Constraining the Baryon Fraction in Extragalactic Diffuse Ionized Gas with 124 Localized Fast Radio Bursts

Technical Summary: Constraining the Baryon Fraction in Extragalactic Diffuse Ionized Gas with 124 Localized Fast Radio Bursts

Problem Statement
The "missing baryon problem" remains a significant challenge in cosmology. While measurements of the Cosmic Microwave Background (CMB) and Big Bang Nucleosynthesis (BBN) indicate that baryonic matter constitutes approximately 5% of the Universe's energy budget, observations of collapsed structures (galaxies, clusters) and the warm-hot intergalactic medium account for only about 70% of this expected content. The remaining ~30% is hypothesized to reside in the diffuse intergalactic medium (IGM) but has eluded direct detection. Fast Radio Bursts (FRBs) offer a promising tool to address this by measuring Dispersion Measures (DM), which encode the integrated column density of ionized baryons along the line of sight. However, previous analyses using FRBs have relied on probability distribution functions (PDFs) for the extragalactic DM component ($DM_{cos}$) that may not accurately reproduce cosmological simulations, potentially introducing systematic biases in the inferred baryon fraction ($f_d$).

Methodology
This study utilizes a sample of 124 localized FRBs (115 from a previous compilation plus 9 new events) to constrain $f_d$, the fraction of baryons in the diffuse ionized gas phase. The analysis employs a joint likelihood approach combining FRB data with complementary cosmological probes: the PantheonPlus Type Ia Supernova (SN Ia) sample, Dark Energy Spectroscopic Instrument (DESI) Baryon Acoustic Oscillation (BAO) data, and Planck CMB measurements.

Key methodological features include:

1. Improved $DM_{cos}$ PDF: Unlike previous studies that used a modified-normal distribution with a power-law tail (as proposed in [75]), this work adopts a PDF for $DM_{cos}$ derived from IllustrisTNG simulations [82]. This new form includes a crucial normalization factor ($1/\langle DM_{cos} \rangle$) previously omitted, which was shown to cause systematic biases exceeding $1\sigma$. The parameters governing the shape of this distribution ($\alpha, \beta, \sigma_d$) are fitted to simulation data across 53 redshift slices and interpolated for the FRB sample.
2. Cosmological Framework: The analysis allows all cosmological parameters to vary freely, testing three models: $\Lambda$CDM, $w$CDM, and the dynamical dark energy $w_0w_a$CDM model. The latter is prioritized due to recent DESI BAO data favoring dynamical dark energy.
3. Component Modeling: The total observed DM is decomposed into contributions from the Milky Way interstellar medium (ISM), the Milky Way halo ($DM_{halo}$), the host galaxy ($DM_{host}$), and the extragalactic IGM ($DM_{cos}$).
   • $DM_{halo}$ is modeled using two truncated Normal distributions based on different literature constraints ($N(65, 15^2)$ and $N(35, 15^2)$).
   • $DM_{host}$ is initially modeled using parameters derived from IllustrisTNG simulations, with a secondary analysis treating the host distribution parameters as free variables.
4. Systematic Checks: The study investigates the impact of baryonic feedback strength (using an alternative log-normal PDF for $DM_{cos}$), DM selection effects (using a sigmoid selection function), and the redshift evolution of $f_d$ (parameterized as $f_d(z) = f_{d,0}(1 + \alpha \frac{z}{1+z})$).

Key Contributions and Results

• High Baryon Fraction: Under a constant $f_d$ model, the analysis finds that more than 90% of baryons reside in the diffuse ionized gas phase. Specifically, for the $N(65, 15^2)$ halo model, $f_d > 0.967$ (68% CL) in $\Lambda$CDM; for the $N(35, 15^2)$ model, $f_d > 0.986$.
• Robustness to Dark Energy: The constraints on $f_d$ are robust against the choice of dark energy parametrization ($\Lambda$CDM, $w$CDM, $w_0w_a$CDM). While cosmological parameters like $H_0$ and $\Omega_{m0}$ shift slightly between models, the inferred $f_d$ remains consistent.
• No Significant Redshift Evolution: The data do not show statistically significant evidence for redshift evolution in $f_d$. The evolution parameter $\alpha$ is consistent with zero, with upper limits of $\alpha < 0.06$ (depending on the halo model). The authors note that these constraints are currently limited by the redshift distribution of the FRB sample, which is concentrated at $z < 1$.
• Systematic Uncertainties: The dominant systematic uncertainties arise from the assumed distributions of the Milky Way halo and the host galaxy DM.
  • A smaller assumed $DM_{halo}$ leads to systematically higher inferred values of $f_d$.
  • When host galaxy parameters are allowed to vary freely (rather than being fixed to simulation predictions), the inferred $f_d$ decreases slightly (by $\sim 0.02\text{--}0.03$), and the dependence on the specific halo model is reduced, though statistical uncertainties increase. The inferred host DM parameters suggest that IllustrisTNG may underestimate the host contribution for non-repeating FRBs.
• Feedback and Selection Effects: The results are insensitive to the adopted baryonic feedback parameters (when modeled via a log-normal PDF) and to the inclusion of a simple DM selection function.

Significance
The paper claims to provide strong evidence that the majority of the "missing baryons" reside in the diffuse ionized intergalactic medium. By utilizing a more accurate PDF for $DM_{cos}$ that aligns with cosmological simulations and correcting for previous normalization errors, the study offers a refined constraint on the baryon fraction. The result that $f_d > 0.9$ is consistent with independent recent constraints (e.g., Connor et al. [28]) and supports the theoretical picture that the missing baryons are located in the warm-hot intergalactic medium. The work highlights that while current FRB data robustly constrain the total baryon fraction, future improvements in constraining the redshift evolution of $f_d$ and reducing systematic uncertainties related to host galaxy and halo contributions will require larger samples with better redshift coverage.