Derivative Financial Instruments and Fair Value Measurements - Fair Value Measurements (Details) - USD ($) $ in Millions	6 Months Ended
Mar. 31, 2024	Sep. 30, 2023
Interest Rate Swap and Interest Rate Cap \| Other current assets
Derivative financial instruments
Fair values of the interest rate swap and cap agreements	$ 15.2	$ 17.2
Interest Rate Swap and Interest Rate Cap \| Other non-current assets
Derivative financial instruments
Fair values of the interest rate swap and cap agreements	27.1	$ 37.5
Interest Rate Swap and Interest Rate Cap \| Other Noncurrent Liabilities
Derivative financial instruments
Fair values of the interest rate swap and cap agreements	0.6
Designated as Hedging Instrument \| Cash Flow Hedging \| Interest Rate Swap
Derivative financial instruments
Losses recognized in income	$ 0.0

Fair values as of the balance sheet date of the net amount of all assets and liabilities resulting from contracts that meet the criteria of being accounted for as derivative instruments.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 45
-Paragraph 5
-SubTopic 10
-Topic 815
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480463/815-10-45-5

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- Definition

Amount of gain (loss) from excluded component of derivative hedge, recognized in earnings. Excludes recognition under systematic and rational method.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 815
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 4C
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480434/815-10-50-4C

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Name Accounting Standards Codification
-Section 45
-Paragraph 1A
-Subparagraph (b)
-SubTopic 20
-Topic 815
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480627/815-20-45-1A

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- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 815
-SubTopic 40
-Name Accounting Standards Codification
-Section 50
-Paragraph 5
-Subparagraph (f)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480237/815-40-50-5

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