Absolute velocity measurements in sunspot umbrae

Context. In sunspot umbrae, convection is largely suppressed by the strong magnetic field. Previous measurements reported on negligible convective flows in umbral cores. Based on this, numerous studies have taken the umbra as zero reference to calculate Doppler velocities of the ambient active region. Aims. We aim to clarify the amount of convective motion in the darkest part of umbrae, by directly measuring Doppler velocities with an unprecedented accuracy and precision. Methods. We performed spectroscopic observations of sunspot umbrae with the Laser Absolute Reference Spectrograph (LARS) at the German Vacuum Tower Telescope. A laser frequency comb enabled the calibration of the high-resolution spectrograph and absolute wavelength positions for 13 observation sequences. A thorough spectral calibration, including the measurement of the reference wavelength, yielded Doppler shifts of the spectral line Ti I 5713.9 Å with an uncertainty of around 5 m s−1. A bisector analysis gave the depth-dependent line asymmetry. Results. The measured Doppler shifts are a composition of umbral convection and magneto-acoustic waves. For the analysis of convective shifts, we temporally averaged each sequence to reduce the superimposed wave signal. Compared to convective blueshifts of up to −350 m s−1 in the quiet Sun, sunspot umbrae yield strongly reduced convective blueshifts around −30 m s−1. We find that the velocity in a sunspot umbra correlates significantly with the magnetic field strength, but also with the umbral temperature defining the depth of the Ti I 5713.9 Å line. The vertical upward motion decreases with increasing field strength. Extrapolating the linear approximation to zero magnetic field reproduces the measured quiet Sun blueshift. In the same manner, we find that the convective blueshift decreases as a function of increasing line depth. Conclusions. Simply taking the sunspot umbra as a zero velocity reference for the calculation of photospheric Dopplergrams can imply a systematic velocity error reaching 100 m s−1, or more. Setting up a relationship between vertical velocities and magnetic field strength provides a remedy for solar spectropolarimetry. We propose a novel approach of substantially increasing the accuracy of the Doppler velocities of a sunspot region by including the magnetic field information to define the umbral reference velocity