Modelling DSA, FAST and CRAFT surveys in a z-DM analysis and constraining a minimum FRB energy

Technical Summary: Modelling DSA, FAST and CRAFT Surveys in a z-DM Analysis and Constraining a Minimum FRB Energy

Problem Statement
Fast Radio Burst (FRB) science aims to elucidate the origins of these bursts and utilize them for cosmological studies, specifically tracing the distribution of ionized baryons and constraining the Hubble constant ($H_0$). Previous analyses using the $z$–DM (redshift–dispersion measure) framework, such as those by James, Ghosh, et al. (2022) and Baptista et al. (2023), successfully modeled instrumental biases and fitted population parameters using data from the Parkes and ASKAP (CRAFT) surveys. However, these studies were limited by small-number statistics and the exclusion of newer, highly sensitive surveys like the Deep Synoptic Array (DSA) and the Five-hundred-meter Aperture Spherical radio Telescope (FAST). Furthermore, previous models often treated Galactic dispersion measure (DM) contributions as fixed values, potentially overestimating the precision of derived cosmological and population parameters.

Methodology
This work extends the $z$DM code to incorporate data from 119 FRBs, including 29 with associated redshifts, by modeling the observational biases of the DSA and FAST surveys alongside updated CRAFT/ICS data.

• Survey Modeling:
  • FAST: Modeled as a spherical single-dish telescope with a 19-beam receiver. The beam pattern was approximated using 19 Gaussian beams with Half-Power Beamwidths (HPBW) derived from Jiang et al. (2020). The analysis included 9 unlocalised FRBs detected in the Commensal Radio Astronomy FAST Survey (CRAFTS) and the Galactic Plane Pulsar Snapshot (GPPS).
  • DSA: Modeled using commissioning data from DSA-110. The beam pattern was approximated as a single Gaussian with a Full-Width Half-Maximum (FWHM) of $2.6^\circ$. To avoid detection bias against high-redshift FRBs (which appear in fainter host galaxies), redshifts were only utilized for FRBs where the extragalactic DM ($DMEG$) was below a threshold ($183 \text{ pc cm}^{-3}$) ensuring a complete sample of localised hosts.
  • CRAFT: Included additional FRBs detected up to the end of 2023, excluding FRB 20171216A due to its Signal-to-Noise Ratio (SNR) falling below the updated threshold.
• Statistical Improvements:
  • Uncertainty in Galactic DM: Unlike previous studies that used fixed values for the Interstellar Medium ($DM_{ISM}$) and Milky Way halo ($DM_{halo}$), this work models $DM_{MW}$ as a probability distribution. $DM_{ISM}$ is modeled as a truncated normal distribution based on the NE2001 model with a standard deviation of 50%, and $DM_{halo}$ is modeled as a normal distribution with a mean of $50 \text{ pc cm}^{-3}$ and $\sigma = 15 \text{ pc cm}^{-3}$.
  • MCMC Implementation: Due to the increased computational load from additional surveys and parameters, the analysis shifted from a grid-based likelihood calculation to a Markov Chain Monte Carlo (MCMC) sampler (EMCEE) running on the OzSTAR supercomputer.
  • Free Parameter $E_{min}$: A hard cutoff for the minimum FRB energy ($E_{min}$) was introduced as a free parameter, allowing the analysis to probe the low-energy turnover of the luminosity function.

Key Results

• Minimum Energy Constraint: The analysis yields a constraint on the minimum FRB energy of $\log E_{min} (\text{erg}) = 39.47^{+0.54}_{-1.28}$. This value is significantly higher than energies detected in strong repeaters (e.g., FRB 20121102A and FRB 20201124A), which are often observed down to $\sim 10^{37}$ erg.
• Population Parameters: The spectral index $\alpha$ prefers a flat value of $0.11^{+0.66}_{-0.60}$, differing from the negative slope preferred in previous ASKAP-only analyses. However, when $H_0$ is allowed to vary freely, the preference shifts back to a negative slope ($\alpha \approx -0.92$).
• Uncertainty Propagation: The inclusion of uncertainty in $DM_{MW}$ leads to larger uncertainties in derived model parameters compared to previous estimates, despite the increased dataset size.
• Predictions for Future Detections:
  • FAST: Predicted to detect 25–41% of its FRBs at $z \gtrsim 2$ and 6–20% at $z \gtrsim 3$. The distribution peaks at $z \approx 1$, with 73–77% of detections beyond $z \gtrsim 1$.
  • DSA: Predicted to detect 2–12% of FRBs at $z \gtrsim 1$.
  • Survey Limits: The current maximum search DM for FAST (3700–5000 $\text{ pc cm}^{-3}$) is predicted to miss 7–18% of possible detections, while DSA's limit of $1500 \text{ pc cm}^{-3}$ is predicted to miss 3–8%.

Significance and Claims
The authors claim this work provides the first constraint on $E_{min}$ derived from a $z$–DM analysis. The high value of $E_{min}$ suggests two possibilities:

1. There is a low-energy turnover (flattening) in the luminosity function of the general FRB population, meaning the surveys are not sensitive enough to detect the lower-energy tail.
2. Strong repeaters possess a fundamentally different luminosity function compared to single-burst detections (or apparent single bursts).

The paper emphasizes that while the new data expands the accessible parameter space to higher redshifts, the inability to robustly localise high-$z$ FRBs with FAST currently limits the ability to obtain associated redshifts. Consequently, the authors state that precise measurements of $DM_{ISM}$ will be critical for future constraints on cosmological parameters like $H_0$. The work serves as a methodological refinement, demonstrating that incorporating uncertainties in Galactic contributions is necessary to avoid artificially skewing the constraining power of low-DM FRBs.