The Time Domain Telescope enables time-critical optical-infrared spectroscopy in an array of ~100, individually steerable, AO-corrected telescopes of (~)2 meter diameter. Optical AO at resolutions of ~0.1" will dilute the sky to ~26th magnitude. Coupled with (almost) read-noise-free detectors per-unit performance will be at g>23, and full-array performance beyond g>25.5. To make the TDT operationally feasible, and to achieve minute-scale flexibility and turn-around times, the TDT will be fully autonomous, making use of AI Agents. The TDT is complementary to the VLT, ELT and ALMA, and addresses the science needs for time-resolved spectroscopy created by the VRO, Euclid and Roman datasets and concurrent facilities such as LISA, ET and Athena. In partnerships the TDT should expand into a global array. To realise the TDT, key technology developments are needed in robotic optical AO, read-noise-free detectors, (photonic) spectroscopy and the use of AI-enabled agents in operations and scheduling. The TDT is planned facility and is being proposed as the next generation ESO facility as part of the ESO expanding horizon 2040 call.

AM CVn systems are rare, ultracompact binaries consisting of a white dwarf primary and a (semi- )degenerate secondary. Only about ~100 AM CVn systems are known. They show orbital periods in a range of 5.4 - 65 min. As these systems evolve from a short orbital period, their mass transfer rate decreases by several orders of magnitude as the orbit widens and the orbital period increases. As ultracompact binaries, they are one of the strongest and most abundant sources of gravitational wave radiation in the LISA regime and some of the them will be verification binaries at launch. The exact formation channel of AM CVn systems is still unknown and three scenarios have been proposed. In the first, two old and completely degenerate white dwarfs start mass transfer, in the second the mass donor is a semi-degenerate helium star and in the third the donor is a well-evolved main-sequence star.

Hot subluminous B stars (sdBs) are core helium-burning stars with very thin hydrogen envelopes and masses around 0.5 Msol. A large fraction of sdBs reside in short period binaries with a low mass main sequence or white dwarf companion. For close binary sdBs common envelope ejection is the most probable formation channel. Evolutionary studies have shown that the orbital period of a hot subdwarf with a white dwarf companion has to be smaller than about 120 min on exit from the last common enveope phase to still have an sdB that is core or shell helium burning when it fills its Roche lobe assuming that the further orbital period evolution is set by the emission of gravitational waves only. In the subsequent evolution, if helium burning is still ongoing, the sdB fills its Roche lobe first and starts to transfer He-rich material onto the white dwarf which could result in a detonation of the white dwarf or formation a stable helium accreting AM CVn type system.

Hot subdwarf stars are known to pulsate with g-modes or p-modes. In all cases photometric amplitudes do not exceed a few percent. Radial mode hot subdwarf pulsators are a new type of pulsator showing typical periods of minutes and spectroscopic properties of hot subdwarfs but pulsate with amplitudes above a few percent. Additionally they show large velocity, temperature and surface gravity variations over the pulsation cycle, typical for radial mode pulsators.