The PAIRS project: a global formation model for planets in binaries. I. Effect of disc truncation on the growth of S-type planets

TL;DR

This paper introduces the PAIRS project and implements a global, pebble-driven planet formation framework for S-type planets by adapting the Bern Model to circumprimary discs under tidal truncation, heating, and companion irradiation. It demonstrates that disc truncation severely limits pebble supply, suppressing core growth and planet formation for binary separations below roughly 160 au, while S-type planets tend to form closer to the primary than to the truncation radius. Through a detailed parameter study, it shows that initial solid mass and disc size largely govern final planet masses, with giant planets requiring wider binaries than Mars-sized planets. The work lays the groundwork for future population synthesis (Paper III) and companion-dynamics analyses (Paper II), advancing quantitative comparisons between observations and theory for planets in binary systems.

Abstract

Binary stars are as common as single stars. The number of detected planets orbiting binaries is rapidly increasing thanks to the synergy between transit surveys, Gaia and high-resolution direct imaging campaigns. However, global planet formation models around binary stars are still underdeveloped, which limits the theoretical understanding of planets orbiting binary star systems. Hereby we introduce the PAIRS project, which aims at building a global planet formation model for planets in binaries, and to produce planet populations synthesis to statistically compare theory and observations. In this first paper, we present the adaptation of the circumstellar disc to simulate the formation of S-type planets. The presence of a secondary star tidally truncates and heats the outer part of the circumprimary disc (and vice-versa for the circumsecondary disc), limiting the material to form planets. We implement and quantify this effect for a range of binary parameters by adapting the Bern Model of planet formation in its pebble-based form and for in-situ planet growth. We find that the disc truncation has a strong impact on reducing the pebble supply for core growth, steadily suppressing planet formation for binary separations below 160 au, when considering all the formed planets more massive than Mars. We find as well that S-type planets tend to form close to the central star with respect to the binary separation and disc truncation radius. Our newly developed model will be the basis of future S-type planet population synthesis studies.

Figures (10)

• Figure 1: Disc truncation radius in units of the binary semi-major axis as a function of the binary mass ratio ($q$), both for the circumprimary (violet lines) and circumsecondary discs (orange lines). The solid lines corresponds to a binary with $e_{\rm bin}=0$, while the dashed lines indicate the case where $e_{\rm bin}=$ 0.5.
• Figure 2: Evolution of the gas disc as a function of orbital distance from the primary, for the nominal disc with binary separations of $a_{\rm bin}=20$ au (left) and $a_{\rm bin}=100$ au (right). The grey background curves correspond to the single-star case. The disc's profiles are shown every $10^5$ years. Top panels display the evolution of the gas surface density, bottom panels the evolution of the disc midplane temperature.
• Figure 3: Evolution of the pebbles' disc as function of orbital distance from the primary, for the nominal disc with binary separations of $a_{\rm bin}=20$ au (left) and $a_{\rm bin}=100$ au (right). The grey background curves correspond to the single-star case. The disc's profiles are shown every $10^5$ years. The top panels indicate the evolution of the pebbles' surface density, while the bottom panels show the evolution of the pebbles' sizes. The abrupt change of the pebbles' size at r$\sim$0.4-5 au for all the profiles and times corresponds to the location of the water iceline. This affects as well the profiles of pebbles' surface density.
• Figure 4: In-situ planet growth by pebble accretion at $a_p=5$ au (top panel) and $a_p =20$ au (bottom panel). The solid lines indicate the evolution of the total planet mass, while the dashed lines the evolution of the core mass. The different colours correspond to different binary separations, as indicated in the labels. After the final planet mass is reached during the disc lifetime (a few million years), the planet evolves during giga-years by cooling and contraction.
• Figure 5: Binary mass ratio vs. binary separation (top panel) and binary mass ratio vs. disc truncation radius (bottom panel) for systems that formed a planet at least more massive than Mars. The colorbar indicates the final planet mass. Shaded contour regions represent areas of highest number planet density, derived from a two-dimensional kernel density estimation (KDE) performed on planets with masses greater than 10 $\text{M}_{\oplus}$. The lack of planets for $R_{\rm trunc}$>400 au stems from the choice of the upper limit on $a_{\rm bin}=1000$ au (see Table \ref{['tab:initialconditions']}).