The magnetic sensitivity of the Ca II H and K lines

Context. The solar chromosphere is a transition layer between the cool, dense photosphere and the hot, rarefied corona. This boundary region plays a key role in regulating energy transport and structuring the magnetic field throughout the solar atmosphere. Understanding its thermodynamic and magnetic properties is essential to model and interpret solar phenomena. Aims. This study investigates the theoretical properties and diagnostic potential of the polarisation signals in the Ca <ns0:sc>II</ns0:sc> H & K lines, with particular emphasis on their capability to probe magnetic fields in the upper chromosphere with the CHROMIS instrument at the Swedish 1-m solar telescope. Methods. We combine semi-empirical atmospheric models with high-resolution solar observations to model the formation of the Ca <ns0:sc>II</ns0:sc> H & K lines using non-local thermodynamic equilibrium radiative transfer calculations. The sensitivity of the lines to the magnetic field is examined through response functions and synthetic inversions, enabling an assessment of their diagnostic performance under realistic chromospheric conditions. Results. For typical chromospheric field strengths, the linear polarisation of the Ca <ns0:sc>II</ns0:sc> H & K lines is less than 1.7%, below the expected detection threshold of CHROMIS. However, their circular polarisation reaches more than 10% in strong-field regions, which is detectable by CHROMIS. Both lines are sensitive to magnetic fields in the upper chromosphere, with the K line forming slightly higher due to its larger opacity, and the H line exhibiting a somewhat stronger Zeeman sensitivity owing to its higher effective Landé factor and longer wavelength. Using the weak-field approximation, the line of sight magnetic field can be reliably inferred around log ξ ≈ −4. These results confirm that the Ca <ns0:sc>II</ns0:sc> H & K lines constitute powerful diagnostics for studying the magnetic structure of the upper solar chromosphere.