COBE Differential Microwave Radiometer Research Articles

Asymmetries in the Cosmic Microwave Background Anisotropy Field

We report on the results from two independent but complementary statistical analyses of the Wilkinson Microwave Anisotropy Probe (WMAP) first-year data, based on the power spectrum and N-point correlation functions. We focus on large and intermediate scales (larger than about 3°) and compare the observed data against Monte Carlo ensembles with WMAP-like properties. In both analyses, we measure the amplitudes of the large-scale fluctuations on opposing hemispheres and study the ratio of the two amplitudes. The power-spectrum analysis shows that this ratio for WMAP, as measured along the axis of maximum asymmetry, is high at the 95%-99% level (depending on the particular multipole range included). The axis of maximum asymmetry of the WMAP data is weakly dependent on the multipole range under consideration but tends to lie close to the ecliptic axis. In the N-point correlation-function analysis, we focus on the northern and southern hemispheres defined in ecliptic coordinates, and we find that the ratio of the large-scale fluctuation amplitudes is high at the 98%-99% level. Furthermore, the results are stable with respect to choice of Galactic cut and also with respect to frequency band. A similar asymmetry is found in the COBE Differential Microwave Radiometer (DMR) map, and the axis of maximum asymmetry is close to the one found in the WMAP data.

Faraday rotation as a diagnostic of Galactic foreground contamination of cosmic microwave background maps

We present a diagnostic test of possible Galactic contamination of cosmic microwave background (CMB) sky maps designed to provide an independent check on the methods used to compile these maps. The method involves a non-parametric measurement of cross-correlation between the Faraday rotation measure (RM) of extragalactic sources and the measured microwave signal at the same angular position. We argue that statistical properties of the observed distribution of rotation measures are consistent with a Galactic origin, an argument reinforced by a direct measurement of cross-correlation between the dust, free-free and synchrotron foreground maps and the RM values, with the strongest correlation being for dust and free-free. We do not find any statistically compelling evidence for correlations between the RM values and the COBE Differential Microwave Radiometer (DMR) maps at any frequency, so there is no evidence of residual contamination in these CMB maps. On the other hand, there is a statistically significant correlation of RM with the preliminary Wilkinson Microwave Anisotropy Probe (WMAP) individual frequency maps which remains significant in the Tegmark et al. Wiener-filtered map, but not in the internal linear combination map produced by the WMAP team.

Measurement of the Cosmic Microwave Background Bispectrum on theCOBEDMR Sky Maps

We measure the angular bispectrum of the cosmic microwave background (CMB) radiation anisotropy from the COBE Differential Microwave Radiometer (DMR) four-year sky maps. The angular bispectrum is the harmonic transform of the three-point correlation function, analogous to the angular power spectrum, the harmonic transform of the two-point correlation function. First, we study statistical properties of the bispectrum and the normalized bispectrum. We find the latter more useful for statistical analysis; the distribution of the normalized bispectrum is very much Gaussian, while the bare bispectrum distribution is highly non-Gaussian. Then, we measure 466 modes of the normalized bispectrum, all independent combinations of three-point configurations up to a maximum multipole of 20, the mode corresponding to the DMR beam size. By measuring 10 times as many modes as the sum of previous work, we test Gaussianity of the DMR maps. We compare the data with the simulated Gaussian realizations, finding no significant detection of the normalized bispectrum on the mode-by-mode basis. We also find that the previously reported detection of the normalized bispectrum is consistent with a statistical fluctuation. By fitting a theoretical prediction to the data for the primary CMB bispectrum, which is motivated by slow-roll inflation, we put a weak constraint on a parameter characterizing non-linearity in inflation. Simultaneously fitting the foreground bispectra estimated from interstellar dust and synchrotron template maps shows that neither dust nor synchrotron emissions significantly contribute to the bispectrum at high Galactic latitude. We conclude that the DMR map is consistent with Gaussianity.

Likelihood Distribution for Models with Cosmological Constant fromCOBEData

Using COBE Differential Microwave Radiometer (DMR) 4 yr data, we find a general expression yielding the likelihood distribution in the three-dimensional parameter space spanned by the spectral index n, the spectral amplitude a10, and the false-vacuum density parameter ΩΛ. Using such simple expression, the range of possible normalizations within a given likelihood interval from top-likelihood normalization is readily found, with fair approximation, for any model with total density parameter Ω0 = 1 and assigned n and ΩΛ.

Cosmological Parameter Determination fromPlanckand Sloan Digital Sky Survey Data in Λ Cold+Hot Dark Matter Cosmologies

We study the complementarity between the cosmological information obtainable with the Planck Surveyor and the large-scale structure (LSS) redshift surveys in Λ cold+hot dark matter (ΛCHDM) cosmologies. We compute the initial full phase-space neutrino distribution function for ΛCHDM models by using numerical simulations. As initial conditions, we adopt the HDM density fluctuation power spectrum normalized on the basis of the analysis of the local cluster X-ray temperature function and derive the initial neutrino phase-space distribution at each spatial wavenumber k by using the Zel'dovich approximation. These initial neutrino phase-space distributions are implemented in the CMBFAST code for the integration of the coupled linearized Einstein, Boltzmann, and fluid equations in k-space. We find that the relative bias between the cosmic microwave background (CMB) temperature fluctuations and the underlying matter density fluctuation power spectrum in COBE Differential Microwave Radiometer normalization is given by the CDM component normalized according to the abundance of rich clusters at the present time. We use the Fisher information matrix approximation to constrain a multidimensional parameterization of the ΛCHDM model by jointly considering CMB and large-scale structure data according to the Planck and the Sloan Digital Sky Survey experimental specifications and by taking into account redshift distortions and nonlinear effects on the matter power spectrum. We found that, although the CMB anisotropy and polarization measurements tend to dominate the constraints on most of the cosmological parameters, the additional small-scale LSS data help to break the parameter degeneracies. This work has been done in the framework of the Planck Low Frequency Instrument activities.

Bumpy power spectra and T/T

With the recent publication of the measurements of the radiation angular power spectrum from the BOOMERanG-98 Antarctic flight, it has become apparent that the currently favoured spatially flat cold dark matter model (matter density parameter Ωm=0.3, flatness being restored by a cosmological constant ΩΛ=0.7, Hubble parameter h=0.65, baryon density parameter Ωbh2=0.02) no longer provides a good fit to the data. We describe a phenomenological approach to resurrecting this paradigm. We consider a primordial power spectrum which incorporates a bump, arbitrarily placed at kb and characterized by a Gaussian in log k of standard deviation σb and amplitude Ab, which is superimposed on to a scale-invariant power spectrum. We generate a range of theoretical models that include a bump at scales consistent with cosmic microwave background (CMB) and large-scale structure observations, and perform a simple χ2 test to compare our models with the COBE Differential Microwave Radiometer (DMR) data and the recently published BOOMERanG-98 and MAXIMA-1 data. Unlike models that include a high baryon content, our models predict a low third acoustic peak. We find that low l observations (20<l<200) are a critical discriminant of the bumps because the transfer function has a sharp cut-off on the high l side of the first acoustic peak. Current galaxy redshift survey data suggest that excess power is required at a scale around 100 Mpc, corresponding to kb∼0.05 h Mpc−1. For the concordance model, use of a bump-like feature to account for this excess is not consistent with the constraints imposed by recent CMB data. We note that models with an appropriately chosen break in the power spectrum provide an alternative model that can give distortions similar to those reported in the automated plate measurement (APM) survey as well as consistency with the CMB data. We prefer, however, to discount the APM data in favour of the less biased decorrelated linear power spectrum recently constructed from the Point Source Catalogue Redshift (PSCz) redshift survey. We show that the concordance cosmology can be resurrected using our phenomenological approach and that our best-fitting model is in agreement with the PSCz observations.

The Angular Power Spectrum of Edinburgh/Durham Southern Galaxy Catalogue Galaxies

We determine the angular power spectrum Cl of the Edinburgh/Durham Southern Galaxy Catalogue (EDSGC) and use this statistic to constrain cosmological parameters. Our methods for determining Cl and the parameters that affect it are based on those developed for the analysis of cosmic microwave background maps. We expect them to be useful for future surveys. Assuming flat cold dark matter models with a cosmological constant (constrained by the COBE Differential Microwave Radiometer experiment and local cluster abundances) and a scale-independent bias b, we find acceptable fits to the EDSGC angular power spectrum with 1.11 < b < 2.35 and 0.2 < Ωm < 0.55 at 95% confidence. These results are not significantly affected by the integral constraint or extinction by interstellar dust but may be by our assumption of Gaussianity.

Constraints on Cosmological Parameters from MAXIMA-1

We set new constraints on a seven-dimensional space of cosmological parameters within the class of inflationary adiabatic models. We use the angular power spectrum of the cosmic microwave background measured over a wide range of l in the first flight of the MAXIMA balloon-borne experiment (MAXIMA-1) and the low-l results from the COBE Differential Microwave Radiometer experiment. We find constraints on the total energy density of the universe, Ω = 1.0img1.gif, the physical density of baryons, Ωbh2 = 0.03 ± 0.01, the physical density of cold dark matter, Ωcdmh2 = 0.2img2.gif, and the spectral index of primordial scalar fluctuations, ns = 1.08 ± 0.1, all at the 95% confidence level. By combining our results with measurements of high-redshift supernovae we constrain the value of the cosmological constant and the fractional amount of pressureless matter in the universe to 0.45 < ΩΛ < 0.75 and 0.25 < Ωm < 0.50, at the 95% confidence level. Our results are consistent with a flat universe and the shape parameter deduced from large-scale structure, and in marginal agreement with the baryon density from big bang nucleosynthesis.

COBE Differential Microwave Radiometer Constraints on an Inflation Model with Nonminimal Scalar Field

We derive the power spectra of the scalar- and tensor-type structures generated in a chaotic-type inflation model based on nonminimally coupled scalar field with a self-interaction. By comparing contributions of both structures to the anisotropy of the cosmic microwave background radiation with the four-year COBE differential microwave radiometer data on quadrupole anisotropy we derive constraints on the ratio of self-coupling and nonminimal coupling constants, and the expansion rate in the inflation era. The requirement for a successful amount of inflation further constrains the relative amount of a tensor-type contribution.

Cosmic Microwave Background Anisotropy Correlation Function and Topology from Simulated Maps forMAP

We have simulated cosmic microwave background (CMB) anisotropy maps for several COBE-Differential Microwave Radiometer experiment normalized cold dark matter (CDM) cosmogonies, to make predictions for the MAP experiment, an upcoming whole-sky CMB anisotropy space mission. We have studied the sensitivity of the simulated MAP data to cosmology, sky coverage, and instrumental noise. Given an accurate knowledge of instrumental noise, MAP data will ably discriminate among the cosmogonies considered, and superbly determine the topology of the initial fluctuations. A correlation function analysis of the simulated MAP data results in a very accurate measurement of the acoustic Hubble radius at decoupling. A low-density open CDM model with Ω0 = 0.4 can be distinguished from the Ω0 = 1 fiducial CDM model or a spatially flat CDM model with a cosmological constant and Ω0 = 0.4 with more than 99% confidence from the location of the acoustic valley in the correlation function. A genus analysis of the simulated MAP data indicates that in cosmogonies with Gaussian random-phase initial conditions, the horizontal shift of the zero-crossing point of the genus curve near the mean temperature threshold level ν = 0 should not exceed |Δν| = 0.01 (0.04) when the total effective FWHM smoothing is 03 (10). The asymmetry of the genus curve at the positive and negative threshold levels should not exceed |Δg/g(ν = ±1)| = 0.8% (4%) at 03 (1°) FWHM smoothing. Deviations of the observed MAP data in excess of these small values will be evidence for non-Gaussian behavior. The amplitude of the genus curve is a measure of the shape of the power spectrum at the smoothing scale. Even with the expected amount of instrumental noise and partial sky coverage (due to the Galaxy), the MAP data should allow discrimination among the cosmogonies considered at more than 99% confidence solely from a genus amplitude analysis.

Simultaneous Observations ofCompton Gamma Ray Observatory–BATSE Gamma‐Ray Bursts with theCOBEDMR

Data acquired with the COBE Differential Microwave Radiometer (DMR) provide a unique opportunity to observe simultaneous emission from cosmic gamma-ray bursts in the previously unexplored microwave region of the spectrum. We have searched the COBE DMR time-ordered data sets for instances when one of the DMR horns (FWHM ~ 7°) was pointing in the direction of a gamma-ray burst at the time of burst occurrence. During the overlap period 1991 April-December corresponding to the first public release of COBE data, 210 Compton Gamma Ray Observatory (CGRO)/BATSE gamma-ray bursts listed in the Third BATSE (3B) Catalog were viewable by the COBE DMR. For five of these events the DMR was pointing within 7° of the burst positions at the exact moment of burst occurrence. For another four events the DMR was pointed within 2° of the BATSE positions within 10 s of the burst trigger time. No obvious microwave emission (at 31.5, 53, or 90 GHz), with upper limits in the 10-100 kJy range, can be associated with any of these events. The COBE DMR has a relatively low sensitivity for the detection of point sources within its field of view. A positive detection of a gamma-ray burst by the COBE DMR would imply that the integrated microwave flux must be of the same order as the energy observed in gamma rays. By extending an acceptance window in time of up to 20 minutes before and after a gamma-ray burst another 60 bursts are sampled by the DMR, whose signals are analyzed statistically. We conclude that the average gamma-ray burst produces less than about 7-42 kJy in simultaneous microwave radiation.

Using Sunyaev‐Zeldovich Infrared Experiment (SuZIE) Arcminute‐Scale Cosmic Microwave Background Anisotropy Data to Probe Open and Flat Λ Cold Dark Matter Cosmogonies

We use arcminute-scale data from the Sunyaev-Zeldovich Infrared Experiment to set limits on anisotropies in cosmic microwave background radiation in open and spatially flat Λ cold dark matter cosmogonies. There are no 2 σ detections for the models tested. The upper limits obtained are consistent with the amplitude of anisotropy detected by the COBE Differential Microwave Radiometer experiment.

How to Make Maps from Cosmic Microwave Background Data without Losing Information

The next generation of cosmic microwave background (CMB) experiments can measure cosmological parameters with unprecedented accuracy—in principle. To achieve this in practice when faced with such gigantic data sets, elaborate data analysis methods are needed to make it computationally feasible. An important step in the data pipeline is to make a map, which typically reduces the size of the data set by orders of magnitude. We compare 10 map-making methods and find that for the Gaussian case, both the method used by the COBE Differential Microwave Radiometer (DMR) team and various forms of Wiener filtering are optimal in the sense that the map retains all cosmological information that was present in the time-ordered data (TOD). Specifically, one obtains just as small error bars on cosmological parameters when estimating them from the map as one could have obtained by estimating them directly from the TOD. The method of simply averaging the observations of each pixel (for total-power detectors), on the contrary, is found generally to destroy information, as does the maximum entropy method and most other nonlinear map-making techniques. Since it is also numerically feasible, the COBE method is the natural choice for large data sets. Other lossless (e.g., Wiener-filtered) maps can then be computed directly from the COBE method map.

Root Mean Square Anisotropy in theCOBEDMR Four‐Year Sky Maps

The sky rms is the simplest model-independent characterization of a cosmological anisotropy signal. We show that the rms temperature fluctuations determined from the COBE Differential Microwave Radiometer (DMR) 4 yr sky maps are frequency independent, consistent with the Planckian spectrum expected for the cosmic microwave background signal and therefore with the hypothesis that they are cosmological in origin. The typical rms amplitude is ~35 ± 2 μK at 7° and ~29 ± 1 μK at 10°. An analysis of the rms anisotropy determined from the data in both Galactic and ecliptic coordinates is used to determine the rms quadrupole normalization, Qrms-PS, for a scale-invariant Harrison-Zeldovich power-law model. Corrections are applied for small biases observed in the likelihood analysis. While there are variations depending on the data selection, all results are consistent with a Qrms-PS normalization of ~18 ± 2 μK. This is also shown to be true for a standard cold dark matter model of cosmological anisotropy. The difference in the normalization amplitudes derived when the quadrupole is either included or excluded from the analysis is attributable to contamination of the observed sky quadrupole by foreground Galactic emission.

Noncosmological Signal Contributions to the [ITAL]COBE[/ITAL] DMR 4 Year Sky Maps

We limit the possible contributions from noncosmological sources to the COBE Differential Microwave Radiometer (DMR) 4 year sky maps. The DMR data are cross-correlated with maps of rich clusters, extragalactic IRAS sources, HEAO 1 A-2 X-ray emission, and 5 GHz radio sources using a Fourier space technique. There is no evidence of significant contamination by such sources at an rms level of ~8 μK [95% confidence level (c.l.) at 7° resolution] in the most sensitive 53 GHz sky map. This level is consistent with previous limits set by analysis of earlier DMR data and by simple extrapolations from existing source models. We place a limit on the rms Comptonization parameter averaged over the high-latitude sky of δy < 1 × 10-6 (95% c.l.). Extragalactic sources have an insignificant effect on the cosmic microwave background power spectrum parameterizations determined from the DMR data.

Microwave Emission at High Galactic Latitudes in the Four-Year DMR Sky Maps

We use the COBE Differential Microwave Radiometers (DMR) 4 yr sky maps to model Galactic microwave emission at high latitudes (|b| > 20°). Cross-correlation of the DMR maps with Galactic template maps detects fluctuations in the high-latitude microwave sky brightness with the angular variation of the DIRBE far-infrared dust maps and a frequency dependence consistent with a superposition of dust and free-free emission. We find no significant correlations between the DMR maps and various synchrotron templates. On the largest angular scales (e.g., quadrupole), Galactic emission is comparable in amplitude to the anisotropy in the cosmic microwave background (CMB). The CMB quadrupole amplitude, after correction for Galactic emission, has amplitude Qrms = 10.7 μK with random uncertainty 3.6 μK and systematic uncertainty 7.1 μK from uncertainty in our knowledge of Galactic microwave emission.

The Angular Power Spectrum of the Four-Year [ITAL]COBE[/ITAL] Data

The angular power spectrum Cℓ is extracted from the 4 yr COBE Differential Microwave Radiometer (DMR) data with a 20° Galactic cut, using the narrowest window functions possible. The average power in eight multipole bands is also computed and plotted together with a compilation of power spectrum measurements from other experiments. The COBE results are found to be consistent with an n = 1 power spectrum with the normalization Qrms, ps = 18 μK reported by the COBE DMR team. Certain nonstandard cosmologies, such as "small universe" models with nontrivial spatial topology, predict power spectra that are not smooth functions. Rather, they contain bumps and wiggles that may not have been detected by other data analysis techniques such as the Hauser-Peebles method, the band-power method, and orthogonalized spherical harmonics, since these methods all give broader window functions that can smear such features out beyond recognition. On the large angular scales probed by COBE, the universe thus appears to be kind to us, presenting a power spectrum that is a simple smooth function.

Band Power Spectra in the [ITAL]COBE[/ITAL] DMR Four-Year Anisotropy Maps

We employ a pixel-based likelihood technique to estimate the angular power spectrum of the COBE Differential Microwave Radiometer (DMR) 4 yr sky maps. The spectrum is consistent with a scale-invariant power-law form with a normalization, expressed in terms of the expected quadrupole anisotropy, of Qrms-PS|n=1 = 18 ± 1.4 μK, and a best-fit spectral index of 1.2 ± 0.3. The normalization is somewhat smaller than we concluded from the 2 yr data, mainly due to additional Galactic modeling. We extend the analysis to investigate the extent to which the small quadrupole observed in our sky is statistically consistent with a power-law spectrum. The most likely quadrupole amplitude ranges between 7 and 10 μK, depending on the details of Galactic modeling and data selection, but in no case is there compelling evidence that the quadrupole is inconsistent with a power-law spectrum. We conclude with a likelihood analysis of the band power amplitude in each of four spectral bands between l = 2 and 40, and find no evidence for deviations from a simple power-law spectrum.

Tests for Non-Gaussian Statistics in the DMR Four-Year Sky Maps

We search the high-latitude portion of the COBE Differential Microwave Radiometer (DMR) 4 yr sky maps for evidence of a non-Gaussian temperature distribution in the cosmic microwave background. The genus, three-point correlation function, and two-point correlation function of temperature maxima and minima are all in excellent agreement with the hypothesis that the CMB anisotropy on angular scales of 7° or larger represents a random-phase Gaussian field. A likelihood comparison of the DMR sky maps to a set of random-phase non-Gaussian toy models selects the exact Gaussian model as most likely. Monte Carlo simulations show that the two-point correlation of the peaks and valleys in the maps provides the greatest discrimination among the class of models tested.

Four-Year [ITAL]COBE[/ITAL] DMR Cosmic Microwave Background Observations: Maps and Basic Results

In this Letter we present a summary of the spatial properties of the cosmic microwave background radiation based on the full 4 yr of COBE Differential Microwave Radiometer (DMR) observations, with additional details in a set of companion Letters. The anisotropy is consistent with a scale-invariant power-law model and Gaussian statistics. With full use of the multifrequency 4 yr DMR data, including our estimate of the effects of Galactic emission, we find a power-law spectral index of n = 1.2 ± 0.3 and a quadrupole normalization Qrms-PS = 15.3−2.8+3.8 μK. For n = 1 the best-fit normalization is Qrms-PS|n=1 = 18 ± 1.6 μK. These values are consistent with both our previous 1 yr and 2 yr results. The results include use of the l = 2 quadrupole term; exclusion of this term gives consistent results, but with larger uncertainties. The final DMR 4 yr sky maps, presented in this Letter, portray an accurate overall visual impression of the anisotropy since the signal-to-noise ratio is ~2 per 10° sky map patch. The improved signal-to-noise ratio of the 4 yr maps also allows for improvements in Galactic modeling and limits on non-Gaussian statistics.