Income taxes - Additional Information (Detail) - USD ($)	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021	Dec. 31, 2021
Income Tax Disclosure [Line Items]
Dividends received from Kronos Worldwide, Inc.			$ 20,074,000	$ 19,017,000
Uncertain tax position	$ 1,515,000		1,515,000		$ 1,724,000
Income tax expense (benefit)	5,576,000	$ (1,054,000)	(3,564,000)	(5,460,000)
Current payable to affiliate	$ 682,000		682,000		$ 691,000
Kronos
Income Tax Disclosure [Line Items]
Dividends received from Kronos Worldwide, Inc.			$ 20,100,000	$ 19,000,000.0