Debt - Senior Credit Agreement (Details) - USD ($)	1 Months Ended	12 Months Ended
	Dec. 31, 2022	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Debt Instrument [Line Items]
Repayments of Debt		$ 920,900,000	$ 38,100,000	$ 800,000,000.0
Term Loan		1,598,100,000
Secured Debt | Line of Credit
Debt Instrument [Line Items]
Term Loan		463,100,000
Payments for Loans		11,900,000	15,000,000
2022 Term Loans | Secured Debt | Line of Credit
Debt Instrument [Line Items]
Principal amount of line of credit		475,000,000
Term of debt	5 years
Debt Instrument, Periodic Payment		5,900,000
2022 Revolver | Revolver | Line of Credit
Debt Instrument [Line Items]
Principal amount of line of credit		475,000,000
Term of debt	5 years
Line of credit, sublimit		100,000,000
Remaining borrowing capacity		471,600,000
Term Loan | Secured Debt | Line of Credit
Debt Instrument [Line Items]
Term Loan		463,100,000	$ 460,000,000.0
Term Loan | Revolver | Line of Credit
Debt Instrument [Line Items]
Letters of credit outstanding		3,400,000
2019 Term Loans | Revolver | Line of Credit
Debt Instrument [Line Items]
Repayments of Debt		445,600,000
2019 Credit Facilities | Revolver | Line of Credit
Debt Instrument [Line Items]
Repayments of Debt		290,000,000
Interest Expense, Debt		1,100,000
2022 Credit Facilities
Debt Instrument [Line Items]
Principal amount of line of credit		$ 950,000,000
2022 Credit Facilities | Minimum | Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate		1.375%
2022 Credit Facilities | Minimum | Base Rate
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate		0.375%
2022 Credit Facilities | Maximum | Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate		2.25%
2022 Credit Facilities | Maximum | Base Rate
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate		1.25%