Chasing Gamma-Ray Signals from Binary Neutron Star Coalescences with the Cherenkov Telescope Array: Prospects and Observing Strategies

1. Problem Statement

The detection of the binary neutron star (BNS) merger GW170817 and its associated short gamma-ray burst (GRB 170817A) established multi-messenger astronomy. However, no Very-High-Energy (VHE; >20 GeV) emission has yet been confirmed from a gravitational wave (GW) event. The Cherenkov Telescope Array Observatory (CTAO) represents the next generation of Imaging Atmospheric Cherenkov Telescopes (IACTs), offering unprecedented sensitivity and rapid slewing capabilities.

The core challenge addressed in this work is determining the detectability prospects of VHE emission from short GRBs associated with BNS mergers during the upcoming LIGO-Virgo-KAGRA (LVK) Observing Run O5 (planned for ~2028). Specifically, the authors aim to:

• Quantify the expected joint detection rate of GWs and VHE GRBs.
• Evaluate how viewing angles (on-axis vs. off-axis) and jet structures affect detectability.
• Develop and optimize observing strategies (tiling, exposure times) to maximize the probability of detecting these transient events given the large sky localization uncertainties typical of GW alerts.

2. Methodology

The authors constructed a comprehensive, multi-step simulation pipeline integrating astrophysical source modeling, GW detection simulation, and instrument response modeling.

A. Simulated GW and BNS Population

• Source: A realistic ensemble of 2,307 simulated BNS mergers based on the LVK O5 sensitivity (Advanced LIGO, Advanced Virgo, KAGRA).
• Parameters: Masses, spins, distances, and sky locations were drawn from realistic astrophysical distributions (e.g., normal distribution for NS masses, isotropic orientation).
• Localization: Sky localization maps (90% credible regions) were generated using the BAYESTAR rapid Bayesian reconstruction code.

B. VHE Emission Modeling (Phenomenological)

Since no TeV short GRBs have been definitively detected, the authors adopted a phenomenological model based on long GRB observations and theoretical jet structures:

• Jet Structure: Assumed a Gaussian structured jet where kinetic energy and Lorentz factor decrease with the angle from the jet axis.
• Emission Physics:
  • Assumed the TeV luminosity ($L_{TeV}$) scales with the isotropic equivalent energy ($E_{\gamma,iso}$) similar to the X-ray afterglow ($L_X$).
  • Light curves were modeled with a rise phase (power-law) to a peak at the deceleration radius, followed by a decay phase.
  • Off-axis effects: The model explicitly calculates the time delay and flux suppression for observers viewing the jet from outside the core opening angle ($\theta_{view} > \theta_{core}$).
• EBL Attenuation: Intrinsic spectra were attenuated by the Extragalactic Background Light (EBL) using the Franceschini & Rodighiero (2017) model.

C. CTAO Instrument Response & Simulation

• Configuration: Simulated the CTAO "Alpha Configuration" (Northern and Southern arrays with LSTs, MSTs, and SSTs).
• IRFs: Used Prod5 Instrument Response Functions (sensitivity, effective area, resolution) for three zenith angles (20°, 40°, 60°).
• Detection Criteria: A 5$\sigma$ detection significance was required. The simulation calculated the exposure time ($t_{exp}$) needed to reach this threshold given a specific latency ($t_L$) from the merger.
• Software: Utilized the custom Python package sensipy (integrating gammapy primitives) to solve for detection times.

D. Observing Strategies (Tiling)

The authors used the tilepy software to simulate follow-up campaigns for poorly localized GW events. They tested five distinct strategies:

1. Fixed Exposure: 1-minute, 5-minute, and 20-minute exposures per pointing.
2. Average-GRB Exposure: Exposure times modulated based on the light curve of an "average" GRB.
3. Adaptive Exposure: Exposure times calculated dynamically for each specific event's light curve (idealized baseline).

• Real-Time Analysis (RTA): Simulated the Science Alert Generation (SAG) pipeline, which can stop the tiling scan and focus on a detected "hotspot" once a 5$\sigma$ signal is found.

3. Key Contributions

• End-to-End Simulation Chain: This is one of the first studies to link GW population synthesis, structured jet phenomenology, and full CTAO instrument response (including tiling and scheduling constraints) in a single framework.
• Quantification of Viewing Angle Bias: The study rigorously demonstrates that viewing angle is the dominant factor in VHE detectability, more so than distance or intrinsic energy.
• Optimization of Tiling Strategies: The paper moves beyond theoretical sensitivity to practical scheduling, evaluating how different exposure durations and latency constraints impact the total number of detections.
• Role of Real-Time Analysis: It highlights the critical importance of the SAG/RTA system in converting a scanning campaign into a targeted observation, significantly boosting detection significance.

4. Key Results

A. Detectability Rates

• Overall Rate: Approximately 18.3% of the simulated GW-associated short GRBs are theoretically detectable by CTAO (assuming ideal pointing).
• Joint Detection Rate: When accounting for realistic scheduling, sky visibility, and latency, the expected joint detection rate for the O5 run is ~4.5% to 5.1%.
• On-Axis vs. Off-Axis:
  • On-axis events ($\theta_{view} < \theta_{core}$) are highly detectable (up to ~73% with 1-min exposure if latency is low).
  • Off-axis events dominate the population (87%) but are much harder to detect. Their detectability drops sharply with latency.

B. Impact of Latency and Exposure

• Critical Time Window: The first 1–4 hours post-merger are critical.
  • For latencies $t_L < 1$ hour, detection is feasible with short exposures (1–10 min).
  • Beyond 4 hours, the fraction of detectable events drops precipitously (to near zero for off-axis events).
• Exposure Time Trade-off:
  • 1-minute campaigns: Cover the sky fastest, allowing multiple revisits to the same source, but may miss fainter events.
  • 20-minute campaigns: Provide deeper sensitivity per pointing but cover less sky area, reducing the chance of hitting the source position quickly.
  • 5-minute campaigns: Identified as the optimal trade-off, achieving the highest detection rate (5.1%) in a fixed 4-hour campaign.

C. The Power of Real-Time Analysis (RTA)

• Implementing RTA (stopping the scan upon a 5$\sigma$ detection) dramatically improves results.
• It increases the median detection significance from ~20$\sigma$ to >90$\sigma$ for on-axis events.
• It allows for extended observation of the source, enabling detailed spectral and light-curve studies that would otherwise be impossible.

D. Parameter Sensitivity

• Viewing Angle ($\theta_{eff}$): The single most important parameter. Even rough estimates of the viewing angle from GW alerts could allow CTAO to prioritize the most promising targets.
• Jet Opening Angle: Smaller opening angles make off-axis detection significantly harder.

5. Significance and Future Outlook

• Strategic Planning: The results provide a concrete roadmap for CTAO operations during O5, recommending a 5-minute tiling strategy with a 4-hour campaign duration as the baseline for GW follow-ups.
• Scientific Return: Even non-detections will place stringent upper limits on VHE emission, constraining jet physics, magnetic field models, and the fraction of BNS mergers that successfully launch jets.
• Synergy: The framework sets the stage for future integration with galaxy catalogs (to prioritize host galaxies) and next-generation GW detectors like the Einstein Telescope, which will detect events at much higher redshifts.
• Multi-Messenger Impact: Confirming VHE emission from BNS mergers would provide unique insights into particle acceleration mechanisms in relativistic jets and the environment of the merger, complementing data from X-ray, optical, and radio counterparts.

In conclusion, this work establishes that while the joint detection of GWs and VHE GRBs is rare (~5%), it is achievable with CTAO. Success depends critically on rapid response, optimized tiling strategies, and the implementation of real-time analysis to capitalize on the fleeting nature of these high-energy transients.