Income taxes - Component of Income Taxes (Detail) - USD ($) $ in Thousands	3 Months Ended	9 Months Ended
Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2023	Sep. 30, 2022
Income taxes
Expected tax expense (benefit), at U.S. federal statutory income tax rate of 21%	$ (62)	$ (2,926)	$ (3,088)	$ 9,550
U.S. federal statutory income tax rate	21.00%	21.00%	21.00%	21.00%
Rate differences on equity in earnings (losses) of Kronos, net of dividends	$ (1,037)	$ (2,712)	$ (3,878)	$ (6,075)
U.S. state income taxes and other, net	134	62	122	89
Income tax expense	$ (965)	$ (5,576)	$ (6,844)	$ 3,564

Income tax reconciliation state income taxes and other net.

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- Definition

Percentage of domestic federal statutory tax rate applicable to pretax income (loss).

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- Definition

Amount of current income tax expense (benefit) and deferred income tax expense (benefit) pertaining to continuing operations.

+ References

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Amount of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to equity in earnings (loss) of unconsolidated subsidiaries exempt from income taxes.

+ References

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- Definition

The amount of income tax expense or benefit for the period computed by applying the domestic federal statutory tax rates to pretax income from continuing operations.

+ References

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