Influence of grain growth on the thermal structure of inner protoplanetary discs

Abstract: Protoplanetary discs surround young stars for the first few million years after their formation and they are the birthplaces of planetary systems. The thermal structure of the discs is regulated by their dust content and the opacity that it provides. The aim of this project is to investigate the effect grain growth has on the structure of the protoplanetary discs. Hydrodynamical simulations have been coupled to a new opacity model, which can calculate the opacity as a function of temperature for a dust population taking into account the particle size, composition and abundance. Single-size simulations are investigated for different turbulent strengths. Full size distributions are also explored that take into account coagulation and fragmentation of dust particles. For the single size simulations it was found that discs with small grains, from 0.1 to 10 μm have similar thermal structures at high turbulence. There exists a slight progressive drop with increasing orbital distance in the temperature or aspect ratio of these discs for the specified grain sizes. On the other hand, discs with grains of 1 mm are around 50% colder at midplane within the first few AU, compared to discs with small grains, but this difference is diminished after approximately 10 AU. The 0.1 mm grains lead to discs that remain 60% hotter even at the outer boundaries of the discs. The location of the iceline depends on the particle size, as it moves inwards as the particles size increases and it is inside 1 AU for the larger particles. In general, decreasing turbulence leads to colder discs and shrinks even further the differences between various grain sizes. The iceline in this case typically moves inside 1 AU even for smaller grain sizes. Two different full grain size distributions were modelled. In the first, the number density follows a power-law inspired by a coagulation/fragmentation equilibrium (Dohnanyi, 1969; Tanaka et al, 1996). The second begins with the same mass distribution, but takes into consideration the relative velocities for particles of different sizes and divides particles into regimes with different slopes for the mass distribution depending on their sizes and therefore aerodynamical properties (Birnstiel et al, 2011). Both models converge near the outer boundaries of the discs simulated here and they show a strong influence from the particles of around 0.1 mm in size. The inner parts of the disc simulated here, show a difference because of the upper boundary of each size distribution. In the more complex model the upper boundary is determined by the fragmentation barrier which leaves only smaller particles in the inner disc. On the contrary, the simple model following the Dohnanyi (1969) distribution has an arbitrarily fixed upper boundary which means that larger particles are present in this case. These have lower opacities and therefore enhance the cooling rate and decrease the disc’s temperature and aspect ratio. The iceline in both of the grain size distribution models is around 3 AU. The grain sizes distribution simulations show that in discs with significant viscous heating, often-used opacity models based on μm-sized dust grains only are not a good approximation in order to create more realistic theoretical models.