Can CTAO/LST-1's delayed signal from GRB 221009A be explained as a pair echo?

A pair echo is delayed light, not a second burst

Very-high-energy gamma-rays travelling from a distant source do not cross intergalactic space undisturbed. On their way they interact with microwave and infrared/optical background photons and convert into electron-positron pairs. Those pairs then scatter Cosmic Microwave Background photons up to lower gamma-ray energies, regenerating a secondary beam. If intergalactic magnetic fields (IGMF) in the voids of the Large Scale Structure deflect the charged pairs, the secondary gamma-rays arrive from slightly different directions and later than the primary signal. That delayed, deflected component is the pair echo.

The delay is what makes the effect measurable. The paper gives the delay as a function of gamma-ray energy, field strength B and correlation length lambda_B, with two regimes: when lambda_B exceeds the electron cooling distance the delay scales as B squared, and when lambda_B is shorter it also scales with lambda_B. The cooling distance itself depends on energy, and at the LST-1 threshold energy of about 0.3 TeV it equals roughly 20 kpc. That single number is why 20 kpc appears as a break point throughout the analysis.

Because the echo is generated by the highest-energy primary photons, the pair echo seen above 300 GeV is produced by primary gamma-rays above 10 TeV. This is the energy range LHAASO measured for GRB 221009A, which is what makes the joint fit in this paper possible.

A transient burst separates echo from afterglow

Active galactic nuclei have been the traditional targets for pair echo searches, but their emission is persistent, which makes it hard to separate an intrinsic signal from a delayed echo. Gamma-ray bursts offer a cleaner geometry: the TeV signal is transient, so a delayed detection can in principle be compared against a well-defined prompt emission window.

GRB 221009A is the brightest burst observed so far and was detected by LHAASO up to energies above 10 TeV. LHAASO recorded the signal over roughly 3000 s from the burst onset, with the brightest emission between 230 s and 900 s after the trigger. The burst sits at redshift z approximately 0.151. Those measured spectra, corrected for absorption on extragalactic background light, are the input the authors use to normalise their pair echo predictions.

The LST-1 telescope of CTAO observed the source from 1.3 to 20 days after the burst. Strong moonlight during the first observation raised the energy threshold from the nominal about 20 GeV to about 300 GeV. At 1.33 days the observation revealed a 4.1 sigma excess in the source direction; later observations produced only upper limits on the flux.

Simulating pair cascades across a cell-like field

The authors model the primary emission with a cut-off power-law spectrum, fitting normalisation, spectral index and cut-off energy to the LHAASO data in two time intervals. They then propagate about 10,000 primary photons in the 1-100 TeV range through intergalactic space using the numerical code CRProp 3.2, following both gamma-rays and the electrons and positrons they produce.

The intergalactic magnetic field is treated as cell-like: constant strength within a cell but randomly oriented from one cell to the next. The explored parameter space covers field strengths from 1e-18 G to 1e-14 G and cell sizes from 1e-4 Mpc to 1 Mpc. GRB 221009A is assumed to be a point source emitting within a jet of 1 degree half-opening angle, inferred from the jet break seen in the LHAASO light curve.

For each combination of B and lambda_B, the model predicts a pair echo light curve and spectrum. The authors then perform a joint fit to the LHAASO and LST-1 spectral data points, assuming Gaussian statistics in each energy bin, and derive profile likelihoods as a function of B for fixed correlation lengths.

The fit prefers a field near 1e-16 G

The profile likelihoods show clear minima, which the authors interpret as the LHAASO and LST-1 data providing a measurement of the IGMF parameters rather than only a bound. The 68% confidence range on B is defined as the interval over which the profile likelihood 2 log(L) drops by less than one from its maximum.

For correlation lengths above 20 kpc, the resulting estimate is log(B/G) = -16.2 +/- 0.7, corresponding to a field of roughly 3e-16 G in the order-of-magnitude sense the authors use in the discussion. For correlation lengths below 20 kpc, the estimate is modified upwards by the square root of (20 kpc / lambda_B). The break at 20 kpc is tied to the cooling distance of the pairs that produce inverse Compton emission at about 0.3 TeV, close to the LST-1 threshold.

In the specific scenario of a short-correlation-length field left over from cosmological phase transitions, the pair echo interpretation of the LST-1 signal implies a field strength between 1e-14 G and 1e-12 G, with a correlation length expected to be shorter than a parsec. The authors note that these parameters are consistent with known constraints on IGMF, including lower bounds from gamma-ray observations of active galactic nuclei.

An intrinsic afterglow could produce the same signal

The central caveat is stated plainly in the paper. A power-law extrapolation of the LHAASO TeV light curve to the time of the first LST-1 observation predicts a flux consistent with the LST-1 measurement within its uncertainty range, and an extrapolation of the Fermi/LAT spectrum into the 0.1-1 TeV range leads to a similar conclusion. A sizeable contribution from the intrinsic source afterglow to the LST-1 signal is therefore possible.

The paper also notes that the pair echo and the intrinsic afterglow could in principle be separated using the characteristic energy dependence of the signal light curve. That test was not possible for GRB 221009A because strong moonlight prevented Cherenkov observations right after the burst. The authors state directly that the LST-1 detection cannot be considered evidence for the pair echo, only that the pair echo can provide an order-of-one contribution to the measured flux.

This is why the result is framed as a measurement under a hypothesis rather than a detection. The field strength quoted is conditional on the pair echo interpretation being the correct one for that 1.33-day signal.

One burst cannot establish the phenomenon

The authors are explicit that a day-scale delayed signal from a single GRB is not, on its own, a discovery of the pair echo phenomenon. What would strengthen the case is repeated detections of similar signals in multiple GRBs and active galactic nuclei, all consistent with the same IGMF parameters. That combination would provide more convincing evidence and a more reliable measurement of the field.

The paper positions the current result as a demonstration of the method's potential for next-generation imaging atmospheric Cherenkov telescopes now under construction, CTAO and LACT. The authors also note a contemporaneous publication reporting a similar IGMF estimate from the same LST-1 signal, and observe that their own analysis differs by addressing the uncertainties on the estimated magnetic field rather than giving only an order-of-magnitude value.

The comparison that matters for a reader is therefore not whether the LST-1 signal is real, but which interpretation of it survives future data. The paper's own threshold is consistency across multiple sources with shared IGMF parameters.

The estimate depends on the assumed correlation length

The field strength is not a single number independent of the model. It is reported as log(B/G) = -16.2 +/- 0.7 only for correlation lengths above 20 kpc; below that scale the central value shifts upward by the square root of (20 kpc / lambda_B). Readers comparing this result with other IGMF constraints need to check which correlation length regime those constraints assume, because the same data imply different field strengths in the two regimes.

The relic-field scenario is a further conditional branch. The 1e-14 G to 1e-12 G range applies specifically to a short-correlation-length field of cosmological origin, where the allowed parameters are obtained by intersecting the pair echo estimate with the theoretical band describing the largest turbulently processed eddy size. That intersection, not the pair echo fit alone, produces the higher field values.

The practical priority this paper sets is therefore to treat the LST-1 signal as a test case for a method, and to read the quoted field strength together with its assumed correlation length and its unresolved degeneracy with an intrinsic afterglow. The decisive next step is the energy-dependence measurement that moonlight blocked here, repeated across more bursts.

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