Do chess players have Q scores?

For those unfamiliar with the concept (or familiar with the concept, but not the name) a "Q Score" measure both the familiarity of a personality and their overall appeal. The higher the score, the more "bankable" the personality.
For the entertainment and advertising industry, the Q score is an important metric, and it has me wondering about potential Q Scores of chess players. Within the chess community I assume that a number of players might have high Q scores, although this would drop (due to lesser recognition) among the wider non-chess community. Fischer and Kasparov would certainly have high recognition levels (as would Nigel Short in the UK) even among non chessplayers. I would even suggest that there Q score might even be higher in the general population, than in the chess population (although Short's might be on the slide!)
Among the chess community Carlsen, Anand and Aronian seem to be both recognised and popular, while Nakamura is an example of a more polarising figure. In the past, Euwe would no doubt be popular in The Netherlands, while Donner might be recognised, but not necessarily popular.
Related to this is an academic paper I have just looked at concerning the correlation between merit and fame. In the paper (which can be found here), the authors measure the historical ELO ratings of players, with their google rankings. At first I thought that this was an odd choice of topic to research, but it a follow up to studies done in other fields. At least the advantage of using chess as a starting point in merit can be measured reasonably accurately (and objectively), something they may not be possible in physics or economics (two other areas looked at),