arXiv subjects

Andrew F. Nelson

Publications and source records attributed to Andrew F. Nelson.

16 recordsLinked to original sources

arXiv2016

Dynamics of Circumstellar Disks III: The case of GG Tau A

(abridged) We present 2-dimensional hydrodynamic simulations using the Smoothed Particle Hydrodynamic (SPH) code, VINE, to model a self-gravitating binary system similar to the GG Tau A system. We simulate systems configured with semi-major axes of either $a=62$~AU (`wide') or $a=32$~AU (`close'), and with eccentricity of either $e=0$ or $e=0.3$. Strong spiral structures are generated with large material streams extending inwards. A small fraction accretes onto the circumstellar disks, with most returning to the torus. Structures also propagate outwards, generating net outwards mass flow and eventually losing coherence at large distances. The torus becomes significantly eccentric in shape. Accretion onto the stars occurs at a rate of a few $\times10^{-8}$\msun/yr implying disk lifetimes shorter than $\sim10^4$~yr, without replenishment. Only wide configurations retain disks by virtue of robust accretion. In eccentric configurations, accretion is episodic, occurs preferentially onto the secondary at wrates peaked near binary periapse. We conclude that the \ggtaua\ torus is strongly self gravitating and that a major contribution to its thermal energy is shock dissipation. We interpret its observed features as manifestations of spiral structures and the low density material surrounding it as an excretion disk created by outward mass flux. We interpret GG Tau A as a coplanar system with an eccentric torus, and account for its supposed mutual inclination as due to degeneracy between the interpretation of inclination and eccentricity. Although the disks persist for long enough to permit planet formation, the environment remains unfavorable due to high temperatures. We conclude that the GG Tau A system is in an eccentric, $a\sim62$~AU orbit.

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arXiv2012

Dynamics of Core Accretion

(shortened) We perform 3D hydrodynamic simulations of gas flowing around a planetary core of mass \mplan=10\me embedded in a near Keplerian background flow, using a modified shearing box approximation. We employ a nested grid hydrodynamic code with as many as six nested grids, providing spatial resolution on the finest grid comparable to the present day diameters of Neptune and Uranus. We find that a strongly dynamically active flow develops such that no static envelope can form. The activity is not sensitive to plausible variations in the rotation curve of the underlying disk. It is sensitive to the thermodynamic treatment of the gas, as modeled by prescribed equations of state (either `locally isothermal' or `locally isentropic') and the temperature of the background disk material. The activity is also sensitive to the shape and depth of the core's gravitational potential, through its mass and gravitational softening coefficient. The varying flow pattern gives rise to large, irregular eruptions of matter from the region around the core which return matter to the background flow: mass in the envelope at one time may not be found in the envelope at any later time. The angular momentum of material in the envelope, relative to the core, varies both in magnitude and in sign on time scales of days to months near the core and on time scales a few years at distances comparable to the Hill radius. We show that material entering the dynamically active environment may suffer intense heating and cooling events the durations of which are as short as a few hours to a few days. Peak temperatures in these events range from $T \sim 1000$ K to as high as $T \sim 3-4000$ K, with densities $ρ\sim 10^{-9}-10^{-8}$ g/cm$^3$. These time scales, densities and temperatures span a range consistent with those required for chondrule formation in the nebular shock model.

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arXiv2009

Interaction of a giant planet in an inclined orbit with a circum-stellar disk

We investigate the dynamical evolution of a Jovian--mass planet injected into an orbit highly inclined with respect to its nesting gaseous disk. Planet--planet scattering induced by convergent planetary migration and mean motion resonances may push a planet into such an out of plane configuration with inclinations as large as $20^\circ-30^\circ$. In this scenario the tidal interaction of the planet with the disk is more complex and, in addition to the usual Lindblad and corotation resonances, it involves also inclination resonances responsible of bending waves. We have performed three--dimensional hydrodynamic simulations of the disk and of its interactions with the planet with a Smoothed Particle Hydrodynamics (SPH) code. A main result is that the initial large eccentricity and inclination of the planetary orbit are rapidly damped on a timescale of the order of $10^3$ yrs, almost independently of the initial semimajor axis and eccentricity of the planet. The disk is warped in response to the planet perturbations and it precesses. Inward migration occurs also when the planet is inclined and it has a drift rate which is intermediate between type I and type II migration. The planet is not able to open a gap until its inclination becomes lower than $\sim 10^\circ$ when it also begins to accrete a significant amount of mass from the disk.

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arXiv2009

VINE -- A numerical code for simulating astrophysical systems using particles I: Description of the physics and the numerical methods

We present a Fortran 95 code for simulating the evolution of astrophysical systems using particles to represent the underlying fluid flow. The code is designed to be versatile, flexible and extensible, with modular options that can be selected either at compile time or at run time. We include a number of general purpose modules describing a variety of physical processes commonly required in the astrophysical community. The code can be used as an N-body code to evolve a set of particles in two or three dimensions using either a Leapfrog or Runge-Kutta-Fehlberg integrator, with or without individual timesteps for each particle. Particles may interact gravitationally as $N$-body particles, and all or any subset may also interact hydrodynamically, using the Smoothed Particle Hydrodynamic (SPH) method. Massive point particles (`stars') which may accrete nearby SPH or $N$-body particles may also be included. The default free boundary conditions can be replaced by a module to include periodic boundaries. Cosmological expansion may also be included. An interface with special purpose `GRAPE' hardware may also be selected. If available, forces obtained from the GRAPE coprocessors may be transparently substituted for those obtained from the default tree based calculation. The code may be run without modification on single processors or in parallel using OpenMP compiler directives on large scale, shared memory parallel machines. In comparison to the Gadget-2 code of Springel 2005, the gravitational force calculation is $\approx 3.5 - 4.8$ times faster with VINE when run on 8 Itanium~2 processors in an SGI Altix, while producing nearly identical outcomes in our test problems. We present simulations of several test problems, including a merger simulation of two elliptical galaxies with 800000 particles.

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arXiv2009

VINE -- A numerical code for simulating astrophysical systems using particles II: Implementation and performance characteristics

We continue our presentation of VINE. We begin with a description of relevant architectural properties of the serial and shared memory parallel computers on which VINE is intended to run, and describe their influences on the design of the code itself. We continue with a detailed description of a number of optimizations made to the layout of the particle data in memory and to our implementation of a binary tree used to access that data for use in gravitational force calculations and searches for SPH neighbor particles. We describe modifications to the code necessary to obtain forces efficiently from special purpose `GRAPE' hardware. We conclude with an extensive series of performance tests, which demonstrate that the code can be run efficiently and without modification in serial on small workstations or in parallel using OpenMP compiler directives on large scale, shared memory parallel machines. We analyze the effects of the code optimizations and estimate that they improve its overall performance by more than an order of magnitude over that obtained by many other tree codes. Scaled parallel performance of the gravity and SPH calculations, together the most costly components of most simulations, is nearly linear up to maximum machine sizes available to us (120 processors on an Origin~3000). At similar accuracy, performance of VINE, used in GRAPE-tree mode, is approximately a factor two slower than that of VINE, used in host-only mode. Optimizations of the GRAPE/host communications could improve the speed by as much as a factor of three, but have not yet been implemented in VINE.

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arXiv2007

Gravitational instability in binary protoplanetary disks

We review the models and results of simulations of self-gravitating, gaseous protoplanetary disks in binary star systems. These models have been calculated by three different groups with three different computational methods, two particle-based and one grid-based. We show that interactions with the companion star can affect the temperature distribution and structural evolution of disks, and discuss the implications for giant planet formation by gravitational instability as well as by core accretion. Complete consensus has not been reached yet on whether the formation of giant planets is promoted or suppressed by tidal interactions with a companion star. While systems with binary separations of order 100 AU or larger appear to behave more or less as in isolation, systems with smaller separations exhibit an increased or decreased susceptibility to fragmentation, depending on the details of thermodynamics, in particular on the inclusion or absence of artificial viscosity, and on the initial conditions. While code comparisons on identical problems need to be carried out (some of which are already in progress) to decide which computer models are more realistic, it is already clear that relatively close binary systems, with separations of order 60 AU or less, should provide strong constraints on how giant planets form in these systems.

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arXiv2006

Numerical requirements for simulations of self gravitating and non-self gravitating disks

(highly abridged) We define three requirements for accurate simulations that attempt to model circumstellar disks and the formation of collapsed objects (e.g. planets) within them. First, we define a resolution requirement based on the wavelength for neutral stability of self gravitating waves in the disk. For particle based or grid based simulations, this criterion takes the form, respectively, of a minimum number of particles per critical (`Toomre') mass or maximum value of a `Toomre number', $T= δx/λ_T$, where the wavelength, $λ_T$, is the wavelength for neutral stability for waves in disks. We apply our criterion to particle simulations and find that in order to prevent numerically induced fragmentation of the disk, the Toomre mass must be resolved by a minimum of six times the average number of neighbor particles used. Second, we require that particle based simulations with self gravity use a variable gravitational softening. We show that using a fixed gravitational softening length can lead either to artificial suppression or enhancement of structure (including fragmentation) in a given disk, or both in different locations of the same disk. Third, we require that 3D SPH simulations resolve the disk's vertical structure with at least $\sim4$ particle smoothing lengths per scale height at the disk midplane and suggest that a similar criterion applies to grid based simulations. Failure to meet this criterion leads to underestimates in the midplane density of up to 30--50% at resolutions common in the literature.

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arXiv2005

A proposed origin for chondrule-forming shocks in the solar nebula

We propose that the nebular shocks currently favored as a model to form chondrules and other annealed silicates in the solar nebula originate in the dynamical activity present in the envelope of forming Jovian planets. In contrast to the classic `core accretion model', our 3D hydrodynamic simulations show that this envelope is not a 1D hydrostatic structure but is instead vigorously active and contains densities and temperatures that appear similar in magnitude and spatial extent to those thought to be responsible for the production of chondrules.

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arXiv2003

A Resolution Requirement for Disk Simulations Modeling Collapse

The accurate simulation of collapsed objects requires that a huge range of spatial scales be well resolved if the result is not to be contaminated by numerically induced fragmentation. In this context, `insufficient resolution' means comparable to the local instability wavelength in the system. I define a minimum resolution criterion for simulations of disk systems, using the critical wavelength appropriate for disks.

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arXiv2003

On the Early Evolution of Forming Jovian Planets I: Initial Conditions, Systematics and Qualitative Comparisons to Theory

(abridged) We analyze the formation and migration of a proto-Jovian companion in a circumstellar disk in 2d, during the period in which the companion makes its transition from `Type I' to `Type II' migration, using a PPM code. Spiral waves are generated by the gravitational torque of the planet on the disk. Their effects are to cause the planet to migrate inward and the disk to form a deep (low surface density) gap. Until a transition to slower Type II migration, the migration rate of the planet is of order 1 AU/10$^3$ yr, and varies by less than a factor of two with a factor twenty change in planet mass, but depends near linearly on the disk mass. Although the disk is stable to self gravitating perturbations (Toomre $Q>5$ everywhere), migration is faster by a factor of two or more when self gravity is suppressed. Migration is equally sensitive to the disk's mass distribution within 1--2 Hill radii of the planet, as demonstrated by our simulations' sensitivity to the planet's assumed gravitational softening parameter. Rapid migration can continue after gap formation. Gaps are typically several AU in width and display the \mplan$^{2/3}$ proportionality predicted by theory. Beginning from an initially unperturbed 0.05\msun disk, planets of mass $M_{\rm pl}> 0.3$\mj can open a gap deep and wide enough to complete the transition to slower \ttwo migration. Lower mass objects continue to migrate rapidly, eventually impacting the inner boundary of our grid. This transition mass is much larger than that predicted as the `Shiva mass' discussed in Ward and Hahn (2000), making the survival of forming planets even more precarious than they would predict.

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arXiv2003

On the Early Evolution of Forming Jovian Planets II: Analysis of Accretion and Gravitational Torques

(abridged) We find that a disk can supply a forming planet with mass at an essentially infinite rate ($\sim1$\mj/25 yr) so that a gap could form very quickly. We show that mass accretion rates faster than $\sim10^{-4}$\mj/yr are not physically reasonable in the limit of either a thin, circumplanetary disk or of a spherical envelope. Planet growth and ultimately survival are therefore limited to the planet's ability to accept additional matter, not by the disk in which it resides. We find that common analytic torque approximations predict values that are a factor $\sim10$ larger than those obtained from the simulations. Accounting for the disk's vertical structure (crudely modeled through a gravitational softening parameter), small shifts in resonance positions due to pressure gradients, to disk self gravity and to inclusion of non-WKB terms in the analysis (Artymowicz 1993) reduce the difference to a factor $\sim3-6$. Torques from the corotation resonances that are positive in sign contribute 20-30% or more of the net torque on the planet. The assumption of linearity underlying theoretical analyses is recovered in the simulations with planets with masses below 0.5\mj, but the assumption that interactions occur only at the resonances is more difficult to support. The detailed shape of the disk's response varies from pattern to pattern, making its true position less clear. We speculate that the finite width allows for overlap and mixing between resonances and may be responsible for the remainder of the differences between torques from theory and simulation, but whether accounting for such overlap in a theory will improve the agreement with the simulations is not clear.

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arXiv2000

Planet formation is unlikely in equal mass binary systems with a ~ 50 AU

We show that planet formation via both gravitational collapse and core accretion is unlikely to occur in equal mass binary systems with moderate (~ 50 AU) semi-major axes. Internal thermal energy generation in the disks is sufficient to heat the gas everywhere so that spiral structures quickly decay rather than grow or fragment. This same heating will inhibit dust coagulation because the temperatures rise above the vaporization temperatures of many volatile materials. We consider other processes not included in the model and conclude that our temperatures are conservatively estimated (low), i.e. planet formation is less likely in real systems than in the model.

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arXiv1999

Dynamics and Observational Appearance of Circumstellar Disks

In my thesis I present a study of the dynamics and observational characteristics of massive circumstellar disks in two dimensions ($r$, $ϕ$) using two complimentary hydrodynamic codes: a `Smoothed Particle Hydrodynamic' (SPH) code and a `Piecewise Parabolic Method' (PPM) code. I also study the detection limits available to radial velocity searches for low mass companions to main sequence stars. The thesis is organized as a series of published or submitted papers, connected by introductory and concluding material and is archived `for posterity'. I recommend that readers of this abstract obtain the published versions of each of these papers. I first outline the progress which has been made in the modeling of the structure and origins of the solar system, then in chapter 2 (ApJ 502,p342) I proceed with numerical simulations of circumstellar disks using both hydrodynamic codes assuming a `locally isothermal' equation of state. In chapter 4 (ApJ submitted) I relax the locally isothermal evolution assumption and instead include simple heating and cooling prescriptions for the system. In chapter 6 (ApJ 500,p940) I examine the limits which may be placed upon the detection of planets, brown dwarfs and low mass stellar companions using radial velocity measurements. In chapter 7, I outline several problems which may be profitably addressed by building on this work.

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arXiv1999

Towards Understanding Jovian Planet Migration

We present 2D hydrodynamic simulations of circumstellar disks around protostars using a `Piecewise Parabolic Method' (PPM) code. We include a point mass embedded within the disk and follow the migration of that point mass through the disk. Companions with masses $M_c\ga 0.5M_J$ can open a gap in the disk sufficient to halt rapid migration through the disk. Lower mass companions open gaps, but migration continues because sufficient disk mass remains close to the disk to exert large tidal torques. We find that the torques which dominate the migration of low mass planets originate within a radial region within 1-2 Hill radii of the planet's orbit radius, a distance smaller than the thickness of the disk. We conclude that a very high resolution 3D treatment will be required to adequately describe the planet's migration.

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arXiv1999

Dynamics of Circumstellar Disks II: Heating and Cooling

We present a series of 2-d ($r,ϕ$) hydrodynamic simulations of marginally self gravitating disks around protostars using an SPH code. We implement simple dynamical heating and we cool each location as a black body, using a photosphere temperature obtained from the local vertical structure. We synthesize SEDs from our simulations and compare them to fiducial SEDs derived from observed systems. These simulations produce less distinct spiral structure than isothermally evolved systems, especially in the inner third of the disk. Pattern are similar further from the star but do not collapse into condensed objects. The photosphere temperature is well fit to a power law in radius with index $q\sim1.1$, which is very steep. Far from the star, internal heating ($PdV$ work and shocks) are not responsible for generating a large fraction of the thermal energy contained in the disk matter. Gravitational torques responsible for such shocks cannot transport mass and angular momentum efficiently in the outer disk. Within $\sim$5--10 AU of the star, rapid break up and reformation of spiral structure causes shocks, which provide sufficient dissipation to power a larger fraction of the near IR energy output. The spatial and size distribution of grains can have marked consequences on the observed near IR SED and can lead to increased emission and variability on $\lesssim 10$ year time scales. When grains are vaporized they do not reform into a size distribution similar to that from which most opacity calculations are based. With rapid grain reformation into the original size distribution, the disk does not emit near infrared photons. With a plausible modification to the opacity, it contributes much more.

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arXiv1998

Dynamics of Circumstellar Disks

We present a series of 2-dimensional hydrodynamic simulations of massive disks around protostars. We simulate the same physical problem using both a `Piecewise Parabolic Method' (PPM) code and a `Smoothed Particle Hydrodynamic' (SPH) code, and analyze their differences. The disks studied here range in mass from $0.05 M_*$ to $1.0 M_*$ and in initial minimum Toomre $Q$ value from 1.1 to 3.0. For this problem, the strengths of the codes overlap only in a limited fashion, but similarities exist in their predictions, including spiral arm pattern speeds and morphological features. Our results represent limiting cases (i.e. systems evolved isothermally) rather than true physical systems. Disks become active from the inner regions outward. From the earliest times, their evolution is a strongly dynamic process rather than a smooth progression toward eventual nonlinear behavior. We calculate approximate growth rates for the spiral patterns; the one-armed ($m=1$) spiral arm is not the fastest growing pattern of most disks. In our SPH simulations, disks with initial minimum $Q=1.5$ or lower break up into proto-binary or proto-planetary clumps. However, these simulations cannot follow the physics important for the flow and must be terminated before the system has completely evolved. At their termination, PPM simulations with similar initial conditions show uneven mass distributions within spiral arms, suggesting that clumping behavior might result if they were carried further. Concern that the point-like nature of SPH exaggerates clumping, that our representation of the gravitational potential in PPM is too coarse, and that our physics assumptions are too simple, suggest caution in interpretation of the clumping in both the disk and torus simulations.

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