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Reading the definitions of T Tauri stars and the Hayashi track one can gather that:

T Tauri stars are pre-main-sequence stars in the process of contracting to the main sequence along the Hayashi track

and that:

After a protostar ends its phase of rapid contraction and becomes a T Tauri star, it is extremely luminous. The star continues to contract, but much more slowly. While slowly contracting, the star follows the Hayashi track

Can we then say that all stars on the Hayashi track are T Tauri stars? And moreover, are all T Tauris on the Hayashi track?

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Very much a case of semantics and what exactly you mean by a T Tauri star.

If a requirement is for the star to have a significant disc, then no, a fair fraction of young stars, particularly those of low mass, have lost their discs before they reach the end of the Hayashi track. The exponential decay timescale for losing a disc is around 3 Myr. The timescale to get to the bottom of the Hayashi track can be 10-100 Myr for stars of 0.5-0.1 solar masses.

If the definition encompasses both "classical" T Tauri stars and "weak-lined" T Tauri stars (those without an active accretion disc), then yes, all young stars on the Hayashi track are T-Tauri stars.

Edit: I realised I hadn't completed the answer. It is also true that many higher mass T-Tauri stars (more than 0.5 solar masses) have left the Hayashi track and still have discs whilst they are on their radiative Henyey tracks.

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