pathos

“... an appeal to the audience’s emotions, and the terms pathetic and empathy are derived from it. It can be in the form of metaphor, simile, a passionate delivery, or even a simple claim that a matter is unjust. Pathos can be particularly powerful if used well, but most speeches do not solely rely on pathos. Pathos is most effective when the author or speaker demonstrates agreement with an underlying value of the reader or listener. ...” (Wikipedia)

see emotional appeal