Expected steepening of synchrotron spectra as particles move from the cluster core in the radial direction from 20 to 140 kpc. All spectra are normalized to unity at ν = 5 × 10⁷ GHz. The magnetic energy density is assumed to follow the ICM pressure profile P_t(r), i.e., B_f²/8π = P_t(r). For these simulations, we adopted a simple power law pressure profile P_t ≈ 2 × 10⁻¹⁰(r/kpc)⁻¹ erg cm⁻³, derived from X-ray observation of the NEST200047 group (Majumder et al. 2025). The solid back curve (marked A) shows the synchrotron spectrum at the initial position at r₁ = 20 kpc. It has a low-frequency slope α₀ = −0.5 and is “aged” in the 15 μG field for 3 × 10⁷ yr so that a break develops in the spectrum. The spectra marked B and C show the evolved spectra at the final position at r₂ = 140 kpc. These spectra represent two extreme limits. In particular, for C, the electrons are moving “in a bubble” from r₁ to r₂ with the velocity v = 500 km s⁻¹ (just below the sound speed in the group ICM c_s ∼ 700 km s⁻¹) and suffer from the adiabatic and radiative losses. In addition to the evolution of the particle spectrum, the magnetic field is lower at r₂. All these effects combined lead to a very steep spectrum at the final position. In contrast, for the “B” spectrum, we assume that electrons quickly propagate “along a static filament” and do not suffer from any losses. The only reason why the spectrum B is steeper than A is that the magnetic field is lower at the final position; hence, a lower critical frequency, ν_c ∝ B. For each curve, the position of the break frequency (defined here as a frequency where the spectral slope is α = α₀ − 1) is shown with a small vertical magenta bar. This plot illustrates that if the initial spectrum has a break around 1 GHz, and no re-acceleration is present, any “subsonic” regime of propagation (blue lines) will result in a very steep spectrum at 100 MHz. If “fast-track” routes are available for a fraction of electrons, this might reduce the apparent steepening dramatically.