Stars as Laboratories for Fundamental Physics - MPP Theory Group

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158 Chapter 4 The gluon in Fig. 4.13 couples to the quarks with the strong finestructure constant α s and the gluon propagator involves an effective mass for which Anand, Goyal, and Iha (1990) used m 2 g = (6α s /π) p 2 F where p F is the Fermi momentum of the quark sea. The axion coupling to quarks is the usual derivative form (C q /2f a ) ψ q γ µ γ 5 ψ q ∂ µ ϕ with q = u, d, s. After a cumbersome but straightforward calculation Anand et al. found for the energy-loss rate in the degenerate limit Q a = 62π2 α 2 s 945 p F T 6 (2f a ) 2 × { C 2 q (I 1 + 2I 2 ) for qq → qqa, (C 2 q + C 2 q ′) I 1 for qq ′ → qq ′ a, (4.84) where the angular integrals are I 1 ≡ 1 ∫ π ∫ 2π dθ dϕ s5 θ (1 + c 4 ϕ) 2π 2 0 0 (s 2 θ s2 ϕ + κ2 ) , 2 I 2 ≡ 1 ∫ π 2π 2 0 ∫ 2π dθ dϕ 0 s 5 θ (s 2 θ s2 ϕ + κ2 )(s 2 θ c2 ϕ + κ2 ) , (4.85) where s θ ≡ sin(θ/2), s ϕ ≡ sin(ϕ/2), c ϕ ≡ cos(ϕ/2), and κ 2 ≡ m 2 g/2p 2 F = 3α s /2π. Numerically, I 1 = 12.3, 4.23, and 2.25 for α s = 0.2, 0.4, and 0.6, while I 2 = 2.34, 1.30, and 0.86, respectively. The total emission rate involves three processes with equal quarks (qq = uu, dd, ss), and three with different ones (qq ′ = ud, us, ds) so that Q a is the prefactor of Eq. (4.84) times (C 2 u + C 2 d + C 2 s )(3I 1 + 2I 2 ), to be compared with Eq. (4.10) for degenerate neutron matter. The ratio between the rates is Q qq a Q nn a = C2 u + C 2 d + C 2 s C 2 n p F,q p F,n αs 2 απ 2 2π (3I 1 + 2I 2 ) G(m π /p F,n ) , (4.86) where the function G(u) was given in Eq. (4.12). The ratio of coupling constants is model dependent (Sect. 14.3.3), the Fermi momenta are approximately equal for equal densities. For a typical value α s = 0.4 one has α 2 s/α 2 π = 0.6×10 −3 while the last factor is about 140 with G = 0.7 (Fig. 4.3) so that the last two factors together are about 0.08. Hence, the emission rate from quark matter is much smaller than that from neutron matter because α π is so large relative to α s . In the inevitable presence of protons in a neutron star, the np process will be even more important than nn (Fig. 4.4), further enhancing the emission rate of nuclear matter relative to quark matter. For neutrino pairs the ratio of the emission rates is about the same as for axions and so quark matter is much less effective at νν emission
Processes in a Nuclear Medium 159 than nuclear matter (Burrows 1979; Anand, Goyal, and Iha 1990). This observation has little effect on the neutrino cooling rate of a quark star because the URCA processes, which are based on charged-current reactions, dominate for both nuclear or quark matter. For axions, however, it may seem that the emission rate is much suppressed relative to nuclear matter. This is certainly true if “axion” stands for any generic pseudoscalar Nambu-Goldstone boson. The QCD axion, however, which was introduced to solve the CP problem of strong interactions (Chapter 14) necessarily has a two-gluon coupling which allows for the gluonic Primakoff effect (Fig. 4.14) which is analogous to the photon Primakoff effect discussed in Sect. 5.2. Fig. 4.14. Axion emission by the gluon Primakoff effect. Altherr (1991) has calculated the emissivity of a hot quark-gluon plasma and found that it was similar to that of a nuclear medium at the same temperature and density. Ellis and Salati (1990) found a much smaller emission rate because they included only the gluonic plasmon decay process g T → g L + γ, much in analogy to the corresponding photonic process discussed in Sect. 5.2.2. This decay process, however, is only part of the axion emissivity by the gluon field fluctuations. For highly degenerate quark matter corresponding to old neutron stars the emission rate has not be calculated as far as I know. 4.9.3 Bubble Phase In a hot lepton-rich neutron star the nuclear medium in the density regime 1 2 ρ 0 to ρ 0 (nuclear matter density ρ 0 = 3×10 14 g cm −3 ) may form a “bubble phase” with regions of low density embedded in the medium. Leinson (1993) has estimated the bremsstrahlung rate for the neutral-current reactions N + bubble → bubble + N + νν. Naturally, he found that only the axial-vector current contributes. Also, it is easy to translate his results into an axion emission rate. Apparently, the bubble phase can be important for early neutron-star cooling.
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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 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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Axions 543 decay into axions. This
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Chapter 15 Miscellaneous Exotica St
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Miscellaneous Exotica 547 Table 15.
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Miscellaneous Exotica 549 15.2.3 Pr
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Miscellaneous Exotica 551 Most rece
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Miscellaneous Exotica 553 Fig. 15.1
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Miscellaneous Exotica 555 A violati
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Miscellaneous Exotica 557 nuclei it
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Miscellaneous Exotica 559 mass, and
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Miscellaneous Exotica 561 backgroun
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Miscellaneous Exotica 563 SN 1987A
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Miscellaneous Exotica 565 which led
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Miscellaneous Exotica 567 For a nar
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Neutrinos: The Bottom Line 569 the
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Neutrinos: The Bottom Line 571 Neut
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Neutrinos: The Bottom Line 573 Apar
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Neutrinos: The Bottom Line 575 is d
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Neutrinos: The Bottom Line 577 of t
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Neutrinos: The Bottom Line 579 siti
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Units and Dimensions 581 In the ast
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Appendix B Neutrino Coupling Consta
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Appendix C Numerical Neutrino Energ
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Numerical Neutrino Energy-Loss Rate
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Numerical Neutrino Energy-Loss Rate
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Appendix D Characteristics of Stell
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Characteristics of Stellar Plasmas
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References 607 Akhmedov, E. Kh., an
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References 609 Bahcall, J. N., Kras
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References 611 Bilenky, S. M., and
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References 613 Cannon, R. D. 1970,
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References 615 Cooper-Sarkar, A. M.
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References 617 Dodelson, S., Friema
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References 619 Fukuda, Y., et al. 1
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References 621 Goyal, A., Dutta, S.
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References 623 Hoogeveen, F., and S
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References 625 Kawakami, H., et al.
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References 627 Landau, L. D., and P
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References 629 Mayle, R. W., and Wi
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References 631 Nieves, J. F., and P
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References 633 Pochoda, P., and Sch
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References 635 Ross, J. E., and All
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References 637 Shlyakhter, A. I. 19
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References 639 Totsuka, Y. 1993, Ne
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References 641 Wiezorek, C., et al.
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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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