Vortices are one of the most promising mechanisms to locally concentrate millimeter dust grains and allow the formation of planetesimals through gravitational collapse. The outer disk around the binary system HD 142527 is known for its large horseshoe structure with azimuthal contrasts of ~3–5 in the gas surface density and of ~50 in the dust. Using 13 CO and C 18 O J = 3–2 transition lines, we detect kinematic deviations to the Keplerian rotation, which are consistent with the presence of a large vortex around the dust crescent, as well as a few spirals in the outer regions of the disk. Comparisons with a vortex model suggest velocity deviations up to 350 m s −1 after deprojection compared to the background Keplerian rotation, as well as an extension of ±40 au radially and ~200° azimuthally, yielding an azimuthal-to-radial aspect ratio of ~5. Another alternative for explaining the vortex-like signal implies artificial velocity deviations generated by beam smearing in association with variations of the gas velocity due to gas pressure gradients at the inner and outer edges of the circumbinary disk. The two scenarios are currently difficult to differentiate and, for this purpose, would probably require the use of multiple lines at a higher spatial resolution. The beam smearing effect, due to the finite spatial resolution of the observations and gradients in the line emission, should be common in observations of protoplanetary disks and may lead to misinterpretations of the gas velocity, in particular around ring-like structures.
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Equations of motion for weakly compressible point vortices
Equations of motion for compressible point vortices in the plane are obtained in the limit of small Mach number, M , using a Rayleigh–Jansen expansion and the method of Matched Asymptotic Expansions. The solution in the region between vortices is matched to solutions around each vortex core. The motion of the vortices is modified over long time scales O ( M 2 log M ) and O ( M 2 ) . Examples are given for co-rotating and co-propagating vortex pairs. The former show a correction to the rotation rate and, in general, to the centre and radius of rotation, while the latter recover the known result that the steady propagation velocity is unchanged. For unsteady configurations, the vortex solution matches to a far field in which acoustic waves are radiated. This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 2)’.
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- Award ID(s):
- 1706934
- NSF-PAR ID:
- 10325030
- Date Published:
- Journal Name:
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Volume:
- 380
- Issue:
- 2226
- ISSN:
- 1364-503X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1098/rsta.2021.0052
