Susana Lizano

Magnetocentrifugally driven flows from young stars and disks. 1: A generalized model

We propose a generalized model for stellar spin-down, disk accretion, and truncation, and the origin of winds, jets, and bipolar outflows from young stellar objects. We consider the steady state dynamics of accretion of matter from a viscous and imperfectly conducting disk onto a young star with a strong magnetic field. For an aligned stellar magnetosphere, shielding currents in the surface layers of the disk prevent stellar field lines from penetrating the disk everywhere except for a range of radii about pi = R(sub x), where the Keplerian angular speed of rotation Omega(sub x) equals the angular speed of the star Omega(sub *). For the low disk accretion rates and high magnetic fields associated with typical T Tauri stars, R(sub x) exceeds the radius of the star R(sub *) by a factor of a few, and the inner disk is effectively truncated at a radius R(sub t) somewhat smaller than R(sub x). Where the closed field lines between R(sub t) and R(sub x) bow sufficiently inward, the accreting gas attaches itself to the field and is funneled dynamically down the effective potential (gravitational plus centrifugal) onto the star. Contrary to common belief, the accompanying magnetic torques associated with this accreting gas may transfer angular momentum mostly to the disk rather than to the star. Thus, the star can spin slowly as long as R(sub x) remains significantly greater than R(sub *). Exterior to R(sub x) field lines threading the disk bow outward, which makes the gas off the mid-plane rotate at super-Keplerian velocities. This combination drives a magnetocentrifugal wind with a mass-loss rate M(sub w) equal to a definite fraction f of the disk accretion rate M(sub D). For high disk accretion rates, R(sub x) is forced down to the stellar surface, the star is spun to breakup, and the wind is generated in a manner identical to that proposed by Shu, Lizano, Ruden, & Najita in a previous communication to this journal. In two companion papers (II and III), we develop a detailed but idealized theory of the magnetocentrifugal acceleration process.

Accretion disks around young objects. I. The Detailed vertical structure

We discuss the properties of an accretion disk around a star with parameters typical of classical T Tauri stars (CTTSs) and with the average accretion rate for these disks. The disk is assumed steady and geometrically thin. The turbulent viscosity coefficient is expressed using the α prescription, and the main heating mechanisms considered are viscous dissipation and irradiation by the central star. The energy is transported by radiation, turbulent conduction, and convection. We find that irradiation from the central star is the main heating agent of the disk, except in the innermost regions, R 5 AU) becomes less dense, optically thin, and almost vertically isothermal, with a temperature distribution T ∝ R-1/2. The decrease in surface density at the outer disk decreases the disk mass by a factor of 4 with respect to a purely viscous case. In addition, irradiation tends to make the outer disk regions stable against gravitational instabilities.

Accretion Disks Around Young Objects. II. Tests of Well-Mixed Models with Ism Dust

We construct detailed vertical structure models of irradiated accretion disks around T Tauri stars with interstellar medium dust uniformly mixed with gas. The dependence of the structure and emission properties on mass accretion rate, viscosity parameter, and disk radius is explored using these models. The theoretical spectral energy distributions (SEDs) and images for all inclinations are compared with observations of the entire population of classical T Tauri stars (CTTSs) and class I objects in Taurus. In particular, we find that the median near-infrared fluxes can be explained within the errors with the most recent values for the median accretion rates for CTTSs. We further show that the majority of the class I sources in Taurus cannot be class II sources viewed edge-on because they are too luminous and their colors would be consistent with disks seen only in a narrow range of inclinations. Our models appear to be too geometrically thick at large radii, as suggested by (1) larger far-infrared disk emission than in the typical SEDs of T Tauri stars, (2) wider dark dust lanes in the model images than in the images of HH 30 and HK Tau/c, and (3) a larger predicted number of stars extincted by edge-on disks than consistent with current surveys. The large thickness of the model is a consequence of the assumption that dust and gas are well mixed, suggesting that some degree of dust settling may be required to explain the observations.

Massive Stars : Their Environment and Formation

Cloud environment is thought to play a critical role in determining the mechanism of formation of massive stars. In this contribution we review the physical characteristics of the environment around recently formed massive stars. Particular emphasis is given to recent high angular resolution obser- vations which have improved our knowledge of the physical conditions and kinematics of compact regions of ionized gas and of dense and hot molecular cores associated with luminous O and B stars. We will show that this large body of data, gathered during the last decade, has allowed signiÐcant progress in the understanding of the physical processes that take place during the formation and early evolution of massive stars.

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. 72 refs.

Heating and Ionization of X-Winds

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, Γmech = αρv3s-1, where ρ and v are the local mass density and wind speed, respectively, s is the distance from the origin, and α is a phenomenological constant. When we consider a partially revealed but active young stellar object, we find that choosing α ~ 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.

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. 51 refs.

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.

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. 45 references.

Gravitational Collapse of Magnetized Clouds. I. Ideal Magnetohydrodynamic Accretion Flow

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.