  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. To clarify the
amount of convective motion in the darkest part of umbrae, we directly measured
Doppler velocities with an unprecedented accuracy and precision. 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. A thorough spectral calibration, including the
measurement of the reference wavelength, yielded Doppler shifts of the spectral
line Ti i 5713.9 {\AA} with an uncertainty of around 5 m s-1. The measured
Doppler shifts are a composition of umbral convection and magneto-acoustic
waves. For the analysis of convective shifts, we temporally average 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 a
strongly reduced convective blueshifts around -30 m s-1. {W}e 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
titanium line. The vertical upward motion decreases with increasing field
strength. Extrapolating the linear approximation to zero magnetic field
reproduces the measured quiet Sun blueshift. Simply taking the sunspot umbra as
a zero velocity reference for the calculation of photospheric Dopplergrams can
imply a systematic velocity error.
