Ice Line Research Articles

The fate of icy pebbles undergoing sublimation in protoplanetary discs

Abstract Icy pebbles may play an important role in planet formation close to the water ice line of protoplanetary discs. There, dust coagulation is more efficient and re-condensation of vapor on pebbles may enhance their growth outside the ice line. Previous theoretical studies showed that disruption of icy pebbles due to sublimation increases the growth rate of pebbles inside and outside the ice line, by freeing small silicate particles back in the dust reservoir of the disc. However, since planet accretion is dependent on the Stokes number of the accreting pebbles, the growth of planetesimals could be enhanced downstream of the ice line if pebbles are not disrupting upon sublimation. We developed two experimental models of icy pebbles using different silicate dusts, and we exposed them to low-temperature and low-pressure conditions in a vacuum chamber. Increasing the temperature inside the chamber, we studied the conditions for which pebbles are preserved through sublimation without disrupting. We find that small silicate particles (<50 μm) and a small quantity of ice (around 15 per cent pebble mass) are optimal conditions for preserving pebbles through sublimation. Furthermore, pebbles with coarse dust distribution (100–300 μm) do not disrupt if a small percentage (10–20 per cent mass) of dust grains are smaller than 50 μm. Our findings highlight how sublimation is not necessarily causing disruption, and that pebbles seem to survive fast sublimation processes effectively.

Molecules with ALMA at Planet-forming Scales (MAPS). VII. Substellar O/H and C/H and Superstellar C/O in Planet-feeding Gas

Abstract The elemental composition of the gas and dust in a protoplanetary disk influences the compositions of the planets that form in it. We use the Molecules with ALMA at Planet-forming Scales (MAPS) data to constrain the elemental composition of the gas at the locations of potentially forming planets. The elemental abundances are inferred by comparing source-specific gas-grain thermochemical models with variable C/O ratios and small-grain abundances from the DALI code with CO and C2H column densities derived from the high-resolution observations of the disks of AS 209, HD 163296, and MWC 480. Elevated C/O ratios (∼2.0), even within the CO ice line, are necessary to match the inferred C2H column densities over most of the pebble disk. Combined with constraints on the CO abundances in these systems, this implies that both the O/H and C/H ratios in the gas are substellar by a factor of 4–10, with the O/H depleted by a factor of 20–50, resulting in the high C/O ratios. This necessitates that even within the CO ice line, most of the volatile carbon and oxygen is still trapped on grains in the midplane. Planets accreting gas in the gaps of the AS 209, HD 163296, and MWC 480 disks will thus acquire very little carbon and oxygen after reaching the pebble isolation mass. In the absence of atmosphere-enriching events, these planets would thus have a strongly substellar O/H and C/H and superstellar C/O atmospheric composition. This paper is part of the MAPS special issue of the Astrophysical Journal Supplement.

Molecules with ALMA at Planet-forming Scales (MAPS). XV. Tracing Protoplanetary Disk Structure within 20 au

Abstract Constraining the distribution of gas and dust in the inner 20 au of protoplanetary disks is difficult. At the same time, this region is thought to be responsible for most planet formation, especially around the water ice line at 3–10 au. Under the assumption that the gas is in a Keplerian disk, we use the exquisite sensitivity of the Molecules with ALMA at Planet-forming Scales (MAPS) ALMA large program to construct radial surface brightness profiles with a ∼3 au effective resolution for the CO isotopologue J = 2–1 lines using the line velocity profile. IM Lup reveals a central depression in 13CO and C18O that is ascribed to a pileup of ∼500 M ⊕ of dust in the inner 20 au, leading to a gas-to-dust ratio of around <10. This pileup is consistent with an efficient drift of grains (≳100 M ⊕ Myr−1) and a local gas-to-dust ratio that suggests that the streaming instability could be active. The CO isotopologue emission in the GM Aur disk is consistent with a small (∼15 au), strongly depleted gas cavity within the ∼40 au dust cavity. The radial surface brightness profiles for both the AS 209 and HD 163296 disks show a local minimum and maximum in the C18O emission at the location of a known dust ring (∼14 au) and gap (∼10 au), respectively. This indicates that the dust ring has a low gas-to-dust ratio (>10) and that the dust gap is gas-rich enough to have optically thick C18O. This paper is part of the MAPS special issue of the Astrophysical Journal Supplement.

A solar C/O and sub-solar metallicity in a hot Jupiter atmosphere.

Measurements of the atmospheric carbon (C) and oxygen (O) relative to hydrogen (H) in hot Jupiters (relative to their host stars) provide insight into their formation location and subsequent orbital migration1,2. Hot Jupiters that form beyond the major volatile (H2O/CO/CO2) ice lines and subsequently migrate post disk-dissipation are predicted have atmospheric carbon-to-oxygen ratios (C/O) near 1 and subsolar metallicities2, whereas planets that migrate through the disk before dissipation are predicted to be heavily polluted by infalling O-rich icy planetesimals, resulting in C/O < 0.5 and super-solar metallicities1,2. Previous observations of hot Jupiters have been able to provide bounded constraints on either H2O (refs. 3-5) or CO (refs. 6,7), but not both for the same planet, leaving uncertain4 the true elemental C and O inventory and subsequent C/O and metallicity determinations. Here we report spectroscopic observations of a typical transiting hot Jupiter, WASP-77Ab. From these, we determine the atmospheric gas volume mixing ratio constraints on both H2O and CO (9.5 × 10-5-1.5 × 10-4 and 1.2 × 10-4-2.6 × 10-4, respectively). From these bounded constraints, we are able to derive the atmospheric C/H ([Formula: see text] × solar) and O/H ([Formula: see text] × solar) abundances and the corresponding atmospheric carbon-to-oxygen ratio (C/O = 0.59 ± 0.08; the solar value is 0.55). The sub-solar (C+O)/H ([Formula: see text] × solar) is suggestive of a metal-depleted atmosphere relative to what is expected for Jovian-like planets1 while the near solar value of C/O rules out the disk-free migration/C-rich2 atmosphere scenario.

Constraints on the ice composition of carbonaceous chondrites from their magnetic mineralogy

Carbonaceous chondrites experienced varying degrees of aqueous alteration on their parent asteroids, which influenced their mineralogies, textures, and bulk chemical and isotopic compositions. Although this alteration was a crucial event in the history of these meteorites, their various alteration pathways are not well understood. One phase that formed during this alteration was magnetite, and its morphology and abundance vary between and within chondrite groups, providing a means of investigating chondrite aqueous alteration. We measured bulk magnetic properties and first-order reversal curve (FORC) diagrams of CM, CI, CO, and ungrouped C2 chondrites to identify the morphology and size range of magnetite present in these meteorites. We identify two predominant pathways of aqueous alteration among these meteorites that can be distinguished by the resultant morphology of magnetite. In WIS 91600, Tagish Lake, and CI chondrites, magnetite forms predominantly from Fe-sulfides as framboids and stacked plaquettes. In CM and CO chondrites, <0.1 μm single-domain (SD) magnetite and 0.1–5 μm vortex (V) state magnetite formed predominantly via the direct replacement of metal and Fe-sulfides. After ruling out differences in temperature, water:rock ratios, terrestrial weathering effects, and starting mineralogy, we hypothesise that the primary factor controlling the pathway of aqueous alteration was the composition of the ice accreted into each chondrite group's parent body. Nebula condensation sequences predict that the most feasible method of appreciably evolving ice concentrations was the condensation of ammonia, which will have formed a more alkaline hydrous fluid upon melting, leading to fundamentally different conditions that may have caused the formation of different magnetite morphologies. As such, we suggest that WIS 91600, Tagish Lake, and the CI chondrites accreted past the ammonia ice line, supporting a more distal or younger accretion of their parent asteroids.

Investigation on the Nonlinear Vibration Characteristics of Current-Carrying Crescent Iced Conductors under Aerodynamic Forces, Ampere’s Forces, and Forced Excitation Conditions

Aiming at the problem of nonlinear vibration of current-carrying iced conductors, the aerodynamic forces are introduced into the previous vibration equation of current-carrying conductors that only considered Ampere’s forces. At the same time, on this basis, a forced excitation load is further introduced to study the influence of dynamic wind on the nonlinear vibration characteristics of current-carrying iced conductors, and a new current-carrying iced conductors system under the combined action of Ampere’s forces, forced excitation, and aerodynamic forces has been established, and the improved theoretical modeling of current-carrying iced transmission lines made the model more in line with practical engineering. Firstly, the model of current-carrying iced conductors was established, and then the vibration equation of the model was derived. And the vibration equation was transformed into a finite dimensional ordinary differential equation by using the Galerkin method. The amplitude-frequency response functions of the nonlinear forced primary resonances and super-harmonic and subharmonic resonances of the system are derived by using the multiscale method. Through numerical calculation, the influence of current-carrying, spacing, wind velocity, tension, and excitation amplitude on the response amplitude when the primary resonance of the system appears is analyzed, and the difference between the two working conditions (considering the aerodynamic forces and without considering aerodynamic forces) is compared. The influence of the variation of current-carrying i on the response amplitude of super-harmonic and subharmonic resonances and the stability of the steady-state solution of forced primary resonance was analyzed. The results show that the response amplitude and the nonlinearilty of system under the action of aerodynamic forces are smaller and weaker than without the action of aerodynamic forces; the variation of line parameters has a certain influence on the response amplitude of conductor and the nonlinearity of system; the response amplitudes of the primary resonance, super-harmonic resonance, and subharmonic resonance increase with the increase in the excitation amplitudes, and the resonance peak is offset towards the negative value of the tuning parameter σ, showing the characteristics of soft spring, and the response amplitudes are accompanied by complex nonlinear dynamic behaviors such as the multivalue and jump phenomenon. The change of current-carrying i has an obvious effect on the nonlinearity of the system. The nonlinear and response amplitudes of the system are also enhanced with the increase in wind velocity. The stability of the system is judged when the primary resonance occurs, and it is found that the response amplitude shows synchronization and the out-of-step phenomenon with the change of tuning parameters. The research results obtained in this paper would help to further improve the theoretical modeling about current-carrying iced lines, and the research of line parameters can give a certain reference value to practical engineering, and it will have a positive effect on the safe operation of high-voltage transmission lines.

How drifting and evaporating pebbles shape giant planets

Upcoming studies of extrasolar gas giants will give precise insights into the composition of planetary atmospheres, with the ultimate goal of linking it to the formation history of the planet. Here, we investigate how drifting and evaporating pebbles that enrich the gas phase of the disk influence the chemical composition of growing and migrating gas giants. To achieve this goal, we perform semi-analytical 1D models of protoplanetary disks, including viscous evolution, pebble drift, and evaporation, to simulate the growth of planets from planetary embryos to Jupiter-mass objects by the accretion of pebbles and gas while they migrate through the disk. The gas phase of the protoplanetary disk is enriched due to the evaporation of inward drifting pebbles crossing evaporation lines, leading to the accretion of large amounts of volatiles into the planetary atmosphere. As a consequence, gas-accreting planets are enriched in volatiles (C, O, N) compared to refractories (e.g., Mg, Si, Fe) by up to a factor of 100, depending on the chemical species, its exact abundance and volatility, and the disk’s viscosity. A simplified model for the formation of Jupiter reveals that its nitrogen content can be explained by inward diffusing nitrogen-rich vapor, implying that Jupiter did not need to form close to the N2evaporation front as indicated by previous simulations. However, our model predicts an excessively low oxygen abundance for Jupiter, implying either Jupiter’s migration across the water ice line (as in the grand tack scenario) or an additional accretion of solids into the atmosphere (which can also increase Jupiter’s carbon abundance, ultimately changing the planetary C/O ratio). The accretion of solids, on the other hand, will increase the refractory-to-volatile ratio in planetary atmospheres substantially. We thus conclude that the volatile-to-refractory ratio in planetary atmospheres can place a strong constraint on planet formation theories (in addition to elemental ratios), especially on the amount of solids accreted into atmospheres, making it an important target for future observations.

Radial Gradients in Dust-to-gas Ratio Lead to Preferred Region for Giant Planet Formation

Abstract The Rosseland mean opacity of dust in protoplanetary disks is often calculated assuming the interstellar medium (ISM) size distribution and a constant dust-to-gas ratio. However, the dust size distribution and dust-to-gas ratio in protoplanetary disks are distinct from those of the ISM. Here we use simple dust evolution models that incorporate grain growth and transport to calculate the time evolution of the mean opacity of dust grains as a function of distance from the star. Dust dynamics and size distribution are sensitive to the assumed value of the turbulence strength α t and the velocity at which grains fragment v frag. For moderate-to-low turbulence strengths of α t ≲ 10−3 and substantial differences in v frag for icy and ice-free grains, we find a spatially nonuniform dust-to-gas ratio and grain size distribution that deviate significantly from the ISM values, in agreement with previous studies. The effect of a nonuniform dust-to-gas ratio on the Rosseland mean opacity dominates over that of the size distribution. This spatially varying—that is, non-monotonic—dust-to-gas ratio creates a region in the protoplanetary disk that is optimal for producing hydrogen-rich planets, potentially explaining the apparent peak in the gas-giant planet occurrence rate at intermediate distances. The enhanced dust-to-gas ratio within the ice line also suppresses gas accretion rates onto sub-Neptune cores, thus stifling their tendency to undergo runaway gas accretion within disk lifetimes. Finally, our work corroborates the idea that low-mass cores with large primordial gaseous envelopes (“super-puffs”) originate beyond the ice line.

Axisymmetric simulations of the convective overstability in protoplanetary discs

ABSTRACT Protoplanetary discs at certain radii exhibit adverse radial entropy gradients that can drive oscillatory convection (‘convective overstability’; COS). The ensuing hydrodynamical activity may reshape the radial thermal structure of the disc while mixing solid material radially and vertically or, alternatively, concentrating it in vortical structures. We perform local axisymmetric simulations of the COS using the code snoopy, showing first how parasites halt the instability’s exponential growth, and secondly, the different saturation routes it takes subsequently. As the Reynolds and (pseudo-) Richardson numbers increase, the system moves successively from (i) a weakly non-linear state characterized by relatively ordered non-linear waves, to (ii) wave turbulence, and finally to (iii) the formation of intermittent and then persistent zonal flows. In three dimensions, we expect the latter flows to spawn vortices in the orbital plane. Given the very high Reynolds numbers in protoplanetary discs, the third regime should be the most prevalent. As a consequence, we argue that the COS is an important dynamical process in planet formation, especially near features such as dead zone edges, ice lines, gaps, and dust rings.

Ice lines as the origin for the gap/ring structure in protoplanetary disks: the issue of the assumed temperature profile

Gaps and rings are commonly seen in recent high-resolution ALMA observations of protoplanetary disks. Ice lines of volatiles are one of the mechanisms proposed to explain the origin for these substructures. To examine the ice line hypothesis, literature studies usually parameterize the mid-plane temperature with the analytic formula of a passively heated, flared disk. The temperature in this simplified expression is basically dependent on the stellar luminosity. I have built a grid of self-consistent radiative transfer models that feature the same stellar properties, but different disk parameters. The mid-plane temperature of these models shows a large dispersion over a wide range of radii, indicating that besides the stellar luminosity, the disk parameters also play an important role in determining the thermal structure. Comparing the mid-plane temperature from radiative transfer simulation with the analytic solution shows a large difference between both approaches. This result suggests that special care on the assumed temperature profile has to be taken in the analysis of gap/ring origins, and conclusions drawn in previous works on the basis of the analytic temperature should be revisited. I further took the AS 209 disk as an example, and conducted a detailed radiative transfer modeling of the spectral energy distribution and the ALMA Band 6 image. The D137, D24 and D9 gaps are associated with the ice lines of major volatiles in the disk according to such a thorough analysis. However, if the temperature profile simply follows the analytic formula, none of these gaps matches the ice lines of the species considered here.

California Legacy Survey. II. Occurrence of Giant Planets beyond the Ice Line

Abstract We used high-precision radial velocity measurements of FGKM stars to determine the occurrence of giant planets as a function of orbital separation spanning 0.03–30 au. Giant planets are more prevalent at orbital distances of 1–10 au compared to orbits interior or exterior of this range. The increase in planet occurrence at ∼1 au by a factor of ∼4 is highly statistically significant. A fall-off in giant planet occurrence at larger orbital distances is favored over models with flat or increasing occurrence. We measure 14.1 − 1.8 + 2.0 giant planets per 100 stars with semimajor axes of 2–8 au and 8.9 − 2.4 + 3.0 giant planets per 100 stars in the range 8–32 au, a decrease in occurrence with increasing orbital separation that is significant at the ∼2σ level. We find that the occurrence rate of sub-Jovian planets (0.1–1 Jupiter masses) is also enhanced for 1–10 au orbits. This suggests that lower-mass planets may share the formation or migration mechanisms that drive the increased prevalence near the water–ice line for their Jovian counterparts. Our measurements of cold gas giant occurrence are consistent with the latest results from direct imaging surveys and gravitational lensing surveys despite different stellar samples. We corroborate previous findings that giant planet occurrence increases with stellar mass and metallicity.

The California Legacy Survey. I. A Catalog of 178 Planets from Precision Radial Velocity Monitoring of 719 Nearby Stars over Three Decades

We present a high-precision radial velocity (RV) survey of 719 FGKM stars, which host 164 known exoplanets and 14 newly discovered or revised exoplanets and substellar companions. This catalog updated the orbital parameters of known exoplanets and long-period candidates, some of which have decades-longer observational baselines than they did upon initial detection. The newly discovered exoplanets range from warm sub-Neptunes and super-Earths to cold gas giants. We present the catalog sample selection criteria, as well as over 100,000 RV measurements, which come from the Keck-HIRES, APF-Levy, and Lick-Hamilton spectrographs. We introduce the new RV search pipeline RVSearch (https://california-planet-search.github.io/rvsearch/) that we used to generate our planet catalog, and we make it available to the public as an open-source Python package. This paper is the first study in a planned series that will measure exoplanet occurrence rates and compare exoplanet populations, including studies of giant planet occurrence beyond the water ice line, and eccentricity distributions to explore giant planet formation pathways. We have made public all radial velocities and associated data that we use in this catalog.

Revision of “Dependence of Climate States of Gray Atmosphere on Solar Constant: From the Runaway Greenhouse to the Snowball States” by Ishiwatari et al. (2007)

AbstractIshiwatari et al. (2007) (https://doi.org/10.1029/2006JD007368) investigated multiple equilibrium solutions of a gray atmosphere for various values of solar constant, utilizing two types of models, namely, a one‐dimensional energy balance model and a general circulation model (GCM) with simplified physical processes, both of which permit existence of the runaway greenhouse state. The study was retracted, since there was a bug in their GCM that affected quantitative aspects of the study. Here, we revise the study with re‐performing all of the GCM experiments using an appropriately corrected model. The results of re‐experiments show that the main features of the climate regime diagram drawn in the solar constant ‐ ice line latitude plane are mostly unchanged, except that the ice‐free equilibrium state, which existed in Ishiwatari et al. (2007) (https://doi.org/10.1029/2006JD007368) now disappears. It is confirmed that there are the partially ice‐covered state, the globally ice‐covered state, and the runaway greenhouse state. These three states coexist for intermediate values of solar constant. The existence of the large ice cap instability is also confirmed, although the critical latitude of the partially ice‐covered state extends equatorward. Also same as before, the small ice cap instability does not seem to appear.

Analysis of stability and modal interaction for multi-modal coupling galloping of iced transmission lines

Considering geometric and aerodynamic nonlinearities, in this work, a reduced dynamic model with crescent-shaped ice accretions has been established to describe the coupling effects of in-plane, out-of-plane and torsional motions on galloping with longitudinal motions limited to in-plane and out-of-plane directions for simplification. Based on natural frequencies and associated eigenfunctions obtained for each of the three directions, motion equations containing two in-plane, two out-of-plane and two torsional components are obtained by Galerkin spatial discretization. By using eigenvalue analysis and numerical methods, galloping stability is investigated at different wind speeds, sags, initial wind attack angles, in-plane damping ratios and torsional damping ratios. The effect laws of different parameters on galloping are analyzed and Hopf bifurcation points are obtained, which denote the upper and lower critical wind speeds where the upper critical wind speed is mainly related to in-plane motion. Then, multi-modal interaction mechanisms with different parameters are discussed in detail. A variety of internal resonance behaviors are observed in the system and their similarities and differences are analyzed. Meanwhile, galloping presents synchronous and limited-amplitude characteristics, the reasons of which are explained. These reveal the occurrence of different energy exchanges among various modes. This research provides a theoretical foundation for the design of transmission lines.

Theoretical Analysis and Experimental Validation on Galloping of Iced Transmission Lines in a Moderating Airflow

Galloping of an iced transmission line subjected to a moderating airflow has been analysed in this study, and a new form of galloping is discovered both theoretically and experimentally. The partial differential equations of the iced transmission line are established based on the Hamilton theory. The Galerkin method is then applied on the continuous model, and a discrete model is derived along with its first two in-plane and torsional modes. A trapezoidal wind field model is built through the superposition of simple harmonic waves. The vibrational amplitude is generally observed to be more violent when the wind velocity decreases, except in the 2nd in-plane mode. Furthermore, the influence of the declining wind velocity rates on galloping is analysed using different postdecline wind velocities and the duration of the decline in wind velocities. Subsequently, an experiment has been carried out on a continuous model of an iced conductor in the wind tunnel dedicated for galloping. The first two in-plane modal profiles are observed, along with their response to the moderating airflow. Different declining rates of the wind velocity are also verified in the wind tunnel, which show good agreement with the results simulated by the mathematical model. The sudden increase in the galloping amplitude poses a significant threat to the transmission system, which also improves the damage mechanism associated with the galloping of a slender, a long structure with a noncircular cross-section.

The water-ice line as a birthplace of planets: implications of a species-dependent dust fragmentation threshold

The thermodynamic structure of protoplanetary discs is determined by dust opacities, which depend on the size of the dust grains and their chemical composition. In the inner regions, the grain sizes are regulated by the level of turbulence (e.g. α viscosity) and by the dust fragmentation velocity that represents the maximal velocity that grains can have at a collision before they fragment. Here, we perform self-consistently calculated 2D hydrodynamical simulations that consider a full grain size distribution of dust grains with a transition in the dust fragmentation velocity at the water-ice line. This approach accounts for the results of previous particle collision laboratory experiments, in which silicate particles typically have a lower dust fragmentation velocity than water-ice particles. Furthermore, we probe the effects of variations in the water abundance, the dust-to-gas ratio, and the turbulence parameter on the disc structure. For the discs with a transition in the dust fragmentation velocity at the water-ice line, we find a narrow but striking zone of planetary outward migration, including for low viscosities. In addition, we find a bump in the radial pressure gradient profile that tends to be located slightly inside the ice line. Both of these features are present for all tested disc parameters. Thus, we conclude that the ice line can function both as a migration trap, which can extend the growth times of planets before they migrate to the inner edge of the protoplanetary disc, and as a pressure trap, where planetesimal formation can be initiated or enhanced.

Dry or water world? How the water contents of inner sub-Neptunes constrain giant planet formation and the location of the water ice line

In the pebble accretion scenario, the pebbles that form planets drift inward from the outer disk regions, carrying water ice with them. At the water ice line, the water ice on the inward drifting pebbles evaporates and is released into the gas phase, resulting in water-rich gas and dry pebbles that move into the inner disk regions. Large planetary cores can block the inward drifting pebbles by forming a pressure bump outside their orbit in the protoplanetary disk. Depending on the relative position of a growing planetary core relative to the water ice line, water-rich pebbles might be blocked outside or inside the water ice line. Pebbles blocked outside the water ice line do not evaporate and thus do not release their water vapor into the gas phase, resulting in a dry inner disk, while pebbles blocked inside the water ice line release their water vapor into the gas phase, resulting in water vapor diffusing into the inner disk. As a consequence, close-in sub-Neptunes that accrete some gas from the disk should be dry or wet, respectively, if outer gas giants are outside or inside the water ice line, assuming that giant planets form fast, as has been suggested for Jupiter in our Solar System. Alternatively, a sub-Neptune could form outside the water ice line, accreting a large amount of icy pebbles and then migrating inward as a very wet sub-Neptune. We suggest that the water content of inner sub-Neptunes in systems with giant planets that can efficiently block the inward drifting pebbles could constrain the formation conditions of these systems, thus making these sub-Neptunes exciting targets for detailed characterization (e.g., with JWST, ELT, or ARIEL). In addition, the search for giant planets in systems with already characterized sub-Neptunes can be used to constrain the formation conditions of giant planets as well.

Cold Traps of Hypervolatiles in the Protosolar Nebula at the Origin of the Peculiar Composition of Comet C/2016 R2 (PanSTARRS)

Abstract Recent observations of the long-period comet C/2016 R2 (PanSTARRS; hereafter R2) indicate an unusually high N2/CO abundance ratio, typically larger than ∼0.05, and at least 2–3 times higher than the one measured in 67P/Churyumov–Gerasimenko. Another striking compositional feature of this comet is its heavy depletion in H2O (H2O/CO ∼ 0.32%), compared to other comets. Here we investigate the formation circumstances of a generic comet whose composition reproduces these two key features. We first envisage the possibility that this comet agglomerated from clathrates, but we find that such a scenario does not explain the observed low water abundance. We then alternatively investigate the possibility that the building blocks of R2 agglomerated from grains and pebbles made of pure condensates via the use of a disk model describing the radial transport of volatiles. We show that N2/CO ratios reproducing the value estimated in this comet can be found in grains condensed in the vicinity of the CO and N2 ice lines. Moreover, high CO/H2O ratios (&gt;100 times the initial gas-phase value) can be found in grains condensed in the vicinity of the CO ice line. If the building blocks of a comet assembled from such grains, they should present N2/CO and CO/H2O ratios consistent with the measurements made in R2’s coma. Our scenario indicates that R2 formed in a colder environment than the other comets that share more usual compositions. Our model also explains the unusual composition of the interstellar comet 2l/Borisov.

Investigation on the Accuracy of Approximate Solutions Obtained by Perturbation Method for Galloping Equation of Iced Transmission Lines

Perturbation method is a commonly used method to solve galloping equation of iced transmission lines, but few scholars have studied the influences of perturbation method on the accuracy of approximate solutions of the galloping equation. In order to analyze the accuracy of approximate solutions obtained by perturbation method for galloping equation of iced transmission lines, the partial differential galloping equation of iced transmission lines with quadratic and cubic nonlinear terms is obtained firstly. Then, the partial differential galloping equation is transformed into ordinary differential galloping equation by Galerkin method. Finally, the approximate solutions of the partial differential galloping equation are obtained by averaging method and first-order, second-order, third-order, and fourth-order multiple scales methods, and the results obtained by these methods are compared systematically. By comparing the numerical solutions and the approximate solutions obtained by averaging method, it can be found that, with the increasing in wind velocity and Young’s modulus of iced transmission lines, the nonlinearity of the system would strengthen and the drift of the vibration center of the system would also increase. The larger the drift is, the greater the error between the approximate solutions obtained by averaging method and the numerical solutions will be. And when the wind velocity reaches 32 m/s, the error would arrive at 17.321%. By comparing the numerical solutions and the approximate solutions obtained by the first-order, the second-order, the third-order, and the fourth-order multiple scales methods, it can be concluded that the first-order multiple scales method is less complex computationally. The accuracy of approximate solutions obtained by the fourth-order multiple scales method is better than that obtained by the first-order, the second-order, and the third-order multiple scales methods, and the error between the approximate solutions obtained by the fourth-order multiple scales method and the numerical solutions is less than 0.639%. The conclusions obtained in this paper would be helpful to the solutions of galloping equation of iced transmission lines and could also give some references to practical engineering.

Planar Nonlinear Galloping of Iced Transmission Lines under Forced Self-Excitation Conditions

In order to study the influence of dynamic wind on the nonlinear galloping characteristics of iced transmission lines, an external excitation load is added to the governing equation of iced transmission lines under the condition of stable wind, and a new forced self-excited system has been established. The frequency-amplitude relationship of the forced self-excited system under weak excitation and strong excitation is obtained by using the multiple-scale method. The principal resonances and superharmonic and subharmonic resonances of the forced self-excited system have also been analyzed. The results show that, in the forced self-excited system under strong excitation, when the excitation frequency is close to the integral and fractional times of the natural frequency, it is easier to produce 1/2-order subharmonic resonance, 2-order superharmonic resonance, and 3-order superharmonic resonance. In addition, numerical techniques provide bifurcation diagrams of different control parameters, which are able to highlight the effects of the simultaneous presence of the sources of excitation. When the control parameters (wind velocity, excitation amplitude, tuning parameter, tension, and Young’s modulus) change, the response amplitudes of the principal resonance and harmonic resonance will have multivalues, jump phenomenon, and hardening behavior. The control parameters can be used as a reference for engineering design. More importantly, as a combination of the Duffing equation and the Rayleigh equation, the forced self-excited system also has high theoretical research value.