What fallacy is represented by using an emotional argument unrelated to the actual topic being discussed?

The fallacy represented by using an emotional argument that is unrelated to the actual topic being discussed is best identified as a Non Sequitur. This fallacy occurs when the conclusion does not logically follow from the premises or when there is a disconnect between the argument's emotional appeal and the topic at hand.

In the context of a debate or discussion, invoking emotions that are not directly linked to the argument can derail the conversation and create confusion about the actual issues being addressed. For example, bringing up a poignant personal story or irrelevant emotional scenario in response to a factual claim does not provide support for or relevant evidence to the argument, thus exemplifying a Non Sequitur. This fallacy underlines the importance of maintaining a logical connection between statements to ensure clarity and relevance in discourse.