Cosmic Background Radiation Field Research Articles

What can be learned from the lensed cosmic microwave background B-mode polarization power spectrum?

The effect of weak gravitational lensing on the cosmic microwave background (CMB) temperature anisotropies and polarization will provide access to cosmological information that cannot be obtained from the primary anisotropies alone. We compare the information content of the lensed B-mode polarization power spectrum, properly accounting for the non-Gaussian correlations between the power on different scales, with that of the unlensed CMB fields and the lensing potential. The latter represent the products of an (idealised) optimal analysis that exploits the lens-induced non-Gaussianity to reconstruct the fields. Compressing the non-Gaussian lensed CMB into power spectra is wasteful and leaves a tight degeneracy between the equation of state of dark energy and neutrino mass that is much stronger than in the more optimal analysis. Despite this, a power spectrum analysis will be a useful first step in analysing future B-mode polarization data. For this reason, we also consider how to extract accurate parameter constraints from the lensed B-mode power spectrum. We show with simulations that for cosmic-variance-limited measurements of the lensed B-mode power, including the non-Gaussian correlations in existing likelihood approximations gives biased parameter results. We develop a more refined likelihood approximation that performs significantly better. This new approximation should also be of more general interest in the wider context of parameter estimation from Gaussian CMB data.

On Star Formation and the Nonexistence of Dark Galaxies

We investigate whether a baryonic dark galaxy or ‘galaxy without stars’ could persist indefinitely in the local universe, while remaining stable against star formation. To this end, a simple model has been constructed to determine the equilibrium distribution and composition of a gaseous protogalactic disk. Specifically, we determine the amount of gas that will transit to a Toomre unstable cold phase via the H2 cooling channel in the presence of a UV—X-ray cosmic background radiation field. All but one of the models are predicted to become unstable to star formation: we find that, in the absence of an internal radiation field, the majority of gas will become Toomre unstable in all putative dark galaxies with baryonic masses greater than 10 9 M⊙, and in at least half of those greater than 10 6 M⊙. Moreover, we find that all our model objects would be detectable via HI line emission, even in the case that star formation is potentially avoided. These results are consistent with the non-detection of isolated extragalactic HI clouds with no optical counterpart (galaxies without stars) by the HI Parkes All-Sky Survey. Additionally, where star formation is predicted to occur, we determine the minimum interstellar radiation field required to restore gravothermal stability, which we then relate to a minimum global star formation rate. This leads to the prediction of a previously undocumented relation between HI mass and star formation rate that is observed for a wide variety of dwarf galaxies in the HI mass range 10 8 —10 10 M⊙. The existence of such a relation strongly supports the notion that the well observed population of dwarf galaxies represent the minimum rates of self-regulating star formation in the universe. Subject headings: Galaxies: Formation — Galaxies: Kinematics and Dynamics — Galaxies: ISM — Stars: Formation — Atomic Processes — Molecular Processes

Cosmic microwave background temperature and polarization pseudo-Cℓestimators and covariances

We develop the pseudo-Cl method for reconstructing the cosmic microwave background (CMB) temperature and polarization auto- and cross-power spectra, and estimate the pseudo-Cl covariance matrix for a realistic experiment on the cut sky. We calculate the full coupling equations for all six possible CMB power spectra, relating the observed pseudo-Cl values to the underlying all-sky Cl values, and test the reconstruction on both full-sky and cut-sky simulated CMB data sets. In particular we consider the reconstruction of the Cl from upcoming ground-based polarization experiments covering areas of a few hundred deg2 and find that the method is fast, unbiased and performs well over a wide range of multipoles from l= 2 to l= 2500. We then calculate the full covariance matrix between the modes of the pseudo-temperature and polarization power spectra, assuming that the underlying CMB fields are Gaussian randomly distributed. The complexity of the covariance matrix prohibits its rapid calculation, required for parameter estimation. Hence we present an approximation for the covariance matrix in terms of convolutions of the underlying power spectra. The coupling matrices in these expressions can be estimated by fitting to numerical simulations, circumventing direct and slow calculation, and further, inaccurate analytic approximations. We show that these coupling matrices are mostly independent of cosmology, and that the full covariance matrix for all six pseudo-Cl power spectra can be quickly and accurately calculated for any given cosmological model using this method. We compare these semi-analytic covariance matrices against simulations and find good agreement, the accuracy of which depends mainly on survey area and the range of cosmological parameters considered.

Does regenerated emission change the high-energy signal from gamma-ray burst afterglows?

We study regenerated high-energy emission from the gamma-ray burst (GRB) afterglows, and compare its flux with the direct component from the same afterglow. When the intrinsic emission spectrum extends to TeV region, these very high-energy photons are significantly absorbed by the cosmic infrared background (CIB) radiation field, creating electron/positron pairs; since these pairs are highly energetic, they can scatter the cosmic microwave background radiation up to GeV energies, which may change the intrinsic afterglow light curve in the GeV region. Using the theoretical modeling given in literature and the reasonable choice of relevant parameters, we calculate the expected light curve due to the regeneration mechanism. As the result, we find that the regenerated emission could only slightly change the original light curve, even if we take a rather large value for the CIB density, independently of the density profile of surrounding medium, i.e., constant or wind-like profile. This ensures us the reliable estimation of the intrinsic GRB parameters when the high-energy observation is accessible, regardless of a large amount of uncertainty concerning the CIB density as well as extragalactic magnetic field strength.

Nonparametric Inference for the Cosmic Microwave Background

The Cosmic Microwave Background (CMB), which permeates the entire Universe, is the radiation left over from just 380,000 years after the Big Bang. On very large scales, the CMB radiation field is smooth and isotropic, but the existence of structure in the Universe - stars, galaxies, clusters of galaxies - suggests that the field should fluctuate on smaller scales. Recent observations, from the Cosmic Microwave Background Explorer to the Wilkinson Microwave Anisotropy Project, have strikingly confirmed this prediction. CMB fluctuations provide clues to the Universe's structure and composition shortly after the Big Bang that are critical for testing cosmological models. For example, CMB data can be used to determine what portion of the Universe is composed of ordinary matter versus the mysterious dark matter and dark energy. To this end, cosmologists usually summarize the fluctuations by the power spectrum, which gives the variance as a function of angular frequency. The spectrum's shape, and in particular the location and height of its peaks, relates directly to the parameters in the cosmological models. Thus, a critical statistical question is how accurately can these peaks be estimated. We use recently developed techniques to construct a nonparametric confidence set for the unknown CMB spectrum. Our estimated spectrum, based on minimal assumptions, closely matches the model-based estimates used by cosmologists, but we can make a wide range of additional inferences. We apply these techniques to test various models and to extract confidence intervals on cosmological parameters of interest. Our analysis shows that, even without parametric assumptions, the first peak is resolved accurately with current data but that the second and third peaks are not.

The sensitivity of infall molecular line profiles to the ambient radiation field

In cold molecular clouds, submillimetre emission lines are excited by the ambient radiation field. The pumping is dominated by the cosmic microwave background (CMB). It is usual in molecular line radiative transfer modelling to assume simply that this is the only incident radiation field. In this paper, a molecular line transport code and a dust radiative transfer code are used to explore the effects of the inclusion of a full interstellar radiation field (ISRF) on a simple test molecular cloud. It is found that in many galactic situations, the shape and strength of the line profiles that result are robust to variations in the ISRF and thus that in most cases, it is safe to adopt the CMB radiation field for the molecular line transport calculations. However, we show that in two examples, the inclusion of a plausible radiation field can have a significant effect on the line profiles. First, in the vicinity of an embedded massive star, there will be an enhanced far-infrared component to the radiation field. Secondly, for molecular clouds at large redshift, the CMB temperature increases and this of course also alters the radiation field. In both these cases, the line profiles are weakened significantly compared with a cloud exposed to a standard radiation field. Therefore this effect should be accounted for when investigating pre-stellar cores in massive star-forming regions and when searching for molecular clouds at high redshift.

M87 – a misaligned synchrotron-proton blazar?

The Fanaroff–Riley (FR) class 1 radio galaxy M87 is widely believed to be a misaligned blazar of BL Lac type. Its unresolved nuclear region is a strong non-thermal emitter of radio to X-ray photons that have been interpreted as synchrotron radiation. The recent detection of TeV-photons by the HEGRA-telescope array, if confirmed, would make it the first radio galaxy detected at TeV-energies. We discuss M87’s core emission in the context of the hadronic Synchrotron-Proton Blazar model. By modeling M87’s non-simultaneous spectral energy distribution we predict the peak power of the γ-ray component at ∼100 GeV at a flux level detectable for the new Cherenkov telescopes H.E.S.S., VERITAS and MAGIC. Thanks to M87’s proximity TeV photon absorption in the cosmic background radiation field is negligible. This offers for the first time the opportunity to directly trace the intrinsic high energy cutoff of a TeV-emitting blazar-like object.

Observational Strategies of Cosmic Microwave Background Temperature and Polarization Interferometry Experiments

We have simulated the interferometric observation of the cosmic microwave background (CMB) temperature and polarization fluctuations. We have constructed data pipelines from the time-ordered raw visibility samples to the CMB power spectra that utilize the methods of data compression, maximum likelihood analysis, and optimal subspace filtering. They are customized for three observational strategies: the single pointing, the mosaicking, and the drift-scanning. For each strategy, derived are the optimal strategy parameters that yield band power estimates with minimum uncertainty. The results are general and can be applied to any close-packed array on a single platform such as the CBI and the forthcoming AMiBA experiments. We have also studied the effect of rotation of the array platform on the band power correlation by simulating the CBI single-pointing observation. It is found that the band power anticorrelations can be reduced by rotating the platform and thus densely sampling the visibility plane. This enables us to increase the resolution of the power spectrum in the l-space down to the limit of the sampling theorem (Δl = 226 ≈ π/θ), which is narrower by a factor of about than the resolution limit (Δl ≈ 300) used in the recent CBI single-pointing observation. The validity of this idea is demonstrated for a two-element interferometer that samples visibilities uniformly in the uv-annulus. From the fact that the visibilities are the Fourier modes of the CMB field convolved with the beam, a fast unbiased estimator (FUE) of the CMB power spectra is developed and tested. It is shown that the FUE gives results very close to those from the quadratic estimator method without requiring large computer resources even though uncertainties in the results increase.

Spectrum and Duration of Delayed MeV–GeV Emission of Gamma‐Ray Bursts in Cosmic Background Radiation Fields

We generally analyze prompt high-energy emission above a few hundreds of GeV due to synchrotron self-Compton scattering in internal shocks. However, such photons cannot be detected because they may collide with cosmic infrared background photons, leading to electron/positron pair production. Inverse-Compton scattering of the resulting electron/positron pairs off cosmic microwave background photons will produce delayed MeV-GeV emission, which may be much stronger than a typical high-energy afterglow in the external shock model. We expand on the Cheng & Cheng model by deriving the emission spectrum and duration in the standard fireball shock model. A typical duration of the emission is ~ 10^3 seconds, and the time-integrated scattered photon spectrum is nu^{-(p+6)/4}, where p is the index of the electron energy distribution behind internal shocks. This is slightly harder than the synchrotron photon spectrum, nu^{-(p+2)/2}. The lower energy property of the scattered photon spectrum is dependent on the spectral energy distribution of the cosmic infrared background radiation. Therefore, future observations on such delayed MeV-GeV emission and the higher-energy spectral cutoff by the Gamma-Ray Large Area Space Telescope (GLAST) would provide a probe of the cosmic infrared background radiation.

Angular trispectra of CMB temperature and polarization

We develop the formalism necessary to study four-point functions of the cosmic microwave background (CMB) temperature and polarization fields. We determine the general form of CMB trispectra, with the constraints imposed by the assumption of statistical isotropy of the CMB fields, and derive expressions for their estimators, as well as their Gaussian noise properties. We apply these techniques to initial non-Gaussianity of a form motivated by inflationary models. Due to the large number of four-point configurations, the sensitivity of the trispectra to initial non-Gaussianity approaches that of the temperature bispectrum at high multipole moment. These trispectra techniques will also be useful in the study of secondary anisotropies induced for example by the gravitational lensing of the CMB by the large scale structure of the universe.

Transformation Properties of External Radiation Fields, Energy‐Loss Rates and Scattered Spectra, and a Model for Blazar Variability

We treat transformation properties of external radiation fields in the proper frame of a plasma moving with constant speed. The specific spectral energy densities of external isotropic and accretion disk radiation fields are derived in the comoving frame of relativistic outflows, such as those thought to be found near black hole jet and gamma-ray burst sources. Nonthermal electrons and positrons Compton-scatter this radiation field, and high-energy protons and ions interact with this field through photomeson and photopair production. We revisit the problem of the Compton-scattered spectrum associated with an external accretion disk radiation field and clarify a past treatment by the authors. Simple expressions for energy-loss rates and Thomson-scattered spectra are given for ambient soft photon fields consisting of either a surrounding external isotropic monochromatic radiation field or an azimuthally symmetric, geometrically thin accretion disk radiation field. A model for blazar emission is presented that displays a characteristic spectral and variability behavior due to the presence of a direct accretion disk component. The disk component and distinct flaring behavior can be bright enough to be detected from flat-spectrum radio quasars with GLAST. Spectral states of blazars are characterized by the relative importance of the accretion disk and scattered radiation fields and, in the extended jet, by the accretion disk, inner jet, and cosmic microwave background radiation fields.

Lensing‐induced Non‐Gaussian Signatures in the Cosmic Microwave Background

We propose a new method for extracting the non-Gaussian signatures on the isotemperature statistics in the cosmic microwave background (CMB) sky, which is induced by the gravitational lensing due to the intervening large-scale structure of the universe. To develop the method, we focus on a specific statistical property of the intrinsic Gaussian CMB field; a field point in the map that has a larger absolute value of the temperature threshold tends to have a larger absolute value of the curvature parameter defined by a trace of second derivative matrix of the temperature field, while the ellipticity parameter similarly defined is uniformly distributed independently of the threshold because of the isotropic nature of the Gaussian field. The weak lensing then causes a stronger distortion effect on the isotemperature contours with higher threshold and especially induces a coherent distribution of the ellipticity parameter correlated with the threshold as a result of the coupling between the CMB curvature parameter and the gravitational tidal shear in the observed map. These characteristic patterns can be statistically picked up by considering three independent characteristic functions, which are obtained from the averages of quadratic combinations of the second derivative fields of CMB over isotemperature contours with each threshold. Consequently, we find that the lensing effect generates non-Gaussian signatures on those functions that have a distinct functional dependence of the threshold. We test the method using numerical simulations of CMB maps and show that the lensing signals can be measured definitely, provided that we use CMB data with sufficiently low noise and high angular resolution.

Determining Cosmic Microwave Background Structure from Its Peak Distribution

We present a new method for time-efficient and accurate extraction of the power spectrum from future cosmic microwave background (CMB) maps based on properties of peaks and troughs of the Gaussian CMB sky. We construct a statistic describing their angular clustering analogously to galaxies, the two-point angular correlation function, ξν(θ). We show that for increasing peak threshold ν, ξν(θ) is strongly amplified and becomes measurable for ν 1 on angular scales ≤10°. Its amplitude at every scale depends uniquely on the CMB temperature correlation function, C(θ), and thus the measured ξν can be uniquely inverted to obtain C(θ) and its Legendre transform, the power spectrum of the CMB field. Because in this method the CMB power spectrum is deduced from high peaks/troughs of the CMB field, the procedure takes only [f(ν)]2N2 operations, where f(ν) is the fraction of pixels with |δT| ≥ ν standard deviations in the map of N pixels and is, e.g., 0.045 and 0.01 for ν = 2 and 2.5, respectively. We develop theoretical formalism for the method and show with detailed simulations, using the Microwave Anisotropy Probe mission parameters, that this method allows us to determine very accurately the CMB power spectrum from the upcoming CMB maps in only ~(10-4 to 10-3) N2 operations.

Evolution of the Extragalactic Infrared-to-Ultraviolet Background and Gamma-Ray Attenuation

We describe a model for the evolution of the cosmic background radiation field from infrared to ultraviolet wavelengths tuned to observations of star formation and including the effects of reprocessing by dust and gas. With this model, we can compute the attenuation of gamma rays from extragalactic sources. The attenuation length for the vast majority of extragalactic gamma-ray sources (blazars and gamma-ray bursts at redshifts of order unity) depends on the evolving optical-to-ultraviolet background, whereas gamma-ray attenuation measurements of nearby sources-such as Mrk 501 probe the infrared background. We focus on the cosmological aspects of the model and discuss the effects of changing cosmological parameters, star formation rate, initial mass function, and dust opacity on the resulting gamma-ray attenuation. A plausible choice of parameters leads to fair agreement between our model in the infrared and the observed attenuation of gamma rays from Mrk 501.

Large-scale jets in active galactic nuclei: multiwavelength mapping

X-ray emission from large-scale extragalactic jets is likely to be as a result of inverse Compton scattering of relativistic particles off seed photons of both the cosmic microwave background field and the blazar nucleus. The first process dominates the observed high-energy emission of large-scale jets if the plasma is moving at highly relativistic speeds and if the jet is aligned with the line of sight, i.e. in powerful flat radio spectrum quasars. The second process is relevant when the plasma is moving at mildly bulk relativistic speeds, and can dominate the high-energy emission in misaligned sources, i.e. in radio galaxies. We show that this scenario satisfactorily accounts for the spectral energy distribution detected by Chandra from the jet and core of PKS 0637–752.

Measuring Cosmological Bulk Flows via the Kinematic Sunyaev-Zeldovich Effect in the Upcoming Cosmic Microwave Background Maps

We propose a new method for measuring the possible large-scale bulk flows in the universe from the cosmic microwave background (CMB) maps from the upcoming missions of the Microwave Anistropy Probe (MAP) and Planck. This can be done by studying the statistical properties of the CMB temperature field at many X-ray cluster positions. At each cluster position, the CMB temperature fluctuation will be a combination of the Sunyaev-Zeldovich (SZ) kinematic and thermal components, the cosmological fluctuations, and the instrument noise term. When averaged over many such clusters, the last three will integrate down, whereas the first one will be dominated by a possible bulk flow component. In particular, we propose to use all-sky X-ray cluster catalogs that should (or could) be available soon from X-ray satellites and then to evaluate the dipole component of the CMB field at the cluster positions. We show that for the MAP and Planck mission parameters, the dominant contributions to the dipole will be from the terms that are due to the SZ kinematic effect produced by the bulk flow (the signal we seek) and the instrument noise (the noise in our signal). Then, by computing the expected signal-to-noise ratio for such measurement, we find that at the 95% confidence level, the bulk flows on scales >/=100 h(-1) Mpc can be probed down to the amplitude of less than 200 km s(-1) with the MAP data and down to only approximately 30 km s(-1) with the Planck mission.

Reconstructing projected matter density power spectrum from cosmic microwave background

Gravitational lensing distorts the cosmic microwave background (CMB) anisotropies and imprints a characteristic pattern onto it. The distortions depend on the projected matter density between today and redshift $z \sim 1100$. In this paper we develop a method for a direct reconstruction of the projected matter density from the CMB anisotropies. This reconstruction is obtained by averaging over quadratic combinations of the derivatives of CMB field. We test the method using simulations and show that it can successfully recover projected density profile of a cluster of galaxies if there are measurable anisotropies on scales smaller than the characteristic cluster size. In the absence of sufficient small scale power the reconstructed maps have low signal to noise on individual structures, but can give a positive detection of the power spectrum or when cross correlated with other maps of large scale structure. We develop an analytic method to reconstruct the power spectrum including the effects of noise and beam smoothing. Tests with Monte Carlo simulations show that we can recover the input power spectrum both on large and small scales, provided that we use maps with sufficiently low noise and high angular resolution.

The cooling of astrophysical media by H2

The results of recent quantum mechanical calculations of cross-sections for rotational transitions within the vibrational ground state of HD are used to evaluate the rate of radiative energy loss from gas containing HD, in addition to H, He and H2. The cooling function for HD (i.e. the rate of cooling per HD molecule) is evaluated in steady state on a grid of values of the relevant parameters of the gas, namely the gas density and temperature, the atomic to molecular hydrogen abundance ratio and the ortho:para-H2 density ratio. The corresponding cooling function for H2, previously computed by Le Bourlot et al., is slightly revised to take account of transitions induced by collisions with ground-state ortho-H2 (J=1). The cooling functions and the data required for their calculation are available from http://ccp7.dur.ac.uk/. We then make a study of the rate of cooling of the primordial gas through collisions with H2 and HD molecules. In this case, radiative transitions induced by the cosmic background radiation field and, in the case of H2, collisional transitions induced by H+ ions should additionally be included.

The Deuterium Chemistry of the Early Universe

The chemistry of deuterium, as well as that of hydrogen and helium, in the postrecombination era of the expanding early universe is presented. A thorough survey of all potentially important gas-phase reactions involving the primordial elements produced in the Big Bang, with a particular emphasis on deuterium, is given. The reaction set, consisting of 144 processes, is used in a nonequilibrium chemistry model to follow the production of primordial molecules in the postrecombination era. It is found that significant deuterium fractionation occurs for HD+, HD, and H2D+, while the abundance of D+ is reduced compared to the proton abundance. Even with the enhanced fractionation of H2D+, its abundance is predicted to be too small to cause any interesting cosmological consequences, such as possible attenuation of spatial anisotropies in the cosmic background radiation field, detections of the epochs of reionization and reheating, or constraints on the primordial deuterium abundance. HD, being the second most abundant primordial molecule after H2, may play a role in subsequent structure formation because of its cooling radiation.

Peculiar Velocity Dipoles of Field Galaxies

The Tully-Fisher (TF) relation is applied to obtain peculiar velocities of field spiral galaxies and to calculate dipoles of the peculiar velocity field to cz8000 km s-1. The field galaxy sample is spatially coextensive with and completely independent of a cluster sample, for which dipole characteristics are given in a separate paper. Dipoles of the peculiar velocity field are obtained separately by applying (1) an inverse version of the TF relation and selecting galaxies by redshift windowing and (2) a direct TF relation, with velocities corrected for the inhomogeneous Malmquist bias and windowing galaxies by TF distance. The two determinations agree, as they do with the cluster sample. When measured in a reference frame in which the Local Group is at rest, the dipole moment of field galaxies farther than ~4000 km s-1 is in substantial agreement, both in amplitude and direction, with that exhibited by the cosmic microwave background radiation field.