EPISODE II: Variability in the CO and H₂O rovibrational absorption lines in a periodically variable protostar EC 53

We present two-epoch JWST NIRSpec and MIRI observations of the young protostar EC 53 (V371 Ser), a periodically variable source with well-characterized quiescent and burst phases. The spectra in both epochs show absorption in the CO overtone ($\sim$2.3 $\mu$m) and fundamental ($\sim$4.6 $\mu$m) bands and the H$_2$O stretching ($\sim$2.7 $\mu$m) and bending ($\sim$6.0 $\mu$m) modes. We also obtained high-resolution ($R\approx45{,}000$) IGRINS spectra during the burst to constrain the CO overtone line profiles. LTE slab modeling yields gas temperatures of $\sim$1800 K (CO overtone) and $\sim$1200 K (CO fundamental), consistent with the overtone tracing hotter gas at smaller radii. The H$_2$O stretching-mode absorption shows no compelling evidence for variability, and the current JWST CO overtone data do not provide a robust constraint on overtone variability. In contrast, the CO fundamental and H$_2$O bending-mode features weaken by a factor of $\sim$2 during the burst, which is most naturally explained by continuum changes rather than large variations in absorbing gas. To quantify continuum dilution, we introduce a ``relative veiling'' that treats the quiescent spectrum as an internal reference and measures the change in the continuum excess between the two epochs. This formalism yields burst-to-quiescent hot-continuum ratios of $2.9\pm0.2$ for the CO overtone and $1.71\pm0.11$ for the CO fundamental. Using a viscous-disk prescription, these imply representative accretion-rate ratios of $\sim$3.6 and $\sim$2.0, respectively. The differing ratios suggest that inner-disk regions traced at different temperatures, and thus radii, respond differently across the burst cycle, consistent with episodic mass buildup in the inner disk during quiescence followed by more efficient transport through the innermost disk onto the protostar during the burst.