Goodwill and Other Intangible Assets - Intangible Assets, Net - Additional Information (Details) - USD ($)	3 Months Ended
Dec. 31, 2021	Dec. 31, 2020
Goodwill And Intangible Assets Disclosure [Abstract]
Impairment of long-lived asset	$ 0
Amortization expense related to intangible assets	5,000,000.0	$ 5,000,000.0
Expected amortization of intangible assets for remainder of 2022	$ 9,600,000

The aggregate expense charged against earnings to allocate the cost of intangible assets (nonphysical assets not used in production) in a systematic and rational manner to the periods expected to benefit from such assets. As a noncash expense, this element is added back to net income when calculating cash provided by or used in operations using the indirect method.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 28
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-URI http://asc.fasb.org/extlink&oid=123570139&loc=d3e3602-108585

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
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Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 30
-Section 45
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-URI http://asc.fasb.org/extlink&oid=6388964&loc=d3e16225-109274

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