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Stock-Based Compensation - Non-options (Details) - Performance-based stock units - $ / shares
12 Months Ended
Sep. 30, 2022
Sep. 30, 2021
Share-based Compensation    
Term of award 10 years  
Number of PSUs    
Balance, Beginning 2,470 2,470
Forfeitures 0 0
Balance, Ending 2,470 2,470
Vested and exercisable 2,470  
Vested and expected to vest 2,470  
Weighted Average Base Price Per Unit    
Balance, Beginning $ 49.97 $ 49.97
Forfeitures 0 0
Balance, Ending 49.97 $ 49.97
Vested and exercisable 49.97  
Vested and expected to vest $ 49.97  
Weighted average remaining contractual term, Outstanding 2 years  
Weighted average remaining contractual term, Vested and exercisable 2 years  
Weighted average remaining contractual term, Vested and expected to vest 2 years