Signals from the epoch of cosmological recombination – Karl Schwarzschild Award Lecture 2008

The physical ingredients to describe the epoch of cosmological recombination are amazingly simple and well‐understood. This fact allows us to take into account a very large variety of physical processes, still finding potentially measurable consequences for the energy spectrum and temperature anisotropies of the Cosmic Microwave Background (CMB). In this contribution we provide a short historical overview in connection with the cosmological recombination epoch and its connection to the CMB. Also we highlight some of the detailed physics that were studied over the past few years in the context of the cosmological recombination of hydrogen and helium. The impact of these considerations is two‐fold: (i) The associated release of photons during this epoch leads to interesting and unique deviations of the CosmicMicrowave Background (CMB) energy spectrum from a perfect blackbody, which, in particular at decimeter wavelength and the Wien part of the CMB spectrum, may become observable in the near future. Despite the fact that the abundance of helium is rather small, it still contributes a sizeable amount of photons to the full recombination spectrum, leading to additional distinct spectral features. Observing the spectral distortions from the epochs of hydrogen and helium recombination, in principle would provide an additional way to determine some of the key parameters of the Universe (e.g. the specific entropy, the CMB monopole temperature and the pre‐stellar abundance of helium). Also it permits us to confront our detailed understanding of the recombination process with direct observational evidence. In this contribution we illustrate how the theoretical spectral template of the cosmological recombination spectrum may be utilized for this purpose. We also show that because hydrogen and helium recombine at very different epochs it is possible to address questions related to the thermal history of our Universe. In particular the cosmological recombination radiation may allow us to distinguish between Compton y ‐distortions that were created by energy release before or after the recombination of the Universe finished. (ii) With the advent of high precision CMB data, e.g. as will be available using the PLANCK Surveyor or CMBPOL, a very accurate theoretical understanding of the ionization history of the Universe becomes necessary for the interpretation of the CMB temperature and polarization anisotropies. Here we show that the uncertainty in the ionization history due to several processes, which until now were not taken in to account in the standard recombination code RECFAST, reaches the percent level. In particular He II → He I recombination occurs significantly faster because of the presence of a tiny fraction of neutral hydrogen at z ∼ 2400. Also recently it was demonstrated that in the case of H I Lyman α photons the timedependence of the emission process and the asymmetry between the emission and absorption profile cannot be ignored. However, it is indeed surprising how inert the cosmological recombination history is even at percent‐level accuracy. Observing the cosmological recombination spectrum should in principle allow us to directly check this conclusion, which until now is purely theoretical. Also it may allow to reconstruct the ionization history using observational data (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

CMB recombination lines of hydrogen: The differential spectrum

We have calculated the distortions of the cosmic microwave background (CMB) spectrum in the wavelength range 2–50 cm due to the superposition of the CMB hydrogen recombination radiation in subordinate lines. The level populations were determined by numerically solving the equation of recombination kinetics together with the statistical equilibrium equations for a 60-level model hydrogen atom. The relative distortions are ≈10^?7–10^?6, with their wavelength dependence having a low-contrast, wavy pattern. However, the contrast increases severalfold and becomes pronounced when passing to the differential distortion spectrum. We study the dependence of the distortions on cosmological parameters.     

How well do we understand cosmological recombination?

The major theoretical limitation for extracting cosmological parameters from the cosmic microwave background (CMB) sky lies in the precision with which we can calculate the cosmological recombination process. Uncertainty in the details of hydrogen and helium recombination could effectively increase the errors or bias the values of the cosmological parameters derived from the Planck satellite, for example. Here, we modify the cosmological recombination code recfast by introducing one more parameter to reproduce the recent numerical results for the speed-up of the helium recombination. Together with the existing hydrogen fudge factor, we vary these two parameters to account for the remaining dominant uncertainties in cosmological recombination. By using the C osmo MC code with Planck forecast data, we find that we need to determine the parameters to better than 10 per cent for He  i and 1 per cent for H, in order to obtain negligible effects on the cosmological parameters. For helium recombination, if the existing studies have calculated the ionization fraction to the 0.1 per cent level by properly including the relevant physical processes, then we already have numerical calculations which are accurate enough for Planck . For hydrogen, setting the fudge factor to speed up low-redshift recombination by 14 per cent appears to be sufficient for Planck . However, more work still needs to be done to carry out comprehensive numerical calculations of all the relevant effects for hydrogen, as well as to check for effects which couple hydrogen and helium recombination through the radiation field.     

Cosmological hydrogen recombination: populations of the high-level substates

We present results for the spectral distortions of the cosmic microwave background (CMB) arising due to bound–bound transitions during the epoch of cosmological hydrogen recombination at frequencies down to  ν∼100 MHz  . We extend our previous treatment of the recombination problem now including the main collisional processes and following the evolution of all the hydrogen angular momentum substates for up to 100 shells. We show that, due to the low baryon density of the Universe, even within the highest considered shell full statistical equilibrium (SE) is not reached and that at low frequencies the recombination spectrum is significantly different when assuming full SE for   n > 2  . We also directly compare our results for the ionization history to the output of the recfast code, showing that especially at low redshifts rather big differences arise. In the vicinity of the Thomson visibility function the electron fraction differs by roughly −0.6 per cent which affects the temperature and polarization power spectra by ≲ 1 per cent. Furthermore, we shortly discuss the influence of free–free absorption and line broadening due to electron scattering on the bound–bound recombination spectrum and the generation of CMB angular fluctuations due to scattering of photons within the high shells.     

Cosmic microwave background polarisation: foreground contrast and component separation

We evaluate the expected level of foreground contamination to the cosmic microwave background (CMB) polarised radiation, focusing on the diffuse emission from our own Galaxy. In particular, we perform a first attempt to simulate an all sky template of polarised emission from thermal dust. This study indicates that the foreground contamination to CMB B-modes is likely to be relevant on all frequencies, and even at high Galactic latitudes. We review the recent developments in the design of data analysis techniques dedicated to the separation of CMB and foreground emissions in multi-frequency observations, exploiting their statistical independence. We argue that the high quality and detail of the present CMB observations represent an almost ideal statistical dataset where these algorithms can operate with excellent performance. We explicitly show that the recovery of CMB B-modes is possible even if they are well below the foreground level, working at the arcminute resolution at an almost null computational cost. This capability well represents the great potentiality of these new data analysis techniques, which should be seriously taken into account for implementation in present and future CMB observations.     

Two-photon 2s ↔ 1s transitions during hydrogen recombination in the universe

Based on the standard cosmological model, we calculate the correction to the rate of two-photon 2s ? 1s transitions in the hydrogen atom under primordial hydrogen plasma recombination conditions that arises when the induced transitions under equilibrium background radiation with a blackbody spectrum and plasma recombination radiation are taken into account.     

Measuring α in the Early Universe

We update the bounds on a time-varying fine structure constant α at the time of BBN (z∼10¹⁰) and CMB (z∼10³) and present the current CMB constraints on α, through a combined analysis of the BOOMERanG, MAXIMA and DASI datasets. We also present a discussion of the constraints on α coming from large-scale structure observations, focusing in particular on the power spectrum from the 2dF survey. Finally we provide a analysis of the degeneracies between α and the other cosmological parameters and discuss ways to break these with both existing and/or forthcoming data. Our results are consistent with no variation in α from the epoch of recombination to the present day, and restrict any such variation to be less than about 4%.We show that the forthcoming MAP and Planck experiments will be able to break most of the currently existing degeneracies between α and other parameters, and measure α to better than percent accuracy. This revised version was published online in July 2006 with corrections to the Cover Date.     

The interaction of matter and radiation in a hot-model universe

In this paper we continue the investigation initiated by Weymann as to the reason why the spectrum of the residual radiation deviates from a Planck curve. We shall consider the distortions of the spectrum resulting from radiation during the recombination of a primeval plasma. Analytical expressions are obtained for the deviation from an equilibrium spectrum due to Compton scattering by hot electrons. On the basis of the observational data it is concluded that a period of neutral hydrogen in the evolution of the universe is unavoidable. It is shown that any injection of energy att>10¹⁰ sec (red shiftz<10⁵) leads to deviation from an equilibrium spectrum.Translated by Peter Foukal.     

Bianchi type I two-fluid cosmological models with a variable G and Λ

This paper presents anisotropic, homogeneous two-fluid cosmological models in a Bianchi type I space–time with a variable gravitational constant G and cosmological constant Λ. In the two-fluid model, one fluid represents the matter content of the universe and another fluid is chosen to model the CMB radiation. We find a variety of solutions in which the cosmological parameter varies inversely with time t. We also discuss in detail the behavior of associated fluid parameters and kinematical parameters. This paper pictures cosmic history when the radiation and matter content of the universe are in an interactive phase. Here, Ω is closing to 1 throughout the cosmic evolution.      

Bayesian foreground analysis with CMB data

The quality of CMB observations has improved dramatically in the last few years, and will continue to do so in the coming decade. Over a wide range of angular scales, the uncertainty due to instrumental noise is now small compared to the cosmic variance. One may claim with some justification that we have entered the era of precision CMB cosmology. However, some caution is still warranted: The errors due to residual foreground contamination in the CMB power spectrum and cosmological parameters remain largely unquantified, and the effect of these errors on important cosmological parameters such as the optical depth τ and spectral index n_s is not obvious. A major goal for current CMB analysis efforts must therefore be to develop methods that allow us to propagate such uncertainties from the raw data through to the final products. Here we review a recently proposed method that may be a first step towards that goal.     

Variation in the Opacity of the Intergalactic Medium During its Reionization

It is now assumed that reionization of the intergalactic medium occurred under the action of ultraviolet radiation from hot stars contained in galaxies that formed early. Regions of ionized hydrogen (H II zones) were formed around such galaxies. The effects of hydrogen recombination and of the simultaneous cosmological expansion of such regions on their opacity are considered. It is shown that regions formed at z _i < 6 are opaque to L _c radiation, while for z _i 5 the intergalactic medium should be transparent at 0 < z < 5. This conclusion is in accord with recent observational data.     

Angular power spectrum of CMB anisotropy from WMAP

The remarkable improvement in the estimates of different cosmological parameters in recent years has been largely spearheaded by accurate measurements of the angular power spectrum of cosmic microwave background (CMB) radiation. This has required removal of foreground contamination as well as detector noise bias with reliability and precision. Recently, a novel model-independent method for the estimation of CMB angular power spectrum from multi-frequency observations has been proposed and implemented on the first year WMAP (WMAP-1) data by Saha et al. [Saha, R., Jain, P., Souradeep, T., 2006. ApJL, 645, L89]. We review the results from WMAP-1 and also present the new angular power spectrum based on three years of the WMAP data (WMAP-3). Previous estimates have depended on foreground templates built using extraneous observational input to remove foreground contamination. This is the first demonstration that the CMB angular spectrum can be reliably estimated with precision from a self contained analysis of the WMAP data. The primary product of WMAP are the observations of CMB in 10 independent difference assemblies (DA) distributed over five frequency bands that have uncorrelated noise. Our method utilizes maximum information available within WMAP data by linearly combining DA maps from different frequencies to remove foregrounds and estimating the power spectrum from the 24 cross-power spectra of clean maps that have independent noise. An important merit of the method is that the expected residual power from unresolved point sources is significantly tempered to a constant offset at large multipoles (in contrast to the l² contribution expected from a Poisson distribution) leading to a small correction at large multipoles. Hence, the power spectrum estimates are less susceptible to uncertainties in the model of point sources.     

On the influence of resonant scattering on cosmic microwave background polarization anisotropies

We implement the theory of resonant scattering in the context of cosmic microwave background (CMB) polarization anisotropies. We compute the changes in the E-mode polarization (EE) and temperature E-mode (TE) CMB power spectra introduced by the scattering on a resonant transition with a given optical depth τ_X and polarization coefficient E ₁. The latter parameter, accounting for how anisotropic the scattering is, depends on the exchange of angular momentum in the transition, enabling observational discrimination between different resonances. We use this formalism in two different scenarios: cosmological recombination and cosmological re-ionization. In the context of cosmological recombination, we compute predictions in frequency and multipole space for the change in the TE and EE power spectra introduced by scattering on the Hα and Pα lines of hydrogen. This constitutes a fundamental test of the standard model of recombination, and the sensitivity it requires is comparable to that needed in measuring the primordial CMB B-mode polarization component. In the context of re-ionization, we study the scattering off metals and ions produced by the first stars, and find that polarization anisotropies, apart from providing a consistency test for intensity measurements, give some insight on how re-ionization evolved. Since polarization anisotropies have memory of how anisotropic the line scattering is, they should be able to discern the O  i 63.2-μm transition from other possible transitions associated to O  iii , N  ii , N  iii , etc. The amplitude of these signals are, however, between 10 and 100 times below the (already challenging) level of CMB B-mode polarization anisotropies.     

Multiband study of NGC 7424 and its two newly discovered ultraluminous X-ray sources

The recombination of hydrogen and helium at   z ∼ 1000–7000  gives unavoidable distortions to the cosmic microwave background (CMB) spectrum. We present a detailed calculation of the line intensities arising from the Lyman α (Lyα) (2p–1s) and two-photon (2s–1s) transitions for the recombination of hydrogen, as well as the corresponding lines from helium. We give an approximate formula for the strength of the main recombination line distortion on the CMB in different cosmologies; this peak occurring at about  170 μm  . We also find a previously undescribed long-wavelength peak (which we call the pre-recombination peak) from the lines of the 2p–1s transitions, which are formed before significant recombination of the corresponding atoms occurred. Detailed calculations of the two-photon emission-line shapes are presented here for the first time. The frequencies of the photons emitted from the two-photon transition have a wide spectrum and this causes the location of the peak of the two-photon line of hydrogen to be located almost at the same wavelength as the main Lyα peak. The helium lines also give distortions at similar wavelengths, so that the combined distortion has a complex shape. The detection of this distortion would provide direct supporting evidence that the Universe was indeed once a plasma. Moreover, the distortions are a sensitive probe of physics during the time of recombination. Although the spectral distortion is overwhelmed by dust emission from the Galaxy, and is maximum at wavelengths roughly where the cosmic far-infrared background peaks, it may be able to tailor an experiment to detect its non-trivial shape.     

Hydrodynamical modes and gravitational instabilities in the Universe during the recombination era

We assume the Universe during the recombination era as a three-component fluid constituted by neutral hydrogen, plasma, and radiation; such fluids are coupled via the effects of photorecombination, photoionization, and Thomson scattering. The hydrodynamical modes are calculated and the relation with the gravitational instabilities is established. In addition to the well-known Jeans's instability modes two additional ones in the neighbourhood of 10¹³ M are obtained in the case of an open Universe.     

Univiewer utility for fast interactive 3D visualization of CMB maps in HEALPix pixelizaton

We describe the Univiewer utility for visualizing the celestialmaps in the HEALPix pixelization scheme, which is widely used in data reduction for various experiments involving observations of the cosmic microwave background radiation (CMB). The utility can be used to view the FITS files containing one or several extensions containing HEALPix maps of temperature, intensities, Stokes parameters, integration time per pixel values, etc. The user can interactively change the visualization parameters, apply a coordinate grid, project sky areas onto a plane for further detailed analyses, and compute power spectra. The utility uses OpenGL and wxWidgets cross-platform libraries.     

Lines in the cosmic microwave background spectrum from the epoch of cosmological hydrogen recombination

We compute the spectral distortions of the cosmic microwave background (CMB) arising during the epoch of cosmological hydrogen recombination within the standard cosmological (concordance) model for frequencies in the range 1–3500 GHz. We follow the evolution of the populations of the hydrogen levels including states up to principle quantum number   n = 30  in the redshift range  500 ≤ z ≤ 3500  . All angular momentum substates are treated individually, resulting in a total number of 465 hydrogen levels. The evolution of the matter temperature and the fraction of electrons coming from He  ii are also included. We present a detailed discussion of the distortions arising from the main dipolar transitions, for example Lyman and Balmer series, as well as the emission due to the two-photon decay of the hydrogen 2s level. Furthermore, we investigate the robusteness of the results against changes in the number of shells considered. The resulting spectral distortions have a characteristic oscillatory behaviour, which might allow experimentalists to separate them from other backgrounds. The relative distortion of the spectrum exceeds a value of 10⁻⁷ at wavelengths longer than 21 cm. Our results also show the importance of detailed follow-up of the angular momentum substates, and their effect on the amplitude of the lines. The effect on the residual electron fraction is only moderate, and mainly occurs at low redshifts. The CMB angular power spectrum is changed by less than 1 per cent. Finally, our computations show that if the primordial radiation field is described by a pure blackbody, then there is no significant emission from any hydrogen transition at redshifts greater than   z ∼ 2000  . This is in contrast to some earlier works, where the existence of a 'pre-recombination' peak was claimed.     

Ionization freeze-out and hydrogen excitation in the SN IIP atmosphere

We study the nonstationary recombination of hydrogen in the atmosphere of SN 1987A by taking into account ion-molecular processes. The hydrogen excitation due to nonstationary recombination is shown to be enough to explain the observed hydrogen lines in a time interval until day 30 in the absence of additional excitation mechanisms. Thus, the problem of a deficit in the hydrogen excitation that has recently been found in modeling the hydrogen spectrum of SN 1987A at an early photospheric stage by assuming statistical ionization equilibrium is resolved. The mass of the radioactive ⁵⁶Ni with a spherically symmetric distribution in the outer layers is shown to be close to 10^?6 M _⊙. Our model predicts the appearance of a blue peak in the Hα profile between days 20 and 30. This peak bears a close similarity to the observed peak known as the Bochum event. The presence of this peak in the model is attributable to nonstationary recombination and to a substantial contribution of hydrogen neutralization involving H^? and H₂.     

GMRT and VLA observations at 49 cm and 20 cm of the HII region near <Emphasis Type="Italic">l</Emphasis> = 24.8°, <Emphasis Type="Italic">b</Emphasis> = 0.1°

We report multi-frequency radio continuum and hydrogen radio recombination line observations of HII regions near l = 24.8°, b = 0.1° using the Giant Metrewave Radio Telescope (GMRT) at 1.28 GHz (n = 172), 0.61 GHz (n = 220) and the Very Large Array (VLA) at 1.42 GHz (n = 166). The region consists of a large number of resolved HII regions and a few compact HII regions as seen in our continuum maps, many of which have associated infrared (IR) point sources. The largest HII region at l = 24.83° and b = 0.1° is a few arcmins in size and has a shell-type morphology. It is a massive HII region enclosing ∼550 M_⊙ with a linear size of 7 pc and an rms electron density of ∼110 cm⁻³ at a kinematic distance of 6 kpc. The required ionization can be provided by a single star of spectral type O5.5. We also report detection of hydrogen recombination lines from the HII region at l = 24.83° and b = 0.1° at all observed frequencies near V _lsr = 100 km s⁻¹. We model the observed integrated line flux density as arising in the diffuse HII region and find that the best fitting model has an electron density comparable to that derived from the continuum. We also report detection of hydrogen recombination lines from two other HII regions in the field.     

Helium radiation diffusion in prominences

The following is shown on the basis of a solution of the integral diffusion equations for radiation in a multilevel helium atom under low-temperature plasma conditions (T _e = 7000 K) in the Vertical slab model: (a) Neutral helium is ionized by coronal radiation mainly in the 100–300 Å spectral region; the degree of helium ionization is maximum at the boundary planes, (b) The photorecombinations to the 2³ S and 2¹ S levels and the photoionizations by the Balmer continuum of the Sun are very nearly balanced and this determines the population of these levels. The 2³ S level is destroyed by electron impacts (this reduces the brightness of the triplet lines), and the 2¹ S level decays via the escape of the quanta of 584 through the 2¹ P level, (c) Emission in the resonance line 584 (2¹ P 1¹ S) occurs due to recombination to 2¹ S with subsequent absorption of quanta of infrared radiation 20581. This is a rare case. (d) The radiation of helium is generated in the vicinity of the boundary planes in the region of penetration of radiation with 200 Å, where the density of matter decreases gradually down to the coronal value. In the subordinate lines, the radiation is conditioned by the quasi-resonance scattering of photospheric radiation, (e) The calculated absolute values of the intensities of the helium and hydrogen lines are in good agreement with the observations (see Figure 6).The helium to hydrogen number ratio is close to 0.05.