Ultra Extreme HEP-BL Lacs (UEHBLs)

• UEHBLs are a subclass of BL Lac objects defined by synchrotron peaks in the MeV range, marking an extreme regime of jet particle acceleration and severe Klein–Nishina suppression.
• The hybrid shock–turbulence acceleration model, using coupled Fokker–Planck equations, accounts for the hard electron spectra and rapid variability observed in these sources.
• Multi-wavelength SED modeling of UEHBLs reveals suppressed GeV–TeV emission and highlights their potential as probes for cosmic background light, intergalactic magnetic fields, and ultra-high-energy cosmic rays.

Ultra Extreme High-Energy-Peaked BL Lacs (UEHBLs) represent an hypothesized and emerging extension of the blazar sequence to the most extreme regimes of jet particle acceleration. Distinguished by their exceptionally high synchrotron peak frequencies, extending into the MeV band, and by suppressed inverse Compton emission due to severe Klein-Nishina effects, UEHBLs provide a new parameter space with strong implications for the physics of relativistic jets, the efficiency of stochastic acceleration, and the observational capabilities of current and future high-energy observatories (Sciaccaluga et al., 12 Nov 2025).

1. Definition, Spectral Properties, and Observational Criteria

UEHBLs push the classic two-hump blazar SED to more extreme energies than the well-established high-energy-peaked BL Lacs (HBLs) and extreme HBLs (EHBLs). In the standard classification, HBLs have their synchrotron peak at $\nu_\mathrm{syn} \lesssim 10^{17}$ Hz ($\sim 0.4$ keV), and EHBLs push into the hard X-ray with $\nu_\mathrm{syn} \gtrsim 10^{18}$ Hz ($\sim 4$ keV). UEHBLs are defined by synchrotron peaks in the MeV regime, i.e., $\nu_\mathrm{syn} \sim (0.2$–$2)\ \text{MeV} \approx 5\times10^{19}$–$5\times10^{20}$ Hz (Sciaccaluga et al., 12 Nov 2025).

Empirically, UEHBLs manifest as extremely hard sources in the Swift-BAT band (15–150 keV), with photon indices $\Gamma_X \lesssim 1.5$, a lack of optical or soft X-ray counterparts, and are effectively undetectable by both Fermi-LAT (GeV) and CTA (TeV) due to the suppression of their high-energy spectral component (Sciaccaluga et al., 12 Nov 2025). This demarcates them from TeV-peaked/ultra-extreme BL Lacs (with $\Gamma_{\mathrm{VHE}}\lesssim2$ and $\nu_{\mathrm{peak}}^{\mathrm{IC}}\gtrsim10^{26}$ Hz), whose Compton dominance and spectra show distinctive behavioral shifts (Costamante, 2019).

Key distinguishing observational properties:

• Synchrotron peak in MeV ($>10^{19}$ Hz), not X-ray/hard X-ray as in EHBLs.
• Swift-BAT spectral hardness ($\Gamma_X<1.5$) and X-ray to optical non-detections.
• Multi-wavelength SED shows suppressed or absent GeV–TeV Compton bump.

2. Physical Models: Hybrid Shock–Turbulence Acceleration

The hybrid shock–turbulence acceleration paradigm underpinning UEHBLs combines direct injection by a weakly magnetized, mildly relativistic recollimation shock with subsequent stochastic (second-order Fermi) acceleration by downstream turbulence (Sciaccaluga et al., 12 Nov 2025).

The system is modeled by coupled Fokker–Planck equations for the particle distribution ($f(p,t)$) and turbulence energy density ($W(k,t)$):

$$\frac{\partial f}{\partial t} = \frac{1}{p^2}\frac{\partial}{\partial p}\left[p^2 D_p \frac{\partial f}{\partial p} + p^2\left(\frac{dp}{dt}\right)_{\text{rad}} f\right] - \frac{f}{t_{\text{esc}}} + I_f$$

$$\frac{\partial W}{\partial t} = \frac{\partial}{\partial k}\left[k^2 D_k \frac{\partial}{\partial k}\left(\frac{W}{k^2}\right)\right] - \frac{W}{t_{\text{dam}}} + I_W$$

Here, the momentum diffusion $D_p$ is derived from quasilinear theory, scaling with $p^2 \beta_a^2$ and integrating over turbulence above the resonant wavenumber. Escape times transition between geometric ($R/c$) and turbulent-diffusive ($R^2/\kappa_\parallel$) limits, and electrons are injected as $$I_n \propto \gamma^{-2} \exp(-\gamma/\gamma_{\text{cut}})$$ with $\gamma_\text{min}=10^3$, $\gamma_\text{cut}=10^5$.

High $\gamma_\mathrm{peak}$ ($\sim10^6$–$10^7$) and high $B \times \delta$ push the synchrotron peak into the MeV range. Particle acceleration occurs close to the theoretical gyroresonant limit, with acceleration timescales $t_{\mathrm{acc}} = \eta\,t_g$ and $\eta$ pushing to $10^4$–$10^5$ for MeV peaks (Sciaccaluga et al., 12 Nov 2025).

3. Spectral Models, SED Realizations, and Physical Parameters

Sciaccaluga et al. (Sciaccaluga et al., 12 Nov 2025) provide three representative SED realizations (Cases A–C):

Case	$\nu_{\text{syn}}$ (MeV)	$B$ (G)	$\delta$	$R$ (cm)	$\gamma_{\text{peak}}$ ($\sim$)
A	2	$1.7 \times 10^{-2}$	25	$2 \times 10^{16}$	few $\times 10^7$
B	0.5	$2.2 \times 10^{-2}$	20	$1.5 \times 10^{16}$	few $\times 10^6$
C	0.2	$3.0 \times 10^{-2}$	16	$1 \times 10^{16}$	few $\times 10^6$

The predicted electron spectra are hard (slope near $-2$) with a high-energy Maxwellian-like pile-up. These parameters are extreme relative to typical EHBLs and are necessary to shift the synchrotron peak into the MeV domain. In every scenario, the strong Klein–Nishina suppression ($\gamma_\text{peak} h\nu_\text{syn}/m_e c^2 \gg 1$) quenches the SSC component at GeV–TeV energies, placing UEHBLs below the detection thresholds of Fermi-LAT and CTA (Sciaccaluga et al., 12 Nov 2025).

4. Multiwavelength Detectability and Candidate Selection

Due to their unique SED shape, UEHBLs evade detection in the GeV–TeV regime. Current and future high-energy facilities have differing prospects:

• Fermi-LAT (10 yr sensitivity): Well below predicted fluxes for all cases, no expected detections.
• CTA North/South (50 h): Unable to detect the suppressed TeV Compton bump (Sciaccaluga et al., 12 Nov 2025).
• MeV Observatories: COSI (2 yr) can detect mid-range peaks (Case B), marginally detect case C, and only reach case A during flares or extended missions; AMEGO-X (3 yr) and e-ASTROGAM (1 yr) comfortably detect all cases across 0.2–10 MeV (Sciaccaluga et al., 12 Nov 2025).

A cross-match in Swift-BAT detected a sample of candidate sources with $F_{15-150\,\mathrm{keV}} \gtrsim 10^{-11}$ erg\,cm$^{-2}$\,s$^{-1}$, $\Gamma_X<1.5$, $|b|>10^\circ$, and no soft X-ray/optical counterpart. Ten such objects, four of which remain unassociated after archival inspection, mirror the SED characteristics of modeled UEHBLs and represent the first credible candidate list (Sciaccaluga et al., 12 Nov 2025).

5. Connection to Hadronic and Alternative Acceleration Models

While all confirmed UEHBLs require extreme particle energies and environments, several emission models exist:

• One-zone leptonic (SSC) models encounter difficulties matching both the narrowness and the energy of the peaks unless one invokes extremely large $\gamma_\text{min}$ or $\delta$ and very low $B$ (Cerruti et al., 2014, Aguilar-Ruiz et al., 2022).
• Hybrid stochastic acceleration—upgrades to the shock–turbulence Fokker–Planck approach—resolve this by self-consistently producing the hardest, highest-$\nu_\mathrm{syn}$ distributions (Sciaccaluga et al., 2022).
• Hadronic scenarios are invoked for ultra-extreme SEDs: proton-synchrotron solutions operate at $B\sim10$–100 G and $E_{p,\text{max}}\sim10^{19}$ eV, whereas lepto-hadronic and cascade models partition emission among multiple zones, at modest (sub-Eddington) jet power, and can explain very hard/flat TeV spectra (Cerruti et al., 2014, Tavecchio, 2013, Tavecchio et al., 2015).

This suggests UEHBLs are critical for testing not only the limits of leptonic but also hadronic blazar emission scenarios.

6. Polarization, Variability, and Jet Plasma Diagnostics

The strong synchrotron-dominated SED architecture of UEHBLs leads to measurable high polarization degrees in the MeV regime (expected to exceed $40\%$) and increasing polarization with frequency. The modeled MeV flux for steady/quiescent states is below the polarization threshold for COSI and AMEGO-X, but e-ASTROGAM could reach detectable limits.

Variability signatures are expected to be driven by radiative thermal instabilities: small, localized increases in $B$ result in pressure collapse and radiative MeV flares via rapid electron overcooling. These events can temporarily boost otherwise marginal sources into the detectability window of MeV missions (Sciaccaluga et al., 12 Nov 2025). The possibility of detecting such rapid, high-amplitude flares provides a critical probe of stochastic acceleration and cooling structures in relativistic jet plasmas.

7. Implications for Jet Particle Acceleration and Cosmological Probes

The existence, or absence, of UEHBLs has major implications:

• Acceleration Physics: Confirmed UEHBLs demonstrate electron acceleration up to Lorentz factors $\gamma \gtrsim 10^7$–$10^8$ on sub-parsec scales, requiring acceleration efficiency parameter $\eta \sim 10^4$–$10^5$, which approaches or saturates the theoretical gyroresonant limit (Sciaccaluga et al., 12 Nov 2025).
• Non-detection: If forthcoming MeV missions fail to detect the expected population, it will imply either that acceleration is significantly less efficient ($\eta \gg 10^5$) or that UEHBLs are intrinsically rare and faint.
• Cosmological Utility: By pushing the synchrotron peak into the MeV regime—well beyond the hard X-ray band—UEHBLs become probes of cosmic EBL and intergalactic magnetic fields, and serve as unique test beds to constrain maximum jet particle energies and probe physics at the edge of QED radiative cooling (Bonnoli et al., 2015, Costamante, 2019).
• Ultra-high-energy cosmic ray (UHECR) context: If hadronic processes dominate, then UEHBLs may also act as sources of UHECRs and PeV–EeV neutrinos (Tavecchio, 2013, Tavecchio et al., 2015, Cerruti et al., 2014).

• "Ultra extreme high-frequency-peaked BL Lacs: a potential population of MeV synchrotron blazars?" (Sciaccaluga et al., 12 Nov 2025)
• "A hadronic origin for ultra-high-frequency-peaked BL Lac objects" (Cerruti et al., 2014)
• "On the hadronic cascade scenario for extreme BL Lacs" (Tavecchio, 2013)
• "A Two-Zone Model as origin of Hard TeV Spectrum in Extreme BL Lacs" (Aguilar-Ruiz et al., 2022)
• "Extreme TeV BL Lacs: a self-consistent stochastic acceleration model" (Sciaccaluga et al., 2022)
• "An emerging population of BL Lacs with extreme properties: towards a class of EBL and cosmic magnetic field probes?" (Bonnoli et al., 2015)
• "Extreme BL Lacs: probes for cosmology and UHECR candidates" (Tavecchio et al., 2015)