arXiv subjects

Alexander Hubbard

Publications and source records attributed to Alexander Hubbard.

At least 19 recordsLinked to original sources

arXiv2018

Dust concentration and chondrule formation

Meteoritical and astrophysical models of planet formation make contradictory predictions for dust concentration factors in chondrule forming regions of the solar nebula. Meteoritical and cosmochemical models strongly suggest that chondrules, a key component of the meteoritical record, formed in regions with solids-to-gas mass ratios orders of magnitude above background. However, models of dust grain dynamics in protoplanetary disks struggle to surpass factors of a few outside of very brief windows in the lifetime of the dust grains. Worse, those models do not predict significant concentration factors for dust grains the size of chondrule precursors. We briefly develop the difficulty in concentrating dust particles in the context of nebular chondrule formation and show that the disagreement is sufficiently stark that cosmochemists should explore ideas that might revise the concentration factor requirements downwards.

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arXiv2017

Making Terrestrial Planets: High Temperatures, FU Orionis Outbursts, Earth, and Planetary System Architectures

Current protoplanetary dust coagulation theory does not predict dry silicate planetesimals, in tension with the Earth. While remedies to this predicament have been proposed, they have generally failed numerical studies, or are in tension with the Earth's (low, volatility dependent) volatile and moderately volatile elemental abundances. Expanding on the work of Boley et al. (2014), we examine the implications of molten grain collisions and find that they may provide a solution to the dry silicate planetesimal problem. Further, the source of the heating, be it the hot inner disk or an FU Orionis scale accretion event, would dictate the location of the resulting planetesimals, potentially controlling subsequent planetary system architectures. We hypothesize that systems which did undergo FU Orionis scale accretion events host planetary systems similar to our own, while ones that did not instead host very close in, tightly packed planets such as seen by Kepler.

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arXiv2016

FU Orionis outbursts, preferential recondensation of water ice, and the formation of giant planets

Ices, including water ice, prefer to recondense onto pre-existing nuclei rather than spontaneously forming grains from a cloud of vapor. Interestingly, different potential recondensation nuclei have very different propensities to actually nucleate water ice at the temperatures associated with freeze-out in protoplanetary discs. Therefore, if a region in a disc is warmed and then recooled, water vapor should not be expected to refreeze evenly onto all available grains. Instead it will preferentially recondense onto the most favorable grains. When the recooling is slow enough, only the most favorable grains will nucleate ice, allowing them to recondense thick ice mantles. We quantify the conditions for preferential recondensation to rapidly create pebble-sized grains in protoplanetary discs and show that FU Orionis type outbursts have the appropriate cooling rates to drive pebble creation in a band about 5 astronomical units wide outside of the quiescent frost line from approximately Jupiter's orbit to Saturn's (about 4 to 10 au). Those pebbles could be of the appropriate size to proceed to planetesimal formation via the Streaming Instability, or to contribute to the growth of planetesimals through pebble accretion. We suggest that this phenomenon contributed to the formation of the gas giants in our own Solar System.

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arXiv2016

Generating potassium abundance variations in the Solar Nebula

An intriguing aspect of chondritic meteorites is that they are complementary: while their separate components have wildly varying abundances, bulk chondrites have nearly solar composition. This implies that the nearly-solar reservoirs in which chondrites were born were in turn assembled from sub-reservoirs of differing compositions that birthed the different components. We focus on explaining the potassium abundance variations between chondrules even within a single chondrite, while maintaining the observed CI $^{41}$K to $^{39}$K ratios. This requires physically separating potassium and chondrules while the temperature is high enough for K to be in the gas phase. We examine several mechanisms which could drive the dust through gas and show that to do so locally would have required long (sub-orbital to many orbits) time scales; with shortest potassium depletion time scales occurring in a scenario where chondrules formed high above the midplane and settled out of the evaporated potassium. While orbital time scales are at odds with laboratory chondrule cooling rate estimates, any other model for the origin for the potassium abundance variation has to wrestle with the severe logistical difficulty of generating a plethora of correlated reservoirs which varied strongly in their potassium abundances, but not in their potassium isotope ratios.

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arXiv2016

Partitioning tungsten between matrix precursors and chondrule precursors through relative settling

Recent studies of chondrites have found a tungsten isotopic anomaly between chondrules and matrix. Given the refractory nature of tungsten, this implies that W was carried into the solar nebula by at least two distinct families of pre-solar grains. The observed chondrule/matrix split requires that the distinct families were kept separate during the dust coagulation process, and that the two families of grain interacted with the chondrule formation mechanism differently. We take the co-existence of different families of solids in the same general orbital region at the chondrule-precursor size as given, and explore the requirements for them to have interacted with the chondrule formation process at significantly different rates. We show that this sorting of families of solids into chondrule and matrix destined dust had to have been at least as powerful a sorting mechanism as the relative settling of aerodynamically distinct grains at at least two scale heights above the midplane. The requirement that the chondrule formation mechanism was correlated in some fashion with a dust grain sorting mechanism argues strongly for spatially localized chondrule formation mechanisms such as turbulent dissipation in non-thermally ionized disk surface layers, and argues against volume filling mechanisms such as planetesimal bow shocks.

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arXiv2016

Ferromagnetism and particle collisions: applications to protoplanetary disks and the meteoritical record

The meteoritical record shows both iron partitioning and tungsten isotopic partitioning between matrix and chondrules. Tungsten is not abundant enough to have driven its own isotopic partitioning, but if tungsten were correlated with iron, then ferromagnetic interactions grains could help explain both observations. We derive a practical parameterization for the increase in particle-particle collision rates caused by mutually attracting particle magnetic dipole moments. While the appropriate magnetic parameters remain uncertain, we show that ambient magnetic fields in protoplanetary disks are expected to be strong enough to magnetize iron metal bearing dust grains sufficiently to drive large increases in their collision rates. Such increased collision rates between iron metal rich grains could help preserve primordial iron and W isotopic inhomogeneities; and would help explain why the meteoritical record shows their partitioning in the solar nebula. The importance of magnetic interactions for larger grains whose growth is balanced by fragmentation is less clear, and will require future laboratory or numerical studies.

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arXiv2015

Turbulent Thermal Diffusion: A Way to Concentrate Dust in Protoplanetary Discs

Turbulence acting on mixes of gas and particles generally evenly diffuses the latter through the former. However, in the presence of background gas temperature gradients a phenomenon known as turbulent thermal diffusion appears as a particle drift velocity (rather than a diffusive term). This process moves particles from hot regions to cold ones. We rederive turbulent thermal diffusion using astrophysical language and demonstrate that it could play a major role in protoplanetary discs by concentrating particles by factors of tens. Such a concentration would set the stage for collective behavior such as the streaming instability and hence planetesimal formation.

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arXiv2015

Photophoresis in a Dilute, Optically Thick Medium and Dust Motion in Protoplanetary Disks

We derive expressions for the photophoretic force on opaque spherical particles in a dilute gas in the optically thick regime where the radiation field is in local thermal equilibrium. Under those conditions, the radiation field has a simple form, leading to well defined analytical approximations for the photophoretic force that also consider both the internal thermal conduction within the particle, and the effects of heat conduction and radiation to the surrounding gas. We derive these results for homogeneous spherical particles; and for the double layered spheres appropriate for modeling solid grains with porous aggregate mantles. Then, as a specific astrophysical application of these general physical results, we explore the parameter space relevant to the photophoresis driven drift of dust in protoplanetary disks. We show that highly porous silicate grains have sufficiently low thermal conductivities that photophoretic effects, such as significant relative velocities between particles with differing porosity or levitation above the midplane, are expected to occur.

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arXiv2015

Compound Chondrules fused Cold

About 4-5% of chondrules are compound: two separate chondrules stuck together. This is commonly believed to be the result of the two component chondrules having collided shortly after forming, while still molten. This allows high velocity impacts to result in sticking. However, at T ~ 1100K, the temperature below which chondrules collide as solids (and hence usually bounce), coalescence times for droplets of appropriate composition are measured in tens of seconds. Even at 1025K, at which temperature theory predicts that the chondrules must have collided extremely slowly to have stuck together, the coalescence time scale is still less than an hour. These coalescence time scales are too short for the collision of molten chondrules to explain the observed frequency of compound chondrules. We suggest instead a scenario where chondrules stuck together in slow collisions while fully solid; and the resulting chondrule pair was subsequently briefly heated to a temperature in the range of 900-1025K. In that temperature window the coalescence time is finite but long, covering a span of hours to a decade. This is particularly interesting because those temperatures are precisely the critical window for thermally ionized MRI activity, so compound chondrules provide a possible probe into that vital regime.

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arXiv2014

Semarkona: Lessons for chondrule and chondrite formation

We consider the evidence presented by the LL3.0 chondrite Semarkona, including its chondrule fraction, chondrule size distribution and matrix thermal history. We show that no more than a modest fraction of the ambient matrix material in the Solar Nebula could have been melted into chondrules; and that much of the unprocessed matrix material must have been filtered out at some stage of Semarkona's parent body formation process. We conclude that agglomerations of many chondrules must have formed in the Solar Nebula, which implies that chondrules and matrix grains had quite different collisional sticking parameters. Further, we note that the absence of large melted objects in Semarkona means that chondrules must have exited the melting zone rapidly, before the chondrule agglomerations could form. The simplest explanation for this rapid exit is that chondrule melting occurred in surface layers of the disk. The newly formed, compact, chondrules then settled out of those layers on short time scales.

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arXiv2014

Explaining Mercury's Density through Magnetic Erosion

In protoplanetary disks, dust grains rich in metallic iron can attract each other magnetically. If they are magnetized to values near saturation, the magnetically induced collision speeds are high enough to knock off the non-magnetized, loosely bound silicates. This process enriches the surviving portions of the dust grains in metallic iron, which further enhances the magnetically mediated collisions. The magnetic enhancement to the collisional cross-section between the iron rich dust results in rapid grain growth leading to planetesimal formation. While this process of knocking off silicates, which we term "magnetic erosion", occurs only in a very limited portion of a protoplanetary disk, it is a possible explanation for Mercury's disproportionately large iron core.

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arXiv2014

Temperature Fluctuations driven by Magnetorotational Instability in Protoplanetary Disks

The magnetorotational instability (MRI) drives magnetized turbulence in sufficiently ionized regions of protoplanetary disks, leading to mass accretion. The dissipation of the potential energy associated with this accretion determines the thermal structure of accreting regions. Until recently, the heating from the turbulence has only been treated in an azimuthally averaged sense, neglecting local fluctuations. However, magnetized turbulence dissipates its energy intermittently in current sheet structures. We study this intermittent energy dissipation using high resolution numerical models including a treatment of radiative thermal diffusion in an optically thick regime. Our models predict that these turbulent current sheets drive order unity temperature variations even where the MRI is damped strongly by Ohmic resistivity. This implies that the current sheet structures where energy dissipation occurs must be well resolved to correctly capture the flow structure in numerical models. Higher resolutions are required to resolve energy dissipation than to resolve the magnetic field strength or accretion stresses. The temperature variations are large enough to have major consequences for mineral formation in disks, including melting chondrules, remelting calcium-aluminum rich inclusions, and annealing silicates; and may drive hysteresis: current sheets in MRI active regions could be significantly more conductive than the remainder of the disk.

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arXiv2014

Radial Stresses and Energy Transport in Accretion Disks

Early in the study of viscous accretion disks it was realized that energy transfers from distant sources must be important, not least because the flow at the disk midplane in the bulk of the disk is likely outwards, out of the gravitational potential well. If the source of the viscosity is powered by accretion, such as in the case of the magneto-rotational instability, such distant energy sources must lie in the innermost regions of the disk, where accretion occurs even at the midplane. We argue here that modulations in this energy supply can alter the accretion rate on dynamical, rather than far longer viscous, time scales. This means that both the steady state value of and fluctuations in the inner disk's accretion rate, depending on the details of the inner boundary condition and occurring on the inner disk's rapid evolution time, can affect the outer disk. This is particularly interesting because observations have shown that disk accretion is not steady (e.g.~EX Lupi type objects). We also note that the power supplied to shearing boxes is set by the boxes themselves rather than the physical energy fluxes in a global disk. That is, their saturated magnetic field is not subject to the full set of energy constraints present in an actual disk. Our analysis suggests that large scale radial transport of energy has a critical impact on the evolution and variability of accretion disks.

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arXiv2014

Protoplanetary dust porosity and FU Orionis Outbursts: Solving the mystery of Earth's missing volatiles

The Earth is known to be depleted in volatile lithophile elements in a fashion that defies easy explanation. We resolve this anomaly with a model that combines the porosity of collisionally grown dust grains in protoplanetary disks with heating from FU Orionis events that dramatically raise protoplanetary disk temperatures. The heating from an FU Orionis event alters the aerodynamical properties of the dust while evaporating the volatiles. This causes the dust to settle, abandoning those volatiles. The success of this model in explaining the elemental composition of the Earth is a strong argument in favor of highly porous collisionally grown dust grains in protoplanetary disks outside our Solar System. Further, it demonstrates how thermal (or condensation based) alterations of dust porosity, and hence aerodynamics, can be a strong factor in planet formation, leading to the onset of rapid gravitational instabilities in the dust disk and the subsequent collapse that forms planetesimals.

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arXiv2014

Convective Overstability in radially stratified accretion disks under thermal relaxation

This letter expands the stability criterion for radially stratified, vertically {unstratified} accretion disks incorporating thermal relaxation. We find a linear amplification of epicyclic oscillations in these disks that depends on the effective cooling time, i.e. an overstability. The growth rates of the overstability vanish for both extreme cases, e.g. infinite cooling time and instantaneous cooling, i.e. the adiabatic and fully isothermal cases. However, for thermal relaxation times $\tau$ on the order of the orbital frequency, $\tau\Omega \sim 1$, modes grow at a rate proportional to the square of the Brunt-V\"ais\"al\"a frequency. The overstability is based on epicyclic motions, with the thermal relaxation causing gas to heat while radially displaced inwards, and cool while radially displaced outwards. This causes the gas to have a lower density when moving outwards compared to when it moves inwards, so it feels the outwards directed pressure force more strongly on that leg of the journey. We suggest the term ``Convective Overstability" for the phenomenon that has already been numerically studied in the non-linear regime in the context of amplifying vortices in disks, under the name ``Subcritical Baroclinic Instability". The point of the present paper is to make clear that vortex formation in three-dimensional disks is neither subcritical, i.e. does not need a finite perturbation, nor is it baroclinic in the sense of geophysical fluid dynamics, which requires on vertical shear. We find that Convective Overstability is a linear instability that will operate under a wide range of physical conditions for circumstellar disks.

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arXiv2014

Ribbons characterize magnetohydrodynamic magnetic fields better than lines: a lesson from dynamo theory

Blackman & Brandenburg argued that magnetic helicity conservation in dynamo theory can in principle be captured by diagrams of mean field dynamos when the magnetic fields are represented by ribbons or tubes, but not by lines. Here we present such a schematic ribbon diagram for the $\alpha^2$ dynamo that tracks magnetic helicity and provides distinct scales of large scale magnetic helicity, small scale magnetic helicity, and kinetic helicity involved in the process. This also motivates our construction of a new "2.5 scale" minimalist generalization of the helicity-evolving equations for the \alpha^2 dynamo that separately allows for these three distinct length scales while keeping only two dynamical equations. We solve these equations and, as in previous studies, find that the large scale field first grows at a rate independent of the magnetic Reynolds number R_M before quenching to an R_M dependent regime. But we also show that the larger the ratio of the wavenumber where the small scale current helicity resides to that of the forcing scale, the earlier the non-linear dynamo quenching occurs, and the weaker the large scale field is at the turnoff from linear growth. The harmony between the theory and the schematic diagram exemplifies a general lesson that magnetic fields in MHD are better visualized as two-dimensional ribbons (or pairs of lines) rather than single lines.

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arXiv2013

Mineral Processing by Short Circuits in Protoplanetary Disks

Meteoritic chondrules were formed in the early solar system by brief heating of silicate dust to melting temperatures. Some highly refractory grains (Type B calcium-aluminum-rich inclusions, CAIs) also show signs of transient heating. A similar process may occur in other protoplanetary disks, as evidenced by observations of spectra characteristic of crystalline silicates. One possible environment for this process is the turbulent magnetohydrodynamic flow thought to drive accretion in these disks. Such flows generally form thin current sheets, which are sites of magnetic reconnection, and dissipate the magnetic fields amplified by a disk dynamo. We suggest that it is possible to heat precursor grains for chondrules and other high-temperature minerals in current sheets that have been concentrated by our recently described short-circuit instability. We extend our work on this process by including the effects of radiative cooling, taking into account the temperature dependence of the opacity; and by examining current sheet geometry in three-dimensional, global models of magnetorotational instability. We find that temperatures above 1600 K can be reached for favorable parameters that match the ideal global models. This mechanism could provide an efficient means of tapping the gravitational potential energy of the protoplanetary disk to heat grains strongly enough to form high-temperature minerals. The volume-filling nature of turbulent magnetic reconnection is compatible with constraints from chondrule-matrix complementarity, chondrule-chondrule complementarity, the occurrence of igneous rims, and compound chondrules. The same short-circuit mechanism may perform other high-temperature mineral processing in protoplanetary disks such as the production of crystalline silicates and CAIs.

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arXiv2013

Turbulence Induced Collision Velocities and Rates between Different Sized Dust Grains

We study the collision rates and velocities for point-particles of different sizes in turbulent flows. We construct fits for the collision rates at specified velocities (effectively a collisional velocity probability distribution) for particle stopping time ratios up to four; already by that point the collisional partners are very poorly correlated and so the results should be robust for even larger stopping time ratios. Significantly, we find that while particles of very different masses have approximately Maxwellian collisional statistics, as the mass ratio shrinks the distribution changes dramatically. At small stopping time ratios, the collisional partners are highly correlated and we find a population of high number density (clustered), low relative-velocity particle pairs. Unlike in the case of identical stopping time collisional partners, this low relative-velocity clustered population is collisional, but the clustering is barely adequate to trigger bulk effects such as the streaming instability. We conclude our analysis by constructing a master fit to the collisional statistics as a function only of the stopping time ratio. Together with our previous work for identical stopping time particle pairs, this provides a recipe for including collisional velocity probability distributions in dust coagulation models for protoplanetary disks. We also include our recipe for determining particle collisional diagnostics from numerical simulations.

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