The 2MIG isolated AGNs -- 4. Linking hot-dust reverberation to spectroscopically predicted BLR scales in IC~5287 and Mrk~845

Abstract

We investigate the relation between directly measured hot-dust reverberation scales and spectroscopically predicted broad-line region (BLR) scales in the isolated Seyfert galaxies IC~5287 and Mrk~845 (MCG+09-25-022), combining ZTF optical light curves, WISE/NEOWISE monitoring, and archival SDSS spectroscopy. Both nuclei show BWB optical variability, RWB MIR behaviour, and delayed MIR responses consistent with circumnuclear dust reprocessing. For IC~5287, interpolated cross-correlation function analysis with flux-randomisation/random-subset-selection uncertainties yields a rest-frame W1 delay of $106_{-39}^{+24}$~d, corresponding to $0.089_{-0.033}^{+0.020}$~pc. The median W2 response occurs at a longer delay, but the lag distributions overlap substantially. The SDSS decomposition reveals strong host dilution and BLR reddening, $E(B-V)_{\rm BLR}=0.612_{-0.066}^{+0.067}$~mag. Applying the same colour excess to the AGN continuum as an illustrative scenario increases the predicted H$β$ BLR lag from approximately 4.8 to 11.7~d and reduces the dust-to-predicted-BLR radius ratios from approximately 20--25 to 8--10. For Mrk~845, transfer-function modelling gives a rest-frame W1 delay of $157_{-8}^{+19}$~d, corresponding to $0.132_{-0.007}^{+0.016}$~pc. Its W2 response occurs at a longer delay, with $P(τ_{\rm W2}>τ_{\rm W1})=0.963$, supporting wavelength-dependent hot-dust structure. The SDSS spectrum shows more moderate BLR reddening, $E(B-V)_{\rm BLR}=0.197_{-0.039}^{+0.046}$~mag. The comparatively large dust-to-predicted-BLR radius ratios in both galaxies therefore primarily reflect the spectroscopically predicted BLR scales. These results emphasise the need to distinguish directly measured dust reverberation radii from BLR radii inferred from single-epoch spectroscopy when interpreting the BLR--dust hierarchy.