"Companion" only in the sense that it helps to make sense of this, not that it's by the same researchers or with any sort of collaboration in mind.

It looked at liberal arts schools, where you'd expect gender discrimination to be at a minimum. Then it looked at the departments with the largest "liberal" reputations as a field--things like English or sociology.

The object of investigation were men and women, both faculty, who had a new baby and who took parental leave. Both had lengthy leaves and had an additional year tacked on to their pre-tenure time. So they had 8 years to tenure instead of 7. In other words, if they did squat in that year but worked as usual in the other 7, they'd be fine.

The researchers looked at distribution of duties as new parents and how the new parents spent their time. Both parents typically gave lip service to equality and equal distribution of duties.

The women tended to say they enjoyed parental activities. This resulted in higher enjoyment ratings (or whatever it was called) even for things like changing diapers.

At the end of the time, there was a profound difference. The men spent far less time on new-father activities than the mothers.

The men had a far larger number of papers submitted for publication, abstracts accepted for conferences, and often had a monograph submitted. At the end of the time period, their CVs had what amounted to more than an additional year's worth of research and publications, while their wives CVs were pretty much flat. The prediction was that the men, upon tenure review, would be much better candidates and quite probably could successfully apply for early review. The women would have 7 years' worth of stuff on their CV after 8 years, if lucky. (Why "if lucky"? Because after the parental leave period expired, the uneven workload continued and their CV-building time was often quality time with child.)

The study in the OP is pretty much par for the course, though. After discounting what can be controlled and looking for evidence of discrimination in what remains, there's not much remaining. The only recourse is to say that the fields that have fewer women in them should have the same pay scale as the fields with more women in them. Or perhaps those women-deficient fields need more outreach.