Estimating Cosmological Parameters from Localized Fast Radio Bursts: A Method for Removing Milky Way Dispersion-Measure Contributions

Technical Summary: Estimating Cosmological Parameters from Localized Fast Radio Bursts via Differential Dispersion Measures

Problem Statement
Fast radio bursts (FRBs) serve as powerful cosmological probes because their dispersion measures (DMs) encode the integrated electron density along the line of sight, providing a direct link to the distribution of ionized matter in the Universe. However, extracting cosmological information from the observed DM ($DM_{obs}$) requires subtracting foreground contributions, specifically the Milky Way interstellar medium ($DM_{ISM}$) and the Galactic halo ($DM_{halo}$). Current methods rely on Galactic electron-density models (e.g., NE2001, YMW16, NE2025) and assumed distributions for the halo contribution. The paper highlights that uncertainties in these models and the lack of a model-independent estimate for $DM_{halo}$ introduce significant systematic errors. Previous studies indicate that different assumptions regarding the Galactic halo can lead to noticeably different constraints on cosmological parameters such as the Hubble constant ($H_0$) and the diffuse baryon fraction ($f_d$).

Methodology
The authors propose a differential DM method designed to eliminate the Milky Way contribution without relying on specific Galactic electron-density models or prior assumptions about $DM_{halo}$. The core logic relies on the assumption that within a sufficiently small sky region, the Milky Way's ISM and halo contributions are approximately constant.

1. Differential Construction: For two localized FRBs located in the same sky region, the method selects the lower-redshift FRB as a reference event. The observed DM of the higher-redshift FRB is subtracted from that of the reference event:
   $$\Delta DM_{obs} = DM_{obs,2} - DM_{obs,1} = \Delta DM_{cos} + \Delta DM_{host}$$
   This operation cancels out the $DM_{ISM}$ and $DM_{halo}$ terms, leaving only the difference in the cosmic component ($\Delta DM_{cos}$) and the host galaxy component ($\Delta DM_{host}$).

2. Likelihood Formulation: A likelihood function is constructed for $\Delta DM_{obs}$ by integrating over the probability distributions of the cosmic and host DM differences. The cosmic DM distribution is modeled using a quasi-Gaussian probability distribution function (PDF) derived from simulations, while the host galaxy DM is assumed to follow a log-normal distribution based on IllustrisTNG simulation results.

3. Sky Partitioning: To ensure the validity of the "constant Milky Way contribution" assumption, the authors test various sky-partitioning schemes using mock data. They employ the coefficient of variation (CV) of the total Milky Way DM ($D_{MW}$) as a metric. An $8 \times 8$ grid partitioning of the sky (excluding the Galactic plane $|b| < 15^\circ$ and the Gum-Vela overdense region) is identified as the optimal scheme, where all regions satisfy the homogeneity criterion ($CV < 0.2$).

4. Parameter Inference: The method is applied to constrain the parameter $\Gamma \equiv \Omega_b H_0 f_d$, which combines the baryon density fraction, the Hubble constant, and the diffuse baryon fraction. Markov Chain Monte Carlo (MCMC) analysis is used to derive posterior distributions for $\Gamma$.

Key Results

• Validation with Mock Data: Using 200 mock FRBs generated with a fiducial $\Gamma = 3.12$ (based on Planck 2018 parameters), the differential method successfully recovered the input parameter, yielding $\Gamma = 3.10 \pm 0.19$. This confirms the method's reliability in removing systematic biases under controlled conditions.
• Application to Observational Data: The method was applied to a sample of 99 localized FRBs (after excluding outliers and FRBs with ambiguous host associations or redshifts outside the calibration range).
  • Differential Method: The analysis yielded $\Gamma = 2.88 \pm 0.33$. Assuming fixed Planck 2018 values for $\Omega_b h^2$ and $H_0$, this corresponds to a diffuse baryon fraction of $f_d = 0.867 \pm 0.099$.
  • Conventional Method: For comparison, the same dataset was analyzed using the traditional approach (subtracting $DM_{ISM}$ via the NE2025 model and treating $DM_{halo}$ as a free parameter). This resulted in $\Gamma = 3.55 \pm 0.17$ and $DM_{halo} = 51^{+8}_{-5} \text{ pc cm}^{-3}$, corresponding to $f_d = 1.069 \pm 0.051$.
• Discrepancy: The value of $\Gamma$ derived from the differential method is lower than that from the conventional method by approximately $1.8\sigma$.

Significance and Claims
The paper claims that the observed discrepancy between the differential and conventional methods highlights the importance of Milky Way DM systematics in FRB cosmology. The authors assert that their differential approach provides a robust way to reduce systematic uncertainties associated with the Milky Way foreground without needing specific Galactic models. While the current statistical precision is limited by the number and sky distribution of localized FRBs (as each region requires at least one low-redshift reference event), the authors conclude that this differential approach offers a promising route for precision cosmology as the sample of localized FRBs grows. The work demonstrates that treating the Milky Way contribution differently can significantly alter cosmological inferences, underscoring the need for model-independent techniques in future large-scale FRB analyses.