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At least 19 records

Discovery of a Similar to 5 Day Characteristic Timescale in the Kepler Power Spectrum of Zw 229-15

We present time series analyses of the full Kepler dataset of Zw 229− 15. This Kepler light curve- with a baseline greater than three years, composed of virtually continuous, evenly sampled 30-minute measurements - is unprecedented in its quality and precision. We utilize two methods of power spectral analysis to investigate the optical variability and search for evidence of a bend frequency associated with a characteristic optical variability timescale. Each method yields similar results. The first interpolates across data gaps to use the standard Fourier periodogram. The second, using the CARMA-based time-domain modeling technique of Kelly et al., does not need evenly-sampled data. Both methods find excess power at high frequencies that may be due to Kepler instrumental effects. More importantly both also show strong bends (delta alpha is approx. 2) at timescales of approx. 5 days, a feature similar to those seen in the X-ray PSDs of AGN but never before in the optical. This observed approx. 5 day timescale may be associated with one of several physical processes potentially responsible for the variability. A plausible association could be made with light -crossing, dynamical or thermal timescales, depending on the assumed value of the accretion disk size and on unobserved disk parameters such as alpha and H¬R. This timescale is not consistent with the viscous timescale, which would be years in a approx. 10(exp7) solar mass AGN such as Zw 229− 15. However there must be a second bend on long (& 1 year) timescales, and that feature could be associated with the viscous timescale.

timescale↗

Characteristic Ultraviolet/Optical Timescales in Active Galactic Nuclei

The UV/optical light curves of active galactic nuclei (AGNs) may be roughly characterized by a periodic fractional flux variations of approx. 10% on timescales of 1 month. The physical mechanism(s) responsible remain ill defined. We present a structure function analysis, i.e., measure the power distribution over a range of timescales tau, of 13 AGNs to constrain the origin of UV/optical emission. On timescales tau approx. 5- 60 days, the mean UV and optical power density spectra (PDS) are equivalent. This may suggest that the underlying energy generating mechanism is identical. The combined W/optical PDS is P(f) proportional to f(sup -alpha)- with alpha = 2.13(sup +0.22, sub -0.06). For sources with measured X-ray PDS indices, we find they are indistinguishable from their UV/optical counterparts. This supports scenarios whereby X-rays are generated via Compton upscattering of UV photons, to later radiatively drive optical variations. At the same time, we present evidence for characteristic variability timescales tau(sub char) of approx. 5-100 days in 10 sources. These variability timescales combined with reverberation based masses M suggest a M - tau(sub char) relationship; higher mass systems have larger characteristic timescales. The UV tau(sub char) may possibly reflect dynamical or accretion disk thermal timescales. We find suggestive evidence for a dichotomy, at tau approx. 30 days and M approx. l0(exp 7) solar mass, between short- and long-time scale optical variations. These optical variations may be attributable to dynamical and accretion disk thermal or starburst activity timescales, respectively.

Collier, Stefan↗

Six-Degree-of-Freedom Trajectory Optimization Utilizing a Two-Timescale Collocation Architecture

Six-degree-of-freedom (6DOF) trajectory optimization of a reentry vehicle is solved using a two-timescale collocation methodology. This class of 6DOF trajectory problems are characterized by two distinct timescales in their governing equations, where a subset of the states have high-frequency dynamics (the rotational equations of motion) while the remaining states (the translational equations of motion) vary comparatively slowly. With conventional collocation methods, the 6DOF problem size becomes extraordinarily large and difficult to solve. Utilizing the two-timescale collocation architecture, the problem size is reduced significantly. The converged solution shows a realistic landing profile and captures the appropriate high-frequency rotational dynamics. A large reduction in the overall problem size (by 55%) is attained with the two-timescale architecture as compared to the conventional single-timescale collocation method. Consequently, optimum 6DOF trajectory problems can now be solved efficiently using collocation, which was not previously possible for a system with two distinct timescales in the governing states.

Desai, Prasun N.↗

Timescales of Soil Moisture Anomalies: Results from Two GCMs

Soil moisture anomalies dissipate over timescales that may span weeks to months. Characterizing the geographical and seasonal variations in these timescales can have important practical benefit; significant soil moisture "memory" allows long-lead forecasts of soil moisture, which have been found in recent studies to be essential for useful Ion--lead forecasts of precipitation in many regions. In this talk, we will present and compare the soil moisture timescales derived in two separate general circulation model (GCM) studies. Both studies employ multiple ensembles of short-term climate simulations. Timescales at a given point are effectively estimated by determining how quickly the soil moisture distribution generated in one ensemble of simulations (characterized by a unique set of initial soil moisture conditions) approaches that produced by another ensemble (characterized by a different set of initial soil moisture conditions). The talk will include a discussion of why the timescales produced by the two GCMs differ in some regions, and it will also describe the impact of soil moisture memory on simulated precipitation.

Koster, Randal D.↗

Candidate Brown-dwarf Microlensing Events with Very Short Timescales and Small Angular Einstein Radii

Short-timescale microlensing events are likely to be produced by substellar brown dwarfs (BDs), but it is difficult to securely identify BD lenses based on only event timescales because short-timescale events can also be produced by stellar lenses with high relative lens-source proper motions. In this paper, we report three strong candidate BD-lens events found from the search for lensing events not only with short timescales (t(E) ≲ 6 days) but also with very small angular Einstein radii (θ(E) ≲ 0.05 mas) among the events that have been found in the 2016–2019 observing seasons. These events include MOA-2017-BLG-147, MOA-2017-BLG-241, and MOA-2019-BLG-256, in which the first two events are produced by single lenses and the last event is produced by a binary lens. From the Monte Carlo simulations of Galactic events conducted with the combined t(E) and θ(E) constraint, it is estimated that the lens masses of the individual events are 0.051 (sup +0.100, sub -0.027) M(ʘ), 0.044 (sup +0.090, sub -0.023) M(ʘ), and 0.046 (sup +0.067, sub -0.023) M(ʘ)/0.038 (sup +0.056, sub -0.019) M(ʘ) and the probability of the lens mass smaller than the lower limit of stars is ~80% for all events. We point out that routine lens mass measurements of short-timescale lensing events require survey-mode space-based observations.

Cheongho Han↗

Recovery Timescales of the Dayside Martian Magnetosphere to IMF Variability

In this work we revisit an event observed by Mars Atmosphere and Volatile Evolution MissioNin the solar wind where the interplanetary magneticfield (IMF) rotates around the Mars‐Sun axis during∼6 min. Based on a time‐dependent LATMOS Hybrid Simulation, we determine recovery timescales of thedayside Martian magnetosphere normalized by the IMF variability timescale. Particularly, wefind thatsuch recovery timescales range between 8 s and 11 min for an∼90° IMF rotation that lasted 50 s (observed aspart of the 6‐min time interval), depending on the considered magnetospheric region. We alsofind thatthe O+plume recovery timescales range between 40 and 120 s, taking greater values for further downstreamdistances (at least up to 1RMdownstream from the terminator plane). This range is on the order of themagnetosheath O+gyroperiod, showing the kinetic nature of the plume recovery process.

Romanelli, N.↗

Guided Plasmaspheric Hiss Interactions with Superthermal Electrons: Resonance Curves and Timescales - Part 1

Under the proper conditions, guided plasmaspheric hiss is shown to be more efficient than Coulomb collisions at scattering electrons in the superthermal energy range of 50 to 500 eV. Broadband, whistler mode hiss becomes guided by plasma density gradients, intensifying the wave energy densities and focusing the wave normal angles. These waves are shown to interact through Cherenkov (Landau) resonance with electrons below 500 eV, and the presented equatorial plane timescales for pitch angle, energy, and mixed diffusion are shown to be faster than Coulomb collision timescales for typical values at the inner edge of the plasmapause and in detached plasma regions. In the latter case, energy diffusion timescales of less than 100 s for small pitch angle electrons between 250 and 500 eV indicate that these waves have the potential to dramatically change the distribution function.

Liemohn, M. W.↗

Guided Plasmaspheric Hiss Interactions with Superthermal Electrons: Resonance Curves and Timescales - 1

Under the proper conditions, guided plasmaspheric hiss is shown to be more efficient than Coulomb collisions at scattering electrons in the superthermal energy range of 50 to 500 eV. Broadband, whistler mode hiss becomes guided by plasma density gradients, intensifying the wave energy densities and focusing the wave normal angles. These waves are shown to interact through Cherenkov (Landau) resonance with electrons below 500 eV, and the presented equatorial plane timescales for pitch angle, energy, and mixed diffusion are shown to be faster than Coulomb collision timescales for typical values at the inner edge of the plasmapause and in detached plasma regions. In the latter case, energy diffusion timescales of less than 100 s for small pitch angle electrons between 250 and 500 eV indicate that these waves have the potential to dramatically change the distribution function.

Liemohn, M. W.↗

Timescales of Land Surface Evapotranspiration Response

Soil and vegetation exert strong control over the evapotranspiration rate, which couples the land surface water and energy balances. A method is presented to quantify the timescale of this surface control using daily general circulation model (GCM) simulation values of evapotranspiration and precipitation. By equating the time history of evaporation efficiency (ratio of actual to potential evapotranspiration) to the convolution of precipitation and a unit kernel (temporal weighting function), response functions are generated that can be used to characterize the timescales of evapotranspiration response for the land surface model (LSM) component of GCMS. The technique is applied to the output of two multiyear simulations of a GCM, one using a Surface-Vegetation-Atmosphere-Transfer (SVAT) scheme and the other a Bucket LSM. The derived response functions show that the Bucket LSM's response is significantly slower than that of the SVAT across the globe. The analysis also shows how the timescales of interception reservoir evaporation, bare soil evaporation, and vegetation transpiration differ within the SVAT LSM.

Scott, Russell↗

A Search for Short Timescale Microvariability in Active Galactic Nuclei in the Ultraviolet

We observed four AGNs (the type-1 Seyfert systems 3C249.1, NGC 6814 and Mrk 205, and the BL Lac object 3C371) using the High Speed Photometer on the Hubble Space Telescope to search for short timescale microvariability in the W. Continuous observations of 3 0 0 0 s duration were obtained for each system on several consecutive HST orbits using a 1 s sample time in a 1400 - 3000 2 bandpass. variability > 0.3 % (0 . 003 mag) was detected in any AGN on timescales shorter than 1500 s. The distribution of photon arrival times observed from each source was consistent with Poisson statistics. Because of HST optical problems, the limit on photometric variability at longer timescales is less precise. These results restrict models of supermassive black holes as the central engine of an AGN and the diskoseismology oscillations of any accretion disk around such a black hole.

Dolan, Joseph F.↗

A Two-Timescale Discretization Scheme for Collocation

The development of a two-timescale discretization scheme for collocation is presented. This scheme allows a larger discretization to be utilized for smoothly varying state variables and a second finer discretization to be utilized for state variables having higher frequency dynamics. As such. the discretization scheme can be tailored to the dynamics of the particular state variables. In so doing. the size of the overall Nonlinear Programming (NLP) problem can be reduced significantly. Two two-timescale discretization architecture schemes are described. Comparison of results between the two-timescale method and conventional collocation show very good agreement. Differences of less than 0.5 percent are observed. Consequently. a significant reduction (by two-thirds) in the number of NLP parameters and iterations required for convergence can be achieved without sacrificing solution accuracy.

Desai, Prasun↗

Microphysical Timescales in Clouds and their Application in Cloud-Resolving Modeling

Computational phenomena (i.e., spurious supersaturation and negative mixing ratio of cloud water) usually exist in cloud-resolving models when the time step for explicit integration is larger than a microphysical timescale in clouds. In this paper, the microphysical timescales in clouds are studied, showing that the timescale of water vapor condensation (or cloud water evaporation) is smaller than 10 s - the order of a typical time step for cloud-resolving models. To avoid spurious computational phenomena in cloud-resolving modeling, it is suggested that moist entropy be used as a prognostic thermodynamic variable, and temperature be diagnosed from that and other prognostic variables. A simple numerical model with moist entropy as a prognostic variable, for example, is presented to show that spurious computational phenomena are removed when moist entropy is used as a prognostic variable.

Zeng, Xi-Ping↗

Transfer of Satellite Rainfall Uncertainty from Gauged to Ungauged Regions at Regional and Seasonal Timescales

Hydrologists and other users need to know the uncertainty of the satellite rainfall data sets across the range of time/space scales over the whole domain of the data set. Here, uncertainty' refers to the general concept of the deviation' of an estimate from the reference (or ground truth) where the deviation may be defined in multiple ways. This uncertainty information can provide insight to the user on the realistic limits of utility, such as hydrologic predictability, that can be achieved with these satellite rainfall data sets. However, satellite rainfall uncertainty estimation requires ground validation (GV) precipitation data. On the other hand, satellite data will be most useful over regions that lack GV data, for example developing countries. This paper addresses the open issues for developing an appropriate uncertainty transfer scheme that can routinely estimate various uncertainty metrics across the globe by leveraging a combination of spatially-dense GV data and temporally sparse surrogate (or proxy) GV data, such as the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar and the Global Precipitation Measurement (GPM) mission Dual-Frequency Precipitation Radar. The TRMM Multi-satellite Precipitation Analysis (TMPA) products over the US spanning a record of 6 years are used as a representative example of satellite rainfall. It is shown that there exists a quantifiable spatial structure in the uncertainty of satellite data for spatial interpolation. Probabilistic analysis of sampling offered by the existing constellation of passive microwave sensors indicate that transfer of uncertainty for hydrologic applications may be effective at daily time scales or higher during the GPM era. Finally, a commonly used spatial interpolation technique (kriging), that leverages the spatial correlation of estimation uncertainty, is assessed at climatologic, seasonal, monthly and weekly timescales. It is found that the effectiveness of kriging is sensitive to the type of uncertainty metric, time scale of transfer and the density of GV data within the transfer domain. Transfer accuracy is lowest at weekly timescales with the error doubling from monthly to weekly.However, at very low GV data density (<20% of the domain), the transfer accuracy is too low to show any distinction as a function of the timescale of transfer.

Tang, Ling↗

Timescale Correlation between Marine Atmospheric Exposure and Accelerated Corrosion Testing - Part 2

Evaluation of metals to predict service life of metal-based structures in corrosive environments has long relied on atmospheric exposure test sites. Traditional accelerated corrosion testing relies on mimicking the exposure conditions, often incorporating salt spray and ultraviolet (UV) radiation, and exposing the metal to continuous or cyclic conditions similar to those of the corrosive environment. Their reliability to correlate to atmospheric exposure test results is often a concern when determining the timescale to which the accelerated tests can be related. Accelerated corrosion testing has yet to be universally accepted as a useful tool in predicting the long-term service life of a metal, despite its ability to rapidly induce corrosion. Although visual and mass loss methods of evaluating corrosion are the standard, and their use is crucial, a method that correlates timescales from accelerated testing to atmospheric exposure would be very valuable. This paper presents work that began with the characterization of the atmospheric environment at the Kennedy Space Center (KSC) Beachside Corrosion Test Site. The chemical changes that occur on low carbon steel, during atmospheric and accelerated corrosion conditions, were investigated using surface chemistry analytical methods. The corrosion rates and behaviors of panels subjected to long-term and accelerated corrosion conditions, involving neutral salt fog and alternating seawater spray, were compared to identify possible timescale correlations between accelerated and long-term corrosion performance. The results, as well as preliminary findings on the correlation investigation, are presented.

Montgomery, Eliza L.↗

Covariability of Climate and Streamflow in the Upper Rio Grande from Interannual to Interdecadal Timescales

Study region: The Upper Rio Grande (URG) flows from its headwaters in Colorado, U.S., and provides an important source of water to millions of people in the U.S. states of Colorado, New Mexico, Texas, and also Mexico. Study focus: We reassess the explanatory power of the relationship of sea surface temperatures (SST) on URG streamflow variability on interannual to interdecadal timescales. We find a significant amount of the variance of spring-summer URG streamflow cannot be fully explained by SST. New hydrological insights: We find that the interdecadal teleconnection between SST and streamflow is more clear than on interannual timescales. The highest ranked years tend to be clustered during positive phases of the Pacific Decadal Oscillation (PDO). During the periods of decadal high flow (1900-1920, and 1979-1995), Pacific SST resembles a positive PDO pattern and the Atlantic a negative Atlantic Multidecadal Oscillation (AMO) pattern; an interbasin pattern shown in prior studies to be conducive to high precipitation and streamflow. To account for the part of streamflow variance not explained by SST, we analyze atmospheric Reanalysis data for the months preceding the highest spring-summer streamflow events. A variety of atmospheric configurations are found to precede the highest flow years through anomalous moisture convergence. This lack of consistency suggests that, on interannual timescales, weather and not climate can dominate the generation of high streamflow events.

AMO↗

Thermodynamic and Diffusion Model Estimates on Metamorphic Temperatures and Timescales for Basaltic Eucrite GRA 98098

Introduction: HED meteorites are thought to rep-resent igneous rocks from Vesta’s basaltic crust and preserve evidence of early crustal metamorphism. Determining the temperatures and timescales of thermal metamorphism is important for reconstructing crustal evolution in the early solar system. Here, we study basaltic eucrite Graves Nunataks (GRA) 98098, which has been identified as a highly metamorphosed eucrite [1]. We present new estimates on metamorphic temperatures determined via thermodynamic modeling as well as the initial results from diffusion models constraining timescales of thermal metamorphism. Sample Description: GRA 98098 is an unbrecciated eucrite with a granoblastic plagioclase and pyroxene mineralogy. Millimeter to cm-long lathes of tridymite cross-cut and poikilitically enclose plagioclase and pyroxene [1,this work]. Pyroxene grains have exsolved into Ca-rich (~Wo38En29Fs33) and Ca-poor (~Wo4.5En36Fs59.5) lamellae. Both unzoned and zoned plagioclase grains are observed. Unzoned plagioclase grains are found solely with tridymite laths. These grains have ~An92 compositions. The cores of the zoned plagioclase grains have the same composition and thin, relatively sodic rims (~An67), (Fig. 1). The bulk sample is unusually enriched in highly in-compatible elements and has one of the most fractionated REE patterns reported [1]. Maximum metamorphic temperatures of 985±78°C have been estimated using two-pyroxene thermometry [2]. Methods: Thermodynamic modeling. Thermodynamic models were constructed using the software Perple_X, which employs a Gibbs free energy minimization in order to determine the most stable phase assemblage for a given bulk rock composition [3]. Bulk composition was calculated using mineral com-positions acquired via EMPA (this study) and the observed abundancies present in the thin section. Two bulk compositions were estimated; 1) includes all phases present in the thin section, (assumes that all phases are present during metamorphism), 2) excludes tridymite from the bulk calculation (assumes that tridymite was not present during metamorphism). In order to determine whether metamorphic equilibria was achieved and estimate temperatures of metamorphism, we compared measured pyroxene compositions with thermodynamically predicted compositions [4, Fig. 2]. Diffusion Modeling. Several time-temperature de-pendent diffusion profiles were calculated in order to determine the best match for XAn chemical profiles observed at the edges of the zoned plagioclase (Fig. 3). We assumed that the start condition was a stepwise gradient at the plagioclase/pyroxene interface. We also assumed an average diffusion coefficient (D) and a constant temperature using the equation in [5]. D was determined for two temperatures (T = 1060ºC; near eucrite solidus [6] and T = 985ºC; metamorphism reported in [4]) and then XAn was calculated as a function of distance from plagioclase core to rim using an error function solution to Fick’s second law. Results: Thermodynamic model results are summarized in Fig. 2. For a bulk composition that includes all phases in the thin section, pyroxene endmember compositions plot in the following temperature ranges: Fs ~660-860ºC, En~1000ºC & 1150ºC, and Wo~760-900ºC (Fig. 2a). For a bulk composition that excludes tridymite from the peak metamorphic assemblage (i.e., the bulk composition minus the contribution from tridymite), a temperature range could not be determined for the Fs component of pyroxene. For Wo, T~760-900ºC and En, T~1000ºC & 1150ºC (Fig. 2b). Fig. 3 summarizes the diffusion model results. For T = 1060°C & 985°C, the most appropriate time interval was estimated based on which diffusion curve most matched (solid lines, Fig. 3) the EMPA data. For T = 1060°C, the best looking match was t = 500 ka. For T = 985°C, the best match was t = 7 Ma. Discussion and future work: Temperature estimates from thermodynamic models are not conclusive because the temperature ranges determined for pyroxene endmember stability do not overlap (colored fields in Fig. 2), thus implying that there is disequilibrium between pyroxene crystals and the bulk composition considered [4]. Thus, additional exploration is needed to define a metamorphically equilibrated do-main that accurately records peak temperature. The utility of defining metamorphically equilibrated do-mains to improve the accuracy and level of detail elucidated regarding the petrogenetic history of metamorphose samples has been demonstrated previously [4,7]. We suggest that in the case of Fig. 2a, the thin section composition is not representative of the length scales over which metamorphic equilibrium was achieve and in the case of Fig. 2b, the assumption that tridymite was not present during metamorphism was incorrect. However, results from thermodynamic models can provide insight into the relative timing of mineral and compositional textures. For example from texture alone, it is unclear whether tridymite was igneous in origin and represents the last bits of melt in a crystallizing magma chamber, or if it formed during (and possibly initiated) open system thermal metamorphism. The latter could be consistent with a partial melt hypothesis [8,9] while the former implies that simple fractional crystallization can yield the textures present in GRA 98098. The lack of coincidence be-tween pyroxene endmember compositions in Fig. 2b suggest that the bulk composition minus tridymite was not the assemblage in equilibrium with the pyroxene, suggesting that tridymite was present during metamorphism and formed during igneous crystallization. We conclude that the development of the Na-rich plagioclase rims likely occurred during or immediately after peak thermal metamorphism, because eucrites of similar metamorphic grade and texture have unzoned plagioclase (~An92) [2,4,8], and Na zoning is only observed in the plagioclase not included in the tridymite. This suggests that the zoning formed after tridymite formation, and therefore after igneous crystallization. Thus, the timescales calculated via diffusion modeling possibly represent the time interval over which thermal metamorphism occurred. Cooling rates approximated for the Vestan crust predict that the crust cooled below 300°C around 35-40 Ma after formation[10]. This is consistent with our modeling results that predict formation of the Na rich plagioclase rims occurring at higher temperatures over a period of 0.5 to 7 Ma years. Future work. Additional thermodynamic modeling work will focus on selecting an equilibrated bulk rock domain in which to elucidate metamorphic conditions. Diffusion models currently provide a minimum time-scale, since diffusion slows down as the system cools. Future work with will focus on integrating cooling into the diffusion models and constraining the depth at which thermal metamorphism occurs because it could be used to determine whether the range of time-scales calculated for thermal metamorphism are consistent with the geologic environment.

J S Gorce↗

Gamma-ray burster recurrence timescales

Three optical transients have been found which are associated with gamma-ray bursters (GRBs). The deduced recurrence timescale for these optical transients (tau sub opt) will depend on the minimum brightness for which a flash would be detected. A detailed analysis using all available data of tau sub opt as a function of E(gamma)/E(opt) is given. For flashes similar to those found in the Harvard archives, the best estimate of tau sub opt is 0.74 years, with a 99% confidence interval from 0.23 years to 4.7 years. It is currently unclear whether the optical transients from GRBs also give rise to gamma-ray events. One way to test this association is to measure the recurrence timescale of gamma-ray events tau sub gamma. A total of 210 gamma-ray error boxes were examined and it was found that the number of observed overlaps is not significantly different from the number expected from chance coincidence. This observation can be used to place limits on tau sub gamma for an assumed luminosity function. It was found that tau sub gamma is approx. 10 yr if bursts are monoenergetic. However, if GRBs have a power law luminosity function with a wide dynamic range, then the limit is tau sub gamma 0.5 yr. Hence, the gamma-ray data do not require tau sub gamma and tau sub opt to be different.

Schaefer, B. E.↗

Timescales for planetary accretion and the structure of the protoplanetary disk

Models of planetary accretion which assume the mass of condensable matter in the protoplanetary disk was equal to that present in the planets today predict accretion timescales for the outer planets approximately or less than 10 to the 8th years. Such timescales are inconsistent with observations of star forming regions, which suggest that most of the gas in disks around one solar mass is removed in a few x 10 to the 6th years. A unified scenario was outlined for solar system formation consistent with astrophysical constraints. Jupiter's core could have grown by runaway accretion of planetesimals to a mass sufficient to initiate rapid accretion of gas in times of order of 500,000 to 5,000,000 years, provided the surface density of solids in its accretion zone was at least 5 to 10 times greater than that required by minimum mass models of the protoplanetary disk. The inner planets and the asteroids can be accounted for in this picture if the surface density of the solar nebula was relatively uniform out to Jupiter's orbit. The formation of such a protoplanetary disk requires significant transport of mass and angular momentum, and is consistent with viscous accretion disk models of the solar nebula.

Lissauer, Jack J.↗