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Volatiles are compounds with low sublimation temperatures, and they make up most of the condensible mass in typical planet-forming environments. They consist of relatively small, often hydrogenated, molecules based on the abundant elements carbon, nitrogen and oxygen. Volatiles are central to the process of planet formation, forming the backbone of a rich chemistry that sets the initial conditions for the formation of planetary atmospheres, and act as a solid mass reservoir catalyzing the formation of planets and planetesimals. This growth has been driven by rapid advances in observations and models of protoplanetary disks, and by a deepening understanding of the cosmochemistry of the solar system. Indeed, it is only in the past few years that representative samples of molecules have been discovered in great abundance throughout protoplanetary disks - enough to begin building a complete budget for the most abundant elements after hydrogen and helium. The spatial distributions of key volatiles are being mapped, snow lines are directly seen and quantified, and distinct chemical regions within protoplanetary disks are being identified, characterized and modeled. Theoretical processes invoked to explain the solar system record are now being observationally constrained in protoplanetary disks, including transport of icy bodies and concentration of bulk condensibles. The balance between chemical reset - processing of inner disk material strong enough to destroy its memory of past chemistry, and inheritance - the chemically gentle accretion of pristine material from the interstellar medium in the outer disk, ultimately determines the final composition of pre-planetary matter. This chapter focuses on making the first steps toward understanding whether the planet formation processes that led to our solar system are universal.
We consider the radial migration of vortices in two-dimensional isothermal gaseous disks. We find that a vortex core, orbiting at the local gas velocity, induces velocity perturbations that propagate away from the vortex as density waves. The resulti
Planet formation is thought to begin with the growth of dust particles in protoplanetary disks from micrometer to millimeter and centimeter sizes. Dust growth is hindered by a number of growth barriers, according to dust evolution theory, while obser
The known exoplanet population displays a great diversity of orbital architectures, and explaining the origin of this is a major challenge for planet formation theories. The gravitational interaction between young planets and their protoplanetary dis
Sulfur is one of the most abundant elements in the Universe, with important roles in astro-, geo-, and biochemistry. Its main reservoirs in planet-forming disks have previously eluded detection: gaseous molecules only account for $<1,$% of total elem
(Abridged) Protoplanetary disks are vital objects in star and planet formation, possessing all the material which may form a planetary system orbiting the new star. We investigate the synthesis of complex organic molecules (COMs) in disks to constrai