tokens: d for the longitudinal field, veiling, and radial velocity (RV), respectively. Modulation is also obvious in Ca ii IRT and He i emission (with periods of 5.82 ± 0.16 d and 5.65 ± 0.08 d, respectively) and longitudinal fields from Ca ii IRT emission (with period of 5.50 ± 0.15 d). Since all periods we derive are quite consistent (within 1.5σ) with the rotation period used to phase our data (5.70 d, see Table 1 ), we report no evidence for differential rotation at the surface of LkCa 15. 4 TOMOGRAPHIC MODELLING OF LkCa 15 We use tomographic imaging, and more specifically Zeeman–Doppler Imaging (ZDI), to simultaneously reconstruct the large-scale magnetic field at the surface of LkCa 15, and the distributions of photospheric brightness and accretion-induced excess emission in Ca ii IRT lines. To achieve this we proceed as in previous studies (e.g. Donati et al. 2011 , 2012 ) where the imaging method was outlined. We thus only recall the main steps in this paper. ZDI iteratively looks for a set of images with lowest information content that fits the data at a given reduced chi-square level, starting from blank images containing no information. Whereas photospheric brightness (with cool spots only) and accretion-induced excess emission (with bright features only) are directly described through their distributions at the surface of the star, the large-scale magnetic field, decomposed into its poloidal and toroidal components, is expressed as a set of spherical harmonics (SH, Donati et al. 2006 ). We assume the field is dominated by odd SH modes (as in, e.g. Donati et al. 2011 ) to ensure that accretion occurs mostly towards the polar regions. The local Stokes I and V profiles of both photospheric lines and Ca ii emission are computed using Unno-Rachkovsky’s analytical solution to the polarized radiative transfer equations, taking into account the local values of the modelled distributions (i.e. the brightness map for photospheric lines, the accretion map for Ca ii emission, and the magnetic map for both sets of lines). Local profiles are then integrated over the visible hemisphere to obtain the synthetic profiles of the rotating star at each observed phase. Our model is able to convincingly reproduce most observed profile distortions and Zeeman signatures, as shown in Fig. 2 . We note that the sharp increase and decrease of the longitudinal field of Ca ii IRT lines are better matched for an inclination angle i of 70° than of 50° (the angle measured for the outer accretion disc, Thalmann et al. 2014 , with no reliable inclination estimate for the inner disc). We also obtain that the data are best fit for km s −1 and for an average radial velocity of LkCa 15 with respect to the Sun of km s −1 . Figure 2. Observed (thick black line) and modelled (thin red line) LSD Stokes I and V profiles of the photospheric lines (lef-handt panels) and of the emission core of IRT lines (right-hand panels) of LkCa 15. Rotation cycles and 3σ error bars (for Stokes V
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