Engineering topics

Bell, K. R.

Publications and source records attributed to Bell, K. R..

11 records

NASA NTRS2004

Selected Papers on Protoplanetary Disks

Three papers present studies of thermal balances, dynamics, and electromagnetic spectra of protoplanetary disks, which comprise gas and dust orbiting young stars. One paper addresses the reprocessing, in a disk, of photons that originate in the disk itself in addition to photons that originate in the stellar object at the center. The shape of the disk is found to strongly affect the redistribution of energy. Another of the three papers reviews an increase in the optical luminosity of the young star FU Orionis. The increase began in the year 1936 and similar increases have since been observed in other stars. The paper summarizes astronomical, meteoric, and theoretical evidence that these increases are caused by increases in mass fluxes through the inner portions of the protoplanetary disks of these stars. The remaining paper presents a mathematical-modeling study of the structures of protostellar accretion disks, with emphasis on limits on disk flaring. Among the conclusions reached in the study are that (1) the radius at which a disk becomes shadowed from its central stellar object depends on radial mass flow and (2) most planet formation has occurred in environments unheated by stellar radiation.

Bell, K. R.↗

NASA NTRS2002

The Center for Star Formation Studies

The Center for Star Formation Studies, a consortium of scientists from the Space Science Division at Ames and the Astronomy Departments of the University of California at Berkeley and Santa Cruz, conducts a coordinated program of theoretical research on star and planet formation. Under the directorship of D. Hollenbach (Ames), the Center supports postdoctoral fellows, senior visitors, and students; meets regularly at Ames to exchange ideas and to present informal seminars on current research; hosts visits of outside scientists; and conducts a week-long workshop on selected aspects of star and planet formation each summer.

Hollenbach, D.↗

NASA NTRS2001

The FU Orionis Phenomenon and Solar Nebula Material

We summarize astronomical, meteoritic, and theoretical evidence relating to the FU Orionis phenomenon. This evidence suggests that at early times (the first few 10(exp 5) yr), the solar nebula experienced a hot phase characterized by high accretion rates (the "FU Ori epoch"), punctuated by episodic outbursts of enhanced mass flow through the inner part of the disk (less than or equal to 0.3 AU). Throughout this epoch, disk midplane temperatures exceeded 1000 K at 1 AU. Diminishing infall from the cloud core led to decreasing mass flux throughout the disk. When mass flow de creased below the value critical for outburst (5 x 10(exp -7) solar mass/yr, as suggested by thermal ionization instability models), outbursts ceased and the T Tauri epoch began. Outburst timescales are too long to explain calcium- and aluminum-rich inclusion (CAI) and chondrule formation. Volatility-dependent fractionation patterns seen in meteoritic materials suggest that solids formed beginning during a hot epoch when temperatures exceeded 1400 K, and the presence of volatiles in chondrites argues that this process continued until the nebula had cooled to below 400 K. The thermal ionization instability model for FU Ori outbursts is in quantitative agreement with astronomical observations. Its results imply that the terrestrial region of the nebula reached the hot end of this range only during a time when mass flow through the disk was high enough to trigger outbursts (i.e., the FU Ori epoch) and reached the cool end of this range only during the later T Tauri epoch. According to the models, heating of material in the terrestrial planet region during individual FU Ori outbursts would be limited to surface layers of the nebula, leaving midplane materials (which are at greater than or equal to 1000 K) largely unaffected. Alternative FU Ori models should be developed, particularly if compositional differences among chondrite clans are attributable to episodic heating.

Bell, K. R.↗

NASA NTRS1995

The FU Orionis outburst as a thermal accretion event: Observational constraints for protostellar disk models

The results of the time-dependent disk models developed in Bell & Lin are compared with observed properties of FU Orionis variables. Specific models are fit to the light curves of Fu Ori, V1515 Cyg, and V1057 Cyg. The slow risetime of V1515 Cyg can be matched by a self-regulated outburst model. The rapid risetimes of FU Ori and V1057 Cyg can be fitted with the application of modest perturbations to the disk surface density. Model disks display spectral features characteristic of observed objects. The color evolution of V1057 Cyg is naturally explained if mass flux drops in the inner disk (r less than 1/4 AU) while remaining steady in the outer disk. The decrease in optical line width (rotational velocity) observed during the decay of V1057 Cyg may be accounted for by an outward-propagating ionization front. We predict that before final decay to the quiescent phase, short-wavelength line widths (lambda less than 1.5 microns) will again increase. It is suggested that FU Orionis outbursts primarily occur to systems during the embedded phase with ages less than several times 10(exp 5) yr.

Bell, K. R.↗

NASA NTRS1994

Is HL Tauri and FU Orionis system in quiescence?

A recent Nobeyama map of HL Tau reveals that gas is infalling in a flattened region approximately 1400 AU around the central star. The apparent motion of the gas provides the necessary condition for the formation of a Keplerian disk with a radius comparable to the size of the primordial solar nebula. The inferred mass infall rate onto the disk is approximately equal to 5 x 10(exp -6) solar mass/yr, which greatly exceeds the maximum estimate of the accretion rate onto the central star (approximately 7 x 10(exp -7) solar mass/yr). Consequently, mass must currently be accumulating in the disk. The estimated age and disk mass of HL Tau suggest that the accumulated matter has been flushed repeatedly on a timescale less than 10(exp 4) yr. Based on the similarites between their evolution patterns, we propose that HL Tau is an FU Orionis system in quiescence. In addition to HL Tau, 14 out of 86 pre-main-sequence stars in the Taurus-Auriga dark clouds have infrared luminosities much greater than their otherwise normal extinction-corrected stellar luminosities. These sources also tend to have flat spectra which may be due to the reprocessing of radiation by dusty, flattened, collapsing envelopes with infall rates a few 10(exp -6) solar mass/yr. Such rates are much larger than estimated central accretion rates for these systems, which suggests that mass must also be accumulating in these disks. If these sources are FU Orionis stars in quiescence, similar to HL Tau, their age and relative abundance imply that the FU Orionis phase occurs over a timescale of approixmately 10(exp 5) yr, and the quiescent phase between each outburst lasts approximately 10(exp 3) =10(exp 4) yr. These inferred properties are compatible with the scenario that FU Orionis outbursts are regulated by a thermal instability in the inner region of the disk.

Lin, D. N. C.↗

NASA NTRS1994

Using FU Orionis outbursts to constrain self-regulated protostellar disk models

One-dimensional, convective, vertical structure models and one dimensional time-dependent, radial diffusion models are combined to create a self-consistent picture in which FU Orionis outbursts occur in young stellar objects (YSOs) as the result of a large-scale, self-regulated, thermal ionization instability in the surrounding protostellar accretion disk. Although active accretion disks have long been postulated to be ubiqitous among low-mass YSOs, few constraints have until now been imposed on physical conditions in these disks. By fitting the results of time-dependent disk models to observed timescales of FU Orionis events, we estimate the magnitude of the effective viscous stress in the inner disk (r approximately less than 1 AU) to be, in accordance with an ad hoc 'alpha' prescription, the product of the local sound speed, pressure scale height, and an efficiency factor alpha of 10(exp -4) where hydrogen is neutral and 10(exp 3) where hydrogen is ionized. We hypothesize that all YSOs receive infall onto their outer disks which is steady (or slowly declining with time) and that FU Orionis outbursts are self-regulated, disk outbursts which occur only in systems which transport matter inward at a rate sufficiently high to cause hydrogen to be ionized in the inner disk. We estimate a critical mass flux of dm(sub crit)/dt = 5 x 10(exp 7) solar mass/yr independent of the magnitude of alpha for systems with one solar mass, three solar radius central objects. Infall accretion rates in the range of dm(sub in)/dt = 1-10) x 10(exp -6) solar mass/yr produce observed FU Orionis timescales consistent with estimates of spherical molecular cloud core collapse rates. Modeled ionization fronts are typically initiated near the inner edge of the disk and propogate out to a distance of several tens of stellar radii. Beyond this region, the disk transports mass steadily inward at the supplied constant infall rate. Mass flowing through the innermost disk annulus is equal to dm(sub in)/dt only in a time-averaged sense and is regulated by the ionization of hydrogen in the inner disk such that long intervals (approximately 1000 yr) of low-mass flux: (1-30) x 10(exp -8) solar mass/yr are punctuated by short intervals (approximately 100 yr) of high-mass flux: (1-30) x 10(exp -5) solar mass/yr. Timescales and mass fluxes derived for quiescent and outburst stages are consistent with estimates from observations of T Tauri and FU Orionis systems, respectively.

Bell, K. R.↗

NASA NTRS1994

The FU Orionis Outburst as a Thermal Disk Accretion Event: Detailed Calculations and Comparison to Observations

FU Orionis outbursts are temporary large increases in luminosity: x (40 - 250) thought to occur repeatedly in all low mass young stellar systems. We discuss detailed calculations of viscous accretion disks suggesting that FU Ori events signify the existence of a protostellar disk transporting mass at a rate of (1 - 10) x 10(exp 6) solar mass / yr, in agreement with theoretical and observational estimates of molecular cloud core collapse rates. Accretion through the inner edge of disks subject to outburst is self-regulated through the thermal ionization instability such that long periods (approx. 1000 yrs) of low mass flux: (1 - 10) x 10(exp -5) solar mass / yr, are punctuated by short periods (approx. 100 yrs) of high mass flux: (1-10) x 10(exp -5) solar mass / yr. The unstable region of the disk extends radially only to a distance of approx. = 1/4 AU. Beyond this region matter is transported stably at the infall rate. In systems for which M(sum *) = 1 solar mass with an inner disk edge of 3 solar radius, the critical rate for outbursts is 5 x 10(exp -7) solar mass / yr independent of the magnitude of the viscous ce parameter consistent with estimates of boundary layer mass flux in T Tauri stars. We use timescales of observed outbursts to constrain the magnitude of the alpha parameter to be 10(exp -4) where hydrogen is neutral and 10(exp -3) where ionized. Light curves of V1515 Cyg, FU Ori, and V1057 Cya are reproduced; the latter two require application of a small perturbation in surface density to produce observed rapid rise times. Detailed reply is made to objections to the accretion disk model for outbursts. Comparison to observations are made of time dependent spectral energy distributions, colors, and line-width velocity evolution.

Bell, K. R.↗

NASA NTRS1994

The FU Orionis Outburst as a Thermal Disk Accretion Event: Detailed Calculations and Comparison to Observations

FU Orionis outbursts are temporary large increases in luminosity: x(40-250) thought to occur repeatedly in all low mass young stellar systems. We discuss detailed calculations of viscous accretion disks suggesting that FU Ori events signify the existence of a protostellar disk transporting mass at a rate of (1-10) x 10(exp -6) Solar Mass/yr, in agreement with theoretical and observational estimates of molecular cloud core collapse rates. Accretion through the inner edge of disks subject to outburst is self-regulated through the thermal ionization instability such that long periods (approximately 1000 yrs) of low mass flux: (1-10) x 10(exp -8) Solar Mass/yr, are punctuated by short periods (approximately 100 yrs) of high mass flux: (1-10) x 10(exp -5) Solar Mass/yr. The unstable region of the disk extends radially only to a distance of approximately 1/4 AU. Beyond this region matter is transported stably at the infall rate. In systems for which M = 1 Solar Mass, with an inner disk edge of 3 Solar Radius, the critical rate for outbursts is 5 x 10(exp -7) Solar Mass/yr independent of the magnitude of the viscous alpha parameter consistent with estimates of boundary layer mass flux in T Tauri stars. We use timescales of observed outbursts to constrain the magnitude of the alpha parameter to be 10(exp -4) where hydrogen is neutral and 10(exp -3) where ionized. Light curves of V1515 Cyg, FU Ori, and V1057 Cyg are reproduced; the latter two require application of a small perturbation in surface density to produce observed rapid rise times. Detailed reply is made to objections to the accretion disk model for outbursts. Comparison to observations are made of time dependent spectral energy distributions, colors, and line-width velocity evolution.

Bell, K. R.↗

NASA NTRS1991

Nonlinear evolution of accretion disks induced by radiative feedback processes

The existence of accretion disks around young stellar objects has recently become widely accepted. The luminosity of some young stellar objects is highly variable and is generally attributed to the release of gravitational energy from matter funneled onto them by accretion disks. The inward transport of matter through these disks is coupled to the outward transfer of angular momentum. This transfer is most likely to be regulated by the mixing of adjacent annuli through the process of large-scale turbulence. Most of the accretion energy generated by this process emerges near the inner edge of the disk. This radiation may be intercepted by the disk and may modify the vertical and viscous evolution of the disk itself. If surface heating can stabilize the disk against the dominant viscous process, then in systems with large accretion rates, angular momentum transport and mass flow through the disk will be quenched. Using this result, it is shown that such a mechanism can induce feedback through the disk which produces oscillations in the luminosity of the central object. This oscillation can become chaotic in certain regimes and might thus explain the highly variable nature of many T Tauri systems and their outbursting counterparts: the FU Orionis objects.

Bell, K. R.↗

NASA NTRS1990

Nonlinear evolution of protostellar disks and light modulations in young stellar objects

An evolutionary model of dynamical processes in protostellar disks is described and illustrated with graphs of typical results. The effective transport mechanisms are discussed, including thermal convection, nonaxisymmetric gravitational instabilities in the outer regions of disks, and wave propagation. Consideration is then given to the stages of dynamical evolution, FU Ori outburst phenomena, unsteady accretion-disk flows, and nonlinear feedback as a mechanism to modulate mass transfer. The simulations show that mass redistribution is determined by angular-momentum transfer, which in turn is regulated by the effective viscosity generated by convectively driven turbulence. Significant mass transfer occurs as a result of mixing of infalling material with disk gas and is affected by the tidal torque associated with the growth of nonaxisymmetric disturbances in the outer disk. The time scale for disk evolution is found to be about 1 Myr.

Lin, D. N. C.↗

NASA NTRS1979

Analysis of surface moisture variations within large field sites

A statistical analysis was made on ground soils to define the general relationship and ranges of values of the field moisture relative to both the variance and coefficient of variation for a given test site and depth increment. The results of the variability study show that: (1) moisture variations within any given large field area are inherent and can either be controlled nor reduced; (2) neither a single value of the standard deviation nor coefficient of variation uniquely define the variability over the complete range of mean field moisture contents examined; and (3) using an upper bound standard deviation parameter clearly defines the maximum range of anticipated moisture variability. 87 percent of all large field moisture content standard deviations were less than 3 percent while about 96 percent of all the computed values had an upper bound of sigma=4 percent for these intensively sampled fields. The limit of accuracy curves of mean soil moisture measurements for large field sites relative to the required number of samples were determined.

Bell, K. R.↗