Least response method to separate CMB spectral distortions from foregrounds

J.-P. Maillard, A. Mihalchenko, D. Novikov, A. Osipova, S. Pilipenko, and J. Silk

Phys. Rev. D 109, 023523 – Published 19 January 2024

Abstract

We present a signal-foreground separation algorithm for filtering observational data to extract spectral distortions of the cosmic microwave background (CMB). Our linear method, called the least response method (LRM), is based on the idea of simultaneously minimizing the response to all possible foregrounds with poorly defined spectral shapes and random noise while maintaining a constant response to the signal of interest. This idea was introduced in detail in our previous paper. Here, we have expanded our analysis by taking into consideration all the main foregrounds. We draw a detailed comparison between our approach and the moment internal linear combination method, which is a modification of the internal linear combination technique previously used for CMB anisotropy maps. We demonstrate advantages of LRM and evaluate the prospects for measuring various types of spectral distortions. Besides, we show that LRM suggests the possibility of its improvements if we use an iterative approach with sequential separation and partial subtraction of foreground components from the observed signal. In addition, we estimate the optimal temperature that the telescope’s optical system should have in order to detect the chemical type $μ$ distortions. We present a design of an instrument where, according to our estimates, the optimal contrast between its thermal emission and the CMB allows us to measure such distortions.

Received 20 October 2023
Accepted 19 December 2023

DOI:https://doi.org/10.1103/PhysRevD.109.023523

Physics Subject Headings (PhySH)

Cosmic microwave background

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

J.-P. Maillard ¹, A. Mihalchenko ^2,3, D. Novikov ², A. Osipova ^2,4, S. Pilipenko ², and J. Silk^1,5,6

¹Institut d’Astrophysique de Paris, UMR 7095, CNRS, Sorbonne Université, 98bis Boulevard Arago, 75014 Paris, France
²Astro-Space Center of P.N. Lebedev Physical Institute, Profsoyusnaya 84/32, Moscow 117997, Russia
³Moscow Institute of Physics and Technology, Institutskiy pereulok, d.9, Dolgoprudny, Moscow 141701, Russia
⁴National Research University Higher School of Economics, 11 Pokrovsky Bulvar, Moscow 109028, Russia
⁵Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA
⁶Beecroft Institute for Particle Astrophysics and Cosmology, Department of Physics, University of Oxford, Oxford OX1 3RH, United Kingdom

Separation of CMB $μ$ spectral distortions from foregrounds with poorly defined spectral shapes

D. I. Novikov and A. O. Mihalchenko

Phys. Rev. D 107, 063506 (2023)

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Issue

Vol. 109, Iss. 2 — 15 January 2024

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Images

Figure 1
MILC and LRM methods for separating $μ$ distortions when only dust and CIB are taken as foregrounds. Panel (a) shows the probability distribution function for $T$ and $β$ parameters. Isocontour lines limit the $Ω$ region of parameter variations. Panel (b) shows MILC response to foreground $| R (F) |$ if $n = 2$ . Dark red indicates the region where the response to the foreground exceeds the response to the $μ$ signal: $| R (F) | \geq 1$ . Panel (c) shows the total MILC $noise + signal$ response $R (F + N)$ if $n = 2$ . Panel (d) $| R (F) |$ for MILC, $n = 3$ . Panel (e) $R (F + N)$ for MILC, $n = 3$ . Panel (f) $| R (F) |$ for MILC, $n = 4$ . Panel (g) $R (F + N)$ for MILC, $n = 4$ . Panel (h) $| R (F) |$ for LRM. Panel (i) $R (F + N)$ for LRM.
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Figure 2
Left panel: red solid line: total response to $foreground + noise$ for MILC as a function of the number of constraints. Red dashed line: Noise response for MILC. Red dash-dotted line: MILC response to foreground. The blue solid, dashed, and dash-dotted lines show LRM responses to $foreground + noise$ , noise, and foreground, respectively. Right panel: responses to noise and foreground as functions of sensitivity for MILC ( $n = 3$ ) and LRM approaches. Solid, dashed, and dash-dotted lines represent the same as in the left panel.
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Figure 3
Left panel: the histogram represents the response to $foreground + noise$ with the sequential addition (one by one from left to right) of various components to the studied signal. Thus, the leftmost column shows the response to $foreground + noise$ in the presence of only dust and CIB radiation as foreground, and the rightmost column shows this response if all the components listed along the horizontal axis are taken into account. Calculations were made for MILC and LRM to separate $μ$ distortions and correspond to the sensitivity $σ = 1 Jy / sr$ . Right panel: the green histogram shows the measure of orthogonality $Γ_{c}$ of the $μ$ signal to each individual component. The red step line is the measure of orthogonality $Γ_{Σ}$ of $μ$ distortion to all components to the left of the step in question (similar to the left panel).
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Figure 4
Left panel: the result of applying the MILC and LRM methods to separate the $μ$ signal. The dependencies of the total $noise + foreground$ response on the sensitivity of the experiment in the presence of all the main foregrounds are shown. The dashed lines show results for an “ideal” experiment with no influence from the instrument optical system. Right panel shows the results of extracting $y_{0}$ , $y_{1}$ and $y_{2}$ signals for the LRM and for MILC approaches. We show the responses to $noise + foreground$ when taking into account all the main foregrounds except the instrument optics (sky difference should be used).
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Figure 5
Solid lines show the response to $foreground + noise$ as a function of the temperature of the instrument optics for different emissivity values. The dashed line corresponds to the value which is inverse to the measure of orthogonality between $I_{μ}$ and a set of signals associated with CMB and optics: $I_{CMBA}, I_{y_{0}}, I_{y_{1}}, I_{y_{2}}, I_{optics}$ .
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Figure 6
SIMBAD instrument.
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