Odd radio circle J1555+2726: Observational evidence for shock re-acceleration of fossil plasma

The gist The observed features suggest that a mixture of electrons with different spectra coexist within ORC4 volume, likely associated with shock re-acceleration of a fossil relativistic reservoir.

Observational Constraints and Data Analysis

The study utilized Low Frequency ARray (LOFAR), upgraded Giant Metrewave Radio Telescope (uGMRT), and MeerKAT radio data across the 50-1284 MHz frequency range to obtain high-resolution images and spectral index maps The brightness contrast between the ring and the filling emission becomes progressively smoother from higher to lower frequencies The integrated spectrum of slope α = 1.06 ± 0.03 was measured, with a radio power of P150 = (5.4 ± 0.5) × 1025 W Hz−1 at 150 MHz However, the inferred spectral index is flatter than previously reported by De Gasperin et al. (2026).

Morphological Characteristics and Frequency Dependence

The morphology of ORC4 is dependent on both the resolution and the observing frequency The main ring is clear at high frequencies, while it becomes progressively less dominant at lower frequencies, where the surface brightness contrast compared to the filling emission is smoother. The 3D geometry of ORC4 is tentatively reconstructed as ellipsoidal (Fig. 8) In this scenario, the main ring traces the equatorial plane of the ellipsoid and is interpreted as the (projected) location of an expanding shock front.

Spectral Distribution and Curvature

The high-resolution spectral index map (143-1260 MHz) reveals that the spectral index flattens outwards along the ring radius, with α ∼ 0.5 at the outermost regions The analysis of the 143-675 MHz and 675-1260 MHz profiles reveals a coherent, but complex, picture for ORC4 where the bulk of the emission is characterised by a moderately convex spectrum, with an average value of SC ∼ −0.2 between radii of ∼ 75 and ∼ 160 kpc. This negative curvature is not predicted by standard DSA and ageing models, as shown by a direct comparison with simulations reported in Appendix C.

Shock Re-acceleration Scenario

The observed spectral properties cannot be explained by shock acceleration of thermal particles and standard ageing The most likely source of acceleration is a shock wave, whose passage is supported by the high concentration of [O II] detected on galactic scales The work provides observational indications for the presence of a pre-existing population of fossil relativistic electrons. Specifically, re-accelerated low-energy fossil electrons are less subjected to radiative losses, thus smoothing brightness and spectral gradients This mixture of re-accelerated fossil electrons with different spectra is broadly in agreement with the spectro-morphological features of the target.

Shock Strength and Physical Interpretation

The Mach number M can be related to spectral indices by the equation M2 = 2αinj + 3/2αinj − 1 = α + 1/α − 1 For ORC4, measurements of α ∼ 1 and αinj ∼ 0.5 formally correspond to an extremely strong shock (M → ∞). However, the paper notes that the observed distribution of M values includes a strong-shock regime. The study suggests that "higher-energy re-accelerated electrons dominate the emission of the ring (close to shock front) at higher frequencies, while lower-energy electrons are diffuse across the whole volume and dominate the emission at lower frequencies".

Conclusion on Formation Scenarios

The study concludes that an expanding shock is the most likely explanation for the overall observed spectral trend Classical DSA followed by standard ageing models fail to predict the high P150 and negative SC of ORC4 Therefore, we propose a scenario in which fossil relativistic electrons have been reaccelerated by the shock passage. The variety of ORC morphologies would be explained primarily in terms of the inclination angle and the combination of resolution and sensitivity required to detect and resolve both the primary and secondary ring. These observations provide a fundamental piece of the puzzle to reconstruct the origin of ORC4. The large amount of data collected for ORC4 revealed some similarities with the archetypical ORC1.

How it works

The analysis involved measuring flux densities within a circular annulus centered on source G of inner and outer radii of 10'' and 1', thus filtering out contamination from the AGN and its surrounding in a circle of diameter ∼ 115 kpc. The spectral index is computed pixel-by-pixel as α = −ln (S 1) − ln (S 2) / ln (ν 1) − ln (ν 2) ± σ ∆S 1/σ S 1!2 + ∆S 2/σ S 2!2. The spectral curvature is defined as SC = (α143-1260 − α675-143) ± q (∆α1260-675) 2 + (∆α675-143) 2. The results show that the spectral index map reveals fine details and that the spectrum flattens outwards along the ring radius, with α ∼ 0.5 at the outermost regions.

Summary of Findings

The study determined that the morphology is dependent on the resolution (Figs. 2, A.1) and the morphology is also dependent on the observing frequency (Figs. 2, 3). The integrated spectrum at 50-1284 MHz is well described by a power law with slope α = 1.06±0.03 The radio power is P150 = (5.4 ± 0.5) × 1025 W Hz−1 at 150 MHz. The high-resolution spectral distribution is characterized by a rapid steepening of the spectral index within the inner ∼ 75 kpc (up to α ∼ 1.5), followed by a progressive flattening at larger radii. The observed distributions provide on average a negative spectral curvature (Figs. 6, 7) of SC ∼ −0.2, implying that the spectrum flattens with increasing frequency.

Implications for Particle Acceleration

The paper strongly supports the possibility that re-accelerated electrons at different energies coexist within the target volume This coexistence is suggested by the negative curvature and peculiar parabolic path in the RCCD, which are not predicted by standard ageing models. The fossil population of electrons is likely the key ingredient for explaining ORC4's radio power, as "higher-energy re-accelerated electrons dominate the emission of the ring (close to shock front) at higher frequencies, while lower-energy electrons are diffuse across the whole volume and dominate the emission at lower frequencies". The data are consistent with a distribution of Mach numbers that includes a strong-shock regime.

Future Directions

Independent constraints on M are important to better test these scenarios, and Optical and X-ray data may constrain the environment and shock Mach number.

1. Improved physical modeling of non-thermal emission in shock environments: The AI system can now incorporate a mixture of electrons with different spectra coexist within ORC4 volume, allowing it to distinguish between high-energy electrons reaccelerated at the shock front and lower-energy reaccelerated electrons uniformly distributed across the source volume.

2. Enhanced morphological classification based on frequency dependence: The system can accurately classify ORC morphologies by analyzing how the brightness contrast between the ring and the filling emission becomes progressively smoother from higher to lower frequencies, enabling better distinction between genuine ORCs and sources resembling them.

3. Constraint of shock physics using spectral curvature analysis: The AI system can evaluate whether observed spectral shapes are consistent with standard models by calculating the spectral curvature, noting that "SC > 0 indicates a standard concave spectrum (steepening at high frequencies) and identifying the observed negative curvature" as evidence against classical DSA models.

4. Predictive modeling of fossil relativistic reservoir effects: The AI can predict the influence of re-accelerated fossil electrons on spectral gradients, specifically recognizing that re-accelerated low-energy fossil electrons are less subjected to radiative losses, thus smoothing brightness and spectral gradients and dominate at low frequencies.

5. Mach number estimation refinement: The system can refine shock strength estimates by utilizing high-frequency data to determine the injection index alphainj, noting that a more reliable measurement of alphainj should be obtained from high-frequency data only to avoid biases from lower frequency components.