Context : The dynamical structure of the atmosphere of Cepheids has been well studied in the optical .
Several authors have found very interesting spectral features in the J band , but little data have been secured beyond 1.6 \mu m. However , such observations can probe different radial velocities and line asymmetry regimes , and are able to provide crucial insights into stellar physics .

Aims : Our goal was to investigate the infrared line-forming region in the K-band domain , and its impact on the projection factor and the k -term of Cepheids .

Methods : We secured CRIRES observations for the long-period Cepheid l Car , with a focus on the unblended spectral line NaI 2 208.969 nm .
We measured the corresponding radial velocities ( by using the first moment method ) and the line asymmetries ( by using the bi-Gaussian method ) .
These quantities are compared to the HARPS visible spectra we previously obtained on l Car .

Results : The optical and infrared radial velocity curves show the same amplitude ( only about 3 % of difference ) , with a slight radial velocity shift of about 0.5 \pm 0.3 \mbox { km s } ^ { -1 } between the two curves .
Around the minimum radius ( phase \simeq 0.9 ) the visible radial velocity curve is found in advance compared to the infrared one ( phase lag ) , which is consistent with an infrared line forming higher in the atmosphere ( compared to the visible line ) and with a compression wave moving from the bottom to the top of the atmosphere during maximum outward velocity .
The asymmetry of the K-band line is also found to be significantly different from that of the optical line .

Conclusions :