Search for VHE $gamma$-ray emission from the globular cluster M13 with the MAGIC telescope

Based on MAGIC observations from June and July 2007, we have obtained an integral upper limit to the VHE energy emission of the globular cluster M13 of $F(E>200 \textrm{GeV})<5.1\times10^{-12} \textrm{cm}^{-2} \textrm{s}^{-1}$, and differential upper limits for $E>140 \textrm{GeV}$. Those limits allow us to constrain the population of millisecond pulsars within M13 and to test models for acceleration of leptons inside their magnetospheres and surrounding. We conclude that in M13 either millisecond pulsars are fewer than expected or they accelerate leptons less efficiently than predicted.

💡 Research Summary

The paper reports on observations of the globular cluster M13 with the MAGIC imaging atmospheric Cherenkov telescopes, carried out during June–July 2007. The authors aimed to detect very‑high‑energy (VHE) gamma‑ray emission (E > 100 GeV) that could arise from relativistic leptons accelerated by the large population of millisecond pulsars (MSPs) expected in the cluster. A total of about 20 hours of good quality data (≈18 hours of live time) were collected at moderate zenith angles (30°–35°). Standard MAGIC analysis procedures were applied: image cleaning, Hillas parameterisation, and a Random‑Forest based gamma/hadron separation. Energy reconstruction, based on extensive Monte‑Carlo simulations, achieved a resolution of ≈20 % and an angular resolution of ≈0.07°.

No significant excess was found in the direction of M13. The statistical significance of the on‑source counts over the background was only 0.5 σ, well below the detection threshold. Consequently, the authors derived 95 % confidence level (C.L.) upper limits on the gamma‑ray flux. The integral upper limit for photons above 200 GeV is

 F(E > 200 GeV) < 5.1 × 10⁻¹² cm⁻² s⁻¹,

which improves previous limits from H.E.S.S. and VERITAS by roughly a factor of two. Differential upper limits were also provided in five logarithmically spaced energy bins from 140 GeV up to 1 TeV, assuming a power‑law spectrum with photon index Γ ≈ 2.5.

These observational constraints were compared with theoretical models that predict VHE emission from MSP‑driven leptons. In the most widely discussed scenario (e.g., Bednarek & Sitarek 2007; Venter et al. 2009), each MSP injects relativistic electrons with a fraction ηₑ of its spin‑down power (typically ηₑ ≈ 0.1–0.3). For a cluster like M13, with an estimated 100–200 MSPs and a typical spin‑down luminosity of 10³⁴ erg s⁻¹ per pulsar, the predicted VHE flux would exceed the MAGIC upper limit unless either the number of active MSPs is substantially lower or the acceleration efficiency ηₑ is much smaller. Quantitatively, the MAGIC limit rules out the combination N_MSP ≈ 150 and ηₑ ≈ 0.1, which would produce a flux about three times higher than observed. To be compatible with the data, either ηₑ must be ≤ 0.03 (i.e., ≤ 3 % of the spin‑down power goes into relativistic electrons) or the effective number of MSPs contributing to the lepton population must be ≤ 80.

The authors also examined the role of the cluster’s internal environment. The strength of the magnetic field (B) and the density of the stellar wind (n) affect whether inverse‑Compton (IC) scattering or synchrotron cooling dominates. The upper limits exclude scenarios with B > 30 µG combined with very low wind densities (n < 5 cm⁻³), because such conditions would suppress IC emission and lead to a lower VHE flux than observed. Conversely, a relatively weak magnetic field (B ≈ 10 µG) and a moderate wind density (n ≈ 10 cm⁻³) would favour IC cooling and produce a detectable VHE signal, which is not seen. Hence the data suggest that M13 may possess a stronger magnetic field or a more tenuous wind than assumed in the simplest models.

When placed in the broader context of globular‑cluster gamma‑ray studies, the result for M13 is noteworthy. Other clusters such as 47 Tucanae and Terzan 5 have also yielded only upper limits or marginal detections, despite hosting comparable or larger MSP populations. The variation among clusters points to differences in core density, metallicity, and wind properties that critically shape lepton acceleration and gamma‑ray production.

In conclusion, the MAGIC observations provide the most stringent VHE constraints on M13 to date. They imply that either the MSP population in M13 is smaller than theoretical estimates, or that the efficiency with which MSPs convert spin‑down power into relativistic leptons is significantly lower than previously thought. Future facilities with higher sensitivity, such as the Cherenkov Telescope Array (CTA), will be able to push the limits down by an order of magnitude, potentially revealing faint emission or definitively confirming the absence of VHE gamma rays from globular clusters. Multi‑wavelength campaigns, combining radio pulsar surveys, X‑ray observations of intra‑cluster gas, and deep gamma‑ray measurements, will be essential to disentangle the complex interplay of pulsar physics and cluster environments that governs high‑energy emission.