Context. It has recently been shown that the infrared (IR) emission of Cepheids, constant over the pulsation cycle, might be due to a pulsating shell of ionized gas with a radius of about 15% of that of the star radius, which could be attributed to the chromospheric activity of Cepheids. Aims. The aim of this paper is to investigate the dynamical structure of the chromosphere of Cepheids along the pulsation cycle and to quantify its size. Methods. We present H α and calcium near-infrared triplet (Ca IR) profile variations using high-resolution spectroscopy with the UVES spectrograph of a sample of 24 Cepheids with a good period coverage from ≈3 to 60 days. After a qualitative analysis of the spectral line profiles, we quantified the Van Hoof effect (velocity gradient between the H α and Ca IR) as a function of the period of the Cepheids. We then used the Schwarzschild mechanism (a line doubling due to a shock wave) to quantify the size of the chromosphere. Results. We find a significant Van Hoof effect for Cepheids with a period larger than P = 10 days. In particular, H α lines are delayed with a velocity gradient up to Δ v ≈ 30 km s −1 compared to Ca IR. By studying the shocks, we find that the size of the chromosphere of long-period Cepheids is of at least ≈50% of the stellar radius, which is consistent at first order with the size of the shell made of ionized gas previously found from the analysis of IR excess. Last, for most of the long-period Cepheids in the sample, we report a motionless absorption feature in the H α line that we attribute to a circumstellar envelope that surrounds the chromosphere. Conclusions. Analyzing the Ca IR lines of Cepheids is of importance to potentially unbias the period-luminosity relation from their IR excess, particularly in the context of forthcoming observations of radial velocity measurements from the Radial Velocity Spectrometer on board Gaia, which could be sensitive to their chromosphere.
