These plots illustrate how varying an inner disk radius ro affects a disk emission line profile. By assuming an opaque disk with an uniform emission and a Keplerian rotation law, the profiles are derived here from a simple histogram of the relative areas associated with a given line-of-sight velocity. The velocities are scaled relative to the maximum projected velocity from a fiducial radius, r=1, i.e. v(r=1)*sin i = 1., with the inclination angle here taken as i=40 deg (about the value inferred for the well-studied Be star, mu Cen). The emission profiles are accordingly plotted over the scaled frequency/velocity range [-1,1], and are scaled such that peaks always have the same height.
The disk figures on the left illustrate the projected spatial distribution of the line-of-sight velocity, as coded by a blue-to-red color scale. In the uppermost case the disk is extended to arbitarily small radii, ro=0 (with, however, projected velocities beyond the chosen fiducial range [-1,1] being blacked out). The 5 other examples below this show results for inner disk radii ro=1,2,3,4, and 4.9.
Note that there is very little difference in the resulting profiles for cases with inner disk radius ro =1 vs. ro =0. However, for large inner disk radii ro >=2, note the gradual reduction in the wing emission, culminating in the “bowl-shape” profile for the “thin-ring” case with ro =4.9. Note also that the emission peaks occur at projected velocities associated with the scaled Keplerian orbital speed of the outer disk radius, i.e. at +/- xm=1/sqrt(5).
These results suggest that:
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- opaque disks that span a relatively narrow radius range of a factor 2-3 should be characterized by a relatively sharp emission edge
- disks that span a wider radius range, e.g. factor 5 or more, should have a quite gradual edge
- in the latter case, line-profiles are not well-suited to determining whether the inner disk radius is detached significantly from the stellar surface
- generally, the velocity separation of the emission peaks should be indicative of the projected orbital velocity near theouter edge of strtong disk emission
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