arXiv subjects

Jeremy Goodman

Publications and source records attributed to Jeremy Goodman.

At least 73 records · Page 4Linked to original sources

arXiv2006

Diffusive Migration of Low-Mass Proto-planets in Turbulent Disks

Torque fluctuations due to magnetorotational turbulence in proto-planetary disks may greatly influence the migration patterns and survival probabilities of nascent planets. Provided that the turbulence is a stationary stochastic process with finite amplitude and correlation time, the resulting diffusive migration can be described with a Fokker-Planck equation, which we reduce to an advection-diffusion equation. We calibrate the coefficients with existing turbulent-disk simulations and mean-migration estimates, and solve the equation both analytically and numerically. Diffusion tends to dominate over advection for planets of low-mass and those in the outer regions of proto-planetary disks, whether they are described by the Minimum Mass Solar Nebula (MMSN) or by T-Tauri alpha disks. Diffusion systematically reduces the lifetime of most planets, yet it allows a declining fraction of them to survive for extended periods of time at large radii. Mean planet lifetimes can even be formally infinite (e.g. in an infinite steady MMSN), though median lifetimes are always finite. Surviving planets may linger near specific radii where the combined effects of advection and diffusion are minimized, or at large radii, depending on model specifics. The stochastic nature of migration in turbulent disks challenges deterministic planet formation scenarios and suggests instead that a wide variety of planetary outcomes are possible from similar initial conditions. This would contribute to the diversity of (extrasolar) planetary systems.

astro-ph↗

arXiv2006

Simulations of Magnetorotational Instability in a Magnetized Couette Flow

In preparation for an experimental study of magnetorotational instability (MRI) in liquid metal, we present non-ideal two-dimensional magnetohydrodynamic simulations of the nonlinear evolution of MRI in the experimental geometry. The simulations adopt initially uniform vertical magnetic fields, conducting radial boundaries, and periodic vertical boundary conditions. No-slip conditions are imposed at the cylinders. Our linear growth rates compare well with existing local and global linear analyses. The MRI saturates nonlinearly with horizontal magnetic fields comparable to the initial axial field. The rate of angular momentum transport increases modestly but significantly over the initial state. For modest fluid and magnetic Reynolds numbers Re, Rm between 100 and 1000, the final state is laminar reduced mean shear except near the radial boundaries, and with poloidal circulation scaling as the square root of resistivity, in partial agreement with the analysis of Knobloch and Julien. A sequence of simulations at Rm=20 and 100 < Re < 25,600 enables extrapolation to the experimental regime (Rm ~ 20, Re ~ 10^7), albeit with unrealistic boundary conditions. MRI should increase the experimentally measured torque substantially over its initial purely hydrodynamic value.

astro-ph↗

arXiv2005

On the nature of the S stars in the Galactic Center

Davies and King have suggested that the bright stars observed on short-period orbits about Sgr A* (``S stars'') are old, low-mass stripped AGB stars rather than young, high-mass main-sequence stars. If the observationally inferred effective temperatures and luminosities of these stars are correct, however, then DK have grossly overestimated the post-AGB lifetimes and hence underestimated the production rate in steady state. In fact, the total mass in stars stripped over the age of the Galaxy would exceed that of the stellar cusp bound to Sgr A*. We take issue also with Davies & King's estimates of the energetics involved in capturing the stars onto their present orbits.

astro-ph↗

arXiv2004

Streaming Instabilities in Protoplanetary Disks

Interpenetrating streams of solids and gas in a Keplerian disk produce a local, linear instability. The two components mutually interact via aerodynamic drag, which generates radial drift and triggers unstable modes. The secular instability does not require self-gravity, yet it generates growing particle density perturbations that could seed planetesimal formation. Growth rates are slower than dynamical, but faster than radial drift, timescales. Growth rates, like streaming velocities, are maximized for marginal coupling (stopping times comparable dynamical times). Fastest growth occurs when the solid to gas density ratio is order unity and feedback is strongest. Curiously, growth is strongly suppressed when the densities are too nearly equal. The relation between background drift and wave properties is explained by analogy with Howard's semicircle theorem. The three-dimensional, two-fluid equations describe a sixth order (in the complex frequency) dispersion relation. A terminal velocity approximation allows simplification to an approximate cubic dispersion relation. To describe the simplest manifestation of this instability, we ignore complicating (but possibly relevant) factors like vertical stratification, dispersion of particle sizes, turbulence, and self-gravity. We consider applications to planetesimal formation and compare our work to other studies of particle-gas dynamics.

astro-ph↗

arXiv2004

Numerical and Experimental Investigation of Circulation in Short Cylinders

In preparation for an experimental study of magnetorotational instability (MRI) in liquid metal, we explore Couette flows having height comparable to the gap between cylinders, centrifugally stable rotation, and high Reynolds number. Experiments in water are compared with numerical simulations. Simulations show that endcaps corotating with the outer cylinder drive a strong poloidal circulation that redistributes angular momentum. Predicted azimuthal flow profiles agree well with experimental measurements. Spin-down times scale with Reynolds number as expected for laminar Ekman circulation; extrapolation from two-dimensional simulations at $Re\le 3200$ agrees remarkably well with experiment at $Re\sim 10^6$. This suggests that turbulence does not dominate the effective viscosity. Further detailed numerical studies reveal a strong radially inward flow near both endcaps. After turning vertically along the inner cylinder, these flows converge at the midplane and depart the boundary in a radial jet. To minimize this circulation in the MRI experiment, endcaps consisting of multiple, differentially rotating rings are proposed. Simulations predict that an adequate approximation to the ideal Couette profile can be obtained with a few rings.

physics.flu-dyn↗

arXiv2004

Low-Mass Proto-Planet Migration in T-Tauri Alpha-Disks

We present detailed estimates of ''type-I'' migration rates for low-mass proto-planets embedded in steady-state T-Tauri alpha-disks, based on Lindblad torque calculations ignoring feedback on the disk. Differences in migration rates for several plausible background disk models are explored and we contrast results obtained using the standard two dimensional formalism of spiral density wave theory with those obtained from a simple treatment of three-dimensional effects. Opacity transitions in the disk result in sudden radial variations of the migration rates. Regions with minimal migration rates may be preferred sites of gravitational interactions between proto-planets. Three-dimensional torques are significantly weaker than two-dimensional ones and they are sensitive to the surface density profile of the background disk. We find that migration times in excess of runaway envelope accretion times or T-Tauri disk lifetimes are possible for Earth-mass proto-planets in some background disk models, even at sub-AU distances. We conclude that an understanding of the background disk structure and ''viscosity'', as well as a proper treatment of three-dimensional effects in torque calculations, are necessary to obtain reliable estimates of ``type-I'' migration rates.

astro-ph↗

arXiv2004

Supermassive Stars in Quasar Disks

We propose that supermassive stars may form in quasar accretion disks, and we discuss possible observational consequences. The structure and stability of very massive stars are reviewed. Because of high accretion rates, quasar disks are massive and the fringes of their optically luminous parts are prone to fragmentation. Starting from a few hundred solar masses, a dominant fragment will grow to the isolation mass, which is a significant fraction of the disk mass, more quickly than the fragment contracts onto the stellar main sequence. A gap will form in the disk and the star will migrate inward on the accretion timescale, which is comparable to the star's main sequence lifetime. By interrupting the gas supply to the inner disk, the gap may temporarily dim and redden the quasar. The final stages of stellar migration will be a strong source of low-frequency gravitational waves.

astro-ph↗

arXiv2003

Blue horizontal branch stars in the Sloan Digital Sky Survey: I. Sample selection and structure in the Galactic halo

We isolate samples of 733 bright (g < 18) and 437 faint (g > 18) high-Galactic latitude blue horizontal branch stars with photometry and spectroscopy in the Sloan Digital Sky Survey (SDSS). Comparison of independent photometric and spectroscopic selection criteria indicates that contamination from F and blue-straggler stars is less than 10% for bright stars (g<18) and about 25% for faint stars (g>18), and this is qualitatively confirmed by proper motions based on the USNO-A catalog as first epoch. Analysis of repeated observations shows that the errors in radial velocity are approximately 26 km/s. A relation between absolute magnitude and color is established using the horizontal branches of halo globular clusters observed by SDSS. Bolometric corrections and colors are synthesized in the SDSS filters from model spectra. The redder stars agree well in absolute magitude with accepted values for RR Lyrae stars. The resulting photometric distances are accurate to about 0.2 magnitudes, with a median of about 25 kpc. Modest clumps in phase space exist and are consistent with the previously reported tidal stream of the Sagittarius dwarf galaxy. The sample is tabulated in electronic form in the online version of this article, or by request to the authors.

astro-ph↗

arXiv2003

Blue horizontal branch stars in the Sloan Digital Sky Survey: II. Kinematics of the Galactic halo

We carry out a maximum-likelihood kinematic analysis of a sample of 1170 blue horizontal branch (BHB) stars from the Sloan Digital Sky Survey presented in Sirko et al. (2003) (Paper I). Monte Carlo simulations and resampling show that the results are robust to distance and velocity errors at least as large as the estimated errors from Paper I. The best-fit velocities of the Sun (circular) and halo (rotational) are 245.9 +/- 13.5 km/s and 23.8 +/- 20.1 km/s but are strongly covariant, so that v_0 - v_halo = 222.1 +/- 7.7 km/s. If one adopts standard values for the local standard of rest and solar motion, then the halo scarcely rotates. The velocity ellipsoid inferred for our sample is much more isotropic [(sigma_r,sigma_theta,sigma_phi) = (101.4 +/- 2.8, 97.7 +/- 16.4, 107.4 +/- 16.6) km/s] than that of halo stars in the solar neighborhood, in agreement with a recent study of the distant halo by Sommer-Larsen et al. (1997). The line-of-sight velocity distribution of the entire sample, corrected for the Sun's motion, is accurately gaussian with a dispersion of 101.6 +/- 3.0 km/s.

astro-ph↗

arXiv2003

Non-Axisymmetric g-Mode and p-Mode Instability in a Hydrodynamic Thin Accretion Disk

It has been suggested that quasi-periodic oscillations of accreting X-ray sources may relate to the modes named in the title. We consider non-axisymmetric linear perturbations to an isentropic, isothermal, unmagnetized thin accretion disk. The radial wave equation, in which the number of vertical nodes (n) appears as a separation constant, admits a wave-action current that is conserved except, in some cases, at corotation. Waves without vertical nodes amplify when reflected by a barrier near corotation. Their action is conserved. As was previously known, this amplification allows the n=0 modes to be unstable under appropriate boundary conditions. In contrast, we find that waves with n >0 are strongly absorbed at corotation rather than amplified; their action is not conserved. Therefore, non-axisymmetric p-modes and g-modes with n>0 are damped and stable even in an inviscid disk. This eliminates a promising explanation for quasi-periodic oscillations in neutron-star and black-hole X-ray binaries.

astro-ph↗

arXiv2002

Spectral energy distributions of selfgravitating QSO discs

We calculate spectral energy distributions (SEDs) of steady accretion discs at high accretion rates, as appropriate for bright QSOs, under the assumption that the outer parts are heated sufficiently to maintain marginal gravitational stability, presumably by massive stars formed within the disc. The SED is independent of the nature of these auxiliary sources if their inputs are completely thermalized. Standard assumptions are made for angular momentum transport, with an alpha parameter less than unity. With these prescriptions, the luminosity of the disc is sensitive to its opacity, in contrast to standard discs powered by release of orbital energy alone. Compared to the latter, our discs have a broader SED, with a second peak in the near-infrared that is energetically comparable to the blue bump. The energy in the second peak increases with the outer radius of the disc, provided that the accretion rate is constant with radius. By comparing our computed SEDs with observed ones, we limit the outer radius of the disc to be less than 10^5 Schwarzschild radii, or about one parsec, in a typical QSO. We also discuss some properties of our minimum-Q discs in the regions where auxiliary heating is dominant (10^3-10^5 Schwarzschild radii).

astro-ph↗

arXiv2002

Selfgravity and QSO disks

It is well known that the outer parts of QSO accretion disks are prone to selfgravity if heated solely by orbital dissipation. Such disks might be expected to form stars rather than accrete onto the black hole. The arguments leading to this conclusion are reviewed. Conversion of a part of the gas into high-mass stars or stellar-mass black holes, and the release of energy in these objects by fusion or accretion, may help to stabilize the remaining gas. If the disk extends beyond a parsec, however, more energy is probably required for stability than is available by turning half the gas into high-mass stars. Small black holes are perhaps marginally viable energy sources, with important implications (not pursued here) for the QSO spectral energy distribution, the metallicity of the gas, microlensing of QSO disks, and perhaps gravitational-wave searches. Other possible palliatives for selfgravity include accretion driven by nonviscous torques that allow near-sonic accretion speeds and hence lower surface densities for a given mass accretion rate. All such modes of accretion face major theoretical difficulties, and in any case merely postpone selfgravity. Alternatively, thin disks may not exist beyond a thousand Schwarzshild radii or so (0.01 parsec), in which case QSOs must be fueled by gas with small specific angular momentum.

astro-ph↗

arXiv2001

Magnetorotational Instability in a Rotating Liquid Metal Annulus

Although the magnetorotational instability (MRI) has been widely accepted as a powerful accretion mechanism in magnetized accretion disks, it has not been realized in the laboratory. The possibility of studying MRI in a rotating liquid-metal annulus (Couette flow) is explored by local and global stability analysis and magnetohydrodynamic (MHD) simulations. Stability diagrams are drawn in dimensionless parameters, and also in terms of the angular velocities at the inner and outer cylinders. It is shown that MRI can be triggered in a moderately rapidly rotating table-top apparatus, using easy-to-handle metals such as gallium. Practical issues of this proposed experiment are discussed.

astro-ph↗

arXiv2001

Magnetorotational instability of dissipative Couette flow

Global axisymmetric stability of viscous, resistive, magnetized Couette flow is re-examined, with the emphasis on flows that would be hydrodynamically stable according to Rayleigh's criterion: opposing gradients of angular velocity and specific angular momentum. In this regime, magnetorotational instabilities [MRI] may occur. Previous work has focused on the Rayleigh-unstable regime. To prepare for an experimental study of MRI, which are of intense astrophysical interest, we solve for global linear modes in a wide gap with realistic dissipation coefficients. Exchange of stability appears to occur through marginal modes. Velocity eigenfunctions of marginal modes are nearly singular at conducting boundaries, but magnetic eigenfunctions are smooth and obey a fourth-order differential equation in the inviscid limit. The viscous marginal system is of tenth order; an eighth-order approximation previously used for Rayleigh-unstable modes does not permit MRI. Peak growth rates are insensitive to boundary conditions. They are predicted with surprising accuracy by WKB methods even for the largest-scale mode. We conclude that MRI is achievable under plausible experimental conditions using easy-to-handle liquid metals such as gallium.

astro-ph↗

arXiv2000

Linear and non-linear theory of a parametric instability of hydrodynamic warps in Keplerian discs

We consider the stability of warping modes in Keplerian discs. We find them to be parametrically unstable using two lines of attack, one based on three-mode couplings and the other on Floquet theory. We confirm the existence of the instability, and investigate its nonlinear development in three dimensions, via numerical experiment. The most rapidly growing non-axisymmetric disturbances are the most nearly axisymmetric (low m) ones. Finally, we offer a simple, somewhat speculative model for the interaction of the parametric instability with the warp. We apply this model to the masing disc in NGC 4258 and show that, provided the warp is not forced too strongly, parametric instability can fix the amplitude of the warp.

astro-ph↗

arXiv2000

Stochastic Coagulation and the Timescale for Runaway Growth

We study the stochastic coagulation equation using simplified models and efficient Monte Carlo simulations. It is known that (i) runaway growth occurs if the two-body coalescence kernel rises faster than linearly in the mass of the heavier particle; and (ii) for such kernels, runaway is instantaneous in the limit that the number of particles tends to infinity at fixed collision time per particle. Superlinear kernels arise in astrophysical systems where gravitational focusing is important, such as the coalescence of planetesimals to form planets or of stars to form supermassive black holes. We find that the time required for runaway decreases as a power of the logarithm of the the initial number of particles. Astrophysical implications are briefly discussed.

astro-ph↗

arXiv2000

Repulsive Dark Matter

It seems necessary to suppress, at least partially, the formation of structure on subgalactic scales. As an alternative to warm or collisional dark matter, I postulate a condensate of massive bosons interacting via a repulsive interparticle potential, plus gravity. This leads to a minimum lengthscale for bound objects, and to superfluidity. Galactic dynamics may differ significantly from that of more generic dark matter in not unwelcome ways, especially in the core. Such particles can be realized as quanta of a relativistic massive scalar field with a quartic self-interaction. At high densities, the equation of state has the same form as that of an ideal relativistic gas despite the interactions. If the nonrelativistic lengthscale is of order a kiloparsec, then the energy density in these particles was comparable to that of photons at early times, but small enough to avoid conflict with primordial nucleosynthesis.

astro-ph↗

arXiv1999

Nonlinear Single-Armed Spiral Density Waves in Nearly Keplerian Disks

Single-armed, stationary density waves can propagate in very weakly self-gravitating gas disks dominated by a central mass. Examples include circumstellar disks of protostars and molecular disks in galactic nuclei. We explore the linear and nonlinear dynamics of such waves. Variational methods yield nonlinear versions of the dispersion relation, angular momentum flux, and propagation velocity in the tight-winding limit. The pitch angle increases with amplitude until the tight-winding approximation breaks down. We also find a series of nonlinear logarithmic spirals which is exact in the limit of small disk mass and which extends to large pitch angle.

astro-ph↗