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Register a new userData Processing and Compression of Cosmic Microwave Background Anisotropies on Board the PLANCK Satellite
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We present a simple way of coding and compressing the data on board the Planck instruments (HFI and LFI) to address the problem of the on board data reduction. This is a critical issue in the Planck mission. The total information that can be downloaded to Earth is severely limited by the telemetry allocation. This limitation could reduce the amount of diagnostics sent on the stability of the radiometers and, as a consequence, curb the final sensitivity of the CMB anisotropy maps. Our proposal to address this problem consists in taking differences of consecutive circles at a given sky pointing. To a good approximation, these differences are independent of the external signal, and are dominated by thermal (white) instrumental noise. Using simulations and analytical predictions we show that high compression rates, $c_r simeq 10$, can be obtained with minor or zero loss of CMB sensitivity. Possible effects of digital distortion are also analized. The proposed scheme allows for flexibility to optimize the relation with other critical aspects of the mission. Thus, this study constitutes an important step towards a more realistic modeling of the final sensitivity of the CMB temperature anisotropy maps.
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Data on board the future PLANCK Low Frequency Instrument (LFI), to measure the Cosmic Microwave Background (CMB) anisotropies, consist of $N$ differential temperature measurements, expanding a range of values we shall call $R$. Preliminary studies and telemetry allocation indicate the need of compressing these data by a ratio of $c_r simgt 10$. Here we present a study of entropy for (correlated multi-Gaussian discrete) noise, showing how the optimal compression $c_{r,opt}$, for a linearly discretized data set with $N_{bits}=log_2{N_{max}}$ bits is given by: $c_r simeq {N_{bits}/log_2(sqrt{2pi e} ~sigma_e/Delta)}$, where $sigma_eequiv (det C)^{1/2N}$ is some effective noise rms given by the covariance matrix $C$ and $Delta equiv R / N_{max}$ is the digital resolution. This $Delta$ only needs to be as small as the instrumental white noise RMS: $Delta simeq sigma_T simeq 2 mK$ (the nominal $mu K$ pixel sensitivity will only be achieved after averaging). Within the currently proposed $N_{bits}=16$ representation, a linear analogue to digital converter (ADC) will allow the digital storage of a large dynamic range of differential temperature $R= N_{max} Delta $ accounting for possible instrument drifts and instabilities (which could be reduced by proper on-board calibration). A well calibrated signal will be dominated by thermal (white) noise in the instrument: $sigma_e simeq sigma_T$, which could yield large compression rates $c_{r,opt} simeq 8$. This is the maximum lossless compression possible. In practice, point sources and $1/f$ noise will produce $sigma_e > sigma_T$ and $c_{r,opt} < 8$. This strategy seems safer than non-linear ADC or data reduction schemes (which could also be used at some stage).
Powerful constraints on theories can already be inferred from existing CMB anisotropy data. But performing an exact analysis of available data is a complicated task and may become prohibitively so for upcoming experiments with gtrsim10^4 pixels. We present a method for approximating the likelihood that takes power spectrum constraints, e.g., ``band-powers, as inputs. We identify a bias which results if one approximates the probability distribution of the band-power errors as Gaussian---as is the usual practice. This bias can be eliminated by using specific approximations to the non-Gaussian form for the distribution specified by three parameters (the maximum likelihood or mode, curvature or variance, and a third quantity). We advocate the calculation of this third quantity by experimenters, to be presented along with the maximum-likelihood band-power and variance. We use this non-Gaussian form to estimate the power spectrum of the CMB in eleven bands from multipole moment ell = 2 (the quadrupole) to ell=3000 from all published band-power data. We investigate the robustness of our power spectrum estimate to changes in these approximations as well as to selective editing of the data.
We present simulations of different scanning strategies for the Planck satellite. We review the properties of slow- and fast-precession strategies in terms of uniformity of the integration time on the sky, the presence of low-redundancy areas, the presence of deep fields, the presence of sharp gradients in the integration time, and the redundancy of the scanning directions. We also compare the results obtained when co-adding all detectors of a given frequency channel. The slow-precession strategies allow a good uniformity of the coverage, while providing two deep fields. On the other hand, they do not allow a wide spread of the scan-crossing directions, which is a feature of the fast-precession strategies. However, the latter suffer from many sharp gradients and low-coverage areas on the sky. On the basis of these results, the strategy for Planck can be selected to be a slow (e.g. 4 month-period) sinusoidal or cycloidal scanning.
Suggestions have been made that the microwave background observed by COBE and WMAP and dubbed Cosmic Microwave Background (CMB) may have an origin within our own Galaxy or Earth. To consider the signal that may be correlated with Earth, a correlate-by-eye exercise was attempted by overlaying the CMB map from Wilkinson Microwave Anisotropy Probe on a topographical map of Earth. Remarkably, several hot spots in the CMB map are found to be well aligned with either large cities on Earth or regions of high altitude. To further study the correlations between Earth and CMB, we performed a complicated cross-correlation analysis in the multipole space. The overall correlations are detected at more than 5 sigma confidence level. These results can be naively interpreted to suggest that large angular scale fluctuations in CMB are generated on Earth by a process that traces the altitude relative to a mean radius. Simply extending our analysis, we suggest that cross-correlations between CMB and any other map of a Solar system body, image of a person, or an image of an animal will be detected at some statistical significance. It is unclear how Occams razor can be applied in such a situation to identify which sources are responsible for CMB fluctuations.
The standard inflationary model presents a simple scenario within which the homogeneity, isotropy and flatness of the universe appear as natural outcomes and, in addition, fluctuations in the energy density are originated during the inflationary phase. These seminal density fluctuations give rise to fluctuations in the temperature of the Cosmic Microwave Background (CMB) at the decoupling surface. Afterward, the CMB photons propagate almost freely, with slight gravitational interactions with the evolving gravitational field present in the large scale structure (LSS) of the matter distribution and a low scattering rate with free electrons after the universe becomes reionized. These secondary effects slightly change the shape of the intensity and polarization angular power spectra (APS) of the radiation. The APS contain very valuable information on the parameters characterizing the background model of the universe and those parametrising the power spectra of both matter density perturbations and gravitational waves. In the last few years data from sensitive experiments have allowed a good determination of the shape of the APS, providing for the first time a model of the universe very close to spatially flat. In particular the WMAP first year data, together with other CMB data at higher resolution and other cosmological data sets, have made possible to determine the cosmological parameters with a precision of a few percent. The most striking aspect of the derived model of the universe is the unknown nature of most of its energy contents. This and other open problems in cosmology represent exciting challenges for the CMB community. The future ESA Planck mission will undoubtely shed some light on these remaining questions.
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