[Paper Review] Monopole and dipole estimation for multi-frequency sky maps by linear regression

I. K. Wehus, U. Fuskeland+10 more|arXiv (Cornell University)|Nov 27, 2014

Geophysics and Gravity Measurements2 references4 citations

TL;DR

This paper presents a linear regression-based method to estimate monopole and dipole offsets in multi-frequency sky maps, using T-T plots to determine spatially varying corrections. The approach enables consistent component separation by lifting degeneracies through spectral index variations, yielding robust estimates for WMAP, Planck, and radio surveys, including a 10–15 μK relative dipole between WMAP and Planck and a 0.15 ± 0.03 K dipole in the 1420 MHz map.

ABSTRACT

We describe a simple but efficient method for deriving a consistent set of monopole and dipole corrections for multi-frequency sky map data sets, allowing robust parametric component separation with the same data set. The computational core of this method is linear regression between pairs of frequency maps, often called "T-T plots". Individual contributions from monopole and dipole terms are determined by performing the regression locally in patches on the sky, while the degeneracy between different frequencies is lifted when ever the dominant foreground component exhibits a significant spatial spectral index variation. Based on this method, we present two different, but each internally consistent, sets of monopole and dipole coefficients for the 9-year WMAP, Planck 2013, SFD 100 um, Haslam 408 MHz and Reich & Reich 1420 MHz maps. The two sets have been derived with different analysis assumptions and data selection, and provides an estimate of residual systematic uncertainties. In general, our values are in good agreement with previously published results. Among the most notable results are a relative dipole between the WMAP and Planck experiments of 10-15 uK (depending on frequency), an estimate of the 408 MHz map monopole of 8.9 +- 1.3 K, and a non-zero dipole in the 1420 MHz map of $0.15 +- 0.03 K pointing towards Galactic coordinates (l,b) = (308,-36) +- 14 degrees. These values represent the sum of any instrumental and data processing offsets, as well as any Galactic or extra-Galactic component that is spectrally uniform over the full sky.

Motivation & Objective

• To address systematic errors in multi-frequency sky maps caused by uncalibrated monopole and dipole offsets that bias component separation.
• To develop a method that determines consistent monopole and dipole corrections across multiple frequency channels using spatial spectral variations.
• To estimate absolute monopole and dipole values for key sky maps, including WMAP, Planck, 408 MHz, and 1420 MHz, with quantified uncertainties.
• To provide two internally consistent offset sets derived under different assumptions, enabling systematic uncertainty estimation.
• To improve the accuracy of cosmological component separation by correcting for instrumental, processing, and astrophysical offsets that are spectrally uniform.

Proposed method

• The method uses linear regression between pairs of frequency maps, known as T-T plots, to estimate monopole and dipole contributions.
• Regression is performed locally in sky patches to resolve spatial variations in monopole and dipole terms.
• Degeneracy between monopole and dipole terms is lifted by leveraging significant spatial spectral index variations in foreground components.
• The approach assumes that the dominant foreground component has a non-uniform spectral index across the sky, enabling separation of offset terms.
• Two independent offset sets are derived using different data selection and analysis assumptions to estimate systematic uncertainties.
• Uncertainties are estimated via an internal bootstrap method, though systematic errors remain challenging to fully capture.

Experimental results

Research questions

• RQ1 What is the magnitude and direction of the dipole offset between the WMAP and Planck experiments across multiple frequencies?
• RQ2 What is the absolute monopole level in the 408 MHz sky map, and how does it compare to previous estimates?
• RQ3 Does the 1420 MHz map contain a non-zero dipole, and if so, what is its amplitude and direction?
• RQ4 How do instrumental and data processing offsets, as well as isotropic astrophysical components, contribute to the observed monopole and dipole values?
• RQ5 To what extent can monopole and dipole corrections be reliably estimated for intermediate CMB frequencies (23–94 GHz) using this method?

Key findings

• The relative dipole between WMAP and Planck is estimated at 10–15 μK, depending on frequency, representing a key systematic uncertainty in CMB component separation.
• The 408 MHz map monopole is estimated at 8.9 ± 1.3 K, consistent with survey data and previous estimates.
• A non-zero dipole of 0.15 ± 0.03 K is detected in the 1420 MHz map, pointing toward Galactic coordinates (l,b) = (308°, -36°) ± 14°.
• The method successfully lifts degeneracies between monopole and dipole terms by exploiting spatial spectral index variations in foregrounds.
• The derived monopole and dipole values represent the sum of instrumental, processing, and astrophysical offsets that are spectrally uniform across the sky.
• The method is less reliable for intermediate CMB frequencies (23–94 GHz) due to overlapping foreground components (synchrotron, free-free, AME), necessitating full parametric fitting instead.