Episodic eruptions of young accreting stars: the key role of disc thermal instability due to Hydrogen ionisation

In the classical grouping of large magnitude episodic variability of young accreting stars, FUORs outshine their stars by a factor of $\sim$ 100, and can last for up to centuries; EXORs are dimmer, and last months to a year. A disc Hydrogen ionisation Thermal Instability (TI) scenario was previously proposed for FUORs but required unrealistically low disc viscosity. In the last decade, many intermediate type objects, e.g., FUOR-like in luminosity and spectra but EXOR-like in duration were found. Here we show that the intermediate type bursters Gaia20eae, PTF14jg, Gaia19bey and Gaia21bty may be naturally explained by the TI scenario with realistic viscosity values. We argue that TI predicts a dearth (desert) of bursts with peak accretion rates between $\dot M \sim 10^{-6} M_\odot$/yr and $\dot M \sim 10^{-5} M_\odot$/yr, and that this desert is seen in the sample of all the bursters with previously determined $\dot M$ burst. Most classic EXORs (FUORs) appear to be on the cold (hot) branch of the S-curve during the peak light of their eruptions; thus TI may play a role in this class differentiation. At the same time, TI is unable to explain how classic FUORs can last for up to centuries, and over-predicts the occurrence rate of short FUORs by at least an order of magnitude. We conclude that TI is a required ingredient of episodic accretion operating at R < 0.1 au, but additional physics must play a role at larger scales. Knowledge of TI inner workings from related disciplines may enable its use as a tool to constrain the nature of this additional physics.