Search for TeV emission from spider millisecond pulsars with HAWC

1. Problem Statement

Millisecond pulsars (MSPs) are rapidly rotating neutron stars, often found in binary systems. A specific subclass, known as "spider" MSPs, consists of systems where the pulsar interacts with a low-mass companion in a tight orbit (period < 1 day). These systems are categorized as Redbacks (companion mass $0.1–0.4 M_\odot$) and Black Widows (companion mass $< 0.1 M_\odot$).

Theoretical models suggest that the interaction between the pulsar wind and the companion's outflow creates strong intrabinary shocks. These shocks could accelerate electron-positron pairs to very high energies, potentially producing Very High Energy (VHE) gamma rays (0.1–100 TeV) via Inverse Compton scattering off the companion's photon field. While young pulsars are known to emit TeV radiation (forming "TeV halos"), no firm detection of TeV emission from MSPs has been established. This study aims to:

• Search for VHE emission from a sample of spider MSPs using HAWC data.
• Determine if Redbacks and Black Widows exhibit different spectral properties.
• Constrain the contribution of MSPs to the Galactic diffuse TeV emission.

2. Methodology

The analysis utilized 2,565 days of data from the High-Altitude Water Cherenkov (HAWC) Gamma-Ray Observatory.

Sample Selection:

• Source List: Derived from the University of Maryland and ATNF catalogs.
• Criteria: Orbital period $P_b < 1$ day; Declination within HAWC's field of view ($-26^\circ < \delta < 64^\circ$); separation $\ge 2^\circ$ from known bright TeV sources (to minimize contamination).
• Final Sample: 43 sources total, comprising 15 Redbacks and 28 Black Widows.

Analysis Techniques:

1. Minimal Source Fit: Each source was fitted individually using a simple power-law spectral model ($\Phi = K(E/E_{piv})^{-p}$) with a fixed spectral index $p=2.7$. The Test Statistic (TS) was calculated to assess significance.
2. Multi-Source Fit: For sources showing a preliminary TS $> 4$, a more complex fit was performed within a 4-degree Region of Interest (ROI). This accounted for:
   • Nearby gamma-ray sources from the 4HWC catalog.
   • Diffuse emission (particularly at low Galactic latitudes).
   • Extended source morphologies (Gaussian distributions).
3. Stacking Analysis: To overcome the faintness of individual sources, a joint likelihood analysis was performed. The likelihoods of individual sources were summed to search for a cumulative signal.
   • Weighting: An equal-weighting scheme was used for all sources to remain model-independent.
   • Subsets: Stacking was performed on the full sample, the Redback subset, and the Black Widow subset separately.
4. Energy Binning: The analysis covered 0.32–100 TeV, divided into five quasi-differential energy bins.

Systematics:
Uncertainties were evaluated by varying the spectral index ($p$ from -2.2 to -3.0) and using alternate detector response models. The total systematic uncertainty was found to be bounded by $\pm 40\%$.

3. Key Results

• Individual Source Detections:
  • No significant detection was found for any of the 43 sources.
  • Three sources (J1952+2630, J1957+2516, and B1957+20) initially showed TS $> 4$ in the minimal fit. However, the multi-source fit revealed that these excesses were caused by contamination from nearby extended sources (e.g., 4HWC J1945+2434) rather than the pulsars themselves. Their final TS values were consistent with background fluctuations.
• Stacking Analysis:
  • The stacked analysis of the full sample, Redbacks, and Black Widows yielded TS values consistent with background fluctuations.
  • No significant difference in TeV emission properties was found between Redbacks and Black Widows given the current sensitivity.
• Upper Limits:
  • Since no signal was detected, 90% confidence level (CL) upper limits on the average flux were derived.
  • For the full energy range (0.32–100 TeV), the average flux upper limit is $3.47 \times 10^{-15} \, \text{cm}^{-2} \, \text{TeV}^{-1} \, \text{s}^{-1}$.
  • In the lowest energy bin (0.32–1.00 TeV), the limit is $6.87 \times 10^{-13} \, \text{TeV}^{-1} \, \text{cm}^{-2} \, \text{s}^{-1}$.

4. Significance and Implications

• Constraints on Models: The derived upper limits are generally 10% to an order of magnitude above optimistic theoretical predictions for Inverse Compton emission from intrabinary shocks. While not yet ruling out standard models, they provide crucial constraints on parameters such as the injection spectral index, companion radiation fields, and shock efficiency.
• Galactic Diffuse Emission: The results suggest that spider MSPs are unlikely to contribute significantly to the Galactic diffuse emission at TeV energies and above.
• Comparison with Other Telescopes: The HAWC limits provide the leading constraints in the 0.3–100 TeV range, surpassing the expected sensitivity of 50 hours of H.E.S.S. observations by nearly an order of magnitude at 10 TeV.
• Future Prospects: The study highlights that while current limits do not yet rule out hadronic emission models (proton acceleration), future improvements in sensitivity (e.g., via the HAWC outrigger array or the Cherenkov Telescope Array Observatory, CTAO) are necessary to potentially detect these sources or further constrain extreme parameter configurations.

Conclusion

This paper presents the first comprehensive search for VHE emission from spider MSPs using HAWC. Despite deep exposure and advanced statistical techniques (including multi-source and stacking analyses), no evidence of TeV emission was found. The study establishes stringent upper limits that guide future theoretical modeling and observational strategies for this class of binary pulsars.