We present the results of medium resolution (Delta v = 60 km/s) spectropolarimetric observations across Halpha of a sample of B[e] and Herbig Be objects. A change in linear polarization across Halpha is detected in a large fraction of the objects. Halpha in the spectra of HD 37806 and HD 50138 each consist of a double-peaked polarized line and a superposed unpolarized single emission peak, suggesting two distinct line-forming regions. Multiple observations of HD 45677 allow for the separation of electron and dust scattering effects for the first time: the data indicate that the dust-scattering region is clumpy. Two unexpected results are the non-detections of Halpha polarization changes in omega Ori, where depolarization has previously been detected, and in MWC 297, which exhibits source elongation at radio wavelengths. In omega Ori time variability is probably responsible such that this stars electron-scattering disk was much weakened at the time of observation. Two hypotheses are advanced that might explain the MWC 297 result. The general findings are that roughly half of the observed Herbig Be stars show polarization changes across Halpha, implying immediately that their ionized envelopes are not spherically symmetric. This pattern, if confirmed by observations of a larger sample, could indicate that the non-detection rate is simply a consequence of sampling randomly-oriented circumstellar disks able to scatter starlight within a few stellar radii. The stars classified as B[e] stars all show startling polarization changes across Halpha. The details in each case are different, but the widely accepted concept of dense Halpha emitting equatorial disks around these objects is supported.
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