Debt (Term Facility and Revolving Credit Facility) (Details) - USD ($) $ in Thousands		3 Months Ended			6 Months Ended
		Mar. 31, 2021		Mar. 31, 2020	Mar. 31, 2021		Mar. 31, 2020	Sep. 30, 2020
Line of Credit Facility [Line Items]
Unamortized discount (premium) and debt issuance costs, net		$ 8,392			$ 8,392			$ 9,436
Total debt		889,427			889,427			885,470
Amortization of debt issuance costs and discounts		518		$ 421	1,044		$ 936
Line of credit facility, remaining borrowing capacity		45,000			45,000			45,000
Revolving Credit Facility
Line of Credit Facility [Line Items]
Line of credit facility, remaining borrowing capacity		125,000			125,000			125,000
First Lien Term Facility, due December 20, 2024
Line of Credit Facility [Line Items]
Unamortized discount (premium) and debt issuance costs, net		(8,392)			(8,392)			(9,436)
First Lien Term Facility, due December 20, 2024 | Other Current Liabilities
Line of Credit Facility [Line Items]
Unamortized discount (premium) and debt issuance costs, net	[1]	(2,147)			(2,147)			(2,112)
First Lien Term Facility, due December 20, 2024 | Other Noncurrent Liabilities
Line of Credit Facility [Line Items]
Unamortized discount (premium) and debt issuance costs, net	[2]	$ (6,245)			$ (6,245)			(7,324)
First Lien Term Facility, due December 20, 2024 | Term Loan
Line of Credit Facility [Line Items]
Debt instrument, interest rate, stated percentage		2.61%			2.61%
Debt instrument, periodic payment, principal					$ 2,369
London Interbank Offered Rate (LIBOR) | First Lien Term Facility, due December 20, 2024 | Term Loan
Line of Credit Facility [Line Items]
Debt instrument, interest rate, stated percentage		2.50%			2.50%
Debt instrument, basis spread on variable rate					0.11%
Revolving Credit Facility
Line of Credit Facility [Line Items]
Total debt		$ 0	[3]		$ 0	[3]		0
First Lien Term Facility, due December 20, 2024
Line of Credit Facility [Line Items]
Total debt		$ 814,538			$ 814,538			$ 819,276

[1] Included in Current portion of debt, net of deferred financing fees on the Consolidated Balance Sheets.

[2] Included in Long-term debt, net of deferred financing fees on the Consolidated Balance Sheets.

[3] On April 1, 2021, the Company paid off the outstanding balance of the First Lien Term Loan (as defined below) and entered into the 2021 Credit Agreement (as defined below). See Note 23, “Subsequent Events” for further discussion.