CosmoDRAGoN III: Shaping the Afterlife -- How Progenitors and Environments Sculpt Radio Galaxy Remnants

Identifying remnant radio-loud active galactic nuclei (AGNs) is challenging due to their diverse morphological and spectral characteristics. Using three-dimensional hydrodynamic simulations of 15 radio galaxies, we investigate how the spectral evolution of remnants depends on progenitor power, active lifetime, environment, and underlying dynamics. The simulations span low-density group and high-density cluster environments re-gridded from smooth-particle-hydrodynamic cosmological simulations. The resulting remnants exhibit a wide range of morphologies, from amorphous structures to double-lobed forms. We find that jet power correlates with the spectral slope. As the remnant lobes evolve, we find surface brightness depends strongly on environment: group remnants are systematically dimmer and more amorphous than cluster remnants, highlighting a potential observational bias against these low-surface-brightness sources. In our models, we estimate that the peak surface brightness of a low-redshift, 50 Myr-old remnant from a low-power progenitor in a 10^{13} M_sun group environment should be routinely detectable at the 3σ level with LOFAR, although 20-30% of the emission would remain undetectable within a reasonable integration time. We find young remnants exhibit low-frequency (150-1400 MHz) spectral indices that overlap with active sources, and follow a consistent and established spectral-evolution sequence: significant curvature (α_{1400}^{6000} - α_{150}^{1400} > 0.5) develops before an ultra-steep low-frequency index (α_{150}^{1400} > 1.2). The results presented in this work are intended as a reference point for current and upcoming low-frequency studies of radio remnants.