Galactic Science with the LiteBIRD satellite: Spectral characterization of diffuse Galactic polarized emission at the angular power spectrum level

Technical Summary: Galactic Science with the LiteBIRD Satellite

Problem Statement
The primary scientific objective of the LiteBIRD satellite is to detect primordial B-mode polarization in the Cosmic Microwave Background (CMB) to constrain the tensor-to-scalar ratio ($r$) and probe inflationary physics. However, this measurement is severely limited by Galactic foregrounds, specifically thermal dust emission (dominant at $\gtrsim 100$ GHz) and synchrotron radiation (dominant at $\lesssim 100$ GHz). While previous missions like Planck characterized these foregrounds, the extreme sensitivity required for LiteBIRD necessitates a more rigorous understanding of the spectral energy distributions (SEDs) of these emissions. Specifically, there is a need to forecast whether LiteBIRD can characterize the spatial variations of dust temperature ($T_d$), dust spectral index ($\beta_d$), synchrotron spectral index ($\beta_s$), and their correlation ($\rho$) at the angular power spectrum level. Furthermore, the paper investigates whether spectral parameters differ between intensity (T), E-mode, and B-mode polarization due to the mixing of emitting regions with varying physical conditions and magnetic field structures along the line of sight (LOS).

Methodology
The authors perform a forecast analysis using simulated LiteBIRD observations across 15 frequency bands (40–402 GHz).

• Sky Simulations: Three levels of Galactic emission complexity are modeled using the Python Sky Model (PySM):
  • Low Complexity: Constant spectral parameters across the sky (d9s4).
  • Medium Complexity: Spatially varying spectral parameters in 2D (d10s5).
  • High Complexity: Spatially varying parameters including LOS superposition of multiple layers to mimic frequency decorrelation (d12s7). Synchrotron models also include curvature in the SED.
• Power Spectrum Analysis: Cross-frequency angular power spectra ($C_\ell$) are computed for Temperature (TT), E-mode (EE), and B-mode (BB) using the NaMaster package. The analysis covers multipoles $\ell < 128$ with 12 bandpowers.
• Covariance Estimation: An analytical covariance matrix is constructed using the iNKA (improved Narrow Kernel Approximation) to account for cosmic variance, instrumental noise (white and 1/f), and cross-correlations between CMB, noise, and foregrounds.
• Fitting Procedure: The cross-spectra are fitted using a parametric model (modified black body for dust, power law for synchrotron) with $\chi^2$ minimization. Two approaches are tested:
  1. A global power-law model for amplitude scaling with $\ell$.
  2. Independent amplitudes for each multipole bin ($\ell$-by-$\ell$).
  3. An extension using the moment expansion formalism to model SED distortions caused by the averaging of spatially varying parameters.
• Discrepancy Search: The study explicitly tests for "E/B-discrepancies" (differences between E and B mode spectral parameters) and "T/P-discrepancies" (differences between intensity and polarization parameters).

Key Contributions and Results

1. Failure of the Power-Law Model: The study finds that the standard power-law model for foreground power spectra (often used for Simons Observatory forecasts) fails to reproduce LiteBIRD data, even for the simplest dust models. The reduced chi-square ($\chi^2_{dof}$) is extremely high ($\sim 593$), indicating that spectral parameters vary significantly with multipole $\ell$ due to the mixing of different emitting regions.
2. Precision Constraints: Using independent amplitudes per bin, LiteBIRD is forecast to measure foreground parameters with unprecedented precision at large scales:
   • Dust temperature: $\sigma(T_d) \sim 0.2$ K (a first for polarization data).
   • Dust spectral index: $\sigma(\beta_d) \sim 0.006$.
   • Synchrotron spectral index: $\sigma(\beta_s) \sim 0.04$.
   • Dust-Synchrotron correlation: $\sigma(\rho) \sim 10^{-2}$.
     These constraints represent improvements of factors 3–12 over Planck sensitivities.
3. Detection of E/B and T/P Discrepancies: For complex models (d12s7), the analysis detects significant discrepancies between spectral parameters in E and B modes, and between intensity and polarization.
   • In the $\ell \approx 16.5$ bin, discrepancies reach $4.2\sigma$ for $T_d$, $11\sigma$ for $\beta_d$, and $2.2\sigma$ for $\beta_s$ between E and B modes.
   • T/P discrepancies are detected at $8.3\sigma$ for $T_d$ and $15\sigma$ for $\beta_d$ between TT and BB spectra.
   • These discrepancies are attributed to the co-variation of physical conditions and magnetic field structures along the LOS, which causes spectral mixing that affects polarization modes differently.
4. Moment Expansion Modeling: The paper demonstrates that the moment expansion formalism successfully models the observed SED distortions and discrepancies. By including first-order moments, the reduced $\chi^2$ becomes compatible with 1, and the theoretical discrepancies derived from the input maps are recovered at the $1\sigma$ level. This confirms that the discrepancies are a physical consequence of the mixing of SEDs with spatially varying parameters.
5. Curvature Detection: While LiteBIRD can detect the effects of synchrotron curvature on the recovery of $\beta_s$, the frequency coverage (40–402 GHz) is insufficient to directly detect the curvature parameter ($c_s$) itself due to degeneracy, highlighting the need for complementary low-frequency data (e.g., from C-BASS or QUIJOTE).

Significance
The paper concludes that LiteBIRD will not only be a premier experiment for cosmology but will also open a "new window" onto the physical conditions of the Interstellar Medium (ISM) in the Milky Way. By moving beyond simple parametric models to include moment expansions, LiteBIRD will be able to:

• Quantify the amplitude of polarized mixing in the Galaxy.
• Detect and characterize the variations of dust temperature and spectral indices across the sky and between different polarization modes.
• Provide the first constraints on dust temperature from polarization data.
• Offer a framework to distinguish between intrinsic variations in grain populations and variations induced by LOS mixing.

The authors emphasize that these advances are crucial not only for Galactic science but also for the accurate subtraction of foregrounds required to isolate the primordial B-mode signal. The study suggests that future analyses must account for spectral complexity and moment expansion to avoid biases in both Galactic and cosmological parameter estimation.