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Chromospheric umbral oscillations produce periodic brightenings in the coreof some spectral lines, known as umbral flashes. They are also accompanied byfluctuations in velocity, temperature, and, according to several recent works,magnetic field. In this study, we aim to ascertain the accuracy of the magneticfield determined from inversions of the Ca II 8542 \AA\ line. We have developednumerical simulations of wave propagation in a sunspot umbra. Synthetic Stokesprofiles emerging from the simulated atmosphere were computed and then invertedusing the NICOLE code. The atmospheres inferred from the inversions have beencompared with the original parameters from the simulations. Our results showthat the inferred chromospheric fluctuations in velocity and temperature matchthe known oscillations from the numerical simulation. In contrast, the verticalmagnetic field obtained from the inversions exhibits an oscillatory patternwith a $\sim$300 G peak-to-peak amplitude which is absent in the simulation. Wehave assessed the error in the inferred parameters by performing numerousinversions with slightly different configurations of the same Stokes profiles.We find that when the atmosphere is approximately at rest, the inversion tendsto favor solutions that underestimate the vertical magnetic field strength. Onthe contrary, during umbral flashes, the values inferred from most of theinversions are concentrated at stronger fields than those from the simulation.Our analysis provides a quantification of the errors associated with theinversions of the Ca II 8542 \AA\ line and suggests caution with theinterpretation of the inferred magnetic field fluctuations.

Limitations of the Ca II 8542 \AA\ line for the determination of magnetic field oscillations