Discriminating Planck Reionisation Histories with the kSZ Effect

Problem Statement
The epoch of reionisation represents a critical phase in cosmic history where the first galaxies ionised the intergalactic medium (IGM). While the Planck satellite has provided robust constraints on the integrated optical depth to reionisation ($\tau$), these measurements are inherently limited by their integrated nature, leaving the detailed evolution, duration, and morphology of the reionisation history poorly constrained. Current cosmic microwave background (CMB) data allows for a wide range of possible reionisation histories ($x_e(z)$). The central question addressed in this work is whether the kinetic Sunyaev–Zel'dovich (kSZ) effect, which probes the distribution and velocity of ionised matter at small angular scales, possesses sufficient discriminatory power to distinguish between the specific reionisation histories currently permitted by Planck data.

Methodology
The authors investigate the kSZ angular power spectrum (APS) using an analytical framework that separates the signal into two distinct components:

1. Late-time kSZ: Arising from bulk flows of ionised gas after reionisation is complete.
2. Patchy kSZ: Generated during reionisation as ionised bubbles form and expand, encoding information about the timing and duration of the epoch.

The study proceeds through the following steps:

• Reionisation Histories: The authors utilize a set of 11 best-fit reionisation history models ($x_e(z)$) derived from a frequentist analysis of Planck PR4 data (Ilić et al. 2025). These models employ various parameterisations (e.g., hyperbolic tangent, power-law, step-based, and interpolation-based) and are categorised into two broad classes based on the duration of reionisation ($\Delta z$): "short" ($\Delta z < 2$) and "long" ($\Delta z > 2$).
• Astrophysical Parameters: To model the electron overdensity power spectrum required for the patchy kSZ calculation, the authors adopt parameters ($\alpha_0$ and $\kappa$) derived from the LORELI II suite of simulations. These simulations vary astrophysical parameters governing galaxy properties (gas conversion timescale, minimum halo mass, and ionising escape fraction). The authors select 319 simulations that fall within the 1-$\sigma$ confidence interval of the optical depth $\tau$.
• Uncertainty Propagation: The authors compute the kSZ APS for the fiducial models and then propagate uncertainties from two sources:
  1. Uncertainties in the reionisation history $x_e(z)$ (using the $\chi^2$ interval from the Planck analysis).
  2. Uncertainties in astrophysical parameters ($\alpha_0, \kappa$) derived from the LORELI II simulation ensemble.
• Comparison with Data: The resulting theoretical envelopes are compared against recent kSZ measurements from the South Pole Telescope (SPT-3G), the Atacama Cosmology Telescope (ACT-DR6), and joint analyses involving Planck.

Key Results

• Distinct Signatures: The analysis reveals that the "short" and "long" reionisation classes produce distinct kSZ signatures. "Long" histories result in spectra dominated by the patchy component, whereas "short" histories are dominated by the late-time contribution.
• Robustness to Uncertainties: Despite propagating uncertainties from both the reionisation history and the astrophysical parameters, the two classes remain clearly separable. The dispersion caused by uncertainties in $x_e(z)$ and the astrophysical parameters ($\alpha_0, \kappa$) are found to be comparable in magnitude.
• Current Data Limitations: Current kSZ measurements, which span a range of approximately $0\text{--}3\,\mu\text{K}^2$, are not yet precise enough to definitively distinguish between the "short" and "long" scenarios. However, most recent analyses (excluding specific SPT fits with the Agora template) tend to favour lower kSZ amplitudes, which align more closely with "short" reionisation models.
• Discrimination Threshold: The authors estimate that a measurement of the kSZ power spectrum at multipole $\ell \sim 2000$ with a sensitivity of approximately $0.4\,\mu\text{K}^2$ would be sufficient to discriminate between the two broad scenarios at a $5\sigma$ level. Variations within a single class (e.g., between different "short" models) are smaller, at the $\sim 10\%$ level, requiring even higher sensitivity to resolve.

Significance and Claims
The paper claims that the kSZ effect serves as a promising probe for reionisation physics that extends beyond the constraints provided by optical depth alone. By demonstrating that the "short" and "long" reionisation scenarios allowed by current Planck data yield distinct kSZ signatures, the work establishes a pathway for future CMB experiments to constrain the duration and morphology of reionisation.

The authors maintain a modest stance regarding current capabilities, noting that while current data hints at a preference for "short" reionisation, the dispersion between analyses and associated systematics prevents firm conclusions. They suggest that joint likelihood analyses combining Planck, ACT, and SPT-3G data could extract maximum information from existing datasets before the advent of Stage 4 and 5 telescopes. Furthermore, they posit that while kSZ measurements could eventually discriminate between models within a specific subgroup, achieving this requires observational sensitivity to match the $\sim 10\%$ level of variation found within those groups. The paper concludes that kSZ measurements, potentially complemented by other probes like the Lyman-$\alpha$ forest or 21 cm signals, offer a critical avenue for refining our understanding of the reionisation epoch.