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Income taxes - Component of Income Taxes (Detail) - USD ($)
$ in Thousands
3 Months Ended 6 Months Ended
Jun. 30, 2024
Jun. 30, 2023
Jun. 30, 2024
Jun. 30, 2023
Income taxes        
Expected tax expense (benefit), at U.S. federal statutory income tax rate of 21% $ 2,048 $ (2,077) $ 3,792 $ (3,026)
Rate differences on equity in earnings (losses) of Kronos, net of dividends (776) (5,146) (1,558) (2,841)
U.S. state income taxes and other, net 30 (77) 56 (12)
Income tax expense (benefit) $ 1,302 $ (7,300) $ 2,290 $ (5,879)