Accumulated Other Comprehensive Loss, Net (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance	$ 1,070.1	$ 904.0	$ 767.5
Other comprehensive income (loss)	38.8	(65.5)	14.8
Amounts reclassified from AOCI, net of tax	0.0	0.0	0.2
Other comprehensive income/(loss)	38.8	(65.5)	15.0
Ending balance	1,379.1	1,070.1	904.0
Foreign Currency Translation Adjustment
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance	(34.4)	(22.7)	(36.0)
Other comprehensive income (loss)	3.2	(11.7)	13.3
Amounts reclassified from AOCI, net of tax			0.0
Other comprehensive income/(loss)	3.2	(11.7)	13.3
Ending balance	(31.2)	(34.4)	(22.7)
Pension Benefits Adjustment
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance	(2.7)	(2.4)	(4.1)
Other comprehensive income (loss)	0.5	(0.3)	1.5
Amounts reclassified from AOCI, net of tax			0.2
Other comprehensive income/(loss)	0.5	(0.3)	1.7
Ending balance	(2.2)	(2.7)	(2.4)
Cash Flow Hedge
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance	(53.5)	0.0	0.0
Other comprehensive income (loss)	35.1	(53.5)	0.0
Amounts reclassified from AOCI, net of tax			0.0
Other comprehensive income/(loss)	35.1	(53.5)	0.0
Ending balance	(18.4)	(53.5)	0.0
Accumulated Other Comprehensive Loss, net
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance	(90.6)	(25.1)	(40.1)
Other comprehensive income/(loss)	38.8	(65.5)	15.0
Ending balance	$ (51.8)	$ (90.6)	$ (25.1)