Spectral distortions of the cosmic microwave background [Elektronische Ressource] / angefertigt von Jens Chluba

Jens Chluba

Sujets

• Astronomie

Informations

• Publié par: ludwig-maximilians-universitat_munchen
• Publié le: 01 janvier 2005
• Nombre de lectures: 20
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

Spectral Distortions of the
Cosmic Microwave Background
Dissertation
der Fakult at fur Physik der
Ludwig-Maximilians-Universit at Munc hen
angefertigt von
Jens Chluba
aus Tralee (Irland)
Munc hen, den 31. M arz 20051. Gutachter: Prof. Dr. Rashid Sunyaev, MPA Garching
2.hter: Prof. Dr. Viatcheslav Mukhanov, LMU Munc hen
Tag der mundlic hen Prufung: 19. Juli 2005Die Sterne
Ich sehe oft um Mitternacht,
wenn ich mein Werk getan
und niemand mehr im Hause wacht,
die Stern am Himmel an.
Sie gehn da, hin und her, zerstreut
als L ammer auf der Flur;
in Rudeln auch, und aufgereiht
wie Perlen an der Schnur;
und funkeln alle weit und breit,
und funkeln rein und sch on;
ich seh die gro e Herrlichkeit,
und kann nicht satt mich sehn...
Dann saget unterm Himmelszelt
mein Herz mir in der Brust;
Es gibt was Bessers in der Welt
als all ihr Schmerz und Lust.
Matthias ClaudiusContents
Abstract ix
1 Introduction 1
1.1 General introduction on CMB . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Spectral distortions of the CMB . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 The SZ e ect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.2 Spectral distortion due to energy release in the early Universe . . . . . . 8
1.3 In this Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 SZ clusters of galaxies: in uence of the motion of the Solar System 13
2.1 General transformation laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 Transformation of the cluster signal . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Multi-frequency observations of clusters . . . . . . . . . . . . . . . . . . . . . . 18
2.3.1 Dipolar asymmetry in the number of observed clusters . . . . . . . . . . 19
2.3.2 Estimates for the dipolar asymmetry in the cluster number counts . . . 19
2.3.3 Source count contribution from non-SZ populations . . . . . . . . . . . 20
2.4 Summary and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3 Spectral distortion of the CMB and the superposition of blackbodies 23
3.1 Basic ingredients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1.1 Compton y-distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1.2 Relation between temperature and intensity . . . . . . . . . . . . . . . . 26
3.2 Small spectral distortions due to the superposition of blackbodies . . . . . . . . 27
3.2.1 Sum of blackbodies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.2 Superposition of Planck spectra . . . . . . . . . . . . . . . . . . . . . . . 33
3.3 Superposition of two Planck spectra . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.1 Sum of two Planck spectra . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.2 Di erence of two Planck spectra . . . . . . . . . . . . . . . . . . . . . . 37
3.4 Spectral distortions due to the CMB dipole . . . . . . . . . . . . . . . . . . . . 37
3.4.1 Whole sky beam spectral distortion . . . . . . . . . . . . . . . . . . . . 38
3.4.2 Beam spectral distortion due to the CMB dipole . . . . . . . . . . . . . 39
3.4.3 Distortion with respect to any T . . . . . . . . . . . . . . . . . . . . . 40ref
3.5 Spectral distortions due to higher multipoles . . . . . . . . . . . . . . . . . . . 43
3.6 Spectral induced in di eren tial measurements . . . . . . . . . . . . . 47
3.7 Cross Calibration of frequency channels . . . . . . . . . . . . . . . . . . . . . . 50
3.7.1 using clusters of galaxies . . . . . . . . . . . . . . . . . . . . 50
3.7.2 Cross calibration using the superposition of blackbodies . . . . . . . . . 51
3.8 Other sources of spectral distortions . . . . . . . . . . . . . . . . . . . . . . . . 54
3.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54ii CONTENTS
4 The double Compton process in mildly relativistic thermal plasmas 57
4.1 The current understanding of the double Compton process . . . . . . . . . . . . 57
4.2 The kinetic equation for DC scattering . . . . . . . . . . . . . . . . . . . . . . . 59
4.2.1 General de nitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2.2 Standard approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.2.3 Kernelh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.3 The DC emission kernelP( ! j ) for thermal electrons . . . . . . . . . . 640 2 1
4.3.1 The DC kernel for cold electrons . . . . . . . . . . . . . . . . . . . . . . 64
4.3.2 The DC kernel for thermal electrons . . . . . . . . . . . . . . . . . . . . 66
4.3.3 Mean photon energy and dispersion of the DC kernel . . . . . . . . . . . 66
4.4 DC emission for monochromatic photons and thermal electrons . . . . . . . . . 67
4.4.1 Cold electrons and soft initial photons . . . . . . . . . . . . . . . . . . . 68
4.4.2 Cold and arbitrary initial photons . . . . . . . . . . . . . . . . 70
4.4.3 Thermal electrons and low energy initial photons . . . . . . . . . . . . . 74
4.4.4 and arbitrary initial . . . . . . . . . . . . . . 77
4.4.5 The DC infrared divergence and the role of the low frequency cuto . . 81
4.4.6 Electron heating and cooling due to DC emission . . . . . . . . . . . . . 83
4.5 Analytical treatment of the full kinetic equation for DC scattering . . . . . . . 83
4.5.1 Analytic approximation for the e ectiv e DC Gaunt factor . . . . . . . . 84
4.5.2 Derivation of the e ectiv e DC Gaunt factor in the soft photon limit . . 86
4.5.3 Beyond the limit 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 88e
4.5.4 Results for di eren t incoming photon spectra . . . . . . . . . . . . . . . 88
4.5.5 Beyond the soft photon limit . . . . . . . . . . . . . . . . . . . . . . . . 90
4.5.6 Discussion of the results for Planck, Bose-Einstein and Wien spectra . . 90
4.6 Summary and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5 Thermalization of CMB spectral distortions 97
5.1 General formulation of the thermalization problem . . . . . . . . . . . . . . . . 97
5.1.1 The Boltzmann equation in the expanding Universe . . . . . . . . . . . 98
5.1.2 Evolution of the number and energy density . . . . . . . . . . . . . . . . 98
5.2 Evolution of the photons in the expanding Universe . . . . . . . . . . . . . . . 99
5.2.1 Compton scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.2.2 Double Compton scattering and Bremsstrahlung . . . . . . . . . . . . . 100
5.2.3 Expansion term . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.3 Evolution of the electrons and baryons in the Universe . . . . . . . . . . . . . . 101
5.3.1 Evolution of the electron temperature . . . . . . . . . . . . . . . . . . . 101
5.3.2 Interactions with the photons . . . . . . . . . . . . . . . . . . . . . . . . 103
5.4 Towards a numerical solution of the problem . . . . . . . . . . . . . . . . . . . 104
5.4.1 Representation of the photon spectrum . . . . . . . . . . . . . . . . . . 104
5.4.2 Compton scattering relativistic corrections . . . . . . . . . . . . . . . . 105
5.4.3 Double Compton and Bremsstrahlung . . . . . . . . . . . . . . . . . . . 105
5.4.4 Electron temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.5 Thermalization of small spectral distortions . . . . . . . . . . . . . . . . . . . . 105
5.5.1 Time evolution of small chemical potential distortions . . . . . . . . . . 106
5.5.2 Solving the time evolution in the limit of small chemical potential . . . 109
5.6 Energy injection by di eren t physical mechanisms . . . . . . . . . . . . . . . . 111
5.6.1 Single energy injection at z . . . . . . . . . . . . . . . . . . . . . . . . . 112h
5.6.2 Energy injection from annihilating relict particles . . . . . . . . . . . . . 113
5.6.3 by unstable relict particles . . . . . . . . . . . . . . . . 113
5.7 Summary and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Conclusions 117CONTENTS iii
A Relativistic Maxwell-Boltzmann distribution 119
A.1 Number and phase space density . . . . . . . . . . . . . . . . . . . . . . . . . . 119
A.2 Low temperature expansion of the relativistic Maxwell-Boltzmann distribution 119
A.3 Energy density and pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
A.4 Heat capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
A.5 Solving integrals over the relativistic Maxwell-Boltzmann distribution . . . . . 121
B Relations for the photon phase space distribution 123
B.1 Pressure, energy and number density . . . . . . . . . . . . . . . . . . . . . . . . 123
B.2 E ectiv e temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
iB.3 Useful relations between n(x;(x)) and its derivatives @ n . . . . . . . . . . . . 124x
C Collection of analytic approximations for the Compton scattering kernel 125
C.1 Compton kernel for cold electrons . . . . . . . . . . . . . . . . . . . . . . . . . . 125
C.1.1 Normalization, mean energy and dispersion of the Compton kernel for
cold electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
C.2 Compton kernel for thermal electrons . . . . . . . . . . . . . . . . . . . . . . . 126
C.2.1 Normalization, mean energy and dispersion of the Compton kernel for
thermal