Article

# Impact on the tensor-to-scalar ratio of incorrect Galactic foreground modelling

Monthly Notices of the Royal Astronomical Society (Impact Factor: 5.11). 03/2012; 424(3). DOI: 10.1111/j.1365-2966.2012.21314.x

Source: arXiv

**ABSTRACT**

A key goal of many cosmic microwave background (CMB) experiments is the detection of gravitational waves, through their B-mode

polarization signal at large scales. To extract such a signal requires modelling contamination from the Galaxy. Using the

Planck experiment as an example, we investigate the impact of incorrectly modelling foregrounds on estimates of the polarized CMB,

quantified by the bias in tensor-to-scalar ratio r, and optical depth τ. We use a Bayesian parameter estimation method to estimate the CMB, synchrotron and thermal dust components

from simulated observations spanning 30–353 GHz, starting from a model that fits the simulated data, returning r < 0.03 at 95 per cent confidence for an r = 0 model and r = 0.09 ± 0.03 for an r = 0.1 model. We then introduce a set of mismatches between the simulated data and assumed model. Including a curvature of

the synchrotron spectral index with frequency, but assuming a power-law model, can bias r high by ∼1σ (δr ∼ 0.03). A similar bias is seen for thermal dust with a modified blackbody frequency dependence, incorrectly modelled as

a power law. If too much freedom is allowed in the model, for example, fitting for spectral indices in 3° pixel over the sky

with physically reasonable priors, we find that r can be biased up to ∼3σ high by effectively setting the indices to the wrong values. Increasing the signal-to-noise ratio

by reducing parameters, or adding additional foreground data, reduces the bias. We also find that neglecting a ∼1 per cent

polarized free–free or spinning dust component has a negligible effect on r. These tests highlight the importance of modelling the foregrounds in a way that allows for sufficient complexity while minimizing

the number of free parameters.

polarization signal at large scales. To extract such a signal requires modelling contamination from the Galaxy. Using the

Planck experiment as an example, we investigate the impact of incorrectly modelling foregrounds on estimates of the polarized CMB,

quantified by the bias in tensor-to-scalar ratio r, and optical depth τ. We use a Bayesian parameter estimation method to estimate the CMB, synchrotron and thermal dust components

from simulated observations spanning 30–353 GHz, starting from a model that fits the simulated data, returning r < 0.03 at 95 per cent confidence for an r = 0 model and r = 0.09 ± 0.03 for an r = 0.1 model. We then introduce a set of mismatches between the simulated data and assumed model. Including a curvature of

the synchrotron spectral index with frequency, but assuming a power-law model, can bias r high by ∼1σ (δr ∼ 0.03). A similar bias is seen for thermal dust with a modified blackbody frequency dependence, incorrectly modelled as

a power law. If too much freedom is allowed in the model, for example, fitting for spectral indices in 3° pixel over the sky

with physically reasonable priors, we find that r can be biased up to ∼3σ high by effectively setting the indices to the wrong values. Increasing the signal-to-noise ratio

by reducing parameters, or adding additional foreground data, reduces the bias. We also find that neglecting a ∼1 per cent

polarized free–free or spinning dust component has a negligible effect on r. These tests highlight the importance of modelling the foregrounds in a way that allows for sufficient complexity while minimizing

the number of free parameters.

Get notified about updates to this publication Follow publication |

Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.

- [Show abstract] [Hide abstract]

**ABSTRACT:**We evaluate the ability of SPIDER, a balloon-borne polarimeter, to detect a divergence-free polarization pattern ("B-modes") in the Cosmic Microwave Background (CMB). In the inflationary scenario, the amplitude of this signal is proportional to that of the primordial scalar perturbations through the tensor-to-scalar ratio r. We show that the expected level of systematic error in the SPIDER instrument is significantly below the amplitude of an interesting cosmological signal with r=0.03. We present a scanning strategy that enables us to minimize uncertainty in the reconstruction of the Stokes parameters used to characterize the CMB, while accessing a relatively wide range of angular scales. Evaluating the amplitude of the polarized Galactic emission in the SPIDER field, we conclude that the polarized emission from interstellar dust is as bright or brighter than the cosmological signal at all SPIDER frequencies (90 GHz, 150 GHz, and 280 GHz), a situation similar to that found in the "Southern Hole." We show that two ~20-day flights of the SPIDER instrument can constrain the amplitude of the B-mode signal to r<0.03 (99% CL) even when foreground contamination is taken into account. In the absence of foregrounds, the same limit can be reached after one 20-day flight. -
##### Article: Planck intermediate results. XV. A study of anomalous microwave emission in Galactic clouds

[Show abstract] [Hide abstract]

**ABSTRACT:**Anomalous microwave emission (AME) is believed to be due to electric dipole radiation from small spinning dust grains. The aim of this paper is a statistical study of the basic properties of AME regions and the environment in which they emit. We used WMAP and Planck maps, combined with ancillary radio and IR data, to construct a sample of 98 candidate AME sources, assembling SEDs for each source using aperture photometry on 1 deg-smoothed maps from 0.408 GHz up to 3000 GHz. Each spectrum is fitted with a simple model of free-free, synchrotron (where necessary), cosmic microwave background (CMB), thermal dust, and spinning dust components. We find that 42 of the 98 sources have significant >5sigma excess emission at frequencies between 20 and 60 GHz. An analysis of the potential contribution of optically thick free-free emission from ultra-compact HII regions, using IR colour criteria, reduces the significant AME sample to 28 regions. The spectrum of the AME is consistent with model spectra of spinning dust. Peak frequencies are in the range 20-35 GHz except for the California Nebula (NGC1499), which appears to have a high spinning dust peak frequency of 50+/-17 GHz. The AME regions tend to be more spatially extended than regions with little or no AME. The AME intensity is strongly correlated with the sub-millimetre/IR flux densities and comparable to previous AME detections in the literature. AME emissivity, defined as the ratio of AME to dust optical depth, varies by an order of magnitude for the AME regions. The AME regions tend to be associated with cooler dust in the range 14-22 K and an average emissivity index, beta of +1.8, while the non-AME regions are typically warmer, at 20-30 K, and have a slightly flatter emissivity index of +1.7. In agreement with previous studies, the AME emissivity appears to decrease with increasing column density...(abridged) - [Show abstract] [Hide abstract]

**ABSTRACT:**The most convincing confirmation that the B-mode polarization signal detected at degree scales by BICEP2 is due to the cosmic microwave background (CMB) would be the measurement of its large-scale counterpart. We assess the requirements for diffuse component separation accuracy over large portions of the sky in order to measure the large-scale B-mode signal corresponding to a tensor-to-scalar ratio of r = 0.1–0.2. We use the method proposed by Bonaldi & Ricciardi to forecast the performances of different simulated experiments taking into account noise and foreground removal issues. We do not consider instrumental systematics, and we implicitly assume that they are not the dominant source of error. If this is the case, the confirmation of an r = 0.1–0.2 signal is achievable by Planck even for conservative assumptions regarding the accuracy of foreground cleaning. Our forecasts suggest that the combination of this experiment with BICEP2 will lead to an improvement of 25–45 per cent in the constraint on r. A next-generation CMB polarization satellite, represented in this work by the Cosmic Origins Explorer experiment, can reduce dramatically (by almost another order of magnitude) the uncertainty on r. In this case, however, the accuracy of foreground removal becomes critical to fully benefit from the increase in sensitivity.