Dynamic Accretion Disk-Corona Connection and Broad Fe K$\alpha$ Variability in Mrk 766 Revealed by Time-Resolved High Resolution X-Ray Spectroscopic Analysis

We present a multi-epoch, primarily X-ray study of the narrow-line Seyfert 1 (NLSy1) galaxy Mrk~766 by combining archival $\mathit{\text{XMM-Newton}}$ observations spanning nearly two decades together with a $\mathit{\text{XRISM}}$ observation obtained during its Performance Verification Phase. We analyzed the absorption and emission features in the soft X-ray spectra from RGS and EPIC-pn data, revealing a stratified multi-phase potentially ionised absorber with a column density varying at a timescale of $\sim$1 day. The covering fraction shows positive correlation with the continuum flux, however with significant intrinsic scatter, between the epochs. Mrk~766 exhibits a multi-component Fe,K$\alpha$ emission line as revealed by fits to the $\mathit{\text{XRISM}}$ data. A quasi-phenomenological model comprising a torus and a broad $\mathit{\text{diskline}}$ component distinguishes the two components and constrains the inner radius of the potential broad line emitting disk substructure between $R_{in}=40-60r_{\mathrm{g}}$. Analysis of multiple epochs of the Fe K$\alpha$ complex across $\mathit{\text{XMM-Newton}}$ observations reveals that the broad component tracks the continuum flux closely and effectively reflects the trend with respect to the continuum. The narrow component is consistent with a distant emitter, potentially the torus. Quasi-simultaneous monitoring with $\mathit{\text{Swift}}$-XRT and UVOT further indicates UV emission lagging the X-rays by $5.9_{-5.7}^{+4.1}$ hours, consistent with disk reprocessing of coronal X-ray fluctuations, and corresponds to a light travel distance of up to ${10}^3{r}_{\mathrm{g}}$. Overall, our analysis maps the extent of the dynamically evolving absorber, the iron line emitter, and the accretion disk in this highly accreting NLSy1 system.