South Pole Telescope
Foreground Mitigation Challenges


Cail Daley

CEA Paris-Saclay

January 17, 2025



  • Introductions:

    • The Cosmic Microwave Background (CMB)

    • The South Pole Telescope (SPT)

  • SPT map processing:

    • point source mitigation

    • component separation

The Cosmic Microwave Background

NAOJ

ESA and the Planck Collaboration

The South Pole
Telescope

3 bands:      95,    150,   220 GHz      resolution:  1.6,     1.2,     1.0 arcmin

Photo Credit: Aman Chokshi

SPT maps

SPT maps

SPT maps

Extragalactic CMB foregrounds

Components:

  • point-sources

    • radio (falling spectrum)

    • dusty (rising spectrum; CIB)

  • Sunyaev Zel’dovich (clusters)

    • temperature (falling*)

    • polarization (same as CMB)

Dunkley et al. (2013)

SPT map filtering

SPT performs constant-decl. scans of the sky; scans recorded as 1D ‘timestreams’.


Timestreams are binned into pixels after various filters are applied:

  • Low-pass

  • High-pass (fit sines & cosines)

  • Polynomial fit

Ignore point source regions when applying filters to avoid “filtering wings.”

  • but doing so couples effective filtering and CMB!

Point source mitigation: inpainting

Replace point sources with Gaussian constrained realization of the CMB:

\[ X_1^{\rm inp} = X_1^{\rm sim} + \vb C_{12} \vb C_{22} ^{-1} \qty(X_1^{\rm data} - X_1^{\rm sim}) \]

Before & after inpainting (credit: Yuuki Omori, thesis)

1

2


Preserves 2-point statistics by construction, but not higher-order information…

\(\implies\) lensing (4-pt) estimator is biased towards zero.


Instead, subtract source template and bias-harden against point sources in the lensing estimator.

Component separation

Scale-dependent linear combination (LC) of frequency bands to:

  • minimize variance noise and foregrounds (MV-LC)

    and optionally,

  • null contribution from a specific frequency response (constrained-LC)

\[ X_{\vbell}^\textrm{MV-LC} = \sum_{i} \mathbb W_{\vbell}^{i} X_{\vbell}^{i} \]

where

\[ \mathbb W_{\vbell} = \frac{\mathbb C_{\vbell} \inv \mathbb A_s}{\mathbb A_s^\dagger \mathbb C_{\vbell} \inv \mathbb A_s}, \qquad \sum_i \mathbb W_{\vbell}^{i} = 1. \]

\(\mathbb A_s = [1 \ 1 \ 1]\)
frequency response of the CMB


\(\mathbb C_{\vbell}\):  \(3 \times 3 \times \ell_{\rm max}\)
per-frequency foreground & noise covariance at each \(\ell\)

Component separation covariance

Reichardt et al. (2021)

Component separation weights

Component separation spectra

Summary

  • Most CMB foregrounds have different spectral response than CMB.

  • SPT foregrounds should be extragalactic, allowing for simple component separation techniques.

    • linear combination of bands using analytic weights

  • Solutions are less obvious for point sources (and interaction with our filtering)

    • exploring source template subtraction

  • If you have critiques of or suggestions to improve these approaches,
    I want to hear them!