arXiv subjects

Frank H. Shu

Publications and source records attributed to Frank H. Shu.

15 recordsLinked to original sources

arXiv2012

Feathering Instability of Spiral Arms. I: Formulation of the Problem

In this paper we study the feathering substructures along spiral arms by considering the perturbational gas response to a spiral shock. Feathers are density fluctuations that jut out from the spiral arm to the inter-arm region at pitch angles given by the quantum numbers of the doubly-periodic structure. In a localized asymptotic approximation, related to the shearing sheet except that the inhomogeneities occur in space rather than in time, we derive the linearized perturbation equations for a razor-thin disk with turbulent interstellar gas, frozen-in magnetic field, and gaseous self-gravity. Apart from the modal quantum numbers, the individual normal modes of the system depend on seven dimensionless quantities that characterize the underlying time-independent axisymmetric state plus its steady, nonlinear, two-armed spiral-shock (TASS) response to a hypothesized background density-wave supported by the disk stars of the galaxy. We show that some of these normal modes have positive growth rates. Their over-density contours in the post-shock region are very reminiscent of observed feathering substructures in full magnetohydrodynamic (MHD) simulations. The feathering substructures are parasitic instabilities intrinsic to the system; thus, their study not only provides potential diagnostics for important parameters that characterize the interstellar medium of external galaxies, but also yields a deeper understanding of the basic mechanism that drives the formation of the giant molecular clouds (GMCs) and the OB stars that outline observed grand-design spirals.

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arXiv2011

Magnetic Interactions in Pre-Main-Sequence Binaries

Young stars typically have strong magnetic fields, so that the magnetospheres of newly formed close binaries can interact, dissipate energy, and produce synchrotron radiation. The V773 Tau A binary system, a pair of T Tauri stars with a 51 day orbit, displays such a signature, with peak emission taking place near periastron. This paper proposes that the observed emission arises from the change in energy stored in the composite magnetic field of the system. We model the fields using the leading order (dipole) components and show that this picture is consistent with current observations. In this model, the observed radiation accounts for a fraction of the available energy of interaction between the magnetic fields from the two stars. Assuming antisymmetry, we compute the interaction energy $E_{\rm int}$ as a function of the stellar radii, the stellar magnetic field strengths, the binary semi-major axis, and orbital eccentricity, all of which can be measured independently of the synchrotron radiation. The variability in time and energetics of the synchrotron radiation depend on the details of the annihilation of magnetic fields through reconnection events, which generate electric fields that accelerate charged particles, and how those charged particles, especially fast electrons, are removed from the interaction region. However, the major qualitative features are well described by the background changes in the global magnetic configuration driven by the orbital motion. The theory can be tested by observing a collection of pre-main-sequence binary systems.

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arXiv2008

Magnetocentrifugally Driven Flows from Young Stars and Disks. VI. Accretion with a Multipole Stellar Field

Previous analyses of magnetospheric accretion and outflow in classical T Tauri stars (CTTSs), within the context of both the X-wind model and other theoretical scenarios, have assumed a dipolar geometry for the stellar magnetic field if it were not perturbed by the presence of an accreting, electrically conducting disk. However, CTTS surveys reveal that accretion hot spots cover a small fraction of the stellar surface, and that the net field polarization on the stellar surface is small. Both facts imply that the magnetic field generated by the star has a complex non-dipolar structure. To address this discrepancy between theory and observations, we re-examine X-wind theory without the dipole constraint. Using simple physical arguments based on the concept of trapped flux, we show that a dipole configuration is in fact not essential. Independent of the precise geometry of the stellar magnetosphere, the requirement for a certain level of trapped flux predicts a definite relationship among various CTTS observables. Moreover, superposition of multipole stellar fields naturally yield small observed hot-spot covering fractions and small net surface polarizations. The generalized X-wind picture remains viable under these conditions, with the outflow from a small annulus near the inner disk edge little affected by the modified geometry, but with inflow highly dependent on the details of how the emergent stellar flux is linked and trapped by the inner disk regions. Our model is consistent with data, including recent spectropolarimetric measurements of the hot spot sizes and field strengths in V2129 Oph and BP Tau.

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arXiv2008

The Challenge of Sub-Keplerian Rotation for Disk Winds

Strong magnetization makes the disks surrounding young stellar objects rotate at rates that are too sub-Keplerian to enable the thermal launching of disk winds from their surfaces unless the rate of gas diffusion across field lines is dynamically fast. This under-appreciated implication of disk magnetization poses a considerable challenge for disk-wind theory.

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arXiv2007

X-winds in Action

The interaction of accretion disks with the magnetospheres of young stars can produce X-winds and funnel flows. With the assumption of axial symmetry and steady state flow, the problem can be formulated in terms of quantities that are conserved along streamlines, such as the Bernoulli integral (BI), plus a partial differential equation (PDE), called the Grad-Shafranov equation (GSE), that governs the distribution of streamlines in the meridional plane. The GSE plus BI yields a PDE of mixed type, elliptic before critical surfaces where the flow speed equals certain characteristic wave speeds are crossed and hyperbolic afterward. The computational difficulties are exacerbated by the locations of the critical surfaces not being known in advance. To overcome these obstacles, we consider a variational principle by which the GSE can be attacked by extremizing an action integral, with all other conserved quantities of the problem explicitly included as part of the overall formulation. To simplify actual applications we adopt the cold limit of a negligibly small ratio of the sound speed to the speed of Keplerian rotation in the disk where the X-wind is launched. We also ignore the obstructing effects of any magnetic fields that might thread a disk approximated to be infinitesimally thin. We then introduce trial functions with adjustable coefficients to minimize the variations that give the GSE. We tabulate the resulting coefficients so that other workers can have analytic forms to reconstruct X-wind solutions for various astronomical, cosmochemical, and meteoritical applications.

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arXiv2007

Ambipolar Diffusion in Molecular Cloud Cores and the Gravomagneto Catastrophe

This paper re-examines the problem of ambipolar diffusion as a mechanism for the production and runaway evolution of centrally condensed molecular cloud cores, a process that has been termed the gravomagneto catastrophe. Our calculation applies in the geometric limit of a highly flattened core and allows for a semi-analytic treatment of the full problem, although physical fixes are required to resolve a poor representation of the central region. A noteworthy feature of the overall formulation is that the solutions for the ambipolar diffusion portion of the evolution for negative times ($t < 0$) match smoothly onto the collapse solutions for positive times ($t > 0$). The treatment shows that the resulting cores display non-zero, but sub-magnetosonic, inward velocities at the end of the diffusion epoch, in agreement with current observations. Another important result is the derivation of an analytic relationship between the dimensionless mass to flux ratio $λ_0\equiv f_0^{-1}$ of the central regions produced by runaway core condensation and the dimensionless measure of the rate of ambipolar diffusion $ε$. In conjunction with previous work showing that ambipolar diffusion takes place more quickly in the presence of turbulent fluctuations, i.e., that the effective value of $ε$ can be enhanced by turbulence, the resultant theory provides a viable working hypothesis for the formation of isolated molecular-cloud cores and their subsequent collapse to form stars and planetary systems.

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arXiv2007

Formation of OB Associations in Galaxies

We consider the formation of OB associations from two perspectives: (a) the fractional gas consumption in star formation,epsilon, per dynamical time scale t_dyn in a galaxy, and (b) the origin of the so-called Kennicutt-Schmidt law that the rate of star formation per unit area is proportional to a power, alpha, of the surface density in HI and H_2 gas when certain thresholds are crossed. The empirical findings that epsilon is approximately 0.01 and alpha is approximately 1.4 or 1.5 have simple explanations if the rate of star formation is magnetically regulated. An empirical test of the ideas resides in an analysis of why giant OB associations are ``strung out like pearls along the arms" of spiral galaxies.

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arXiv2007

Mean-Field Magnetohydrodynamics of Accretion Disks

We consider the accretion process in a disk with magnetic fields that are dragged in from the interstellar medium by gravitational collapse. Two diffusive processes are at work in the system: (1) "viscous" torques exerted by turbulent and magnetic stresses, and (2) "resistive" redistribution of mass with respect to the magnetic flux arising from the imperfect conduction of current. In steady state, self-consistency between the two rates of drift requires that a relationship exists between the coefficients of turbulent viscosity and turbulent resistivity. Ignoring any interactions with a stellar magnetosphere, we solve the steady-state equations for a magnetized disk under the gravitational attraction of a mass point and threaded by an amount of magnetic flux consistent with calculations of magnetized gravitational collapse in star formation. Our model mean-field equations have an exact analytical solution that corresponds to magnetically diluted Keplerian rotation about the central mass point. The solution yields the strength of the magnetic field and the surface density as functions of radial position in the disk and their connection with the departure from pure Keplerian rotation in representative cases. We compare the predictions of the theory with the available observations concerning T Tauri stars, FU Orionis stars, and low- and high-mass protostars. Finally, we speculate on the physical causes for high and low states of the accretion disks that surround young stellar objects. One of the more important results of this study is the physical derivation of analytic expressions for the turbulent viscosity and turbulent resistivity.

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arXiv2005

The Irradiation Origin of Beryllium Radioisotopes and Other Short-lived Radionuclides

Two explanations exist for the short-lived radionuclides present in the solar system when the CAIs first formed. They originated either from the ejecta of a supernova or by the in situ irradiation of nebular dust by energetic particles. With a half-life of only 53 days, Beryllium-7 is then the key discriminant, since it can be made only by irradiation. We calculate the yield of Be-7. Within model uncertainties associated mainly with nuclear cross sections, we obtain agreement with the experimental value. Moreover, if Be-7 and Be-10 have the same origin, the irradiation time must be short. The x-wind model provides a natural astrophysical setting that gives the requisite conditions. The decoupling of the Al-26 and Be-10 observed in some rare CAIs receives a quantitative explanation when rare gradual events are considered. Finally, we show that the presence of supernova-produced Fe-60 in the solar accretion disk does not necessarily mean that other short-lived radionuclides have a stellar origin.

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arXiv2004

Nonaxisymmetric Neutral Modes in Relativistic Disks

We perform a linear stability analysis of the axisymmetric, relativistic, self-similar isothermal disk against non-axisymmetric perturbations. Two sets of neutral modes are discovered. The first set corresponds to marginally unstable perturbations driven by gravitational radiation, and the other signals the onset of bifurcation to non-axisymmetric equilibrium solutions to the Einstein equations.

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arXiv2003

Does Magnetic Levitation or Suspension Define the Masses of Forming Stars?

We investigate whether magnetic tension can define the masses of forming stars by holding up the subcritical envelope of a molecular cloud that suffers gravitational collapse of its supercritical core. We perform an equilibrium analysis of the initial and final states assuming perfect field freezing, no rotation, isothermality, and a completely flattened configuration. The sheet geometry allows us to separate the magnetic tension into a levitation associated with the split monopole formed by the trapped flux of the central star and a suspension associated with curved field lines that thread the static pseudodisk and envelope of material external to the star. We find solutions where the eigenvalue for the stellar mass is a fixed multiple of the initial core mass of the cloud. We verify the analytically derived result by an explicit numerical simulation of a closely related 3-D axisymmetric system. However, with field freezing, the implied surface magnetic fields much exceed measured values for young stars. If the pinch by the central split monopole were to be eliminated by magnetic reconnection, then magnetic suspension alone cannot keep the subcritical envelope (i.e., the entire model cloud) from falling onto the star. We argue that this answer has general validity, even if the initial state lacked any kind of symmetry, possessed rotation, and had a substantial level of turbulence. These findings strongly support a picture for the halt of infall that invokes dynamic levitation by YSO winds and jets, but the breakdown of ideal magnetohydrodynamics is required to allow the appearance in the problem of a rapidly rotating, centrifugally supported disk. We use these results to calculate the initial mass function and star formation efficiency for the distributed and clustered modes of star formation.

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arXiv2003

Relativistic Singular Isothermal Toroids

We construct self-similar, axisymmetric, time-independent solutions to Einstein's field equations for an isothermal gas with a flat rotation curve in the equatorial plane. The metric scales as $ds^2 \to a^2 ds^2$ under the transformation $r\to a r$ and $t \to a^{1-n} t$, where $n$ is a dimensionless measure of the strength of the gravitational field. The solution space forms a two-parameter family characterized by the ratios of the isothermal sound speed and the equatorial rotation speed to the speed of light. The isodensity surfaces are toroids, empty of matter along the rotation axis. Unlike the Newtonian case, the velocity field is not constant on a cylindrical radius. As the configuration rotates faster, an ergoregion develops in the form of the exterior of a cone centered about the rotation axis. The sequence of solutions terminates when frame dragging becomes infinite and the ergocone closes onto the axis. The fluid velocity of the last solution has finite value in the midplane but reaches the speed of light on the axis.

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arXiv2002

Planetesimal Formation by Gravitational Instability

We investigate the formation of planetesimals via the gravitational instability of solids that have settled to the midplane of a circumstellar disk. Vertical shear between the gas and a subdisk of solids induces turbulent mixing which inhibits gravitational instability. Working in the limit of small, well-coupled particles, we find that the mixing becomes ineffective when the surface density ratio of solids to gas exceeds a critical value. Solids in excess of this precipitation limit can undergo midplane gravitational instability and form planetesimals. However, this saturation effect typically requires increasing the local ratio of solid to gaseous surface density by factors of two to ten times cosmic abundances, depending on the exact properties of the gas disk. We discuss existing astrophysical mechanisms for augmenting the ratio of solids to gas in protoplanetary disks by such factors, and investigate a particular process that depends on the radial variations of orbital drift speeds induced by gas drag. This mechanism can concentrate millimeter sized chondrules to the supercritical surface density in < few x 10^6 years, a suggestive timescale for the disappearance of dusty disks in T Tauri stars. We discuss the relevance of our results to some outstanding puzzles in planet formation theory: the size of the observed solar system, and the rapid type I migration of Earth mass bodies.

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arXiv2001

Relativistic Self-similar Disks

We formulate and solve by semi-analytic means the axisymmetric equilibria of relativistic self-similar disks of infinitesimal vertical thickness. These disks are supported in the horizontal directions against their self-gravity by a combination of isothermal (two-dimensional) pressure and a flat rotation curve. The dragging of inertial frames restricts possible solutions to rotation speeds that are always less than 0.438 times the speed of light, a result first obtained by Lynden-Bell and Pineault in 1978 for a cold disk. We show that prograde circular orbits of massive test particles exist and are stable for all of our model disks, but retrograde circular orbits cannot be maintained with particle velocities less than the speed of light once the disk develops an ergoregion. We also compute photon trajectories, planar and non-planar, in the resulting spacetime, for disks with and without ergoregions. We find that all photon orbits, except for a set of measure zero, tend to be focused by the gravity of the flattened mass-energy distribution toward the plane of the disk. This result suggests that strongly relativistic, rapidly rotating, compact objects may have difficulty ejecting collimated beams of matter or light along the rotation axes until the flows get well beyond the flattened parts of the relativistic mass distribution (which cannot happen in the self-similar models considered in this paper).

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arXiv2000

Singular Isothermal Disks: II. Nonaxisymmetric Bifurcations and Equilibria

We review the difficulties of the classical fission and fragmentation hypotheses for the formation of binary and multiple stars. A crucial missing ingredient in previous theoretical studies is the inclusion of dynamically important levels of magnetic fields. As a minimal model for a candidate presursor to the formation of binary and multiple stars, we therefore formulate and solve the problem of the equilibria of isopedically magnetized, singular isothermal disks, without the assumption of axial symmetry. Considerable analytical progress can be made if we restrict our attention to models that are scale-free, i.e., that have surface densities that vary inversely with distance from the rotation axis of the system. In agreement with earlier analysis by Syer and Tremaine, we find that lopsided (M=1) configurations exist at any dimensionless rotation rate, including zero. Multiple-lobed (M = 2, 3, 4, ...) configurations bifurcate from an underlying axisymmetric sequence at progressively higher dimensionless rates of rotation, but such nonaxisymmetric sequences always terminate in shockwaves before they have a chance to fission into M=2, 3, 4, ... separate bodies. On the basis of our experience in this paper, and the preceding Paper I, we advance the hypothesis that binary and multiple star-formation from smooth (i.e., not highly turbulent) starting states that are supercritical but in unstable mechanical balance requires the rapid (i.e., dynamical) loss of magnetic flux at some stage of the ensuing gravitational collapse.

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