Science communication is changing. It is increasingly directed not only at peers but at the public in general. Accordingly, understanding the circumstances under which audience members engage with scientific content is crucial to improving science communication. In this article, we investigate the role of affect on audience engagement with a modern form of science communication: TED talks. We examined how affect valence---a net positive or negative affect---and density---the proportion of affective words---are associated with a talk's popularity---reflecting views and likes---and polarity---reflecting dislikes and comments. We found that the valence of TED talks was associated with both popularity and polarity, with positive valence being linked to higher talk popularity and lower talk polarity. Density, on the other hand, was only associated with popularity, with higher affective density being linked to higher popularity---even more so than valence---but not polarity. Moreover, we observed that the association between affect and engagement was partially moderated by talk topic. Specifically, whereas higher density was related to higher popularity across most topics, valence seemed to particularly impact the popularity and polarity of TED talks on social topics, which regularly discuss polarizing issues such as race or political conflicts. We discuss implications of our findings for increasing the effectiveness of science communication.