Characterising the surface magnetic fields of T Tauri stars with high-resolution near-infrared spectroscopy

Aims. In this paper, we aim to characterise the surface magnetic fields of a sample of eight T Tauri stars from high-resolution near-infrared spectroscopy. Some stars in our sample are known to be magnetic from previous spectroscopic or spectropolarimetric studies. Our goals are firstly to apply Zeeman broadening modelling to T Tauri stars with high-resolution data, secondly to expand the sample of stars with measured surface magnetic field strengths, thirdly to investigate possible rotational or long-term magnetic variability by comparing spectral time series of given targets, and fourthly to compare the magnetic field modulus < B > tracing small-scale magnetic fields to those of large-scale magnetic fields derived by Stokes V Zeeman Doppler Imaging (ZDI) studies. Methods. We modelled the Zeeman broadening of magnetically sensitive spectral lines in the near-infrared K-band from high-resolution spectra by using magnetic spectrum synthesis based on realistic model atmospheres and by using different descriptions of the surface magnetic field. We developped a Bayesian framework that selects the complexity of the magnetic field prescription based on the information contained in the data. Results. We obtain individual magnetic field measurements for each star in our sample using four different models. We find that the Bayesian Model 4 performs best in the range of magnetic fields measured on the sample (from 1.5 kG to 4.4 kG). We do not detect a strong rotational variation of < B > with a mean peak-to-peak variation of 0.3 kG. Our confidence intervals are of the same order of magnitude, which suggests that the Zeeman broadening is produced by a small-scale magnetic field homogeneously distributed over stellar surfaces. A comparison of our results with mean large-scale magnetic field measurements from Stokes V ZDI show different fractions of mean field strength being recovered, from 25-42% for relatively simple poloidal axisymmetric field topologies to 2-11% for more complex fields.