The Astrophysical Distance Scale: V. A 2% Distance to the Local Group Spiral M33 via the JAGB Method, Tip of the Red Giant Branch, and Leavitt Law

The J-region asymptotic giant branch (JAGB) method is a new standard candle that is based on the stable intrinsic J-band magnitude of color-selected carbon stars, and has a precision comparable to other primary distance indicators such as Cepheids and the TRGB. We further test the accuracy of the JAGB method in the Local Group Galaxy M33. M33's moderate inclination, low metallicity, and nearby proximity make it an ideal laboratory for tests of systematics in local distance indicators. Using high-precision optical BVI and near-infrared JHK photometry, we explore the application of three independent distance indicators: the JAGB method, the Cepheid Leavitt Law, and the TRGB. We find: $\mu_0$ (TRGB I) = 24.72 +/- 0.02 (stat) +/- 0.07 (sys) mag, $\mu_0$ (TRGB NIR) = 24.72 +/- 0.04 (stat) +/- 0.10 (sys) mag, $\mu_0$ (JAGB) = 24.67 +/- 0.03 (stat) +/- 0.04 (sys) mag, $\mu_0$ (Cepheid) = 24.71 +/- 0.04 (stat) +/- 0.01 (sys) mag. For the first time, we also directly compare a JAGB distance using ground-based and space-based photometry. We measure: $\mu_0$ (JAGB F110W) = 24.71 +/- 0.06 (stat) +/- 0.05 (sys) mag using the (F814-F110W) color combination to effectively isolate the JAGB stars. In this paper, we measure a distance to M33 accurate to 2% and provide further evidence that the JAGB method is a powerful extragalactic distance indicator that can effectively probe a local measurement of the Hubble constant using spaced-based observations. We expect to measure the Hubble constant via the JAGB method in the near future, using observations from JWST.