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Semi-blind component separation for measurement of CMB B-mode polarisation

By: Tran Hoang Viet

Supervisor: Guillaume Patanchon - APC, Université Paris Cité

With the help of: Michele Citran, Benjamin Beringue

CMB France #7

15th October 2025

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Contents

Scientific context: CMB B-mode and component separation

Strategies for semi-blind component separation

Summary & outlooks

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1. Scientific context

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Cosmology and the LiteBIRD mission

LiteBIRD is a satellite mission under development by an international collaboration led by JAXA

( Tristram et al. 2022, combining BK18 and Planck PR4)

Hazumi, M. et al. (2019). “LiteBIRD: A Satellite for the Studies of B-Mode Polarization and Inflation from Cosmic Background Radiation Detection.”

(for r = 0, without systematics and delensing)

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Foregrounds emission and component separation

Context: Other sources of contamination are foreground emissions: dust & synchrotron polarization

These are the most important effects when it comes to polarization measurement

E-mode

Primordial B-mode

Lensing B-mode

Foregrounds

Component separation methods are needed !

These methods utilize the fact that we have measurement of the components in multiple different frequencies

Credits: Josquin Errard

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Foregrounds emission and component separation

Context: Other sources of contamination are foreground emissions: dust & synchrotron polarization

These are the most important effects when it comes to polarization measurement

Component separation methods are needed !

These methods utilize the fact that we have measurement of the components in multiple different frequencies

Credits: Josquin Errard

Polarized thermal dust amplitude map @ 353 GHz

Polarized synchrotron amplitude map @ 30 GHz

Planck collaboration, “Planck 2018 results IV. Diffuse component separation” (2020)

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Spectral Matching ICA

From these parameters we can build the set of comp sep weights

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SMICA in the context of component separation

SMICA was developed at APC

Reference method for temperature in Planck

SMICA should be able to achieve the requirement for component separation in LiteBIRD

LiteBIRD expected component separation result for B-mode.

Method in use was FGBuster – a parametric method

Component separation can be roughly divided into 2 classes:

Parametric: makes strong assumption on mixing matrix, doesn’t make assumption on the component - FGBuster
Blind: use statistical techniques, no assumption on foregrounds emission - ILC

SMICA lies between these two classes of method

LiteBIRD collaboration, “Probing cosmic inflation with the LiteBIRD cosmic microwave background polarization survey”, PTEP 2023

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Simulation setup

The simulations (200 random realizations of CMB + noise) are based on LiteBIRD baseline configuration with 15 frequency bands from 40 - 402 GHz (LiteBIRD collaboration, PTEP 2023)

We implement a 2-component (dust + synchrotron) foreground, created from the library PySM

Simplest model: d0s0 - constant SED parameters across the sky

A more realistic model: d1s1 - SED parameters varies smoothly across the sky

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Simple foregrounds d0s0 case

Assumptions: fixed CMB emission, white noise, 2 foreground components

Likelihood (fsky scaling log-likelihood) on r for this residual

*as the instrument’s configuration is under rescope

PRELIMINARY*

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2. Strategies for semi-blind component separation

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SMICA for complex foregrounds

SMICA basic framework does not take into account the spatial variation

Complex foregrounds can be decomposed into a number of modes (depending on the sensitivity & the complexity of the sky), which can be interpreted as “components”

=> Adding more components into SMICA maybe able to solve the spatial variation

With LiteBIRD sensitivity + d1s1 foregrounds: Across the concerned multipole range (2-128), fitting for 3 foregrounds components absorb a lot the bias coming from spatial variation

A.Carones. “Optimization of foreground moment deprojection for semi-blind CMB polarization reconstruction” https://arxiv.org/pdf/2402.17579

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SMICA with independent components

Applying to a complex sky example (d1s1), featuring some spatial variation of the mixing matrix A on the sky (deviating away from SMICA assumption)

SMICA filtered spectrum (r = 0 in simulation), the bias at all scales is reduced when an additional component is introduced

Likelihood on r, calculated from the SMICA filtered maps spectrum (using a Planck 40 mask) for 3 and 4 foreground components.

*as the instrument’s configuration is under rescope

PRELIMINARY*

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SMICA on subset of pixels

Instead of assuming constant SED across the entire sky, we just force it to be constant within certain regions of the sky (e.g. Healpix superpixel)

=> Run SMICA locally on each subsets of pixels

Using the SMICA-fitted parameters: mixing matrix, component spectra, noise spectra, we can reconstruct the CMB signal on the sky patch using a filtering operation

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SMICA on subset of pixels

A proof of concept with simple d0s0 foreground: apply the procedure for each patch & combine to get the final map

Cleaned CMB map on an example Heapix superpixel

Combined cleaned CMB map

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SMICA on subset of pixels

Evaluating the power spectrum of the cleaned map

Similar constraints to the full sky d0s0: in this case, the operation have little impact on the recovery of r

*as the instrument’s configuration is under rescope

PRELIMINARY*

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Applied on d1s1 simulations: We use Healpix superpixels of nside 2 (48 patches) => Improvements at large scale (at a a cost of smaller scales…)

*as the instrument’s configuration is under rescope

PRELIMINARY*

SMICA on subset of pixels

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Comparison of fgs residual

Full-sky

Heapix superpixels

The residual are large scales !!!

Smaller and more centralized area of contamination

SMICA on subset of pixels

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Ideal mask: Massive improvement at large scale leading to a reduction of bias on r

*as the instrument’s configuration is under rescope

PRELIMINARY*

SMICA on subset of pixels

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3. Summary & outlooks

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We’re able to improve the performance of SMICA for LiteBIRD on complex foregrounds, resulting in a good constraint on r !

Optimization: to be done

Masking strategy & marginalization over systematic residual
Different, more optimized patch selection scheme (K-means, realistic subsets built from data…)

Achieve requirements for component separation and contribute to the data analysis pipeline of LiteBIRD

Other possible developments:

SMICA under systematic effects
From SMICA likelihood to spectra in the case of a masked sky
Non-gaussian SMICA (Michele’s talk on Monday)

Summary & outlooks

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THANKS FOR LISTENING

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BACK UP SLIDES

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SMICA with clusters

Evaluating the power spectrum of the cleaned map

Similar constraints to the full sky d0s0: in this case, the operation does not have an impact on the recovery of r

*as the instrument’s configuration is under rescope

PRELIMINARY*

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Simple foregrounds d0s0 case

Assumptions: fixed CMB emission, white noise

Likelihood (a simple scaling log-likelihood) on r for this residual

*as the instrument’s configuration is under rescope

PRELIMINARY*

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Foreground cleaning

Date

Conference

1/N

Date

Conference

“Multi-Clustering technique” (extension of xForecast)
Distribution of the recovered r in 1000 simulations with input r = 0, with and without foreground residuals
Bias from foreground (PySM d1s1) residuals is found to be small
Final value: r = (3.3 ± 6.2)×10^-4

The plot shows the bias on r when the input value is r=0 (vertical dashed black line) and the associated distribution of sigma_r from 1000 simulations with r=0 and foreground residuals (orange histogram). 1000 simulations are run, which include foregrounds given by the PySM s1d1 sky model, which are fixed in all simulations, and a realization of CMB+noise. A parametric component separation technique, FGBuster, is applied in each realization, and as a result a value of r and sigma_r is obtained in each simulation. The black dashed line shows the mean of r in the 1000 simulations (3.3e-4), and then this can be regarded as a bias. The orange histogram shows the distribution of sigma_r in the 1000 simulations, and the blue dashed line marks the mean of sigma_r (6.2e-4). The red dashed line shows the mean of a the Fisher approach (5.2e-4=, in which the likelihood is approximated by a Gaussian around its peak. These two approaches (direct sigma_r from the simulations and from the Fisher approach) agree to within 20%, but here we conservatively adopt the highest value, and quote a final value of (3.3 +/- 6.2)*1e-4.

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SMICA with clusters

Frequency maps

Divide into Healpix patches

Calculate covariance matrices

Run SMICA on each patches independently

Fit for A, Rs, RN

Filter to build map for each patches using fitted A, Rs, RN

Recombine the patches and retrieve the full sky map

Cl and r analysis

Removing biases…

A proof of concept with simple d0s0 foregrounds

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SMICA with clusters

Frequency maps

Divide into Healpix patches

Calculate covariance matrices

Run SMICA on each patches independently

Fit for A, Rs, RN

Filter to build map for each patches using fitted A, Rs, RN

Sum up the results to create a full sky map

Cl and r analysis

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SMICA with clusters

Frequency maps

Divide into Healpix patches

Calculate covariance matrices

Run SMICA on each patches independently

Fit for A, Rs, RN

Filter to build map for each patches using fitted A, Rs, RN

Sum up the results to create a full sky map

Cl and r analysis

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SMICA with clusters

Frequency maps

Divide into Healpix patches

Calculate covariance matrices

Run SMICA on each patches independently

Fit for A, Rs, RN

Filter to build map for each patches using fitted A, Rs, RN

Sum up the results to create a full sky map

Cl and r analysis

Removing biases…

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SMICA with clusters

Frequency maps

Divide into Healpix patches

Calculate covariance matrices

Run SMICA on each patches independently

Fit for A, Rs, RN

Filter to build map for each patches using fitted A, Rs, RN

Sum up the results to create a full sky map

Cl and r analysis

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SMICA with independent components

SMICA model:

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SMICA with independent components

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Wiener vs GLS

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SMICA with systematic effects

Exploring systematics effects with SMICA: Beam perturbation - one of the most important effect in LiteBIRD currently

Very brief result following an established structure and comparing to the result of a more matured pipeline in LiteBIRD (NILC)

Plots show you the level of beam calibration in each frequency needed to achieve the required tensor-to-scalar ratio measurement in LiteBIRD

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Simple foregrounds d0s0 case

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SMICA procedure

“Fully blind” case: mixing matrix, component spectra, noise spectra all free => Doesn’t work

Must develop a procedure to fit all these elements

Close-form (estimated explicit solution in 1D case) to estimate power spectra.

Release constraint on noise spectra

Repeat until no noticeable change in the parameters

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Treatment of masked polarization maps

Masking Stokes parameter maps cause mixing between E & B-mode spectra => We opted to try a procedure to remove this:

Extract T, E & B spectra from map
Use E spectra with spin 1 to create “E-mode map”, similar for B
Mask these E and B maps => Generate from this the E and B-mode spectra

Mixing of E & B removed

E-mode

Lensing B-mode

Lensing B-mode with leakage from E-mode