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Income taxes - Component of Income Taxes (Detail) - USD ($)
$ in Thousands
3 Months Ended 9 Months Ended
Sep. 30, 2024
Sep. 30, 2023
Sep. 30, 2024
Sep. 30, 2023
Income taxes        
Expected tax expense (benefit), at U.S. federal statutory income tax rate of 21% $ 9,425 $ (62) $ 13,217 $ (3,088)
Rate differences on equity in earnings (losses) of Kronos, net of dividends (954) (1,037) (2,512) (3,878)
U.S. state income taxes and other, net 37 134 93 122
Income tax expense (benefit) $ 8,508 $ (965) $ 10,798 $ (6,844)