The most direct evidence for the existence of asphericities in stellar winds is the intrinsic polarization observed in many hot stars. This intrinsic polarization is often time variable, and the polarization position angle can be either stochastic, indicating clumps in the wind (usually supergiants and WR stars), or time independent, which is indicative of an axisymmetric or disk-like geometry (e.g., Oe/Be stars). Clumps may arise as a result of the instabilities inherent in radiatively driven winds (Lucy & Solomon 1970, ApJ, 159, 879).
Rotation can also cause equatorial density enhancements. When the star rotates rapidly, the stellar wind is directed towards the equator and forms a shock-compressed disk, which may be the origin of the disks around Oe/Be stars (Bjorkman & Cassinelli 1993, ApJ, 409, 429; Owocki, Cranmer, & Blondin 1994, ApJ, 424, 887). However, Ignace, Cassinelli, & Bjorkman (1996, ApJ, 459, 671) showed that it is not necessary that the star rotate rapidly. They found that a WR star with a slowly accelerating wind can have a factor of three increase in the equatorial density at a rotation rate of only 15% of the critical rotation speed.
One of the many features of Wolf Rayet stars is observational data indicating the presence of dust grains in the circumstellar environment of WC9 and WC10 stars (Williams 1995, IAU Symp. 163, 335). Spherically symmetric models predict radiative equilibrium temperatures that are higher than the dust condensation temperature out to a radius of 100AU, at which point the wind density is too small to enable the growth of dust grains (Williams, van der Hucht, & Thé 1987,A&A, 182, 91). Thus, the survival of dust around these hot stars is a puzzling theoretical problem and several explanations have been proposed. For those that show transient dust features, it has been suggested that these stars are in binary systems, and the dust forms at periastron in a compressed region between the two stellar winds (Williams 1995). For single stars the dust may be formed in clumps within the wind (Moffat & Robert 1992, ASPC, 22, 303), or in a rotationally compressed zone surrounding the star (Cassinelli, Ignace, & Bjorkman 1994, IAU Symp. 163, 191). The common feature of these models that permits dust formation is the existence of a high density region where the material is either shielded from the direct stellar radiation field or the high density increases the radiative cooling rate, enabling the local temperature to drop below the dust formation threshold. No matter whether this region arises due to compression of two colliding stellar winds, clumping in the wind of a single star, or an equatorially compressed zone, a thorough investigation of this problem requires non-spherical radiation transfer.
Other systems that clearly require non-spherical radiation transfer are rapidly rotating O and B stars. One of the ongoing problems with Be star observations is that the mass loss rate measured from UV absorption line profiles is typically 2–-3 orders of magnitude smaller than that measured from observations of the IR excess (Waters, Coté, & Lamers 1987, A&A, 185, 206). One proposed solution to this discrepancy is a two-component wind model, comprised of a fast, diffuse polar wind where the UV wind lines are formed, and a dense disk whose free-free emission produces the IR excess (see Waters & Marlborough 1994, IAU Symp. 162, 399 ). Given that the rotation rates of Be stars are so high, it is quite likely that the mass loss is not spherically symmetric, so model line profiles really should be calculated using an axisymmetric model in order to produce more reliable mass loss rates.
A relevant result from EUVE observations is that a B giant star, e CMa (B2 II), has a photospheric flux in the 500–-700 Å range that is a factor of 30 larger than model predictions (Cassinelli et al. 1996, ApJ, 460, 949). Najarro et al. (1996, A&A, 306, 892) have found that by including the effects of wind expansion, the extra flux can be explained by NLTE effects, but only if the mass loss rate is a factor of 10 above that estimated from UV wind lines. Increasing the mass loss rate of a B2 V star by an order of magnitude, we find that over its main-sequence lifetime it will lose 3% of its initial mass. This mass is returned to the ISM. If the mass return rates during all B star phases are increased by an order of magnitude, then the B star contribution will begin to compete with the supernova return rate. Furthermore, if for all B stars the ionization fraction of C IV were as small as 0.01, as suggested by Bjorkman et al. (1994, ApJ, 435, 416) in their study of HD93521, then the mass lost in the B main-sequence stage could be as much as 30% of the total mass.
Intrinsic polarization in hot stars is attributed to electron scattering in a non-spherical circumstellar envelopes (Coyne 1976, IAU Symp., 70, 233). Electron scattering is wavelength independent; however, the scattered radiation is subject to attenuation by both continuum and line opacity sources within the circumstellar envelope, yielding a wavelength dependence for the observed polarization. When one observes the polarized flux, one is preferentially selecting photons that are scattered in the circumstellar disk. Therefore, these photons must traverse the disk both before and after they are scattered. Hence spectropolarimetry provides a valuable probe of the column densities of the various absorbers within the disk itself. For example, the polarized spectra of Be stars (obtained with the University of Wisconsin Pine Bluff Observatory, PBO, and the Wisconsin Ultraviolet Photo-Polarimeter Experiment, WUPPE, on the Astro-2 space shuttle mission) show the signature of continuous hydrogen absorption with large jumps in the level of polarization across the Balmer and Paschen edges . Fitting the level of the polarization determines the total number of scatterers (i.e., total mass) in the disk, while the size of the polarization Balmer jump determines the density in the disk. The combination of these two allows us to determine the geometrical thickness of the disk. Our fits, indicate that Be stars are surrounded by extremely thin disks (Wood, Bjorkman & Bjorkman 1997, ApJ, 477, 926).
There are many indications of the presence of non-spherical envelopes around Herbig Ae/Be stars, which are intermediate-mass, pre-main-sequence stars. In particular, Herbig Ae/Be stars show non-periodic Algol-type photometric minima accompanied by increasing optical polarization. Grinin et al. (1991, Ap&SS, 186, 283) proposed that these effects are produced by circumstellar dust clouds that occasionally occult the stellar radiation. In addition, the observation of time variable polarization implies that the system is intrinsically polarized, which requires a non-spherical distribution of dust around the star. Millimeter-wave continuum observations of A-type Herbig stars also imply the presence of orbiting material in disk-like configurations (Mannings & Sargent 1997, ApJ, in press). Finally, the hydrogen Balmer line profiles of many of these objects are double-peaked, similar to those observed in Be stars, which are known to have highly flattened rotating gaseous envelopes.
However, the kinematics of the gaseous envelopes around Herbig Ae/Be stars is much more complex than that of Be stars. The highly time variable UV resonance line profiles sometimes show redshifted absorption indicative of accretion (Grady et al. 1996, A&AS, 120, 157), while at the same time there can be time variable blueshifted P Cygni absorption in the Balmer lines indicative of a strong stellar wind in combination with a circumstellar disk (Pogodin 1992, Sov.Astr.Let., 18, 1066). Thus we see that in addition to the disk, there appears to be simultaneous accretion and outflow from these stars. Mass loss rates for these systems are usually based on pure stellar wind models. Because the accreting matter “contaminates” the line profiles produced by the outflow, the current estimates of mass loss rates are very unreliable. To produce better estimates of the accretion and mass loss rates we require 2-D NLTE radiation transfer models.
We use a 3-D Monte Carlo radiation transfer code and a NLTE Sobolev code (to calculate level populations of different atoms existing in circumstellar envelopes) to determine ioinization and temperature structure of non-spherical circumstellar envelopes around early-type stars. Our basic approach will be to determine the intensity moments throughout the circumstellar envelope, using the Monte Carlo technique, and use these results to determine the NLTE level populations, temperature, and ionization structure. In particular, we are going to: