Astronomy:Rossby wave instability in astrophysical discs

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Short description: Rossby
Rossby wave instability in a Keplerian disk.[1]

Rossby Wave Instability (RWI) is a concept related to astrophysical accretion discs. In non-self-gravitating discs, for example around newly forming stars, the instability can be triggered by an axisymmetric bump, at some radius [math]\displaystyle{ r_0 }[/math], in the disc surface mass-density. It gives rise to exponentially growing non-axisymmetric perturbation in the vicinity of [math]\displaystyle{ r_0 }[/math] consisting of anticyclonic vortices. These vortices are regions of high pressure and consequently act to trap dust particles which in turn can facilitate planetesimal growth in proto-planetary discs.[2] The Rossby vortices in the discs around stars and black holes may cause the observed quasi-periodic modulations of the disc's thermal emission.

The theory of the Rossby wave instability in accretion discs was developed by Lovelace et al.[3] and Li et al.[4] for thin Keplerian discs with negligible self-gravity and earlier by Lovelace and Hohlfeld[5] for thin disc galaxies where the self-gravity may or may not be important and where the rotation is in general non-Keplerian.

Rossby waves, named after Carl-Gustaf Arvid Rossby, are important in planetary atmospheres and oceans and are also known as planetary waves.[6][7][8][9] These waves have a significant role in the transport of heat from equatorial to polar regions of the Earth. They may have a role in the formation of the long-lived ([math]\displaystyle{ \gt 300 }[/math] yr) Great Red Spot on Jupiter which is an anticyclonic vortex.[10] The Rossby waves have the notable property of having the phase velocity opposite to the direction of motion of the atmosphere or disc in the comoving frame of the fluid.[2][6]

The Rossby wave instability occurs because of the local wave trapping in a disc. It is related to the Papaloizou and Pringle instability;[11][12] where the wave is trapped between the inner and outer radii of a disc or torus.

References

  1. ↑ Lovelace, R V E.; Romanova, M. M. (2014). "Rossby wave instability in astrophysical discs". Fluid Dynamics Research 46 (4): 041401. doi:10.1088/0169-5983/46/4/041401. Bibcode: 2014FlDyR..46d1401L. 
  2. ↑ 2.0 2.1 Lyra, W.; Johansen, J.; Zsom, A.; Klahr, H.; Piskunov, N. (April 2009). "Planet formation bursts at the borders of the dead zone in 2D numerical simulations of circumstellar disks". Astronomy & Astrophysics 497 (3): 869–888. doi:10.1051/0004-6361/200811265. Bibcode: 2009A&A...497..869L. 
  3. ↑ Lovelace, R. V. E.; Li, H.; Colgate, S. A.; Nelson, A. F. (March 1999). "Rossby Wave Instability of Keplerian Accretion Disks". The Astrophysical Journal 513 (2): 805–810. doi:10.1086/306900. Bibcode: 1999ApJ...513..805L. 
  4. ↑ Li, H.; Finn, J. M.; Lovelace, R. V. E.; Colgate, S. A. (2000). "Rossby Wave Instability of Thin Accretion Disks. II. Detailed Linear Theory". The Astrophysical Journal 533 (2): 1023–1034. doi:10.1086/308693. Bibcode: 2000ApJ...533.1023L. 
  5. ↑ Lovelace, R. V. E.; Hohlfeld, R. G. (1978). "Negative mass instability of flat galaxies". The Astrophysical Journal 221: 51. doi:10.1086/156004. Bibcode: 1978ApJ...221...51L. 
  6. ↑ 6.0 6.1 Rossby, C.-G. (1939). "Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centers of action". Journal of Marine Research 2: 38–55. doi:10.1357/002224039806649023. 
  7. ↑ Brekhovskikh, Leonid; Goncharov, Valery (1985). "Waves in Rotating Fluids". Mechanics of Continua and Wave Dynamics. Springer Series on Wave Phenomena. 1. pp. 236–261. doi:10.1007/978-3-642-96861-7_11. ISBN 978-3-642-96863-1. 
  8. ↑ Chelton, D. B.; Schlax, M. G. (1996). "Global Observations of Oceanic Rossby Waves". Science 272 (5259): 234–238. doi:10.1126/science.272.5259.234. Bibcode: 1996Sci...272..234C. http://www.ocean.washington.edu/courses/oc513/Chelton.Science.1996.pdf. 
  9. ↑ Lindzen, Richard S. (1988). "Instability of plane parallel shear flow (toward a mechanistic picture of how it works)". Pure and Applied Geophysics 126 (1): 103–121. doi:10.1007/BF00876917. Bibcode: 1988PApGe.126..103L. 
  10. ↑ Marcus, Philip S. (1993). "Jupiter's Great Red Spot and Other Vortices". Annual Review of Astronomy and Astrophysics 31: 523–569. doi:10.1146/annurev.aa.31.090193.002515. Bibcode: 1993ARA&A..31..523M. 
  11. ↑ Papaloizou, J. C. B.; Pringle, J. E. (1984). "The dynamical stability of differentially rotating discs with constant specific angular momentum". Monthly Notices of the Royal Astronomical Society 208 (4): 721–750. doi:10.1093/mnras/208.4.721. Bibcode: 1984MNRAS.208..721P. 
  12. ↑ Papaloizou, J. C. B.; Pringle, J. E. (1985). "The dynamical stability of differentially rotating discs - II". Monthly Notices of the Royal Astronomical Society 213 (4): 799–820. doi:10.1093/mnras/213.4.799. Bibcode: 1985MNRAS.213..799P. 

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