The Einstein Probe (EP) soft X-ray transient EP241113a — with isotropic energy Eγ,iso∼1051E_{\gamma,\rm iso}\sim10^{51} erg comparable to classical gamma-ray bursts (GRBs) but a bulk Lorentz factor of only Γ∼20\Gamma\sim20 — is the prototype of the long-predicted 'dirty fireball'. Dai, Wang & Zhang (2026) explained its sub-keV spectral peak as dissipative photospheric emission and argued that such a heavily baryon-loaded jet is plausibly powered by neutrino–antineutrino annihilation in a hyperaccreting neutrino-dominated accretion flow (NDAF), while restricting their calculation to steady, weakly magnetized outflows and noting that the EP sample with redshifts is too small for population tests. The surviving open problem is to determine which engine(s) launch energetic dirty fireballs: whether weakly magnetized Blandford–Znajek (BZ) jets can reach η∼few\eta\sim{\rm few}–20 at the observed luminosities, what the relative NDAF-versus-BZ contributions to the dirty-fireball population are, and whether the dissipative-photosphere predictions survive extension to unsteady and magnetized outflows.

Background

In the standard fireball picture of gamma-ray bursts (GRBs), a compact central engine deposits ∼1050\sim10^{50}–105210^{52} erg into a small volume, producing an outflow whose terminal speed is limited only by the amount of baryonic matter entrained. Baryon loading is conventionally measured by the dimensionless entropy η\eta, the ratio of outflow energy to entrained baryon rest-mass energy, which sets the terminal bulk Lorentz factor Γ\Gamma (the relativistic speed of the outflow). Classical long GRBs are 'clean' fireballs with Γ≳100\Gamma\gtrsim100. Decades ago it was hypothesized that explosions of comparable energy but much heavier baryon loading — 'dirty fireballs' with η∼few\eta\sim{\rm few}–100 — should also exist, radiating softer prompt emission, but secure examples were lacking until recently. Long GRBs obey an empirical correlation between the rest-frame spectral peak energy EpE_{\rm p} and the isotropic-equivalent radiated energy Eγ,isoE_{\gamma,\rm iso}, roughly Ep∝Eγ,iso1/2E_{\rm p}\propto E_{\gamma,\rm iso}^{1/2}, known as the Amati relation. The Einstein Probe (EP), a Chinese-led wide-field soft X-ray (0.5–4 keV) monitor launched in 2024, is revealing a population of fast X-ray transients (FXTs), many without gamma-ray counterparts, whose relation to GRBs is actively being established. EP241113a, detected in November 2024, has Eγ,iso≃1.4×1051E_{\gamma,\rm iso}\simeq1.4\times10^{51} erg yet a spectral peak below a few keV, deviating from the Amati relation at >3σ>3\sigma; modeling of its faint X-ray afterglow plateau implies a low bulk Lorentz factor, Γ∼20\Gamma\sim20, making it the prototype energetic dirty fireball (Dai et al. 2026, arXiv:2603.26213). Dai, Wang & Zhang (2026, ApJL, arXiv:2608.03043) proposed that its low EpE_{\rm p} arises from a dissipative photosphere: as Γ\Gamma decreases, the Thomson photosphere (the radius at which the scattering optical depth falls to unity) shifts outward while the internal-shock dissipation radius shifts inward, so dissipation occurs deep below the photosphere, where repeated Compton scatterings keep radiation and matter coupled and the spectral peak is set at a lower temperature in a larger thermalization zone; the weaker Lorentz boosting then shifts the observed EpE_{\rm p} into the soft X-ray band. For the engine, two channels are standard for collapsing massive stars (collapsars) hosting a hyperaccreting stellar-mass black hole. In a neutrino-dominated accretion flow (NDAF) — a disk accreting at ∼0.01\sim0.01–1 M⊙ s−11\,M_\odot\,{\rm s^{-1}} and cooled by neutrino emission — neutrino–antineutrino (ννˉ\nu\bar\nu) annihilation above the disk can power a bipolar jet, and neutrino heating of the disk atmosphere drives a baryonic wind that mass-loads the outflow, reducing its terminal η\eta. In the Blandford–Znajek (BZ) mechanism, rotational energy is extracted electromagnetically from the spinning black hole by magnetic field lines threading the horizon; the magnetically supported polar region is expected to leak fewer baryons, giving a cleaner jet. The quantitative baseline is Lei, Zhang & Liang (2013), who computed minimum baryon loads for both channels and found that ννˉ\nu\bar\nu-annihilation fireballs are typically dirtier while magnetically dominated BZ jets can be much cleaner, concluding that at least a good fraction of classical GRBs require magnetically dominated engines. However, that calculation treated the magnetically dominated BZ limit; the weakly magnetized BZ regime relevant to η∼few\eta\sim{\rm few}–20 outflows at Lγ,iso∼1048L_{\gamma,\rm iso}\sim10^{48}–1051 erg s−110^{51}\,{\rm erg\,s^{-1}} was not mapped, and no decomposition of the newly accessible dirty-fireball population by engine type exists. The Letter's own population synthesis of EpE_{\rm p}–Eγ,isoE_{\gamma,\rm iso} is NDAF-only, applies to steady and weakly magnetized outflows (subphotospheric synchrotron photons from shock-heated electrons are neglected), and its authors state that EP241113a is only 'likely' launched by a weakly magnetized, neutrino-annihilation-dominated engine — while a companion analysis lists BZ jets, proto-neutron-star neutrino winds, unclean polar funnels, and envelope mixing as alternative routes to dirty fireballs, and EP population studies (O'Connor et al. 2025) establish the collapsar connection without discriminating engines. What remains unresolved is therefore the launching mechanism of this new class: which engines can produce such baryon-loaded, low-Γ\Gamma jets at the observed luminosities, and in what proportions they contribute to the population.

Problem Statement

Determine which central engine(s) launch energetic dirty fireballs — baryon-loaded jets with η∼few\eta\sim{\rm few}–20 and Eγ,iso∼1049E_{\gamma,\rm iso}\sim10^{49}–105110^{51} erg, exemplified by EP241113a (Γ∼20\Gamma\sim20, Eγ,iso≃1.4×1051E_{\gamma,\rm iso}\simeq1.4\times10^{51} erg) and possibly EP240414a (η∼few\eta\sim{\rm few}, Lγ,iso∼1048 erg s−1L_{\gamma,\rm iso}\sim10^{48}\,{\rm erg\,s^{-1}}) — and quantify the relative contributions of the NDAF neutrino–antineutrino-annihilation channel and the Blandford–Znajek channel to their population. Concretely: (1) calculate (or otherwise establish) whether a BZ jet with weak magnetization can achieve baryon loading as heavy as η∼few\eta\sim{\rm few}–20 at Lγ,iso∼1048L_{\gamma,\rm iso}\sim10^{48}–1051 erg s−110^{51}\,{\rm erg\,s^{-1}}, or whether such low-Γ\Gamma outflows require neutrino-driven wind entrainment in a hyperaccreting NDAF; (2) derive the observable discriminants (e.g. positions in the EpE_{\rm p}–Eγ,isoE_{\gamma,\rm iso} plane, luminosity functions, event rates) that separate these engine channels, and use them to decompose the observed population of energetic soft fast X-ray transients (if the observed sample is too small for a statistical decomposition, state the required sample size and instead give a model-based expectation for the relative contributions), thereby testing whether high-accretion-rate NDAF phases are intrinsically rare or short-lived; and (3) assess whether the dissipative-photosphere interpretation of their soft spectra survives the model extensions the source Letter itself flags — unsteady jets with internal-collision-induced density and dissipation fluctuations, and magnetized outflows in which synchrotron emission from shock-heated electrons provides additional subphotospheric soft photons and can modify the thermalization condition. An answer should state, with uncertainties, which engine(s) can produce the observed class and in what relative proportions; parts (1)–(3) above are all required for a complete answer.

References

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