Borrowings - Components of the Carrying Value of Notes (Details) - USD ($)	Mar. 31, 2024	Sep. 30, 2023	Aug. 15, 2023	May 18, 2021	Feb. 25, 2020
Debt Instrument [Line Items]
Unamortized financing costs	$ (6,001,000)	$ (7,076,000)
Net carrying value	1,635,642,000	1,600,731,000
2025 Notes
Debt Instrument [Line Items]
Principal	300,000,000.0	300,000,000.0			$ 300,000,000
Unamortized financing costs	(700,000)	(1,100,000)
Unaccreted discount	(500,000)	(700,000)			$ (2,500,000)
Interest rate swap fair value adjustment	0	0
Net carrying value	298,800,000	298,200,000
Fair Value	293,600,000	286,400,000
2027 Notes
Debt Instrument [Line Items]
Principal	350,000,000.0	350,000,000.0		$ 350,000,000
Unamortized financing costs	(2,100,000)	(2,500,000)
Unaccreted discount	(500,000)	(600,000)		$ (1,000,000)
Interest rate swap fair value adjustment	(32,500,000)	(40,500,000)
Net carrying value	314,900,000	306,400,000
Fair Value	317,700,000	301,800,000
2029 Notes
Debt Instrument [Line Items]
Principal	300,000,000.0	300,000,000.0	$ 300,000,000
Unamortized financing costs	(3,200,000)	(3,500,000)
Unaccreted discount	(3,100,000)	(3,400,000)	$ (3,500,000)
Interest rate swap fair value adjustment	(1,800,000)	(7,000,000.0)
Net carrying value	291,900,000	286,100,000
Fair Value	$ 311,100,000	$ 290,000,000.0