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Income taxes - Component of Income Taxes (Detail) - USD ($)
$ in Thousands
3 Months Ended 6 Months Ended 18 Months Ended
Jun. 30, 2023
Jun. 30, 2022
Jun. 30, 2023
Jun. 30, 2022
Jun. 30, 2023
Income taxes          
Expected tax expense (benefit), at U.S. federal statutory income tax rate of 21% $ (2,077) $ 7,873 $ (3,026) $ 12,475  
U.S. federal statutory income tax rate         21.00%
Rate differences on equity in earnings (losses) of Kronos, net of dividends (5,146) (1,449) (2,841) (3,363)  
U.S. state income taxes and other, net (77) 11 (12) 28  
Income tax expense $ (7,300) $ 6,435 $ (5,879) $ 9,140