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This work reports the discovery of cycle-to-cycle modulated spectral line andatmospheric velocity gradient variability in long-period Cepheids based on 925high-resolution optical spectra of $\ell$ Carinae (P $\sim$ 35.5 d) recordedduring three heavy duty-cycle monitoring campaigns (in 2014, 2015, and 2016).Spectral line variability is investigated via cross-correlation functions(CCFs) computed using three sets of spectral lines (weak, solar, strong). Ametallic line velocity gradient, {\delta}v$_r$ (t), is computed as thedifference between weak and strong-line RVs. CCF shape indicators BIS(asymmetry), FWHM, and depth all exhibit clear phase-dependent variabilitypatterns that differ from one pulsation cycle to the next. Weak-line CCFsexhibit these effects more clearly than strong-line CCFs. BIS exhibits the mostpeculiar modulated variability and can be used to identify the presence ofcycle-to-cycle modulated line profile variations. {\delta}v$_r$ (t) clearlyexhibits cycle-to-cycle differences that correlate very closely with modulatedBIS variability, suggesting perturbations of the atmospheric velocity field asthe cause for modulated spectral line variability. These perturbations are mostsignificant during contraction and are not in phase with the pulsation,transmitting information between consecutive pulsation cycles. This work showsRV curve modulation to be a consequence of atmospheric velocity gradientperturbations. Possible origins of these perturbations and their impact onCepheid RV measurements as well as the projection factor used inBaade-Wesselink-type distance determinations are discussed.

Discovery of Cycle-to-cycle Modulated Spectral Line Variability and Velocity Gradients in Long-period Cepheids