The quest for Magrathea planets I: formation of second generation exoplanets around double white dwarfs

The evolution of binaries that become double white dwarf (DWD) can cause the ejection of high amounts of dust and gas. Such material can give rise to circumbinary discs and become the cradle of new planets, yet no studies so far have focused on the formation of circumbinary planets around DWDs. These binaries will be the main sources of gravitational waves (GWs) detectable by the ESA Laser Interferometer Space Antenna (LISA) mission, opening the possibility to detect circumbinary planets around short-period DWDs everywhere in the Milky Way. We investigate the formation of Magrathea planets by simulating multiple planet formation tracks to explore how seeds growing first by pebble accretion, and then by gas accretion, are affected by the disc environments surrounding DWDs. We present both planetary formation tracks taking place in steady-state discs, and formation tracks taking place in discs evolving with time. The time-dependent tracks account for both the disc accretion rate onto the central binary and the disc photoevaporation rate caused by stellar irradiation. Our results show that planetary formation in circumbinary discs around DWDs can be possible. In particular, the extreme planetary formation environment implies three main significant results: (i) the accretion rate and the metallicity of the disc should be high in order to form sub-stellar objects with masses up to 31 M$_J$, this is achieved only if planet formation starts soon after the onset of the disc and if first generation seeds are present in the disc; (ii) seeds formed within 0.1 Myr, or within 1 Myr, from the onset of the disc can only produce sub-Neptune and Neptunian planets, unless the disc accommodates first generation seeds with mass 10 M$_{\oplus}$; (iii) most of the planets are finally located within 1 au from the disc centre, while they are still undergoing the gas accretion phase.