Differential Microwave Radiometer Research Articles

Nobel Lecture: From the Big Bang to the Nobel Prize and beyond

NASA's Cosmic Background Explorer satellite mission, the COBE, laid the foundations for modern cosmology by measuring the spectrum and anisotropy of the cosmic microwave background radiation and discovering the cosmic infrared background radiation. I describe the history of the COBE project, its scientific context, the people who built it, and the scientific results. The COBE observed the universe on the largest scales possible by mapping the cosmic microwave and infrared background radiation fields and determining their spectra. It produced conclusive evidence that the hot Big Bang theory of the early universe is correct, showed that the early universe was very uniform but not perfectly so, and that the total luminosity of post--Big Bang objects is twice as great as previously believed. The COBE concept was developed by a Mission Definition Study Team appointed by NASA in 1976, based on three competing proposals submitted in 1974. The COBE was built in-house by Goddard Space Flight Center, with a helium cryostat provided by Ball Aerospace, and was launched on a Delta rocket built by McDonnell Douglas. It is in a circular orbit $900\phantom{\rule{0.3em}{0ex}}\mathrm{km}$ above the Earth, in a plane inclined 99\ifmmode^\circ\else\textdegree\fi{} to the equator and roughly perpendicular to the line to the Sun. It carried three instruments, a far infrared absolute spectrophotometer (FIRAS), a differential microwave radiometer with three channels (DMR), and a diffuse infrared background experiment (DIRBE). The helium cryostat cooled the FIRAS and DIRBE for $10\phantom{\rule{0.3em}{0ex}}\text{months}$ until the helium was exhausted, but operations continued for a total of $4\phantom{\rule{0.3em}{0ex}}\text{years}$. Subsequent observations have confirmed the COBE results and led to measurements of the main cosmological parameters with a precision of a few percent.

Global, exact cosmic microwave background data analysis using Gibbs sampling

We describe an efficient and exact method that enables global Bayesian analysis of cosmic microwave background (CMB) data. The method reveals the joint posterior density (or likelihood for flat priors) of the power spectrum ${C}_{\ensuremath{\ell}}$ and the CMB signal. Foregrounds and instrumental parameters can be simultaneously inferred from the data. The method allows the specification of a wide range of foreground priors. We explicitly show how to propagate the non-Gaussian dependency structure of the ${C}_{\ensuremath{\ell}}$ posterior through to the posterior density of the parameters. If desired, the analysis can be coupled to theoretical (cosmological) priors and can yield the posterior density of cosmological parameter estimates directly from the time-ordered data. The method does not hinge on special assumptions about the survey geometry or noise properties, etc., It is based on a Monte Carlo approach and hence parallelizes trivially. No trace or determinant evaluations are necessary. The feasibility of this approach rests on the ability to solve the systems of linear equations which arise. These are of the same size and computational complexity as the map-making equations. We describe a preconditioned conjugate gradient technique that solves this problem and demonstrate in a numerical example that the computational time required for each Monte Carlo sample scales as ${n}_{p}^{3/2}$ with the number of pixels ${n}_{p}$. We use our method to analyze the data from the Differential Microwave Radiometer on the Cosmic Background Explorer and explore the non-Gaussian joint posterior density of the ${C}_{\ensuremath{\ell}}$ from the Differential Microwave Radiometer on the Cosmic Background Explorer in several projections.

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.

Astrophysical component separation of COBE-DMR 4-yr data with FastICA

We present an application of the Fast Independent Component Analysis (FastICA) method to the Cosmic Background Explorer Differential Microwave Radiometer (COBE-DMR) 4-yr data. Although the signal-to-noise (S/N) ratio in the COBE-DMR data is typically ∼1, the approach is able to extract the cosmic microwave background (CMB) signal with high confidence from high galactic latitude regions. However, the foreground emission components have too low a S/N ratio to be reconstructed by this method (moreover, the number of components which can be reconstructed is directly limited by the number of input channels). The reconstructed CMB map shows the expected frequency scaling of the CMB and, fitting for the rms quadrupole normalization Qrms-PS and primordial spectral index n we find results in excellent agreement with those derived from the minimum-noise combination of the 90- and 53-GHz DMR channels without galactic emission correction. We extend the analysis by including additional channels (priors): the Haslam map of radio emission at 408 MHz and the Diffuse Infrared Background Experiment (DIRBE) 140-μm map of galactic infrared emission. The FastICA algorithm is now able to both detect galactic foreground emission and separate it from the dominant CMB signal. Fitting again for Qrms-PS and n we find good agreement with the results of Górski et al. where galactic emission has been taken into account by means of correlation analysis of the DMR signal. We investigate the ability of FastICA to evaluate the extent of foreground contamination in the COBE-DMR data further including an all-sky Hα survey to determine a reliable free-free. The derived frequency scalings of the recovered foregrounds are consistent with previous correlation studies. After subtraction of the thermal dust emission as in model 7 of Finkbeiner, Davis & Schlegel, we find a clear indication of an anomalous dust-correlated component which is the dominant foreground emission at 31.5 GHz and which is well fitted by a power-law spectral shape ν−β with β∼ 2.5 in agreement with Banday et al.

The Optical Design and Characterization of theMicrowave Anisotropy Probe

The primary goal of the MAP satellite, now in orbit, is to make high-fidelity polarization-sensitive maps of the full sky in five frequency bands between 20 and 100 GHz. From these maps we will characterize the properties of the cosmic microwave background (CMB) anisotropy and Galactic and extragalactic emission on angular scales ranging from the effective beam size, less than 023, to the full sky. MAP is a differential microwave radiometer. Two back-to-back shaped offset Gregorian telescopes feed two mirror symmetric arrays of 10 corrugated feeds. We describe the prelaunch design and characterization of the optical system, compare the optical models to the measurements, and consider multiple possible sources of systematic error.

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.

A Bayesian Estimate of the Skewness of the Cosmic Microwave Background

We propose a formalism for estimating the skewness and angular power spectrum of a general Cosmic Microwave Background data set. We use the Edgeworth Expansion to define a non-Gaussian likelihood function that takes into account the anisotropic nature of the noise and the incompleteness of the sky coverage. The formalism is then applied to estimate the skewness of the publicly available 4 year Cosmic Background Explorer (COBE) Differential Microwave Radiometer data. We find that the data is consistent with a Gaussian skewness, and with isotropy. Inclusion of non Gaussian degrees of freedom has essentially no effect on estimates of the power spectrum, if each $C_\ell$ is regarded as a separate parameter or if the angular power spectrum is parametrized in terms of an amplitude (Q) and spectral index (n). Fixing the value of the angular power spectrum at its maxiumum likelihood estimate, the best fit skewness is $S=6.5\pm6.0\times10^4(\muK)^3$; marginalizing over Q the estimate of the skewness is $S=6.5\pm8.4\times10^4(\muK)^3$ and marginalizing over n one has $S=6.5\pm8.5\times10^4(\muK)^3$.

Cosmic Microwave Background Anisotropy Constraints on Open and Flat‐Λ Cold Dark Matter Cosmogonies from UCSB South Pole, ARGO, MAX, White Dish, and SuZIE Data

We use combinations of 10 small-scale cosmic microwave background anisotropy data sets from the UCSB South Pole 1994, ARGO, MAX 4 and 5, White Dish, and SuZIE experiments to constrain cosmogonies. We consider open and spatially flat-? cold dark matter cosmogonies with nonrelativistic mass density parameter ?0 in the range 0.1-1, baryonic mass density parameter ?B in the range 0.005-0.029 h-2, and age of the universe t0 in the range 10-20 Gyr. Marginalizing over all parameters but ?0, the combined data favor a ?01 (1) open (flat-?) model. Excluding the smallest angular scale SuZIE data, an ?00.3 (1) open (flat-?) model is favored. Considering only multifrequency data with error bars consistent with sample variance and noise considerations, i.e., the South Pole 1994 Ka band, the MAX 4 ? Draconis, and the MAX 5 HR5127 data, an ?00.1 (1) open (flat-?) model is favored. For both open and flat-? models and for all three combinations of data sets, after marginalizing over all other parameters, a lower ?Bh2 (~0.005) or younger (t0~10 Gyr) universe is favored. However, the data do not rule out other values of ?0 in the flat-? model and other values of ?Bh2 in both models. At 2 ? confidence, model normalizations deduced from the small-scale data are consistent with those derived from the Differential Microwave Radiometer data. We emphasize that since we consider only a small number of data sets, these results are tentative.

What Have We Already Learned from the Cosmic Microwave Background?

ABSTRACTThe Cosmic Background Explorer (COBE) satellite, and the Differential Microwave Radiometer (DMR) experiment in particular, was extraordinarily successful. However, the DMR results were announced about 7 years ago, during which time a great deal more has been learned about anisotropies in the cosmic microwave background (CMB). We assess the current state of knowledge and discuss where we might be going. The CMB experiments currently being designed and built, including long‐duration balloons, interferometers, and two space missions, promise to address several fundamental cosmological issues. We present our evaluation of what we already know, what we are beginning to learn now, and what the future may bring.

ARGO Cosmic Microwave Background Anisotropy Measurement Constraints on Open and Flat‐Λ Cold Dark Matter Cosmogonies

We use data from the ARGO cosmic microwave background (CMB) anisotropy experiment to constrain cosmogonies. We account for the ARGO beamwidth and calibration uncertainties, and we marginalize over the offset removed from the data. Our derived amplitudes of the CMB anisotropy detected by the ARGO experiment are smaller than those derived previously. We consider open and spatially flat-Λ cold dark matter cosmogonies, with the clustered-mass density parameter Ω0 in the range 0.1-1, the baryonic-mass density parameter ΩB in the range 0.005-0.029 h−2, and the age of the universe t0 in the range 10-20 Gyr. Marginalizing over all parameters but Ω0, the ARGO data favor an open (spatially flat-Λ) model with Ω0=0.23 (0.1). However, these numerical values are model dependent. At the 2 σ confidence level, model normalizations deduced from the ARGO data are consistent with those drawn from the UCSB South Pole 1994, MAX 4+5, White Dish, and SuZIE data sets. The ARGO open-model normalizations are also consistent with those deduced from the Differential Microwave Radiometer (DMR) data. However, for most spatially flat-Λ models, the DMR normalizations are more than 2 σ above the ARGO ones.

Determination of Cosmological Parameters by Cosmic Microwave Background

After the sensational discovery of Cosmic Microwave Background (CMB) anisotropies by Differential Microwave Radiometer (DMR) boarded on the Cosmic Background Explore (COBE) (Smoot et al. 1992), the number of observational data of temperature fluctuations have been rapidly increasing (see e.g., White, Scott and Silk 1994) together with the understanding of physical processes of evolution of CMB anisotropies. Nowadays, CMB anisotropies are becoming one of the key observational object in the modern cosmology. CMB anisotropies provide us direct information at last scattering surface, i.e., redshift z ≈ 1000. Since the shape of the angular power spectrum of CMB anisotropies is highly sensitive to geometry of the universe, cosmological models and cosmological parameters, i.e., density parameter Ω0, Hubble constant h which is normalized by 100km/s/Mpc, cosmological constant Λ, baryon density ΩB and so on, CMB anisotropies are expected to be a new tool to understand our universe. Moreover, we can obtain information of thermal history of the universe after recombination (through the formation of secondary fluctuations and damping of primary fluctuations), physics of clusters of galaxies (through the Sunyaev-Zeldovich effect) and non-linear structure of the universe (through the gravitational lensing effect) from CMB anisotropies.

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.

Evidence for Scale-Scale Correlations in the Cosmic Microwave Background Radiation

We perform a discrete wavelet analysis of the Cosmic Background Explorer differential microwave radiometer (DMR) 4-yr sky maps and find a significant scale-scale correlation on angular scales from about 11\ifmmode^\circ\else\textdegree\fi{} to 22\ifmmode^\circ\else\textdegree\fi{}, only in the DMR face centered on the north galactic pole. This non-Gaussian signature does not arise either from the known foregrounds or the correlated noise maps, nor is it consistent with upper limits on the residual systematic errors in the DMR maps. Either the scale-scale correlations are caused by an unknown foreground contaminate or systematic errors on angular scales as large as 22\ifmmode^\circ\else\textdegree\fi{}, or the standard inflation plus cold dark matter paradigm is ruled out at the $&gt;99%$ confidence level.

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.