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Summary of Significant Accounting Policies - Equity Method Investments (Details) - USD ($) $ in Thousands |  |  |  | 12 Months Ended |
--- | --- | --- | --- | --- | ---
Sep. 30, 2020 | Jul. 06, 2020 | Oct. 10, 2018 | Sep. 30, 2020 | Sep. 30, 2019 | Sep. 30, 2018 | Jul. 01, 2020
Schedule of Equity Method Investments [Line Items] |  |  |  |  |  |  |
Equity in earnings (losses) of investees |  |  |  | $ 1,545 | $ 719 | $ (578) |
Distributions from equity method investments |  |  |  | 736 | 549 | 174 |
Impairment loss on Tremont Mortgage Trust investment |  |  |  | 0 | 6,213 | 4,359 |
Quoted market value | $ 12,152 |  |  | 12,152 | 3,682 |  |
Unrealized gain (loss) on investment, fair value option |  |  |  | $ 3,151 | (4,700) | 0 |
TA |  |  |  |  |  |  |
Schedule of Equity Method Investments [Line Items] |  |  |  |  |  |  |
Ownership percentage by noncontrolling owners | 4.60% |  |  | 4.60% |  |  |
TA | RMR LLC |  |  |  |  |  |  |
Schedule of Equity Method Investments [Line Items] |  |  |  |  |  |  |
Number of shares owned (in shares) | 621,853 |  |  | 621,853 |  |  |
Ownership percentage | 4.30% |  |  | 4.30% |  |  |
Share purchase from related party (in shares) | 104,738 | 218,577 | 298,538 |  |  |  |
Ownership percentage by noncontrolling owners | 4.30% |  |  | 4.30% |  |  |
Purchase from related party | $ 2,259 | $ 3,060 | $ 8,382 |  |  |  |
TRMT |  |  |  |  |  |  |
Schedule of Equity Method Investments [Line Items] |  |  |  |  |  |  |
Equity in earnings (losses) of investees |  |  |  | $ 1,545 | 719 | (545) |
Distributions from equity method investments |  |  |  | $ 736 | 549 | 0 |
Impairment loss on Tremont Mortgage Trust investment |  |  |  |  | 6,213 | 4,359 |
TRMT | Tremont Advisors |  |  |  |  |  |  |
Schedule of Equity Method Investments [Line Items] |  |  |  |  |  |  |
Number of shares owned (in shares) | 1,600,100 |  |  | 1,600,100 |  |  |
Ownership percentage | 19.30% |  |  | 19.30% |  |  |
Open End Fund |  |  |  |  |  |  |
Schedule of Equity Method Investments [Line Items] |  |  |  |  |  |  |
Ownership percentage |  |  |  |  |  |  | 0.50%
Equity in earnings (losses) of investees |  |  |  | $ 0 | $ 0 | (33) |
Distributions from equity method investments |  |  |  |  |  | $ 174 |

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