A data tree is a tree whose every node carries a label from a finite alphabet and a datum from some infinite domain. We introduce a new model of automata over unranked data trees with a decidable emptiness problem. It is essentially a bottom-up alternating automaton with one register, enriched with epsilon-transitions that perform tests on the data values of the subtree. We show that it captures the expressive power of the vertical fragment of XPath -- containing the child, descendant, parent and ancestor axes -- obtaining thus a decision procedure for its satisfiability problem.