Mixing of blackbodies: entropy production and dissipation of sound waves in the early Universe

Abstract

Mixing of blackbodies with different temperatures creates a spectral distortion which, at lowest order, is a y-type distortion, indistinguishable from the thermal y-type distortion produced by the scattering of CMB photons by hot electrons residing in clusters of galaxies. This process occurs in the radiation-pressure dominated early Universe, when the primordial perturbations excite standing sound waves on entering the sound horizon. Photons from different phases of the sound waves, having different temperatures, diffuse through the electron-baryon plasma and mix together. This diffusion, with the length defined by Thomson scattering, dissipates sound waves and creates spectral distortions in the CMB. Of the total dissipated energy, 2/3 raises the average temperature of the blackbody part of spectrum, while 1/3 creates a distortion of y-type. It is well known that at redshifts 10^5< z< 2x10^6, comptonization rapidly transforms y-distortions into a Bose-Einstein spectrum. The chemical potential of the Bose-Einstein spectrum is again 1/3 the value we would get if all the dissipated energy was injected into a blackbody spectrum but no extra photons were added. We study the mixing of blackbody spectra, emphasizing the thermodynamic point of view, and identifying spectral distortions with entropy creation. This allows us to obtain the main results connected with the dissipation of sound waves in the early Universe in a very simple way. We also show that mixing of blackbodies in general, and dissipation of sound waves in particular, leads to creation of entropy.

References in corpus (23)

• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Cosmological Perturbation Theory in the Synchronous vs. Conformal Newtonian Gauge
• Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges
• The Cosmic Microwave Background Spectrum from the Full COBE/FIRAS Data Set
• 4-Year COBE DMR Cosmic Microwave Background Observations: Maps and Basic Results
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Sky Maps, Systematic Errors, and Basic Results
• The Primordial Inflation Explorer (PIXIE): A Nulling Polarimeter for Cosmic Microwave Background Observations
• Anisotropies in the Cosmic Microwave Background: An Analytic Approach
• The evolution of CMB spectral distortions in the early Universe
• Power Spectrum Constraints from Spectral Distortions in the Cosmic Microwave Background
• Analytic approach to the polarization of the cosmic microwave background in flat and open universes
• Reionization and cosmic microwave background distortions: a complete treatment of second order Compton scattering
• A New Window on Primordial non-Gaussianity
• Scale-dependent bias of galaxies and mu-type distortion of the cosmic microwave background spectrum from single-field inflation with a modified initial state
• CMB Anisotropies at Second-Order II: Analytical Approach
• Lines in the cosmic microwave background spectrum from the epoch of cosmological helium recombination
• The radiative transfer at second order: a full treatment of the Boltzmann equation with polarization
• Free-bound emission from cosmological hydrogen recombination
• Creation of the CMB spectrum: precise analytic solutions for the blackbody photosphere
• Superposition of blackbodies and the dipole anisotropy: A possibility to calibrate CMB experiments
• Does Bose-Einstein condensation of CMB photons cancel μ distortions created by dissipation of sound waves in the early Universe?
• Cosmological constraints from CMB distortion
• A numerical code for the solution of the Kompaneets equation in cosmological context

Cited by in corpus (50)

• Massive Primordial Black Holes from Hybrid Inflation as Dark Matter and the seeds of Galaxies
• Features and New Physical Scales in Primordial Observables: Theory and Observation
• PRISM (Polarized Radiation Imaging and Spectroscopy Mission): An Extended White Paper
• Beyond y and μ: the shape of the CMB spectral distortions in the intermediate epoch, 1.5x10^4 < z < 2x10^5
• Distinguishing different scenarios of early energy release with spectral distortions of the cosmic microwave background
• CMB spectral distortions from small-scale isocurvature fluctuations
• The synergy between CMB spectral distortions and anisotropies
• The blackness of the cosmic microwave background spectrum as a probe of the distance-duality relation
• Constraining primordial magnetic fields with distortions of the black-body spectrum of the cosmic microwave background: pre- and post-decoupling contributions
• Unavoidable CMB spectral features and blackbody photosphere of our Universe
• A Hydrodynamical Approach to CMB mu-distortions
• Forecasts for CMB μ- and i-type spectral distortion constraints on the primordial power spectrum on scales 8 < k < 10^4 Mpc^-1 with the future Pixie-like experiments
• $\mu$-Distortions or Running: A Guaranteed Discovery from CMB Spectrometry
• Testing Inflation and Curvaton Scenarios with CMB Distortions
• Critical point Higgs inflation in the Palatini formulation
• Rich structure of non-thermal relativistic CMB spectral distortions from high energy particle cascades at redshifts $z\lesssim 2\times 10^5$
• Using CMB spectral distortions to distinguish between dark matter solutions to the small-scale crisis
• CMB $\mu$ distortion from primordial gravitational waves
• Kinetic Sunyaev Zeldovich effect in an anisotropic CMB model: measuring low multipoles of the CMB at higher redshifts using intensity and polarization spectral distortions
• Polarized anisotropic spectral distortions of the CMB: Galactic and extragalactic constraints on photon-axion conversion
• Probing correlations of early magnetic fields using mu-distortion
• A new probe of Axion-Like Particles: CMB polarization distortions due to cluster magnetic fields
• CMB spectral distortions from the decay of causally generated magnetic fields
• CMB Distortions from Damping of Acoustic Waves Produced by Cosmic Strings
• New CMB spectral distortion constraints on decaying dark matter with full evolution of electromagnetic cascades before recombination
• Cosmological constraints from $\mu E$ cross-correlations
• Limits on the fluctuating part of $y$-type distortion monopole from Planck and SPT results
• Impact of EDGES 21cm Global Signal on Primordial Power Spectrum
• Constraints on non-resonant photon-axion conversion from the Planck satellite data
• Can accreting primordial black holes explain the excess radio background?
• The effects of the small-scale behaviour of dark matter power spectrum on CMB spectral distortion
• Anisotropic CMB distortions from non-Gaussian isocurvature perturbations
• The general relativistic equations of radiation hydrodynamics in the viscous limit
• Probing early-universe phase transitions with CMB spectral distortions
• FSD: Frequency Space Differential measurement of CMB spectral distortions
• CMB spectral distortions as solutions to the Boltzmann equations
• New Horizons in Cosmology with Spectral Distortions of the Cosmic Microwave Background
• Recent developments in astrophysical and cosmological exploitation of microwave surveys
• Probing small-scale non-Gaussianity from anisotropies in acoustic reheating
• Robust μ-distortion constraints on primordial supermassive black holes from cubic (gNL) non-Gaussian perturbations
• Motion induced second order temperature and y-type anisotropies after the subtraction of linear dipole in the CMB maps
• Testing kinetically coupled inflation models with CMB distortions
• Non-thermal Sunyaev-Zeldovich signal from radio galaxy lobes
• Cosmology with Recombination Spectrum
• Spectral Distortion in a Radially Inhomogeneous Cosmology
• Effects on the CMB from magnetic field dissipation before recombination
• Revisiting constraints on primordial magnetic fields from spectral distortions of cosmic microwave background
• Secondary isocurvature perturbations from acoustic reheating
• E and B modes of the CMB y-type distortions: polarised kinetic Sunyaev-Zeldovich effect from the reionisation and post-reionisation eras
• The non-thermal secondary CMB anisotropies from a cosmic distribution of radio galaxy lobes