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Context. Bright heads of penumbral filaments, penumbral grains (PGs), showapparent horizontal motions inwards, towards the umbra, or outwards, away fromthe umbra.  Aims. We aim to prove statistically whether the direction of PGs' apparentmotion is related to the inclination of the surrounding magnetic field.  Methods. We use spectropolarimetric observations of five sunspot penumbrae tocompare magnetic inclinations inside PGs with those in their surroundings. Thedata are taken by three observatories: Hinode satellite, Swedish SolarTelescope, and GREGOR solar telescope. The direction of PGs' motion isdetermined by feature tracking. The atmospheric conditions in PGs and theirsurroundings, including the magnetic field information, are retrieved by meansof height-stratified spectropolarimetric inversions.  Results. On a sample of 444 inward- and 269 outward-moving PGs we show that43% of the inward-moving PGs have magnetic inclination larger by $8^\circ \pm4^\circ$ than the inclination in their surroundings and 51% of theoutward-moving PGs have the inclination smaller by $13^\circ \pm 7^\circ$ thanthe surrounding one. The opposite relation of inclinations is observed at onlyone-fifth of the inward- and outward-moving PGs.  Conclusions. Rising hot plasma in PGs surrounded by a less inclined magneticfield may adapt its trajectory to be more vertical, causing an inward apparentmotion of PGs. Oppositely, it may be dragged by a more horizontal surroundingmagnetic field such that an outward apparent motion is observed.

Relation between magnetic field inclination and apparent motion of penumbral grains