In a cosmos of blazars, the jet is a lighthouse beaming photons and, sometimes, elusive neutrinos toward us. For decades, scientists have wrestled with what exactly powers the bright, bungling glow of these faraway engines, and whether protons, electrons, or a hybrid cocktail lead the dance. A collaboration led by Narine Sahakyan of Bar-Ilan University (Israel) and ICRANet-Armenia (and involving several international partners) has pushed the frontier by teaching a data-driven surrogate to imitate the intricate physics of hadronic models. The aim isn’t to replace physics, but to turn a centuries‑old puzzle into something researchers can explore, quickly and exhaustively, like a telescope you can tune rather than rebuild from scratch each time.
The team’s work sits at the intersection of multimessenger astronomy—where light from radio to gamma rays meets the neutrinos marching through space—and modern machine learning’s appetite for speed. By training a surrogate model on a vast library of simulations generated by SOPRANO, a time‑dependent kinetic code, they can reproduce the full electromagnetic and neutrino output of blazar jets. In other words: they built a fast, faithful stand‑in for a very heavy calculation, so scientists can sift through how a jet’s inner physics would look across millions of parameter sets without grinding through months of processor time. This is especially valuable when you want to test whether protons in the jet could be the culprits behind observed neutrinos, or whether a purely leptonic picture could suffice.
These aren’t abstract questions. The authors apply their surrogate to two famous blazars linked to IceCube neutrino detections—TXS 0506+059 and PKS 0735+178—and show how the same data can be fit under different energetic stories. The result is not a single verdict, but a demonstration of how a fast, self-consistent modeling approach can sharpen our inferences about jet composition and energy budgets. The work takes place in the real world of data, where electromagnetic observations and neutrino counts must be reconciled within a common framework. It’s the kind of tool that could become as routine as fitting a spectrum, just more multi‑messenger and more physics-laden.
A neural shortcut through blazar physics
What if you could teach a machine to imitate complex physics without re solving the equations from scratch? That’s the core idea here. The surrogate model is trained on an enormous catalog of spectra produced by SOPRANO, a self‑consistent, time‑dependent solver that follows electrons, protons, and a chorus of secondary particles as they radiate and interact inside a blazar’s jet. SOPRANO handles proton synchrotron emission, Bethe‑Heitler pair production, photo‑pion processes, and all the messy cooling and cascading that follows. It’s a physics engine, but it’s also computationally expensive—perfect motivation for a fast, data‑driven mimic that can interpolate between many possible jet states.
To capture the full breadth of hadronic and hybrid scenarios, the authors generate an immense dataset—7 million spectra—covering a wide swath of jet parameters. They don’t just sample the space randomly; they use Latin hypercube sampling to ensure the coverage is uniform across dimensions. The resulting surrogate isn’t a single model; it’s a small fleet of specialized estimators, each tuned for a region of the parameter space that includes both proton‑synchrotron dominance and mixed, lepto‑hadronic states. When the four photon regions overlap, the outputs are averaged to keep predictions smooth at the boundaries. In short: the surrogate is crafted to stay faithful across the terrain of possibilities, not just in a single, tidy corner of parameter space.
Crucially, the surrogate doesn’t merely spit out a spectrum. The training includes not only the photon flux but also the accompanying neutrino output, since neutrinos are the smoking guns of hadronic processes. The team trained separate networks for the photon bands and a dedicated network for each neutrino flavor, all while maintaining a physically grounded normalization and energy scale. The result is a fast, self‑consistent tool that can be plugged into a Bayesian fitting engine to extract jet parameters from real data. The lead authors and coauthors—Sahakyan, Bégué, Casotto, Dereli‑Bégué, Vardanyan, Khachatryan, Giommi, and Pe’er—showcase a method that scales with the era of multimessenger astronomy, not against it.
The model’s architecture is guided by physical intuition: the jet is treated as a compact, magnetized blob moving toward us, with electrons and protons injected in a power‑law distribution bounded by minimum and maximum Lorentz factors. The realism matters: the same run that reproduces the radio through X‑ray spectrum must also predict the potential neutrino flux that IceCube could observe. It’s this coupling of spectra and neutrinos that elevates the surrogate beyond a simple spectrum generator. The paper also foregrounds practical choices—e.g., limiting the dynamic range for some parameters, incorporating absorption by the extragalactic background light, and handling neutrino oscillations—so that the predictions map onto what telescopes actually see.
Two neutrino-bright blazars tested
The two testbeds are not random picks. TXS 0506+059 and PKS 0735+178 are among the clearest blazar candidates linked to neutrino events detected by IceCube, Baikal‑GVD, KM3NeT, and others. The authors push the surrogate through two distinct fitting approaches for TXS 0506+059: a Gaussian likelihood for the neutrino flux in two energy bands and a Poisson likelihood that uses the number of detected events over a year. The same surrogate is then used to fit PKS 0735+178 under a Poisson neutrino likelihood. The result is a window onto how different statistical treatments of the same multimessenger data can tilt the inferred jet physics toward different energetic regimes.
For TXS 0506+059, the two strategies tell complementary stories. When the neutrino flux is treated as a Gaussian, the best fit leans toward a hybrid model: electrons and protons share the workload, with protons carrying most of the jet’s luminous power. The fit suggests a proton luminosity far outstripping the electrons and even the magnetic field’s energy budget, with the Doppler factor around a modest tens and a magnetic field of only a few hundredths of a gauss. In this picture, the high‑energy emission is shaped not just by proton synchrotron radiation but also by secondary particles born in photohadronic interactions, weaving a rich electromagnetic tapestry that also accommodates the neutrinos. The proton maximum Lorentz factor climbs high enough to keep the beam efficient in the gamma range, but the energetics wallop the Eddington limit when you push the numbers to their extremes. It’s a provocative hint that in at least some blazars, protons are not just passengers but major energy carriers in the jet.
When the analysis switches to a Poisson likelihood—essentially asking how many neutrinos we would expect to see given one detected event in a year—the favored solution shifts toward a proton‑synchrotron (P‑syn) dominated scenario. Here the magnetic field is lower, the emission region is larger, and the neutrino production sits at a different energy sweet spot. The result underscores a recurring theme in multimessenger modeling: different statistical lenses on the same data can illuminate different corners of the jet’s physics, and only by combining the electromagnetic portrait with neutrino counts can we begin to constrain the true energy partition inside the jet.
PKS 0735+178 yields a similar, if nuanced, story. The Poisson‑based fit places the HE emission squarely in the realm of proton radiation in a compact, magnetized zone, with a robust proton luminosity and a magnetic field that can be dramatically stronger than in TXS. Yet the posterior for PKS 0735+178 is bimodal: one mode resembles a hadronic/hybrid hybrid, while the other resembles a more proton‑synchrotron‑only picture. In other words, the data for this source admit more than one plausible energetic arrangement, a reminder that current observations aren’t yet definitive for every object. The authors emphasize that to decisively distinguish the two scenarios, we’ll need more high‑energy photon data and, crucially, more neutrino statistics from next‑gen detectors.
Implications for the era of multimessenger astronomy
What does it all mean for how we study the universe now—and in the years ahead? For one, the surrogate technology dramatically lowers the barrier to exploring blazar jet physics under hadronic and lepto‑hadronic models. The full physics, including proton cascades and secondary particle production, is computationally expensive; having a fast, faithful stand‑in means researchers can sweep the parameter space far more thoroughly and repeatedly test different data sets or instrumental assumptions. The authors even integrate the surrogate with a Bayesian inference engine to deliver posterior distributions for each jet parameter. In practical terms, this is a game changer for planning observations, testing scenarios, and quantifying what multimessenger data can—and cannot—tell us about jet composition and energetics.
The work is also a reminder that a single blazar can harbor different energy “modes.” The TXS 0506+059 analyses show that both a hybrid and a pure hadronic—proton‑driven—interpretation can fit the electromagnetic data, with neutrino expectations guiding the choices. This tension highlights how neutrino observations act as a crucial discriminator for jet content. In the larger picture, the study nudges us toward the possibility that proton‑loaded jets may be common in the era of strong multimessenger detections, at least under certain conditions of compactness and photon density. Yet the PKS 0735+178 results warn that the data are not yet decisive for every source; the same source can host multiple viable configurations depending on how we weigh the neutrino information and how we treat high‑energy photons.
Beyond the science of blazars themselves, the paper points to a brighter, more collaborative future for astronomy. The trained surrogate has been integrated into the Markarian Multiwavelength Data Center (MMDC), a web platform designed to let researchers upload data, run fits, and visualize multimessenger predictions. That portal is more than a convenience: it democratizes access to sophisticated, self‑consistent modeling for both electromagnetic and neutrino data. When next‑generation facilities—CTAO for very high energy gamma rays, KM3NeT, IceCube‑Gen2, and other detectors—enter the scene, this kind of surrogate modeling could keep pace with data volumes and enable rapid hypothesis testing across many sources. The authors’ broader aim is clear: give the astrophysical community a fast, robust, and reusable tool to explore how jets accelerate particles, how those particles radiate, and how neutrinos reveal the hidden, proton‑driven engines at work.
There are caveats, of course. The surrogate currently omits external photon fields that can be important in some blazars with dense ambient light, such as certain flat‑spectrum radio quasars. Including those could shift cooling rates and secondary production in meaningful ways, so the authors plan a future version that incorporates external radiation fields or multi‑zone physics. And as the posterior landscapes for some sources remain bimodal, more discriminating data—especially in the highest photon energies and, of course, more neutrino counts—will be essential to pin down which energy budget really powers a given jet. Even so, the study demonstrates a powerful pattern: when you couple rich, time‑dependent physics with scalable, data‑driven surrogates, you open up a practical path to learning from the cosmos’s most extreme laboratories.
At its core, the paper is a story about collaboration between computation and observation, theory and data. It is about turning a daunting set of equations into a tool that can keep up with 21st‑century data streams, and about asking the right questions in the right way: not only what is the emission from a blazar, but what does that emission tell us about the jet’s content, about how energy is transported across cosmic distances, and about whether the universe truly runs on protons as well as electrons when the conditions are just so. As the authors note, the era of multimessenger astronomy has arrived, and with it a practical, scalable way to test the most compelling ideas about how the most powerful engines in the universe work.
