Magnetic fields play a significant role throughout the life of low-mass stars¹⁾; for instance, they are very efficient at spinning down Sun-like stars by dissipating their angular momentum through magnetic braking, via mass loss from magnetically-driven winds. Magnetic fields have the largest impact in early phases of evolution, when stars and their planets form from collapsing parsec-sized molecular clouds, progressively flattening into large-scale magnetized accretion discs and finally settling as pre-main- sequence (PMS) stars surrounded by protoplanetary discs. At an age of 1-10 Myr, low-mass PMS stars have emerged from their dust cocoons and are still in a phase of gravitational contraction towards the main sequence (MS). They are either classical T-Tauri stars (cTTSs) when still surrounded by a massive (presumably planet-forming) accretion disc or weak-line T-Tauri stars (wTTSs) when their disc has mostly dissipated. TTSs have been the subject of intense scrutiny at all wavelengths in recent decades given their interest for benchmarking the scenarios currently invoked to explain low-mass star and planet formations²⁾.

Magnetic fields of TTSs play a key role in the accretion, outflow and angular momentum evolution. Large-scale fields of cTTSs can evacuate the central regions of accretion discs, funnel the disc material onto the stars, and enforce corotation between cTTSs and their inner-disc Keplerian flows, thus allowing cTTSs to rotate much more slowly than expected from the contraction and accretion of the high-angular-momentum disc material. Although first detected more than 10 yr ago³⁾⁴⁾, the magnetic topologies of TTSs remained elusive for a long time. In particular, the large-scale fields of cTTSs have only recently been unveiled for a first sample of 15 cTTSs⁵⁾⁶⁾. This small survey revealed that the large-scale fields of cTTSs depend mostly on the internal structure of the PMS star. More specifically, these large-scale fields, although often more complex than pure dipoles and featuring a significant (sometimes dominant) octupolar component, remain rather simple when the PMS star is still fully or largely convective, but become much more complex when the PMS star turns mostly radiative⁷⁾. This survey also showed that these fields are likely of dynamo origin, being variable on timescales of years⁸⁾ and similar to those of mature stars with comparable internal structures⁹⁾¹⁰⁾. These new results have stimulated more realistic models of magnetospheric accretion¹¹⁾.

Comparatively little is known on the large-scale magnetic topologies of wTTSs, with only 1 such PMS star imaged to date (namely V410 Tau). Yet, being the missing link between cTTSs and MS low-mass stars, wTTSs are key targets to study the magnetic topologies and associated winds with which these disc-less PMS stars initiate their unleashed spin-up as they contract towards the MS. The results obtained for V410 Tau showing a complex field with a significant toroidal and a non-axisymmetric poloidal component¹²⁾ despite being fully convective, are in surprising contrast with those for largely- and fully-convective cTTSs and mature M dwarfs, harbouring rather simple fields¹³⁾¹⁴⁾. Observing a significant number of wTTSs in a few of the nearest star forming regions is needed to have a better view of their magnetic topologies. It will also allow us to study in a quantitative way the magnetic winds of wTTSs and the corresponding spin-down rates¹⁵⁾, and to filter-out most of the activity jitter from radial velocity (RV) curves of wTTSs (using spectropolarimetry as the most reliable proxy of surface activity) for potentially detecting hot Jupiters (hJs) around wTTSs.

The 3 main issues on which MaTYSSE is focussed are as follows:

• are large-scale magnetic fields of wTTSs similar to those of cTTSs? In particular, are the magnetic topologies of cTTSs typical initial magnetic conditions of wTTSs as they start their unleashed acceleration towards the MS, as a combined result of the radius contraction and of the vanishing magnetic brake from the disc (mostly dissipated at the wTTS stage)? Or are they significantly different, eg as a result of accretion and of the star/disc coupling torque modifying dynamo processes in accreting stars and consequently the large-scale field topology? This is essential information for consistently explaining the rotational history of low-mass stars once on the MS, usually invoking magnetic braking as the main cause of their later spin down;
• is disc migration the main process for producing hJs and are magnetospheric gaps & winds key factors for their survival? If this is the case, one can expect to find at least as many hJs in TTSs than in mature stars, and possibly significantly more if we account for all those that did not resist the subsequent tidal-induced forces from the disc-less protostar over the whole contraction phase. Although technically very difficult for cTTSs (given their very high level of intrinsic accretion-induced variability), detecting hJs is potentially feasible for wTTSs whose spectral variability (mostly due to magnetic activity) is much easier to model and thus subtract from radial velocity (RV) curves; detecting even one single hJ around a TTS would be a major observational step forward for our understanding of the formation / migration of hJs;
• by how much do magnetospheric gaps & winds vary with time as a result of the non- stationary dynamos operating in cTTSs? Magnetospheric gaps / winds are expected to vary in size / strength with time, reflecting changes in the large-scale magnetic topologies of cTTSs on timescales of a few yr. By monitoring selected cTTSs (those that already showed time-variable large-scale fields in particular) over the whole LP, we can work out how variable magnetospheric gaps / winds are and whether this variability is compatible with the survival of hJs.

MaTYSSE aims at addressing these major issues through a detailed spectropolarimetric & photometric survey of ~40 wTTSs as well as a regular monitoring of ~5 cTTSs.