Quenching pathways in the green valley at low redshift: confronting SDSS AGN hosts with IllustrisTNG and EAGLE

We compare low-redshift ($z<0.1$) BPT-selected pure optical AGN hosts in SDSS DR7 to colour-selected "green-valley" analogue central galaxies in IllustrisTNG100 and EAGLE Ref-L0100N1504. To reduce cross-dataset systematics, we define the green valley internally using $(g-r)$ percentiles: for galaxies with $\log_{10}(M_\star/M_\odot)>10$, we select the 75th-95th percentiles (SDSS observed-frame fibre colours; simulations rest-frame synthetic colours within 30 kpc). SDSS hosts are linked to the MPA-JHU catalogue for stellar masses and aperture-corrected total SFRs. TNG green-valley centrals are almost entirely quenched, with a sharp pile-up at the imposed SFR floor and median $\log_{10}\mathrm{sSFR}\simeq-14.85$ ($\sim$3.5 dex below SDSS). EAGLE instead produces a broad, continuous distribution with median $\log_{10}\mathrm{sSFR}\simeq-11.71$ and substantial overlap with SDSS, robust to varying the lower percentile between 60 and 90. At fixed mass, TNG yields higher green-valley occupancy fractions (reaching $\gtrsim60$ per cent near $M_\star\sim10^{11}M_\odot$) than EAGLE (20-40 per cent). A simple forward model of nebular line ratios places EAGLE analogues across the star-forming and composite loci in the BPT plane, while TNG analogues concentrate in a LINER-like, low-sSFR regime. We infer that TNG's kinetic mode drives an efficient, near-binary shutdown of star formation, whereas EAGLE's stochastic thermal feedback supports a slower decline more consistent with local AGN hosts. All catalogues and analysis scripts are publicly released.