Searching for Balmer-dominated Type Ia Supernova Remnants in M33

We searched for Balmer-dominated Type Ia supernova remnants (SNRs) in M33 by selecting thermal X-ray sources with ${L}_{{\rm{X}}}\geqslant 5\times {10}^{35}$ erg s^-1, identifying associated Hα emission features, and checking their [S II] and [O III] emission properties. Our search did not find any Balmer-dominated Type Ia SNRs in M33. This result is puzzling because M33 is 2-3 times more massive than the Large Magellanic Cloud (LMC), yet the LMC hosts five Balmer-dominated Type Ia SNRs and M33 has none. We have considered observational biases; interstellar densities and ionization conditions; the Type Ia SN rate expected from the star formation history and Type Ia SN delay time distribution function; and the metallicity effect. None of these can explain the absence of X-ray-bright Balmer-dominated Type Ia SNRs in M33. It is intriguing that the Galaxy has X-ray-bright and thermal Type Ia SNRs (Kepler and Tycho), as well as X-ray-faint and nonthermal Type Ia SNRs (G1.9+0.3, SN1006, and RCW86), while the LMC does not have the X-ray-faint and nonthermal ones and M33 does not have the X-ray-bright and thermal ones.