 462 and 463:
C. Tables Table C.26. Millimetre an
Page 464 and 465:
Table C.27 (continued) Satellite La
Page 466 and 467:
468 Answers to Exercises 6.2 a = 1.
Page 468 and 469:
470 Answers to Exercises Chapter 17
Page 470 and 471:
472 Further Reading Morrison (ed.):
Page 472 and 473:
474 Further Reading Maps and Catalo
Page 474 and 475:
Name and Subject Index A aberration
Page 476 and 477:
coherent radiation 95 Cold Dark Mat
Page 478 and 479:
forbidden transition 101, 332 four-
Page 480 and 481:
Kellman, Edith 212 Kepler’s equat
Page 482 and 483:
nautical mile 15 nautical triangle
Page 484 and 485:
Reber, Grote 69 recombination 95, 9
Page 486 and 487:
synchronous rotation 135 synchrotro
Page 488 and 489:
Colour Supplement 491
Page 490 and 491:
Plate 14. The first view from the s
Page 492 and 493:
Plate 1 Plate 2 Colour Supplement 4
Page 494 and 495:
Plate 6 Plate 5 Colour Supplement 4
Page 496 and 497:
Plate 9 Colour Supplement Plate 10
Page 498 and 499:
Page 500 and 501:
Page 502 and 503:
Plate 23 Plate 24 Colour Supplement
Page 504 and 505:
Colour Supplement Plate 29 507
Page 506 and 507:
show all

Fundamental Astronomy

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?