Stockholders' Equity - Accumulated Other Comprehensive Income (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019
Increase (Decrease) in Accumulated Other Comprehensive Income [Roll Forward]
Beginning Balance	$ 1,213,614	$ 1,138,954	$ 717,832
Ending Balance	1,325,334	1,213,614	1,138,954
Accumulated Other Comprehensive Income
Increase (Decrease) in Accumulated Other Comprehensive Income [Roll Forward]
Beginning Balance	21,919	3,511	13,587
Other comprehensive (loss) income before reclassifications	(2,589)	18,379	(9,971)
Amounts reclassified from accumulated other comprehensive income	21	29	(105)
Ending Balance	19,351	21,919	3,511
Currency Translation Adjustments
Increase (Decrease) in Accumulated Other Comprehensive Income [Roll Forward]
Beginning Balance	23,061	4,184	13,517
Other comprehensive (loss) income before reclassifications	(2,922)	18,877	(9,333)
Ending Balance	20,139	23,061	4,184
Unrealized Gains (Losses) on Available-for-Sale Securities
Increase (Decrease) in Accumulated Other Comprehensive Income [Roll Forward]
Beginning Balance	(1)	(8)	(112)
Other comprehensive (loss) income before reclassifications		5	244
Amounts reclassified from accumulated other comprehensive income		2	(140)
Ending Balance	(1)	(1)	(8)
Pension Liability Adjustments
Increase (Decrease) in Accumulated Other Comprehensive Income [Roll Forward]
Beginning Balance	(1,141)	(665)	182
Other comprehensive (loss) income before reclassifications	333	(503)	(882)
Amounts reclassified from accumulated other comprehensive income	21	27	35
Ending Balance	$ (787)	$ (1,141)	$ (665)