ALBERT

Description: These are exciting times in the study of planetary system formation with a steadily expanding inventory of exo-planet detections, and imaging of dust disks around nearby young and main sequence stars. While these discoveries imply that our Solar System is far from unique, linking the data for the protoplanetary and debris disks to mature planetary systems requires a demonstration that disk evolution proceeds via planetesimal production and growth to the formation of planets. Theoretical studies of planet formation indicate that planetesimals grow, via runaway accretion, to lunar-sized (approx. = 2000 km) embryos in 10(exp 5) years. Recent gas giant planet formation studies have suggested that most of the action in planet formation occurs over 1-16 Myr, with formation of planets similar to Jupiter in t less than 10 Myr, within the time interval that infrared (IR) and optical emission line studies have demonstrated that circumstellar material remains detectable around both solar mass and intermediate mass stars. Direct imaging of exo-planetesimals is not feasible with current and foreseeable technology, since such bodies have substantially less surface area than micron-sized grains distributed in a disk, and thus are inefficient IR emitters. However, such bodies may be indirectly detectable.

Description: Infrared spectroscopy of pre-main sequence stars with dusty protostellar disks provide information about the evolution of refractory materials in such systems. These systems exhibit varying degrees of strength and structure in the silicate emission band situated at 10 microns wavelength. Band strength is affected by the mean grain size, while band structure is determined by the chemical composition and degree of crystallinity. In some objects, the silicate band is strong and featureless, similar to that seen in the interstellar medium. In others, the band is often weaker, and exhibits structure consistent with the presence of crystalline olivine. In these latter objects, the band is similar to that of some solar system comets. The strength and structure of the silicate band may be related to the processing history of the system.

Description: The debris disks surrounding the pre-main-sequence stars HD 31648 and HD 163296 were observed spectroscopically between 3 and 14 microns. Both stars possess a silicate emission feature at 10 Am that resembles that of the star P Pictoris and those observed in solar system comets. The structure of the band is consistent with a mixture of olivine and pyroxene material, plus an underlying continuum of unspecified origin. The similarity in both size and structure of the silicate band suggests that the material in these systems had a processing history similar to that in our own solar system prior to the time that the grains were incorporated into comets.

Description: The debris disks surrounding the pre-main-sequence stars HD 31648 and HD 163296 were observed spectroscopically between 3 and 14 microns. Both stars possess a silicate emission feature at 10 microns that resembles that of the star beta Pictoris and those observed in solar system comets. The structure of the band is consistent with a mixture of olivine and pyroxene material, plus an underlying continuum of unspecified origin. The similarity in both size and structure of the silicate band suggests that the material in these systems had a processing history similar to that in our own solar system prior to the time that the grains were incorporated into comets.

Description: The purpose of this grant is to study parametric instability. The simplest example of parametric instability is a harmonic oscillator with a periodic modulation of the spring constant. If the modulation frequency is close to twice the natural frequency of the oscillator, the amplitude of oscillation tends to grow exponentially. The growth rate is proportional to the strength of the modulation, but it also depends upon the closeness to resonance of the two frequencies, and upon natural damping rate or "Q" of the oscillator. Parametric instabilities are very common in physics. A familiar example is a jogger's ponytail--normally a very strongly damped pendulum, it can be destabilized by the variation in effective gravity during the jogger's stride. Observation confirms that the period of the pendulum is half that of the jogger's vertical motion. In astrophysics, parametric instability may occur by external tidal forcing, or by interaction among eigenmodes. In the latter case, an energetic eigenmode may destabilize modes of half its frequency, provided some weak nonlinearity exists to couple them. Under a previous Astrophysical Theory grant (NAGW-2419), the PI discovered a parametric instability of tidally forced disks such as the accretion disks in cataclysmic variables and X ray binaries [2]. The destabilized modes are tightly-wound, incompressible, three-dimensional waves analogous to g-modes and r-modes in stars. Later work has confirmed our analysis [4]. It was hoped that these modes might provide a source of turbulence and angular momentum transport in accretion disks. However, a follow-up investigation of this instability by local numerical simulations, although confirming the analytically estimated growth rates, found negligible angular momentum flux [3]. Other work, partly supported by the ATP, now strongly indicates that the transport mechanism in such disks is magnetohydrodynamic turbulence [6]. Nevertheless, the parametric mechanism may truncate the outer edges of disks in close binaries [2], and it may be important in disks of very low ionization such as protostellar disks, or even cataclysmic-variable disks in quiescence where the MHD mechanism may be ineffective [5]. All analyses up to 1996 were done in a local approximation where the orbital frequency, shear rate, and tidal field were treated as constants. The locally computed growth rate turns out to depend strongly on radius, and it was unclear how to average these local rates to obtain the correct global rate. This is a critical issue for accretion disks in close binaries, because the local growth rate is comparable to the orbital frequency towards the outer edge of the disk but decreases rapidly inwards. Paper #1 examined this issue in a simplified global model where the destabilizing terms vary with position. We found that the global growth rate is essentially equal to the maximum local rate, provided that the latter is smoothed over a radial range equal to the distance that the destabilized wave propagates at its group speed in one growth time. Thus, in an accretion disk, waves would grow rapidly in the outer parts but would propagate both inwards and outwards at a maximum group speed of order the disk thickness divided by the orbital period.