Aims. To understand the morphology of the chromosphere in sunspot umbra. We investigate if the horizontal structures observed in the spectral core of the Ca II H line are ephemeral visuals caused by the shock dynamics of more stable structures, and examine their relationship with observables in the H-alpha line. Methods. Filtergrams in the core of the Ca II H and H-alpha lines as observed with the Swedish 1-m Solar Telescope are employed. We utilise a technique that creates composite images and tracks the flash propagation horizontally. Results. We find 0"15 wide horizontal structures, in all of the three target sunspots, for every flash where the seeing was moderate to good. Discrete dark structures are identified that are stable for at least two umbral flashes, as well as systems of structures that live for up to 24 minutes. We find cases of extremely extended structures with similar stability, with one such structure showing an extent of 5". Some of these structures have a correspondence in H-alpha but we were unable to find a one to one correspondence for every occurrence. If the dark streaks are formed at the same heights as umbral flashes then there are systems of structures with strong departures from the vertical for all three analysed sunspots. Conclusions. Long-lived Ca II H filamentary horizontal structures are a common and likely ever-present feature in the umbra of sunspots. If the magnetic field in the chromosphere of the umbra is indeed aligned with the structures, then the present theoretical understanding of the typical umbra needs to be revisited.

Accepted to Astronomy and Astrophysics. Online material (Fig3.mov and Fig4.mov) will be available at A&A