On the evolution of the snow line in protoplanetary discs

ABSTRACT Volatile species in protoplanetary discs can undergo a phase change from vapour to solid. These ‘snow lines’ can play vital roles in planet formation at all scales, from dust coagulation to planetary migration. In the outer regions of protoplanetary discs, the temperature profile is set by the absorption of reprocessed stellar light by the solids. Further, the temperature profile sets the distribution of solids through sublimation and condensation at various snow lines. Hence, the snow line position depends on the temperature profile and vice versa. We show that this coupling can be thermally unstable, such that a patch of the disc at a snow line will produce either runaway sublimation or condensation. This thermal instability arises at moderate optical depths, where heating by absorption of reprocessed stellar light from the disc’s atmosphere is optically thick, yet cooling is optically thin. Since volatiles in the solid phase drift much faster than volatiles in the vapour phase, this thermal instability results in a limit cycle. The snow line progressively moves in, condensing volatiles, before receding, as the volatiles sublimate. Using numerical simulations, we study the evolution of the carbon monoxide (CO) snow line. We find the CO snow line is thermally unstable under typical disc conditions and evolves inwards from ∼50 to ∼30 au on time-scales from 1000 to 10 000 yr. The CO snow line spends between ${\sim}10{{\ \rm per\ cent}}\,\mathrm{ and}\,50{{\ \rm per\ cent}}$ of its time at smaller separations, where the exact value is sensitive to the total opacity and turbulent viscosity. The evolving snow line also creates ring-like structures in the solid distribution interior to the snow line. Multiple ring-like structures created by moving snow lines could potentially explain the substructures seen in many ALMA images.

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On the evolution of the snow line in protoplanetary discs – II. Analytic approximations

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stt1051 ◽

2013 ◽

Vol 434 (1) ◽

pp. 633-638 ◽

Cited By ~ 24

Author(s):

Rebecca G. Martin ◽

Mario Livio

Keyword(s):

Analytic Approximations ◽

Snow Line ◽

Protoplanetary Discs

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Self-induced dust traps around snow lines in protoplanetary discs

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz3444 ◽

2019 ◽

Vol 492 (1) ◽

pp. 210-222 ◽

Cited By ~ 3

Author(s):

Arnaud Vericel ◽

Jean-François Gonzalez

Keyword(s):

Carbon Monoxide ◽

The Self ◽

Dust Particles ◽

Parameter Study ◽

Volatile Species ◽

Dust Trap ◽

Multiple Observations ◽

Snow Line ◽

Dust Evolution ◽

Protoplanetary Discs

ABSTRACT Dust particles need to grow efficiently from micrometre sizes to thousands of kilometres to form planets. With the growth of millimetre to metre sizes being hindered by a number of barriers, the recent discovery that dust evolution is able to create ‘self-induced’ dust traps shows promises. The condensation and sublimation of volatile species at certain locations, called snow lines, are also thought to be important parts of planet formation scenarios. Given that dust sticking properties change across a snow line, this raises the question: how do snow lines affect the self-induced dust trap formation mechanism? The question is particularly relevant with the multiple observations of the carbon monoxide (CO) snow line in protoplanetary discs, since its effect on dust growth and dynamics is yet to be understood. In this paper, we present the effects of snow lines in general on the formation of self-induced dust traps in a parameter study, and then focus on the CO snow line. We find that for a range of parameters, a dust trap forms at the snow line where the dust accumulates and slowly grows, as found for the water snow line in a previous work. We also find that, depending on the grains’ sticking properties on either side of the CO snow line, it could be either a starting or braking point for dust growth and drift. This could provide clues to understand the link between dust distributions and snow lines in protoplanetary disc observations.

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Warm millimetre dust in protoplanetary discs near massive stars

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab728 ◽

2021 ◽

Author(s):

Thomas J Haworth

Keyword(s):

Massive Stars ◽

External Source ◽

Central Star ◽

Equilibrium Temperature ◽

Initial Assessment ◽

Snow Line ◽

Close Proximity ◽

Dust Mass ◽

External Sources ◽

Protoplanetary Discs

Abstract Dust plays a key role in the formation of planets and its emission also provides one of our most accessible views of protoplanetary discs. If set by radiative equilibrium with the central star, the temperature of dust in the disc plateaus at around 10 − 20 K in the outer regions. However sufficiently nearby massive stars can heat the outer disc to substantially higher temperatures. In this paper we study the radiative equilibrium temperature of discs in the presence of massive external sources and gauge the effect that it has on millimetre dust mass estimates. Since millimetre grains are not entrained in any wind we focus on geometrically simple 2D-axisymmetric disc models using radiative transfer calculations with both the host star and an external source. Recent surveys have searched for evidence of massive stars influencing disc evolution using disc properties as a function of projected separation. In assuming a disc temperature of 20 K for a disc a distance D from a strong radiation source, disc masses are overestimated by a factor that scales with D−1/2 interior to the separation that external heating becomes important. This could significantly alter dust mass estimates of discs in close proximity to θ1C in the Orion Nebular Cluster. We also make an initial assessment of the effect upon snow lines. Within a parsec of an O star like θ1C a CO snow line no longer exists, though the water snow line is virtually unaffected except for very close separations of ≤0.01 pc.

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Is water ice an efficient facilitator for dust coagulation?

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa2467 ◽

2020 ◽

Vol 498 (2) ◽

pp. 1801-1813

Author(s):

Hiroshi Kimura ◽

Koji Wada ◽

Hiroshi Kobayashi ◽

Hiroki Senshu ◽

Takayuki Hirai ◽

...

Keyword(s):

Numerical Simulations ◽

Water Vapour ◽

Molecular Clouds ◽

Laboratory Experiments ◽

Systematic Investigation ◽

Dust Particles ◽

Water Ice ◽

Snow Line ◽

Quasi Liquid Layer ◽

Protoplanetary Discs

ABSTRACT Beyond the snow line of protoplanetary discs and inside the dense core of molecular clouds, the temperature of gas is low enough for water vapour to condense into amorphous ices on the surface of pre-existing refractory dust particles. Recent numerical simulations and laboratory experiments suggest that condensation of the vapour promotes dust coagulation in such a cold region. However, in the numerical simulations, cohesion of refractory materials is often underestimated, while in the laboratory experiments, water vapour collides with surfaces at more frequent intervals compared to the real conditions. Therefore, to re-examine the role of water ice in dust coagulation, we carry out systematic investigation of available data on coagulation of water-ice particles by making full use of appropriate theories in contact mechanics and tribology. We find that the majority of experimental data are reasonably well explained by lubrication theories, owing to the presence of a quasi-liquid layer (QLL). Only exceptions are the results of dynamic collisions between particles at low temperatures, which are, instead, consistent with the JKR theory, because QLLs are too thin to dissipate their kinetic energies. By considering the vacuum conditions in protoplanetary discs and molecular clouds, the formation of amorphous water ice on the surface of refractory particles does not necessarily aid their collisional growth as currently expected. While crystallization of water ice around but outside the snow line eases coagulation of ice-coated particles, sublimation of water ice inside the snow line is deemed to facilitate coagulation of bare refractory particles.

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On the evolution of the Snow Line in Protoplanetary Discs

Proceedings of the International Astronomical Union ◽

10.1017/s1743921313008235 ◽

2013 ◽

Vol 8 (S299) ◽

pp. 167-168

Author(s):

Rebecca G. Martin ◽

Mario Livio

Keyword(s):

Steady State ◽

Accretion Rate ◽

Dead Zone ◽

Giant Planets ◽

Rotational Instability ◽

Sufficient Time ◽

The Earth ◽

Snow Line ◽

The Dead ◽

Protoplanetary Discs

AbstractWe examine the evolution of the snow line in a protoplanetary disc. If the magneto-rotational instability (MRI) drives turbulence throughout the disc, there is a unique snow line outside of which the disc is icy. The snow line moves closer to the star as the infall accretion rate drops. Because the snow line moves inside the radius of the Earth's orbit, the formation of our water-devoid planet is difficult with this model. However, protoplanetary discs are not likely to be sufficiently ionised to be fully turbulent. A dead zone at the mid-plane slows the flow of material through the disc and a global steady state cannot be achieved. We model the evolution of the snow line also in a disc with a dead zone. As the mass is accumulating, the outer parts of the dead zone become self gravitating, heat the massive disc and thus the outer snow line does not come inside the radius of the Earth's orbit. With this model there is sufficient time and mass in the disc for the Earth to form from water-devoid planetesimals at a radius of 1AU. Furthermore, the additional inner icy region within the dead zone predicted by this model may allow for the formation of giant planets close to their host star without the need for much migration.

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Oxygen isotope systematics of chondrules in the Paris CM2 chondrite: Indication for a single large formation region across snow line

Geochimica et Cosmochimica Acta ◽

10.1016/j.gca.2021.02.012 ◽

2021 ◽

Vol 299 ◽

pp. 199-218 ◽

Cited By ~ 1

Author(s):

Noël Chaumard ◽

Céline Defouilloy ◽

Andreas T. Hertwig ◽

Noriko T. Kita

Keyword(s):

Oxygen Isotope ◽

Formation Region ◽

Snow Line ◽

Isotope Systematics ◽

Large Formation

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MRI-active inner regions of protoplanetary discs. I. A detailed model of disc structure

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab920 ◽

2021 ◽

Vol 504 (1) ◽

pp. 280-299

Author(s):

Marija R Jankovic ◽

James E Owen ◽

Subhanjoy Mohanty ◽

Jonathan C Tan

Keyword(s):

Energy Transport ◽

Threshold Temperature ◽

Mass Star ◽

Dust Grains ◽

Solar Mass ◽

Detailed Model ◽

Short Period ◽

Pressure Maximum ◽

Ion Emission ◽

Protoplanetary Discs

ABSTRACT Short-period super-Earth-sized planets are common. Explaining how they form near their present orbits requires understanding the structure of the inner regions of protoplanetary discs. Previous studies have argued that the hot inner protoplanetary disc is unstable to the magnetorotational instability (MRI) due to thermal ionization of potassium, and that a local gas pressure maximum forms at the outer edge of this MRI-active zone. Here we present a steady-state model for inner discs accreting viscously, primarily due to the MRI. The structure and MRI-viscosity of the inner disc are fully coupled in our model; moreover, we account for many processes omitted in previous such models, including disc heating by both accretion and stellar irradiation, vertical energy transport, realistic dust opacities, dust effects on disc ionization, and non-thermal sources of ionization. For a disc around a solar-mass star with a standard gas accretion rate ($\dot{M}\, \sim \, 10^{-8}$ M⊙ yr−1) and small dust grains, we find that the inner disc is optically thick, and the accretion heat is primarily released near the mid-plane. As a result, both the disc mid-plane temperature and the location of the pressure maximum are only marginally affected by stellar irradiation, and the inner disc is also convectively unstable. As previously suggested, the inner disc is primarily ionized through thermionic and potassium ion emission from dust grains, which, at high temperatures, counteract adsorption of free charges on to grains. Our results show that the location of the pressure maximum is determined by the threshold temperature above which thermionic and ion emission become efficient.

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