Search

This article discusses quantitatively how to stop and reverse climate change. To stop climate change, we must transition from burning fossil fuels to using clean energy resources that do not involve the emission of CO2. We discuss the advantages and disadvantages of renewable energy sources, such as wind, water, and solar, relative to nuclear fission and the continued burning of fossil fuels, coupled to CO2 capture and sequestration of the flue gas. A plot of the energy per unit mass, e, against the energy per unit volume, e, shows many orders of magnitude difference between changes in the mechanical state of ordinary matter versus chemical reactions versus nuclear transformations. These differences raise an apparent paradox concerning how the price of electricity can be roughly competitive for the commercial technologies based on the very different fuel types. Explicit and implicit subsidies for politically favored fuels give a partial explanation, but the turbines that turn flowing fluids into flowing electricity account for most of the result.

The theory of spiral density waves had its origin approximately six decades ago in an attempt to reconcile the winding dilemma of material spiral arms in flattened disk galaxies. We begin with the earliest calculations of linear and nonlinear spiral density waves in disk galaxies, in which the hypothesis of quasi-stationary spiral structure (QSSS) plays a central role. The earliest success was the prediction of the nonlinear compression of the interstellar medium and its embedded magnetic field; the earliest failure, seemingly, was not detecting color gradients associated with the migration of OB stars whose formation is triggered downstream from the spiral shock front. We give the reasons for this apparent failure with an update on the current status of the problem of OB star formation, including its relationship to the feathering substructure of galactic spiral arms. Infrared images can show two-armed, grand design spirals, even when the optical and UV images show flocculent structures. We suggest how the nonlinear response of the interstellar gas, coupled with overlapping subharmonic resonances, might introduce chaotic behavior in the dynamics of the interstellar medium and Population I objects, even though the underlying forces to which they are subject are regular. We then move to a discussion of resonantly forced spiral density waves in a planetary ring and their relationship to the ideas of disk truncation, and the shepherding of narrow rings by satellites orbiting nearby. The back reaction of the rings on the satellites led to the prediction of planet migration in protoplanetary disks, which has had widespread application in the exploding data sets concerning hot Jupiters and extrasolar planetary systems. We then return to the issue of global normal modes in the stellar disk of spiral galaxies and its relationship to the QSSS hypothesis, where the central theoretical concepts involve waves with negative and positive surface densities of energy and angular momentum in the regions interior and exterior, respectively, to the corotation circle; the consequent transmission and overreflection of propagating spiral density waves incident on the corotation circle; and the role of feedback from the central regions.

We review the theory of the formation and gravitational collapse of magnetized molecular cloud cores, leading to the birth of T Tauri stars surrounded by quasi-Keplerian disks whose accretion is driven by the magnetorotational instability (MRI). Some loss of magnetic flux during the collapse results typically in a dimensionless mass-to-flux ratio for the star plus disk of λ0≈ 4. Most of the mass ends up in the star, while almost all of the flux and the angular momentum ends up in the disk; therefore, a known mass for the central star implies a computable flux in the surrounding disk. A self-contained theory of the MRI that drives the viscous/resistive spreading in such circumstances then yields the disk radius needed to contain the flux trapped in the disk as a function of the aget. This theory yields analytic predictions of the distributions with distance ϖ from the central star of the surface density Σ(ϖ), the vertical magnetic fieldBz(ϖ), and the (sub-Keplerian) angular rotation rate Ω (ϖ). We discuss the implications of this picture for disk-winds, X-winds, and funnel flows, and we summarize the global situation by giving the energy and angular-momentum budget for the overall problem.

We study the self-similar collapse of an isothermal magnetized rotating cloud in the ideal magnetohydrodynamic (MHD) regime. In the limit of small distance from the accreting protostar, we find an analytic solution that corresponds to free fall onto a central mass point. The density distribution is not spherically symmetric but depends on the mass loading of magnetic field lines, which can be obtained by matching our inner solution to an outer collapse solution previously computed by Allen et al. The concentration of magnetic field trapped by the central mass point under field freezing, independent on the details of the starting state, creates a split-monopole configuration in which the magnetic field strength increases as the inverse square of the distance from the center. Under such conditions, the inflow eventually becomes sub-Alfvenic and the outward transfer of angular momentum by magnetic braking very efficient, thus preventing the formation of a centrifugally supported disk. Instead, the azimuthal velocity of the infalling gas decreases to zero at the center, and the gas spirals into the star. Therefore, the dissipation of dynamically important levels of magnetic field is a fundamental requisite for the formation of protoplanetary disks around young stars.

We study the gravitational collapse of a relativistic singular isothermal sphere that is initially in unstable equilibrium. In the subsequent collapse, the dynamic spacetime is self-similar. The infall proceeds in an inside-out fashion, mimicking its Newtonian counterpart in star formation. A spherical expansion wave propagates outward at the speed of sound, initiating an inward collapse relative to local static observers. Outside of the expansion wave front, matter remains in local equilibrium. Inside, fluid elements are accelerated from rest toward the expanding black hole event horizon. When the singular isothermal sphere is initially threaded by a uniform but weak magnetic field, the frozen-in field lines accumulate above the horizon according to a distant observer, while assuming a split-monopole configuration on a larger scale. When the magnetized system also possesses rotation, such a configuration may naturally develop a vigorous outflow in the simultaneous presence of an accretion inflow. We speculate that such a process underlies the well-known relationship between mass and bulge velocity dispersion of supermassive black holes in the nuclei of galaxies.

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., to appear in ApJ v611

We calculate the centimeter wavelength free-free emission of the jets of young stellar objects (YSOs) with the X-wind model enhanced by a variety of physical processes. Using parameters characteristic of a Class I YSO with a mass-loss rate of ~10-6 M☉ yr-1, we obtain a 3.6 cm map and a spectral index that compare well with high spatial resolution observations of L1551 IRS 5. Models with lower mass-loss rates, appropriate for Class II YSOs with revealed optical jets, produce radio jets that are too weak to be detected at current sensitivity levels. In addition to demonstrating the consistency of the density distribution of the X-wind model with observations, we are able to obtain information on the processes that heat and ionize the inner jet, i.e., X-ray ionization and shock heating and ionization.

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., 47 pages, 7 figures

We study numerically the collapse of rotating, magnetized molecular cloud cores, focusing on rotation and magnetic braking during the main accretion phase of isolated star formation. Motivated by previous numerical work and analytic considerations, we idealize the pre-collapse core as a magnetized singular isothermal toroid, with a constant rotational speed everywhere. The collapse starts from the center, and propagates outwards in an inside-out fashion, satisfying exact self-similarity in space and time. For rotation rates and field strengths typical of dense low-mass cores, the main feature remains the flattening of the mass distribution along field lines -- the formation of a pseudodisk, as in the nonrotating cases. The density distribution of the pseudodisk is little affected by rotation. On the other hand, the rotation rate is strongly modified by pseudodisk formation. Most of the centrally accreted material reaches the vicinity of the protostar through the pseudodisk. The specific angular momentum can be greatly reduced on the way, by an order of magnitude or more, even when the pre-collapse field strength is substantially below the critical value for dominant cloud support. The efficient magnetic braking is due to the pinched geometry of the magnetic field in the pseudodisk, which strengthens the magnetic field and lengthens the level arm for braking. Both effects enhance the magnetic transport of angular momentum from inside to outside. The excess angular momentum is carried away in a low-speed outflow that has, despite claims made by other workers, little in common with observed bipolar molecular outflows. We discuss the implications of our calculations for the formation of true disks that are supported against gravity by rotation., Comment: 38 pages, 9 figures. To appear in v599 n1 ApJ December 10, 2003 issue

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., Comment: 49 pages, 11 figures, LaTeX, needs aaspp4.sty. The Astrophysical Journal, in press

We study the eUects of self-shielding in the X-wind model of protosolar cosmic-ray irradiation of early solar-system rocks. We adopt a two-component picture of protoCAIs consisting of cores with the elemental abundances of type B1 CAIs (calcium-aluminum-rich inclusions) and mantles of less refractory material. The cores have a power-law distribution of sizes between and The mantles have a R min R max . uniform thickness, whose value is chosen to bring the total inventory of elements at least as refractory as sulfur to cosmic abundances for the entire population of protoCAIs. Each object is irradiated with a —uence consistent with the product of their residence time in the reconnection ring and the —ux of solar cosmic rays obtained by a scaling of impulsive —ares from the hard X-rays observed from low-mass protostars. For in the 50 km regime and in the few centimeter regime, which corresponds to the R min R max range of sizes of observed CAIs in micrometeorites and chondrites, we recover approximately the canonical values quoted for the ratios 26Al/27Al, 53Mn/55Mn, and 41Ca/40Ca in CV3 meteorites. Moreover, the excess 138La (denoted as 138La*) produced by proton bombardment of 138Ba lies within the CAI range obtained in the experiments of Shen et al. When we include fragmentation reactions that produce 10Be from the impact of protons, alphas, and 3He on the 16O that is bound up in rocks, we further obtain a level of 10Be/9Be that agrees approximately with the report of McKeegan et al. for a CAI from the Allende meteorite. Similar calculations for the expected anomalies in the stable isotopes of lithium show rough consistency with the measured values and further support our interpretation. The value for 10Be/9Be is particularly difficult to produce by any other astrophysical mechanism. Thus, the 10Be discovery greatly strengthens the case for an origin in early solar-system irradiation, rather than external stellar seeding, for the shortest-lived radionuclides inferred from CAIs in chondritic meteorites.

Examples of calcium-aluminum-rich inclusions (CAIs) surrounded by thick chondrule mantles have been found in chondritic meteorites and cast doubt on the conventional belief that CAIs and chondrules possessed different spacetime origins in the primitive solar nebula. We study specific processes by which such objects, and the more common ordinary CAIs and chondrules, might have formed by flare heating of primitive rocks interior to the inner edge of a gaseous accretion disk that has been truncated by magnetized funnel flow onto the central proto-Sun. Motivated by the appearance of the chains of Herbig-Haro knots that define collimated optical jets from many young stellar objects (YSOs), we adopt the model of a fluctuating X-wind, where the inner edge of the solar nebula undergoes periodic radial excursions on a timescale of ~30 yr, perhaps in response to protosolar magnetic cycles. Flares induced by the stressing of magnetic fields threading both the star and the inner edge of the fluctuating disk melt or partially melt solids in the transition zone between the base of the funnel flow and the reconnection ring, and in the reconnection ring itself. The rock melts stick when they collide at low velocities. Surface tension pulls the melt aggregate into a quasi-spherical core/mantle structure, where the core consists mainly of refractories and the mantle mainly of moderate volatiles. Orbital drift of rocks past the inner edge of the disk or infall of large objects from the funnel flow replaces the steady loss of material by the plasma drag of the coronal gas that corotates with the stellar magnetosphere. In quasi-steady state, agglomeration of molten or heat-softened rocks leads to a differential size-distribution in radius R proportional to R-3e, where tL ~ 20 yr is the drift time of an object of fiducial radius L ≡ 1 cm and t is the time since the last inward excursion of the base of the funnel flow and X-wind. Thus, during the ~30 yr interval between successive flushing of the reconnection ring, flash-heated and irradiated rocks have a chance to grow to millimeter and centimeter sizes. The evaporation of the moderately volatile mantles above large refractory cores, or the dissolving of small refractory cores inside thick ferromagnesian mantles before launch, plus extended heating in the X-wind produce the CAIs or chondrules that end up at planetary distances in the parent bodies of chondritic meteorites.

We idealize giant molecular clouds as flattened sheets, incorporating the concepts of strong magnetization, star formation from dense cores, and efficient bipolar outflows. This toy model reproduces the observed tendency of molecular clouds to form filaments without the need to invoke large-scale overall gravitational collapse that would yield a rate of star formation far in excess of empirical Galactic values. It yields line width-size relationships that are in rough accord with observations, although better simulations are needed that remove the imposition of periodic boundary conditions and allow for a more systematic treatment of subgrid turbulence. The model lends credence to earlier ideas concerning the self-regulation of star formation by turbulence and photoionization.

We discuss the interaction between the magnetosphere of a young star and its surrounding accretion disk. We consider how an X-wind can be driven magnetocentrifugally from the inner edge of the disk where accreting gas is diverted onto stellar field lines either to flow onto the Sun or to be flung outwards with the wind. The X-wind satisfies many observational tests concerning optical jets, Herbig-Haro objects, and molecular outflows. Connections may exist between primitive solar system materials and X-winds. Chondrules and calcium-aluminum-rich inclusions (CAIs) experienced short melting events uncharacteristic of the asteroid belt where meteorites originate. The inner edge of the solar nebula has the shortest orbital timescale available to the system, a few days. Protosolar flares introduce another timescale, tens of minutes to hours. CAIs may form when solids are lifted from shaded portions of the disk close to the Sun and are exposed to its intense light for a day or so before they are flung by the X-wind to much larger distances. Chondrules were melted, perhaps many times, by flares at larger distances from the Sun before being launched and annealed, but not remelted, in the X-wind. Aerodynamic sorting explains the narrow range of sizes with which CAIs and chondrules are found in chondritic meteorites. Flare-generated cosmic-rays may induce spallation reactions that produce some of the short-lived radioactivities associated with primitive solar system rocks.

We investigate the equilibrium properties of self-gravitating magnetized clouds with polytropic equations of state with negative index n. In particular, we consider scale-free isopedic configurations that have constant dimensionless spherical mass-to-flux ratio lambda_r and that may constitute ``pivotal'' states for subsequent dynamical collapse to form groups or clusters of stars. For given Gamma = 1 + 1/n, equilibria with smaller values of lambda_r are more flattened, ranging from spherical configurations with lambda_r = infinity to completely flattened states for lambda_r=1. For a given amount of support provided by the magnetic field as measured by the dimensionless parameter H_0, equilibria with smaller values of Gamma are more flattened. However, logatropic (defined by Gamma = 0) disks do not exist. The only possible scale-free isopedic equilibria with logatropic equation of state are spherical uniformly magnetized clouds.

Calcium-aluminum-rich inclusions (CAIs) and chondrules of chondritic meteorites may originate with the melting of dustballs launched by a magnetically driven bipolar outflow from the inner edge of the primitive solar nebula. Bombardment by protostellar cosmic rays may make the rock precursors of CAIs and chondrules radioactive, producing radionuclides found in meteorites that are difficult to obtain with other mechanisms. Reasonable scalings from the observed hard X-rays for the cosmic-ray protons released by flares in young stellar objects yield the correct amounts of 41Ca,53Mn, and 138La inferred for meteorites, but proton- and α-induced transformations underproduce 26Al by a factor of about 20. The missing 26Al may be synthesized by 3He nuclei accelerated in impulsive flares reacting primarily with 24Mg, an abundant isotope in the target precursor rocks. The mechanism allows a simple explanation for the very different ratios of 26Al/27Al inferred for normal CAIs, CAIs with fractionated and unidentified nuclear (FUN) anomalies, and chondrules. The overproduction of 41Ca by analogous 3He reactions and the case of 60Fe inferred for eucritic meteorites require special interpretations in this picture.

We construct synthetic images and long-slit spectra of protostellar jets modeled as steady state X-winds. Assuming uniform ionization fractions and electron temperatures, we calculate non-LTE level populations for five-level atoms. Synthetic images in the [S II] λ6716/λ6731 and [O I] λ6300/λ6364 lines have roughly the same surface brightness as observed jets if we ignore their knotty structure. Long-slit spectra taken with the slit placed along the central axis of the jet, or slightly displaced laterally from it, provide strong evidence in support of the X-wind theory. In both the models and the actual objects, wide line profiles, containing both large positive and negative velocities, are often seen at the base of the flow, indicative of a wide-angle wind. As one progresses up the length of the slit, the line profiles narrow to straddle the projected velocity of a highly collimated jet.

Protostars emit more x-rays, hard and soft, than young sunlike stars in more advanced stages of formation. The x-ray emission becomes harder and stronger during flares. The excess x-rays may arise as a result of the time-dependent interaction of an accretion disk with the magnetosphere of the central star. Flares produced by such fluctuations have important implications for the x-wind model of protostellar jets, for the flash-heating of the chondrules found in chondritic meteorites, and for the production of short-lived radioactivities through the bombardment of primitive rocks by solar cosmic rays.

We consider the magnetic forces in electrically conducting thin disks threaded by magnetic fields originating in the external (interstellar) medium. We focus on disks that have dimensionless ratios λ of the mass to flux that are spatially constant, a condition that we term isopedic. For arbitrary distributions of the surface density Σ (which can be nonaxisymmetric and time dependent), we show that the magnetic tension exerts a force in the plane of the disk equal to -1/λ2 times the self-gravitational force. In addition, if the disk maintains magnetostatic equilibrium in the vertical direction, the magnetic pressure, integrated over the z-height of the disk, may be approximated as (1 + η2)/(λ2 + η2) times the gas pressure integrated over z, where η ≡ f||/2πGΣ and f${b f}$ -->|| is the component of the local gravitational field parallel to the plane of the disk. We apply these results to the problem of the stability of magnetized isothermal disks to gravitational fragmentation into subcondensations of a size comparable to the vertical scale height of the disk. Contrary to common belief, such dynamical fragmentation probably does not occur. In particular, the case of the magnetized singular isothermal disk undergoes not dynamical fragmentation into many subcondensations, but inside-out collapse into a single compact object, a self similar problem that is studied in a companion paper (Li & Shu 1997).

We study the gravitational collapse of an isothermal disk which is isopedically magnetized (i.e., with a mass-to-flux ratio that is spatially constant). The two theorems concerning magnetic forces in such a disk proven in a companion paper (Shu & Li 1997), plus the self-similar nature of the overall problem, allow a semianalytical treatment. The inflow occurs in an inside-out manner similar to that which applies in the collapse of the unmagnetized singular isothermal sphere (Shu 1977). These two cases (singular sphere and disk) bracket the range of possible collapse behaviors expected for the family of isopedic singular isothermal toroids described by Li & Shu (1996b). Although the strong magnetic fields dilute the effects of self-gravity in the isopedic isothermal disk, they do not prevent its outer parts (envelope) from falling onto the central condensed object (protostar) at a fixed infall rate , even when the field is perfectly frozen to the matter. Indeed, the higher densities supported by the fields in the equilibrium state increase during collapse in comparison with the unmagnetized case. The larger effective speed of sound due to magnetization produces a smaller effect. The flattened geometry enforced by the strong magnetic fields introduces a complication: the appearance of an outwardly propagating shock wave that runs ahead of the region of infall (also studied by Tsai & Hsu 1995 in a different context). We discuss the implications of our results for the magnetic-flux problem and for the formation of centrifugally supported disks in the presence of rotation.

We review current ideas and models in the problem of star formation from molecular cloud cores that are relatively isolated from the influences of other forming stars. We discuss the time scales, flow dynamics, and density and temperature structures applicable to each of the four stages of the entire process: (a) formation of a magnetized cloud core by ambipolar diffusion and evolution to a pivotal state of gravomagneto catastrophe; (b) self-similar collapse of the pivotal configuration and the formation of protostars, disks, and pseudo-disks; (c) onset of a magnetocentrifugally driven, lightly ionized wind from the interaction of an accretion disk and the magnetosphere of the central star, and the driving of bipolar molecular outflows; (d) evolution of pre-main-sequnce stars surrounded by dusty accretion disks. For each of these stages and processes, we consider the characteristics of the molecular diagnostics needed to investigate the crucial aspects of the observational problem.

We review the theory of x-winds in young stellar objects (YSOs). In particular, we consider how a model where the central star does not corotate with the inner edge of the accretion disk may help to explain the enhanced emission of X-rays from embedded protostars. We argue, however, that the departure from corotation is not large, so a mathematical formulation that treats the long-term average state as steady and axisymmetric represents a useful approximation. Magnetocentrifugally driven x-winds of this description collimate into jets, and their interactions with the surrounding molecular cloud cores of YSOs yield bipolar molecular outflows.

We consider the end states for a quasi-magnetostatic phase of evolution of molecular cloud cores by ambipolar diffusion. The models yield good initial states for fully dynamical collapse to isolated proto-stellar systems. These pivotal transition states are self-gravitating, magnetized, isothermal masses of gas in which the density scales with spherical radius r as r–2 and the magnetic field as r–1. The dependences of these quantities with angle θ satisfy the constraints of magnetostatic equilibrium. Under these circumstances, we find a linear sequence of possible pivotal states, each member characterized by a separate value of the differential mass-to-flux ratio in dimensionless form, λ≡ 2πG1/2dM/dΦ ≥ 1. In general, the pivotal states are toroids, with the density distribution on a circle of constant r in the meridional plane declining from a maximum value on the magnetic equator, θ = π/2, to zero over the magnetic poles, θ = 0 and θ = π. For λ 1, the pivotal configurations approach the unmagnetized singular isothermal sphere, with volume density ρ = (a2/2πG)r–2. For λ close to 1, the pivotal configurations flatten to a thin disk, with surface density Σ = [(1 + H0) a2/πG]r−1, where H0 is a number 1. We comment on the implications of these results for observations and other theoretical investigations.

The chondrules, calcium-aluminum-rich inclusions (CAIs), and rims in chondritic meteorites could be formed when solid bodies are lifted by the aerodynamic drag of a magnetocentrifugally driven wind out of the relative cool of a shaded disk close to the star into the heat of direct sunlight. For reasonable self-consistent parameters of the bipolar outflow, the base and peak temperatures reached by solid bodies resemble those needed to melt CAIs and chondrules. The process also yields a natural sorting mechanism that explains the size distribution of CAIs and chondrules, as well as their fine-grained and coarse-grained rims. After reentry at great distances from the original launch radius, the CAIs, chondrules, and their rims would be compacted with the ambient nebular dust comprising the matrices, forming the observed chondritic bodies.

We consider the formation of planetesimals via gravitational instability. While minimum solar nebula (MSN) models are known to be gravitationally stable, we find that sufficiently metal enriched and/or colder discs can yield planetesimals by the Goldreich-Ward mechanism (GWM). This is because the shear between gas and solids, previously believed to render the GWM ineffective, can only stir a finite amount of solids.

We review the prevailing theories for the formation of the jovian planets and comment that they do not provide a natural explanation for the oft-noted subdivision into two separate classes: the gas-rich giants, Jupiter and Saturn, and the gas-poor giants, Uranus and Neptune. To account for the observed differences in envelope mass relative to core mass, the conventional discriminants would seem to require special timing for the phases: assemblage of the protoplanetary cores, runaway accretion of gas, and the dispersal of nebular gases. We propose a discriminant that relies on photoevaporation by Lyman continuum photons of the outer parts of the disk as the primary hydrogen (and helium) loss mechanism. We show that Saturn's orbit constitutes the natural transitional radius between gas retainage and loss in this sort of picture and that the evaporative wind in the Uranus and Neptune regions would have been large enough to get rid of the hydrogen and helium gas before these planets assembled a critical core mass for runaway gas accretion, if the primitive Sun had an enhanced extreme ultraviolet luminosity for a duration comparable to those estimated for classical T Tauri stars.

We summarize recent work addressing the role of magnetic fields in the process of star formation and disk accretion. After a short review of the basic observational results, we concentrate on the efficiency of magnetic braking during cloud collapse and its consequences on the formation of centrifugally supported disks around young stars. Then, we relate this issue to the well‐known magnetic flux problem of star formation, and we show that the introduction of non‐ideal MHD effects is a necessary step toward the development of self‐consistent models for the collapse of molecular clouds and the formation of disks. Finally, we discuss the structure and evolution of magnetized accretion disks around young stars that have dragged their magnetic field in the phase of gravitational collapse and we focus on two main diffusive processes: viscous stresses that redistribute mass and angular momentum, and the resistive diffusion of mass across magnetic field lines.

The X-wind model for magnetospheric accretion and outflow in classical T Tauri stars (CTTS) has gained credence in recent years for a variety of theoretical and observational reasons. However, both this model as well as other theoretical scenarios for explaining magnetospheric disk accretion assume that the stellar field, were it not perturbed by an electrically conducting accretion disk, would have a dipolar geometry (e.g., [5]; OS95 hereafter). Observations of accretion hot spot sizes and net field polarization on the surface of CTTS, however, clearly indicate that the stellar field has a complex multipolar structure. To overcome this discrepancy between theory and data, we reformulate X-wind theory without the dipole constraint. This contribution represents a brief summary of the paper by Mohanty and Shu [6]. In Sect. 1 we present the fundamental physical ideas of the generalized theory, and the associated equations; in Sect. 2 we compare the resulting theoretical prediction to recent observations, and provide some illustrative numerical simulations with multipole stellar fields.

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., 4 pages, accepted by ApJL

Many problems in the theory of star formation are amenable to a complementary attack in which the analytical approach is used to reduce the governing equations to a form amenable to efficient numerical solution. This strategy has proven very useful in helping to resolve several astrophysical puzzles which arise because the bulk of star formation today is observed to occur, with relatively low efficiency, in giant molecular cloud complexes. How does a cloud of 105-106M⊙) know how to form stars of mass ≈ 1 M⊙)? How does the interstellar medium know, to one or two orders of magnitude, that roughly (hc/Gm H 2 3/2 hydrogen atoms of mass mH are needed to yield thermonuclear fusion in a self-gravitating ball of gas? Why have radio astronomers not detected unambiguous evidence for the collapse motions attendant to star formation? Why has a true protostar, the “holy grail” of infrared astronomy, been so hard to find? Why do young stellar objects almost universally exhibit powerful outflows? Why is the geometry for these outflows often bipolar? Why do T Tauri stars have such active chromospheres? In this review we suggest that these puzzles all have a related resolution, in the nature of how gravitational collapse is initiated and terminated in the slowly rotating cores of molecular clouds.

We consider models of the processes by which a molecular cloud acquires dense cores, a (magnetized) rotating core collapses to give a protostar plus nebular disk, and a powerful stellar wind sets in to reverse the accretion flow and reveal the central object as a pre-main-sequence star. At each stage, we rely on a combination of theory and observation to fix the basic parameters of the model. We show that core formation in a molecular cloud is an inevitable byproduct of ambipolar diffusion in a magnetized self-gravitating medium of low fractional ionization. We find that the gravitational collapse of a uniformly-rotating isothermal core, which possesses a 1/r2 density profile in its inner parts, has simple analytic properties. And we propose that strong stellar winds in T Tauri stars represent a phase of readjustment in the angular momentum distribution after deuterium burning drives convection throughout a strongly differentially-rotating protostar. We conclude that the major missing link in this picture is the evolutionary behavior of massive nebular disks that may accumulate around protostars. Otherwise, there seems to be a satisfying connection between the cloud cores observed by molecular-line radio astronomers and the active stellar atmospheres of young stars studied by optical and x-ray astronomers.

We present models of the spectral energy distributions for an evolutionary sequence of young stellar objects, from protostars to pre-main-sequence stars. The protostellar theory, characterized by a central star and disk embedded within an infalling envelope of dust and gas, can explain the observed infrared spectra of embedded IRAS sources associated with molecular cloud cores. Next, we find that T Tauri stars with near- and mid-infrared excesses can be understood as young stars surrounded by nebular disks. The disks in T Tauri systems are found in two varieties: passive disks which have no intrinsic luminosity and merely intercept and re-radiate stellar photons, and active disks which have appreciable intrinsic luminosity. In addition, there is another class of objects in which a residual dust shell still surrounds the star and disk.

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., Comment: ApJ accepted; 47 pages (submission format), 7 figures

Understanding how stars like the sun formed constitutes one of the principal challenges confronting modern astrophysics. In recent years, advances in observational technology, particularly at infrared and millimeter wavelengths, have produced an avalanche of critical data and unexpected discoveries about the process of star formation, which is blocked from external view at optical and shorter wavelengths by an obscuring blanket of interstellar dust. Fueled by this new knowledge, a comprehensive empirical picture of stellar genesis is beginning to emerge, laying the foundations for a coherent theory of the birth of sunlike stars.

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., 31 pages, 8 figures. Accepted for publication in ApJ

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., Comment: The Astrophysical Journal, in press

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., Comment: The Astrophysical Journal Letters, in press

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 $\lambda_0\equiv f_0^{-1}$ of the central regions produced by runaway core condensation and the dimensionless measure of the rate of ambipolar diffusion $\epsilon$. 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 $\epsilon$ 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., Comment: 49 pages including 8 figures and 1 table; accepted for publication in ApJ

We formulate the problem of magnetic field dissipation during the accretion phase of low-mass star formation, and we carry out the first step of an iterative solution procedure by assuming that the gas is in free-fall along radial field lines. This so-called ``kinematic approximation'' ignores the back reaction of the Lorentz force on the accretion flow. In quasi steady-state, and assuming the resistivity coefficient to be spatially uniform, the problem is analytically soluble in terms of Legendre's polynomials and confluent hypergeometric functions. The dissipation of the magnetic field occurs inside a region of radius inversely proportional to the mass of the central star (the ``Ohm radius''), where the magnetic field becomes asymptotically straight and uniform. In our solution, the magnetic flux problem of star formation is avoided because the magnetic flux dragged in the accreting protostar is always zero. Our results imply that the effective resistivity of the infalling gas must be higher by several orders of magnitude than the microscopic electric resistivity, to avoid conflict with measurements of paleomagnetism in meteorites and with the observed luminosity of regions of low-mass star formation., 20 pages, 4 figures, The Astrophysical Journal, in press

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., Comment: 18 pages, 6 figures, 2 tables. ApJ in press

We review spiral density-wave theory and its realtionship to the disordered appearance of population I objects in some disk galaxies. We discuss mechanisms proposed for the formation of (a) feathers by gravitational instability behind galactic shocks, (b) branches by the action of ultraharmonic resonances, (c) spurs by reflection of leading waves off sharp features induced by nonlinear dredging, and (d) flocculence by the chaos produced from overlapping resonances. We conclude that disorder arises in spiral galaxies not so much from disorderly causes as from too sensitive a response of the interstellar medium to an orderly but nonlinear spiral gravitational field.

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., 11 pages, 8 figures

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., 34 pages, 9 .eps figures (included), accepted by ApJ

(Abridged) We consider the expansion of an initially self-gravitating, static, singular, isothermal cloud core. For t>0, the gas is ionized and heated to a higher uniform temperature by the formation of a luminous, but massless, star in its center. The approximation that the mass and gravity of the central star is negligible for the subsequent motion of the HII region holds for distances much greater than about 100 AU and for the massive cloud cores that give rise to high-mass stars. If the initial ionization and heating is approximated to occur instantaneously at t=0, then the subsequent flow (for r >> 100 AU) caused by the resulting imbalance between self-gravity and thermal pressure is self-similar. Because of the steep density profile, pressure gradients produce a shock front that travels into the cloud, accelerating the gas to supersonic velocities in what has been called the ``champagne phase.'' We then study the self-similar solutions of the expansion of HII regions embedded in molecular clouds characterized by more general power-law density distributions with exponent 3/2 < n < 3. In these cases, the shock velocity is an increasing function of the exponent n, and diverges as n tends to 3. We show that this happens because the model includes an origin, where the pressure driving the shock diverges because the enclosed heated mass is infinite. Our results imply that the continued photoevaporation of massive reservoirs of neutral gas (e.g., surrounding disks and/or globules) nearby to the embedded ionizing source is required in order to maintain over a significant timescale the emission measure observed in champagne flows., 29 pages, 5 figures. The Astrophysical Journal, in press

In order to compare the x-wind with observations, one needs to be able to calculate its thermal and ionization properties. We formulate the physical basis for the streamline-by-streamline integration of the ionization and heat equations of the steady x-wind. In addition to the well-known processes associated with the interaction of stellar and accretion-funnel hot-spot radiation with the wind, we include X-ray heating and ionization, mechanical heating, and a revised calculation of ambipolar diffusion heating. The mechanical heating arises from fluctuations produced by star-disk interactions of the time dependent x-wind that are carried by the wind to large distances where they are dissipated in shocks, MHD waves, and turbulent cascades. We model the time-averaged heating by the scale-free volumetric heating rate, $\Gamma_{\rm mech} = \alpha \rho v^3 s^{-1}$, where $\rho$ and $v$ are the local mass density and wind speed, respectively, $s$ is the distance from the origin, and $\alpha$ is a phenomenological constant. When we consider a partially-revealed but active young stellar object, we find that choosing $\alpha \sim 10^{-3}$ in our numerical calculations produces temperatures and electron fractions that are high enough for the x-wind jet to radiate in the optical forbidden lines at the level and on the spatial scales that are observed. We also discuss a variety of applications of our thermal-chemical calculations that can lead to further observational checks of x-wind theory., Comment: 48 pages, 5 figures, ApJ in press. For better figures, go to http://www.asiss.sinica.edu.tw/theory/prints.html