Rises in suicide rates following media reports of the deaths by suicide of public figures are a well-documented phenomenon. However, it remains unclear why, or by what exact mechanism, celebrity suicides act to increase suicidal risk in the wider public due to the lack of data showing how the public understands and reacts to the suicide of well-known figures. This study used a supervised machine learning approach to investigate the emotional content of almost 1 million messages sent on Twitter related to the suicides of 18 prominent individuals in Japan between 2010 and 2014. The results revealed that different demographic characteristics of the deceased person (age, gender, and occupation) resulted in significant differences in emotional response; notably that the suicides of younger people, of women and of people in entertainment careers created more emotional responses (measured as a ratio of emotionally-coded tweets within the overall volume of tweets for each case) than for older people, men, and those in other careers. Moreover, certain types of emotional response were shown to correlate to subsequent rises in the national suicide counts, with "surprised" reactions being positively correlated with the suicide counts, while a high proportion of polite messages of condolence were negatively correlated. The study demonstrates the importance of, and describes a methodology for, considering the content of social media messages, not just their volume, in research into the mechanism by which these widely-reported deaths increase suicide risk in the broader public.