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Stock-Based Compensation (Tables) | 6 Months Ended
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Mar. 31, 2023
Disclosure of Compensation Related Costs, Share-based Payments [Abstract] |
Summary of stock-based compensation expense | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Three Months Ended March 31, | ​ | Six Months Ended March 31, | ​
​ |  | 2023 |  | 2022 |  | 2023 |  | 2022 |
Restricted stock units | ​ | $ | 3,634 | ​ | $ | 8,058 | ​ | $ | 5,393 | ​ | $ | 15,255 | ​
Employee stock purchase plan | ​ |  | 356 | ​ |  | 599 | ​ |  | 703 | ​ |  | 1,293 | ​
Total stock-based compensation expense | ​ | $ | 3,990 | ​ | $ | 8,657 | ​ | $ | 6,096 | ​ | $ | 16,548 | ​
​
Restricted Stock Unit Activity | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | ​ |  | Time-Based |  | Stock |  | Performance-
​ | ​ | Total Units | ​ | Units | ​ | Grants | ​ | Based Units
Six months ended March 31, 2023 |  | 572,111 |  | 356,410 |  | — |  | 215,701
Six months ended March 31, 2022 |  | 228,468 | ​ | 101,706 |  | 16,286 |  | 110,476
​ ​
​ | ​ | ​ | ​ | ​ | ​
​ |  | ​ |  | Weighted
​ | ​ | ​ | ​ | Average
​ | ​ | ​ | ​ | Grant-Date
​ | ​ | Shares | ​ | Fair Value
Outstanding at September 30, 2022 |  | 538,238 | ​ | $ | 71.99
Granted |  | 572,111 | ​ | ​ | 58.21
Vested |  | (261,618) | ​ | ​ | 55.66
Forfeited |  | (81,878) | ​ | ​ | 78.66
Outstanding at March 31, 2023 |  | 766,853 | ​ | ​ | 67.68
​

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- Definition Tabular disclosure of cost recognized for award under share-based payment arrangement by plan. Includes, but is not limited to, related tax benefit. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (h)(1) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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- Definition Tabular disclosure of the number and weighted-average grant date fair value for restricted stock units that were outstanding at the beginning and end of the year, and the number of restricted stock units that were granted, vested, or forfeited during the year. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (c)(1) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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