A Radiatively D riven Orbital M ass Ejection

model for formation of circumstellar disks in Be stars

Be stars are characterized by emission in Hydrogen Balmer lines thought to originate from a circumstellar disk. Recent observations by Rivinius et al. show that episodic brightenings in circumstellar emission are often correlated with period of positive overlap between distinct modes of Non-Radial Pulsation (NRP).

NRP Line-Profile Variability loop Here is an animation illustrating how NRP oscillations are diagnosed by variations in photospheric absorption lines. (The amplitude of the variations and distortions of the surface are greatly exaggerated to emphasize the effects.)

NRP Resonance l=4, m=2 Here is an animation showing how distinct NRP modes "beat" into intervals of reinforcement and cancellation.

Bright spot with rotation The velocity amplitude of pulsation is generally only on order of a few tens of km/s, much less than the speed needed to achieve orbit, which is typically about 500 km/s. However, Be stars are typically rapid rotators, with surface rotations of order 250 km/s or more, that is, half or more the speed to achieve orbit. Thus, for example, if material on the stellar surface could somehow be propelled outward at velocity > 500-250=250 km/s from the stellar surface, then that material that happens to be heading in the prograde direction of rotation can have sufficient speed to remain in orbit, while other material ejected upward or in a retrograde direction will simply fall back onto the star.

Kroll SPH sim In a Ph. D. thesis, P. Kroll used smoothed-particle hydrodynamics to model the effect of a localized "outburst" or explosion on the surface of a critically rotating stellar surface. The material was simply assumed to have an initial outward expansion velocity of order 100 km/s. The figure at the left illustrates the resulting time evolution of ejected material, as viewed from both the pole and equator.

What is not clear from these models is what driving mechanism can propel material to these kind of orbital escape speeds.

I have recently been examining the potential role of radiative driving in such orbital outbursts. Be stars are hot, bright stars with a radiatively driven stellar wind. Such winds can attain speeds of more than 1000 km/s, that is, far above the sufrace escape speed, which itself is factor Sqrt[2] higher than the requjired orbital speed. However,. in such winds,  material is primarily driven radially outward, and so lacks the directed azimuthal acceleration that gives material the required angular momentum to achieve circumstellar momentum.

But if we consider the possibility of localized bright spots on the stellar surface, then we can examine the dynamics of the radiative driven mass outflow from such spots. For this I have adapted radiation hydrodynamics computer codes I have used previously to study structure in line-driven stellar winds to examine now such localized spot outflows. A key feature of this code is to compute a vector extension of usual CAK/Sobolev form for the line-force, including in particular the azimuthal force component that may be able to propel material in the direction of the star's rotation from a localized spot, and thus possibly into circumstellar orbit.

The link here shows an animation of such an outflow from a spot that is factor 10 brighter than the ambient star, and covering a circle approximately 10 degrees radius located at the equator of a star rotating at 350 km/s, with orbital speed 500 km/s. Note that for this case of isotropic emission from the bright spot, the net outcome is to produce a spiral stream of outwardly flowing enhanced density, with essentially no material being left in a circumstellar orbit.

RDOME sequence from limb-brightened spot From further numerical experiments, I have found that it is generally important to limit the radial, outward components of the driving force, to prevent material from being driven entirely away from the star. For example, the illustration at the right shows the time evolution (time labeled in ksec) of the density in a bright spot with a highly limb-brightened emission, i.e. with strong lateral emission from the sides of the spot, but little upward emission. (Such a radiative configuration is somewhat reminiscent of the emission from a quiescent solar prominence, which appears bright at the solar limb, but dark when viewed against the solar disk.). Click here for an animation of this case.

Other cases I have studied include spots with a prograde-biased emission (click here for animation),  and a complete line-force cutoff above some radius (perhaps reflecting a change in ionization that abruptly reduces the effectiveness of line-opacity; click here for animation for case with force cutoff above r=1.25 R).

Finally, perhaps the most visual striking example comes from a model with 4 prograde spots arranged around the stellar equator. (click here for animation). Some of my friends and colleagues have suggested this would make an entertaining screen-saver! :)

While this RDOME scenario thus demonstrates that radiative driving can, in principle, expel surface material into a circumstellar disk, I caution that the conditions assumed in these simulations are quite extreme, with brightness variations that are far stronger than have typically been thought to be possible on such stars. More study is thus needed to determine whether what role radiative driving actually might play in such episodic mass ejections of material into circumstellar orbit.

This research has not yet been published in any journal, but I have given several talks on the general probem of forming Be disks, with the somewhat whimsical title "The Rocket Science of Launching Stellar Disks", which you can access here in the original Powerpoint , or as a PDF document. You can also view an exported html slide show version of this talk by clicking here.

Finally, you may also access a PDF version of a recently funded NSF grant proposa l to develop models of Be disk formation.