Differential Microwave Radiometer Research Articles

Estimating the power spectrum of the cosmic microwave background

We develop two methods for estimating the power spectrum, ${C}_{\mathcal{l}},$ of the cosmic microwave background from data and apply them to the Cosmic Background Explorer Differential Microwave Radiometer and Saskatoon datasets. One method involves a direct evaluation of the likelihood function, and the other is an estimator that is a minimum-variance weighted quadratic function of the data. Applied iteratively, the quadratic estimator is not distinct from likelihood analysis, but is rather a rapid means of finding the power spectrum that maximizes the likelihood function. Our results bear this out: direct evaluation and quadratic estimation converge to the same ${C}_{\mathcal{l}}$s. The quadratic estimator can also be used to determine directly cosmological parameters and their uncertainties. While the two methods both require ${O(N}^{3})$ operations, the quadratic is much faster, and both are applicable to datasets with arbitrary chopping patterns and noise correlations. We also discuss approximations that may reduce it to ${O(N}^{2})$ thus making it practical for forthcoming megapixel datasets.

Cosmic microwave background theory

A long-standing goal of theorists has been to constrain cosmological parameters that define the structure formation theory from cosmic microwave background (CMB) anisotropy experiments and large-scale structure (LSS) observations. The status and future promise of this enterprise is described. Current band-powers in -space are consistent with a DeltaT flat in frequency and broadly follow inflation-based expectations. That the levels are approximately (10(-5))2 provides strong support for the gravitational instability theory, while the Far Infrared Absolute Spectrophotometer (FIRAS) constraints on energy injection rule out cosmic explosions as a dominant source of LSS. Band-powers at 100 suggest that the universe could not have re-ionized too early. To get the LSS of Cosmic Background Explorer (COBE)-normalized fluctuations right provides encouraging support that the initial fluctuation spectrum was not far off the scale invariant form that inflation models prefer: e.g., for tilted Lambda cold dark matter sequences of fixed 13-Gyr age (with the Hubble constant H0 marginalized), ns = 1.17 +/- 0.3 for Differential Microwave Radiometer (DMR) only; 1.15 +/- 0.08 for DMR plus the SK95 experiment; 1.00 +/- 0.04 for DMR plus all smaller angle experiments; 1.00 +/- 0.05 when LSS constraints are included as well. The CMB alone currently gives weak constraints on Lambda and moderate constraints on Omegatot, but theoretical forecasts of future long duration balloon and satellite experiments are shown which predict percent-level accuracy among a large fraction of the 10+ parameters characterizing the cosmic structure formation theory, at least if it is an inflation variant.

A Search for Millimetric Emission from Gamma‐Ray Bursts

We have used the 2- year Differential Microwave Radiometer data from the COsmic Background Explorer (COBE) satellite to systematically search for millimetric (31 - 90 GHz) emission from the Gamma Ray Bursts (GRBs) in the Burst And Transient Source Experiment (BATSE) GRB 3B catalog. The large beamsize of the COBE instrument (7 degs FWHM) allows for an efficient search of the large GRB positional error boxes, although it also means that fluxes from (point source) GRB objects will be somewhat diluted. A likelihood analysis has been used to look for a change in the level of millimetric emission from the locations of 81 GRB events during the first two years (1990 & 1991) of the COBE mission. The likelihood analysis determined that we did not find any significant millimetric signal before or after the occurance of the GRB. We find 95% confidence level upper limits of 175, 192 and 645 Jy or, in terms of fluxes, of 9.6, 16.3 and 54.8 10^{-13} erg/cm^2/s, respectively at 31, 53 and 90 GHz. We also look separately at different classes of GRBs, including a study of the top ten (in peak flux) GRBs, the short burst and long burst subsets, finding similar upper limits. While these limits may be somewhat higher than one would like, we estimate that using this technique with future planned missions could push these limits down to \sim 1 mJy.

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.

Limits to global rotation and shear from the COBE DMR four-year sky maps

Small departures from a homogeneous isotropic spacetime create observable features in the large-scale anisotropy of the cosmic microwave background. We cross correlate the maps of the cosmic microwave background anisotropy from the Cosmic Background Explorer Differential Microwave Radiometers four-year data set with template maps from Bianchi type VII${}_{h}$ cosmological models to limit global rotation or shear in the early universe. On the largest scales, spacetime is well described by the Friedmann-Robertson-Walker metric, with departures from isotropy about each spatial point limited to shear $\ensuremath{\sigma}{/H}_{0}<{10}^{\ensuremath{-}9}$ and rotation $\ensuremath{\omega}{/H}_{0}<6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$ for $0.1<~{\ensuremath{\Omega}}_{0}<~1$.

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.

The Dipole Observed in the COBE DMR 4 Year Data

The largest anisotropy in the cosmic microwave background (CMB) is the $\approx 3$ mK dipole assumed to be due to our velocity with respect to the CMB. Using the four year data set from all six channels of the COBE Differential Microwave Radiometers (DMR), we obtain a best-fit dipole amplitude $3.358 \pm 0.001 \pm 0.023$ mK in the direction $(l,b)=(264\deg.31 \pm 0\deg.04 \pm 0\deg.16, +48\deg.05 \pm 0\deg.02 \pm 0\deg.09)$, where the first uncertainties are statistical and the second include calibration and combined systematic uncertainties. This measurement is consistent with previous DMR and FIRAS results

Calibration and Systematic Error Analysis for the COBE DMR 4 Year Sky Maps

The Differential Microwave Radiometers (DMR) instrument aboard the Cosmic Background Explorer (CO BE) has mapped the full microwave sky to mean sensitivity 26 μK per 7° field of view. The absolute calibration is determined to 0.7% with drifts smaller than 0.2% per year. We have analyzed both the raw differential data and the pixelized sky maps for evidence of contaminating sources such as solar system foregrounds, instrumental susceptibilities, and artifacts from data recovery and processing. Most systematic effects couple only weakly to the sky maps. The largest uncertainties in the maps result from the instrument susceptibility to Earth's magnetic field, microwave emission from Earth, and upper limits to potential effects at the spacecraft spin period. Systematic effects in the maps are small compared to either the noise or the celestial signal: the 95% confidence upper limit for the pixel-pixel rms from all identified systematics is less than 6 μK in the worst channel. A power spectrum analysis of the (A - B)/2 difference maps shows no evidence for additional undetected systematic effects.

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.

Gaussian nature of the COBE data from multipoint correlations.

Important information about the early universe can be obtained from a study of the cosmic background radiation (CBR) in the microwave range. We study high-order correlation and structure functions of temperature fluctuations collected from the first two years of Differential Microwave Radiometer (DMR) observations from the Cosmic Background Explorer (COBE) satellite. The intent is to determine whether the radiation data possess significant deviations from Gaussianity. The most difficult problem in drawing meaningful conclusions is the presence of instrumental noise, which is quite strong even after a two-year averaging has been performed. We have taken into account the noise in various ways. Within the limitations imposed by the noise, our study shows that the fluctuations are quite likely to be Gaussian-like. The results can, therefore, be said to favor the inflation scenario of the universe.

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.

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.

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.

The Wiener-filtered COBE DMR Data and Predictions for the Tenerife Experiment

view Abstract Citations (112) References (32) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Wiener-filtered COBE DMR Data and Predictions for the Tenerife Experiment Bunn, Emory F. ; Hoffman, Yehuda ; Silk, Joseph Abstract We apply a Wiener filter to the two-year COBE Differential Microwave Radiometer (DMR) data. The resulting sky map has significantly reduced noise levels compared to the raw data: the most prominent hot and cold spots are significant at the 4 (7 level. Furthermore, the entire covariance matrix of the errors in the filtered sky map is known, and it is therefore possible to make constrained realizations of the microwave sky with the correct a posteriori probability distribution. The filtered DMR sky map is used to make predictions for the Tenerife experiment. Two prominent features are predicted in a region of the sky not yet analyzed by the Tenerife group. The presence of these features is a robust prediction of the standard cosmological paradigm; if these features are not observed, some of our fundamental assumptions must be incorrect. Publication: The Astrophysical Journal Pub Date: June 1996 DOI: 10.1086/177294 arXiv: arXiv:astro-ph/9509045 Bibcode: 1996ApJ...464....1B Keywords: COSMOLOGY: COSMIC MICROWAVE BACKGROUND; METHODS: DATA ANALYSIS; METHODS: STATISTICAL; Astrophysics E-Print: 15 pages of uuencoded compressed PostScript. A PostScript file including figures is available at ftp://pac2.berkeley.edu/pub/bunn/wienerten/ full text sources arXiv | ADS |

Tentative Appraisal of Compatibility of Small-Scale Cosmic Microwave Background Anisotropy Detections in the Context of [ITAL]COBE[/ITAL]-DMR–normalized Open and Flat-Λ Cold Dark Matter Cosmogonies

Goodness-of-fit statistics are used to quantitatively establish the compatibility of cosmic microwave background (CMB) anisotropy predictions in a wide range of Differential Microwave Radiometer (DMR) normalized, open and spatially flat Λ, cold dark matter cosmogonies with the set of all presently available small-scale CMB anisotropy detection data. Conclusions regarding model viability depend sensitively on the prescription used to account for the 1 σ uncertainty in the assumed value of the DMR normalization, except for low-density, Ω0 ~ 0.3-0.4, open models, which are compatible with the data for all prescriptions used. While old, large baryon density, low-density, flat-Λ models (t0 15-16 Gyr, ΩB 0.0175 h-2, Ω0 ~ 0.2-0.4) might be incompatible, no model is incompatible with the data for all prescriptions. In fact, some open models seem to fit the data better than should be expected, and this might be an indication that some error bars are mildly overconservative.

High-Latitude Galactic Emission in the COBE Differential Microwave Radiometer 2 Year Sky Maps

view Abstract Citations (248) References (32) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS High-Latitude Galactic Emission in the COBE Differential Microwave Radiometer 2 Year Sky Maps Kogut, A. ; Banday, A. J. ; Bennett, C. L. ; Gorski, K. M. ; Hinshaw, G. ; Reach, W. T. Abstract We cross-correlate the COBE6 DMR 2 year sky maps with spatial templates from long-wavelength radio surveys and the far-infrared COBE DIRBE maps. We place an upper limit on the spectral index of synchrotron radiation βsynch < -2.9 between 408 MHz and 31.5 GHz. We obtain a statistically significant cross-correlation with the DIRBE maps, whose dependence on the DMR frequencies indicates a superposition of dust and free-free emission. The high-latitude dust emission (|b| > 30°) is well fitted by a single dust component with temperature T = 18+3-7 K and emissivity ν ∝ (υ/ν0)β with β = 1.9+3.0-0.5. The free-free emission is spatially correlated with the dust on angular scales larger than the 70 DMR beam, with rms variations 5.3±1.8 μK at 53 GHz and angular power spectrum p ∝ l-3. If this correlation persists to smaller angular scales, free-free emission should not be a significant contaminant to measurements of the cosmic microwave anisotropy at degree angular scales for frequencies above 20 GHz. Publication: The Astrophysical Journal Pub Date: March 1996 DOI: 10.1086/176947 Bibcode: 1996ApJ...460....1K Keywords: COSMOLOGY: COSMIC MICROWAVE BACKGROUND; ISM: DUST; EXTINCTION; RADIO CONTINUUM: ISM full text sources ADS |

Measurement and Implications of the Cosmic Microwave Background Spectrum

The Cosmic Background Explorer (COBE) was developed by NASA Goddard Space Flight Center to measure the diffuse infrared and microwave radiation from the early universe. It also measured emission from nearby sources such as the stars, dust, molecules, atoms, ions, and electrons in the Milky Way, and dust and comets in the Solar System. It was launched 18 November 1989 on a Delta rocket, carrying one microwave instrument and two cryogenically cooled infrared instruments. The Far Infrared Absolute Spectrophotometer (FIRAS) mapped the sky at wavelengths from 0.01 to 1 cm, and compared the CMBR to a precise blackbody. The spectrum of the CMBR differs from a blackbody by less than 0.03%. The Differential Microwave Radiometers (DMR) measured the fluctuations in the CMBR originating in the Big Bang, with a total amplitude of 11 parts per million on a 10° scale. These fluctuations are consistent with scale-invariant primordial fluctuations. The Diffuse Infrared Background Experiment (DIRBE) spanned the wavelength range from 1.2 to 240 μm and mapped the sky at a wide range of solar elongation angles to distinguish foreground sources from a possible extragalactic Cosmic Infrared Background Radiation (CIBR). In this paper we summarize the COBE mission and describe the results from the FIRAS instrument. The results from the DMR and DIRBE were described by Smoot and Hauser at this Symposium.