Stars as Laboratories for Fundamental Physics - MPP Theory Group

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594 Appendix D of antifermions is given by the same expression with µ → −µ. Then µ is implicitly given by the phase-space integral ∫ n f = 2 d 3 ( ) p 1 (2π) 3 e (E p−µ)/T + 1 − 1 , (D.5) e (E p+µ)/T + 1 where the second term represents antifermions and the factor 2 is for the two spin degrees of freedom. Again, the fermion density is understood to mean the density of fermions minus that of antifermions. At vanishing temperature, f p becomes a step function Θ(µ − E p ). If µ > 0 so that n f > 0, i.e. an excess of fermions over antifermions, there are no antifermions at all at T = 0. The fermion integral yields n f = p 3 F/3π 2 , (D.6) where the Fermi momentum is defined by µ 2 0 = p 2 F + m 2 with µ 0 the zero-temperature chemical potential. The Fermi energy is defined by E 2 F = p 2 F + m 2 e, i.e. E F = µ 0 . Equation D.6 is taken as the definition of the Fermi momentum even at T > 0; it is a useful parameter to characterize the fermion density, whether or not they are degenerate. Numerically it is p F = 5.15 keV (Y e ρ) 1/3 (D.7) for electrons with the mass density ρ in units of g cm −3 . In general, Eq. (D.5) cannot be made explicit for µ; it has to be solved numerically or by an approximation method. In the ρ-T -plane, contours for the electron chemical potential are shown in Fig. D.3. Above the main plot, the electron density is characterized by p F . On the right side, the temperature is shown in units of keV. Recall that 10 7 K = 0.8621 keV (Appendix A). For nonrelativistic electrons the contours in Fig. D.3 are very sensitive to the exact value of µ. Therefore, in this regime the nonrelativistic chemical potential ˆµ ≡ µ − m (D.8) is a more appropriate parameter. Often ˆµ is referred to as the chemical potential. This can be very confusing when relativistic effects are important. In terms of ˆµ, the relativistic Fermi-Dirac distribution is f p = 1 e (E kin−ˆµ)/T + 1 , (D.9) with the kinetic energy E kin = E p −m → p 2 /2m (nonrelativistic limit).
Characteristics of Stellar Plasmas 595 Fig. D.3. Contours for the electron chemical potential µ. The solid lines are marked with the relevant value for µ, the dotted lines with µ − m e . Fig. D.4. Contours for the electron degeneracy parameter η = (µ − m e )/T . Also shown are the loci of the stellar models of Fig. D.1.
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Georg G. Raffelt Stars as Laborator
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Table of Contents Preface (xiv) Ack
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Table of Contents vii 4.5 Neutrino
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Table of Contents ix 8. Neutrino Os
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Table of Contents xi 12. Radiative
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Table of Contents xiii 16.3 New Int
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Preface xv Second, particles from d
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Preface xvii search for proton deca
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Preface xix cuts of higher-order gr
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Preface xxi quoted “astrophysical
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Chapter 1 The Energy-Loss Argument
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The Energy-Loss Argument 3 example
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The Energy-Loss Argument 5 trinos,
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The Energy-Loss Argument 7 As a sim
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The Energy-Loss Argument 9 The most
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The Energy-Loss Argument 11 against
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The Energy-Loss Argument 13 ing M;
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The Energy-Loss Argument 15 M ′ (
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The Energy-Loss Argument 17 Table 1
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The Energy-Loss Argument 19 ing to
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The Energy-Loss Argument 21 scalars
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Chapter 2 Anomalous Stellar Energy
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Anomalous Stellar Energy Losses Bou
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Chapter 3 Particles Interacting wit
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Particles Interacting with Electron
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Chapter 4 Processes in a Nuclear Me
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Processes in a Nuclear Medium 119 t
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Processes in a Nuclear Medium 121 f
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Processes in a Nuclear Medium 123 F
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Processes in a Nuclear Medium 129 v
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Processes in a Nuclear Medium 131 4
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Processes in a Nuclear Medium 133 i
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Processes in a Nuclear Medium 135 H
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Processes in a Nuclear Medium 137 I
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Processes in a Nuclear Medium 143 i
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Processes in a Nuclear Medium 145 s
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Processes in a Nuclear Medium 147 E
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Processes in a Nuclear Medium 149 a
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Processes in a Nuclear Medium 151 T
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Processes in a Nuclear Medium 153 r
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Processes in a Nuclear Medium 155 4
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Processes in a Nuclear Medium 157 I
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Processes in a Nuclear Medium 159 t
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Processes in a Nuclear Medium 161 A
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Processes in a Nuclear Medium 163 R
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Chapter 5 Two-Photon Coupling of Lo
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Two-Photon Coupling of Low-Mass Bos
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Chapter 6 Particle Dispersion and D
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Particle Dispersion and Decays in M
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Chapter 7 Nonstandard Neutrinos The
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Nonstandard Neutrinos 253 (“spont
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Nonstandard Neutrinos 255 kinematic
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Nonstandard Neutrinos 257 95% CL ma
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Nonstandard Neutrinos 259 Fig. 7.2.
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Nonstandard Neutrinos 261 In three-
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Nonstandard Neutrinos 263 Flavor mi
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Nonstandard Neutrinos 267 The quant
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Nonstandard Neutrinos 269 dipole mo
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Nonstandard Neutrinos 271 component
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Nonstandard Neutrinos 275 moments.
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Nonstandard Neutrinos 277 7.5.2 Spi
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Nonstandard Neutrinos 279 where m
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Neutrino Oscillations 281 and hence
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Neutrino Oscillations 283 As usual
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Neutrino Oscillations 285 two-flavo
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Neutrino Oscillations 287 Fig. 8.2.
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Neutrino Oscillations 289 8.2.4 Exp
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Neutrino Oscillations 293 Apparentl
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Neutrino Oscillations 297 when the
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Neutrino Oscillations 299 If the ne
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Neutrino Oscillations 301 8.3.5 The
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Neutrino Oscillations 303 It is als
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Neutrino Oscillations 305 system, h
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Neutrino Oscillations 307 say, betw
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Neutrino Oscillations 309 1991). Th
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Oscillations of Trapped Neutrinos 3
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Chapter 10 Solar Neutrinos The curr
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Solar Neutrinos 343 Fig. 10.1. Sola
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Solar Neutrinos 345 There exist vas
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Solar Neutrinos 347 10.2 Calculated
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Solar Neutrinos 349 Fig. 10.3. Norm
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Solar Neutrinos 351 a certain range
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Solar Neutrinos 353 While helium an
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Solar Neutrinos 355 Bahcall and Pin
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Solar Neutrinos 357 Xu et al. (1994
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Solar Neutrinos 359 Table 10.4. Spe
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Solar Neutrinos 361 Table 10.5. Pre
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Solar Neutrinos 363 rates attribute
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Solar Neutrinos 365 10.3.4 Water Ch
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Solar Neutrinos 367 Fig. 10.10. Dif
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Solar Neutrinos 369 Fig. 10.13. Mea
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Solar Neutrinos 371 Table 10.9. Cur
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Solar Neutrinos 373 of order the an
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Solar Neutrinos 375 Fig. 10.16. 37
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Solar Neutrinos 377 GALLEX, or Home
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Solar Neutrinos 379 Table 10.10. Me
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Solar Neutrinos 381 deficits in all
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Solar Neutrinos 383 The ν e surviv
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Solar Neutrinos 385 The allowed ran
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Solar Neutrinos 387 10.7 Spin and S
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Solar Neutrinos 389 10.8 Neutrino D
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Solar Neutrinos 391 The small- and
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Solar Neutrinos 393 flux above its
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Chapter 11 Supernova Neutrinos The
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Supernova Neutrinos 397 Fig. 11.1.
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Supernova Neutrinos 399 beyond the
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Supernova Neutrinos 401 ate neutrin
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Supernova Neutrinos 403 Convection
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Supernova Neutrinos 405 Hayes, and
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Supernova Neutrinos 407 11.2 Predic
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Supernova Neutrinos 409 must then b
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Supernova Neutrinos 411 Figure 11.6
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Supernova Neutrinos 413 signal (Sec
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Supernova Neutrinos 415 time) on 23
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Supernova Neutrinos 417 All of the
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Supernova Neutrinos 419 to multiple
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Supernova Neutrinos 421 the final-s
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Supernova Neutrinos 423 ter of 53 e
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Supernova Neutrinos 425 Given these
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Supernova Neutrinos 427 thorough st
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Supernova Neutrinos 429 The forward
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Supernova Neutrinos 431 Another int
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Supernova Neutrinos 433 ber of ν e
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Supernova Neutrinos 435 A “normal
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Supernova Neutrinos 437 Fig. 11.19.
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Supernova Neutrinos 439 The approxi
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Supernova Neutrinos 441 be taken to
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Supernova Neutrinos 443 sense that
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Supernova Neutrinos 445 presence of
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Supernova Neutrinos 447 An even mor
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Chapter 12 Radiative Particle Decay
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Radiative Particle Decays 451 one c
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Radiative Particle Decays 453 corre
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Radiative Particle Decays 455 is no
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Radiative Particle Decays 457 Fig.
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Radiative Particle Decays 461 12.3.
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Radiative Particle Decays 463 emiss
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Radiative Particle Decays 465 range
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Radiative Particle Decays 469 weak
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Radiative Particle Decays 471 value
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Radiative Particle Decays 473 ignor
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Radiative Particle Decays 479 Table
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Radiative Particle Decays 481 In or
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Radiative Particle Decays 485 while
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Radiative Particle Decays 487 h 100
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Radiative Particle Decays 491 still
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Chapter 13 What Have We Learned fro
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What Have We Learned from SN 1987A
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Axions 525 Table 14.1. Particle mag
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Axions 527 or axion decay constant.
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Axions 529 The Yukawa coupling h is
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Axions 531 14.2.3 Pseudoscalar vs.
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Axions 533 Notably, the Higgs field
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Axions 535 otic heavy quarks: only
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Axions 537 Various axion models dif
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Axions 539 Bounds on the Yukawa cou
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Axions 541 Fig. 14.5. Astrophysical
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Page 611 and 612: Appendix D Characteristics of Stell
Page 613: Characteristics of Stellar Plasmas
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Page 629 and 630: References 609 Bahcall, J. N., Kras
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Page 635 and 636: References 615 Cooper-Sarkar, A. M.
Page 637 and 638: References 617 Dodelson, S., Friema
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Page 641 and 642: References 621 Goyal, A., Dutta, S.
Page 643 and 644: References 623 Hoogeveen, F., and S
Page 645 and 646: References 625 Kawakami, H., et al.
Page 647 and 648: References 627 Landau, L. D., and P
Page 649 and 650: References 629 Mayle, R. W., and Wi
Page 651 and 652: References 631 Nieves, J. F., and P
Page 653 and 654: References 633 Pochoda, P., and Sch
Page 655 and 656: References 635 Ross, J. E., and All
Page 657 and 658: References 637 Shlyakhter, A. I. 19
Page 659 and 660: References 639 Totsuka, Y. 1993, Ne
Page 661 and 662: References 641 Wiezorek, C., et al.
Page 663 and 664: Acronyms 643 L l.h. l.h.s. ly LMC L
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Symbols 645 dp differential in phas
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Symbols 647 X j Peccei-Quinn charge
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Subject Index A α-Ori 189 A665, A1
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Subject Index 651 Coulomb gauge 204
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Subject Index 653 H Hayashi line 32
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Subject Index 655 multiple scatteri
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Subject Index 657 neutrino radiativ
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Subject Index 659 Primakoff process
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Subject Index 661 SN 1987A bounds (
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Subject Index 663 supernova core bi
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