Engineering topics

Shu, Frank H.

Publications and source records attributed to Shu, Frank H..

At least 19 records

NASA NTRS2000

Singular Isothermal Disks and the Formation of Multiple Stars

A crucial missing ingredient in previous theoretical studies of fragmentation 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 consider the equilibrium configuration of isopedically magnetized, scale-free, singular isothermal disks, without the assumption of axial symmetry. 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 separate bodies. 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.

Galli, Daniele↗

NASA NTRS2000

Singular Isothermal Disks: Nonaxiymmetric Bifurcations and Equilibria - Paper 2

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 omega 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, 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.

Galli, Danielle↗

NASA NTRS1996

Toward an Astrophysical Theory of Chondrites

Sunlike stars are born with disks. Based on our recently developed model to understand how a magnetized new star interacts with its surrounding accretion disk, we advanced an astrophysical theory for the early solar system. The aerodynamic drag of a magnetocentrifugally driven wind out of the inner edge of a shaded disk could expose solid bodies lifted into the heat of direct sunlight, when material is still accreting onto the protosun. Chondrules, calcium-aluminum-rich inclusions (CAI's), and rims could form along the flight for typical self-consistent parameters of the outflow in different stages of star formation. The process gives a natural sorting mechanism that explains the size distribution of CAI's and chondrules, as well as their associated rims. Chondritic bodies then subsequently form by compaction of the processed solids with the ambient nebular dust comprising the matrices after their reentry at great distances from the original launch radius.

Shang, Hsien↗

NASA NTRS1994

Magnetocentrifugally driven flows from young stars and disks. 2: Formulation of the dynamical problem

We formulate the dynamical problem of a cool wind centrifugally driven from the magnetic interface of a young star and an adjoining Keplerian disk. We examine the situation for mildly accreting T Tauri stars that rotate slowly as well as rapidly accreting protostars that rotate near break-up. In both cases a wind can be driven from a small X-region just outside the stellar magnetopause, where the field lines assume an open geometry and are rooted to material that rotates at an angular speed equal both to the local Keplerian value and to the stellar angular speed. Assuming axial symmetry for the ideal magnetohydrodynamic flow, which requires us to postpone asking how the (lightly ionized) gas is loaded onto field lines, we can formally integrate all the governing equations analytically except for a partial equation that describes how streamlines spread in the meridional plane. Apart from the difficulty of dealing with PDEs of mixed type, finding the functional forms of the conserved quantities along streamlines - the ratio beta of magnetic field to mass flux, the specific energy H of the fluid in the rotating frame, and the total specific angular momentum J carried in the matter and the field - constitutes a standard difficulty in this kind of (Grad-Shafranov) formalism. Fortunately, because the ratio of the thermal speed of the mass-loss regions to the Keplerian speed of rotation of the interface constitutes a small parameter epsilon, we can attack the overall problem by the method of matched asymptotic expansions. This procedure leads to a natural and systematic technique for obtaining the relevant functional dependences of beta, H, and J. Moreover, we are able to solve analytically for the properties of the flow emergent from the small transsonic region driven by gas pressure without having to specify the detailed form of any of the conserved functions, beta, H, and J. This analytical solution provides inner boundary conditions for the numerical computation in a companion paper by Najita & Shu of the larger region where the main acceleration to terminal speeds occurs.

Shu, Frank H.↗

NASA NTRS1994

Magnetocentrifugally driven flows from young stars and disks. 3: Numerical solution of the sub-Alfvenic region

We construct steady, axisymmetric, numerical models of the sub-Alfvenic regions of cool winds driven by the X-celerator mechanism. We find that smooth acceleration to speeds of the order of the escape speed accompanied by substantial collimation of the flow can be achieved within the Alfven surface, located characteristically at several stellar radii. We apply the nondimensional results to winds which emerge from the equator of magnetized YSOs rotating at breakup and from circumstellar disks interacting with the magnetospheres of slowly rotating T Tauri stars. Stellar magnetic fields of kilogauss strength can drive wind mass-loss rates of 10(exp -6) solar mass/year from rapidly accreting YSOs and 10(exp -8) solar mass/year from slowly accreting T Tauri stars. The X-celerator mechanism can accelerate winds from these systems to velocities of hundreds of km/sec within a few stellar radii in the case of embedded YSOs and approximately 10 stellar radii in the case of T Tauri stars.

Najita, Joan R.↗

NASA NTRS1993

The inner-disk and stellar properties of the young stellar object WL 16

We present kinematic evidence for a rapidly rotating circumstellar disk around the young stellar object WL 16, based on new high-velocity-resolution data of the v = 2-0 CO bandhead emission. A Keplerian disk provides an excellent fit to the observed profile and requires a projected velocity for the CO-emitting region of roughly 250 km/s at the inner radius and 140 km/s at the outer radius, giving a ratio of the inner to the outer radius of about 0.3. We show that satisfying the constraints imposed by the gas kinematics, the observed CO flux, and the total source luminosity requires the mass of WL 16 to lie between 1.4 and 2.5 solar mass. The inner disk radius for the CO emission must be less than 8 solar radii.

Carr, John S.↗

NASA NTRS1992

Near-resonant excitation and propagation of eccentric density waves by external forcing

An overview is presented of the astronomical evidence that relatively massive, distended, gaseous disks form as a natural by-product of the process of star formation, and also the numerical evidence that SLING-amplified eccentric modes in the outer parts of such disks can drive one-armed spiral density waves in the inner parts by near-resonant excitation and propagation. An ordinary differential equation (ODE) of the second order that approximately governs the nonlocalized forcing of waves in a disk satisfying Lindblad resonance almost everywhere is derived. When transformed and appended with an extra model term, this ODE implies, for free waves, the usual asymptotic results of the WKBJ dispersion relationship and the propagation Goldreich-Tremaine (1978) formula for the resonant torque exerted on a localized Lindblad resonance. An analytical solution is given for the rate of energy and angular momentum transfer by nonlocalized near-resonant forcing in the case when the disk has power-law dependences on the radius of the surface density and temperature.

Ostriker, Eve C.↗

NASA NTRS1991

Star formation and the nature of bipolar outflows

This paper presents a simple physical model for the bipolar molecular outflows that frequently accompany star formation. The model forges an intrinsic link between the bipolar flow phenomenon and the process of star formation, and it helps to explain many of the systematics known for existing sources.

Shu, Frank H.↗

NASA NTRS1991

Star formation - A theoretician's view

The present evaluation of the hypothesis that the birth of a sunlike star occurs in four stages, with a critical bipolar outflow phase, notes that observed molecular outflows cannot be initiated from circumstellar disks and must instead represent swept-up shells of gas that are driven by strong protostellar winds. The star can resolve its growing angular-momentum problem only by rejecting a fraction of the material that is fed through the disk in a powerful, magnetocentrifugally-driven wind. Empirical properties measured for well-collimated outflow sources can be accounted for by the interaction of this anisotropic wind with the ambient molecular cloud core.

Shu, Frank H.↗

NASA NTRS1990

Thermal structure of neutral winds from young stellar objects

The physical processes that control the thermal structure of lightly ionized winds from cool protostars are discussed. Attention is concentrated on the hydrogen gas, and the heating, cooling, and chemical processes that affect the neutral and ionic species of atomic and molecular hydrogen are examined. Warm silicate dust may condense out of the cooling wind and may heat the gas through collisions. Singly ionized sodium atoms, which do not recombine for the mass-loss rates considered, set a lower limit to the ionization fraction in the wind. Magnetic fields, which are presumed to accelerate the wind, couple directly to the ionic component of the gas and transfer momentum and energy to the neutral component through collisions. This process of ambipolar diffusion is found to be the dominant source of heat input to the gas.

Ruden, Steven P.↗

NASA NTRS1990

Sling amplification and eccentric gravitational instabilities in gaseous disks

An analytical description is presented of the modal mechanisms relevant to a recently discovered type of eccentric gravitational instability in nearly Keplerian disks. A quantum condition is derived which accurately predicts the pattern speeds for these modes. The growth rates for the modes are determined, and it is shown that the mode can grow when the disk is safely stable to axisymmetric disturbances. The case of marginal stability for the outside edge is discussed, and the implications of the results for the formation of binary companions and/or giant planets within disks associated with young stellar objects are considered.

Shu, Frank H.↗

NASA NTRS1990

The dense interstellar medium and the birthplaces of OB stars

A review is presented of Stromgren's research on the relationships among atomic, ionized, and molecular hydrogen in the Galaxy and the spatial distribution and kinematics of OB stars. Particular attention is given to the development of density-wave theory, the implication that the pattern of the formation of OB stars in a spiral galaxy should rotate at a constant angular speed, which differs generally from the mean material speed of the interstellar gas. Other theories involving the mechanical support of molecular clouds; triggered star formation; and the relationships among H2, H I, and H II are discussed.

Shu, Frank H.↗

NASA NTRS1990

Star formation and the lunar initiative

The paper considers the opportunities offered by proposed lunar observatories for studies of the origin of stars and related objects. The principal advantages to be gained by astronomical observations from the moon are summarized. An outline of the working hypothesis that present-day star formation in the Galaxy involves four conceptually distinct stages is given. It is concluded that the greatest strides forward in understanding will probably come from interferometric investigations that can be carried out with at least 10 milliarcsecond angular resolution at submillimeter and far-infrared wavelengths, and 10 microarcsecond resolution at ultraviolet, optical, and near-infrared wavelengths.

Shu, Frank H.↗

NASA NTRS1989

Eccentric gravitational instabilities in nearly Keplerian disks

The growth of global gravitational instabilities in young stellar objects (YSOs) with associated circumstellar disks is studied. The possibility that the accretion ultimately owes its origin to the growth of spiral gravitational instabilities is explored. The results indicate that YSO disks will be unstable to the growth of eccentric distortions which have growth rates comparable to the orbital frequency at the outer edge of the disk. Thus, the distortions grow on nearly a dynamical time scale. Perturbations with m = 1 force the star to move from the center of mass and thereby transfer angular momentum to the stellar orbit. Depending on whether or not an axisymmetric stability parameter Q barrier exists near the corotation radius of the disturbance, this coupling may lead to mass accretion or to the formation of a binary companion from the disk, or both.

Adams, Fred C.↗

NASA NTRS1989

Molecular cloud cores and bimodal star formation

The phenomenon of bimodal star formation is reviewed in the context of supercritical and subcritical states for molecular clouds that are supported against their self-gravitation by magnetic fields. The governing set of equations is derived subject to the quasi-static and axisymmetric approximations. The method of numerical solution and tests of the resultant computer code are outlined. The results of the evolutionary calculations are discussed, emphasizing time scales, masses, and typical sizes of modeled cores that can be compared with observations. For a fixed mass, it is found that the level or turbulent support determines whether a dense core forms or not. This is used to generalize the concept of a critical mass to account for the contributions of turbulence and thermal pressures to the support of a cloud.

Lizano, Susana↗

NASA NTRS1988

Neutral stellar winds that drive bipolar outflows in low-mass protostars

The Arecibo radio telescope at the 21-cm line of atomic hydrogen has been used to detect a neutral atomic wind in the bipolar flow source HH 7-11. An atomic mass of about 0.015 solar associated with the rapidly flowing gas is deduced. The stellar mass-loss rate is roughly 3 x 10 to the -6th solar mass/yr if the crossing time of the decelerating wind is 5000 yr. The excess emission in the H I line core gives a total duration of the outflow of about 70,000 yr. A detailed analysis of the H I line shape yields a reasonable deceleration rate for the atomic wind if the stellar wind continuously entrains ambient molecular gas as it propagates from the protostar. A stellar wind with the described characteristics and a terminal velocity of 170 km/s would be more than sufficient to drive the known extended CO bipolar outflow in HH 7-11.

Lizano, Susana↗

NASA NTRS1988

Mass loss from rapidly rotating magnetic protostars

It is proposed that bipolar outflows from young stellar objects originate from a protostar rotating at breakup at its equator because it is being spun up by an adjoining accretion disk. Mass outflow at an appreciable fraction of the infall rate from a surrounding molecular cloud core onto the star and disk can be driven centrifugally if the protostar has a sufficiently strong magnetic field. The expansion of the flow toward the rotational poles may provide a collimation mechanism for focusing an ordinary stellar wind into optical jets.

Shu, Frank H.↗

NASA NTRS1988

The disks of T Tauri stars with flat infrared spectra

The energy distributions of T Tauri stars with flat infrared spectra is modeled by assuming that they have spatially thin disks with unorthodox radial gradients of temperature. Derived model parameters show that the disks associated with the flat-spectrum sources must contain intrinsic luminosity in addition to the energy intercepted and reprocessed from the central star, i.e., the disks must be active. Self-gravity may provide a possible source for this activity.

Adams, Fred C.↗