Modelling the time dependence of the TeV Gamma-ray source at the Galactic Centre

The physical mechanism behind the TeV gamma-ray source observed at the centre of the Galaxy is still unknown. One intriguing possibility is that the accretion flow onto the central supermassive black hole is responsible for accelerating protons to TeV energies which then diffuse outward to interact with molecular gas at distances of 1 pc. Here, we build on our earlier detailed calculations of the proton transport to consider the time and energy dependence of the TeV signal following a burst of particle acceleration at Sgr A*. We find that, due to the strong energy dependence of the proton diffusion, any variability in the particle acceleration rate will only be visible in the TeV signal after a delay of ~ 10 yrs, and only at energies > 10 TeV. If the accelerator is long-lived it must have been running for at least 10^4 yrs and have a hard proton injection spectrum of \alpha=0.7 (where dn/dE_inj \propto E^{-\alpha}) in order to produce the correct amount of high energy gamma-ray flux. This rapid diffusion of high energy protons also rules out the possibility that the observed TeV source is directly related to the period of increased activity of Sgr A* that ended ~ 100 yrs ago. However, a good fit to the observed H.E.S.S. data was found with \alpha=2.7 for the scenario of a brief (few year long) burst of particle acceleration that occurred ~ 10 yrs ago. If such bursts are common then they will keep the TeV source energised and will likely produce spectral variability at > 10 TeV on <~ 5 yr timescales. This model also implies that particle acceleration may be an important mechanism in reducing the radiative efficiency of weakly accreting black holes.

💡 Research Summary

The paper investigates the origin of the TeV gamma‑ray source at the Galactic Centre by modeling the transport of relativistic protons accelerated in the accretion flow of the supermassive black hole Sgr A*. Building on earlier detailed calculations of proton diffusion, the authors explore how the gamma‑ray signal evolves in time and energy after a burst of particle acceleration. A key physical ingredient is the strong energy dependence of the diffusion coefficient, (D(E) \propto E^{\delta}) with (\delta \approx 0.5–0.6). Consequently, low‑energy protons (∼1 TeV) take thousands of years to reach the dense molecular gas at ∼1 pc, whereas high‑energy protons (≥10 TeV) can traverse the same distance in a few decades. This disparity creates a characteristic time lag: any change in the proton injection rate becomes visible in the gamma‑ray flux only after roughly ten years, and only at energies above ∼10 TeV.

Two distinct acceleration scenarios are examined. In the “long‑lived” case, the accelerator must have been active for at least (10^{4}) yr. To reproduce the H.E.S.S. spectrum under this assumption, the injected proton spectrum must be extremely hard, with an index (\alpha \simeq 0.7) (i.e., (dn/dE_{\rm inj} \propto E^{-\alpha})). Such a hard spectrum ensures that a sufficient number of high‑energy protons diffuse rapidly enough to interact with the surrounding gas and generate the observed high‑energy gamma‑ray flux. The model predicts a relatively steady TeV emission at low energies, while any variability would be confined to the >10 TeV band on timescales of decades.

In the “burst” scenario, acceleration occurs only for a brief interval of a few years. Here a much softer injection spectrum ((\alpha \approx 2.7)) can match the data provided the burst happened roughly ten years ago. In this case the high‑energy gamma‑ray component is still in the diffusion phase, so the model anticipates observable spectral variability above ∼10 TeV on timescales of ≤5 yr. The low‑energy (∼1 TeV) component would evolve more slowly, changing only over centuries.

The authors also address the possibility that the present TeV source is a relic of the heightened activity of Sgr A* that ended ∼100 yr ago. Because protons of the relevant energies would have already diffused beyond the 1 pc interaction region, the model rules out a direct connection between that historic flare and the current gamma‑ray emission.

Beyond explaining the TeV source, the study suggests a broader astrophysical implication: efficient proton acceleration in a weakly accreting black hole can divert a substantial fraction of the accretion power into non‑radiative channels. Accelerated protons carry away energy that would otherwise emerge as X‑ray or radio radiation, thereby reducing the radiative efficiency of the system. This mechanism may be a generic feature of low‑luminosity active galactic nuclei and could help explain their under‑luminous nature.

Overall, the paper provides a quantitative framework linking proton acceleration, energy‑dependent diffusion, and delayed gamma‑ray response. It predicts that future high‑resolution TeV observations, especially those capable of monitoring spectral changes on yearly timescales, can discriminate between the long‑lived hard‑spectrum accelerator and the short‑burst soft‑spectrum scenario. Detection of rapid (>10 TeV) variability would strongly support the burst model, while a stable high‑energy spectrum would favor a persistent, hard accelerator operating over Myr timescales. The work thus offers clear, testable predictions for forthcoming observations with CTA and next‑generation gamma‑ray facilities.