## Vorticity generation in large-scale structure caustics
^{1} CITA, 60 St. George Street, Toronto, Ontario M5S 1A7, Canada^{2} Astronomisches Institut Universitaet Basel, Venusstrasse 7 CH-4102 Binningen, Switzerland,^{3} Institut d'Astrophysique de Paris, 98 bis Boulevard d'Arago, F-75014 Paris, France^{4} Centre d'étude de Saclay, Service de Physique Théorique, F-91191 Gif-sur-Yvette, France
A fundamental hypothesis for the interpretation of the measured large-scale line-of-sight peculiar velocities of galaxies is that the large-scale cosmic flows are irrotational. In order to assess the validity of this assumption, we estimate, within the frame of the gravitational instability scenario, the amount of vorticity generated after the first shell crossings in large-scale caustics. In the Zel'dovich approximation the first emerging singularities form sheet like structures. Here we compute the expectation profile of an initial overdensity under the constraint that it goes through its first shell crossing at the present time. We find that this profile corresponds to rather oblate structures in Lagrangian space. Assuming the Zel'dovich approximation is still adequate not only at the first stages of the evolution but also slightly after the first shell crossing, we calculate the size and shape of those caustics and their vorticity content as a function of time and for different cosmologies. The average vorticity created in these caustics is small: of the order of one (in units of the Hubble constant). To illustrate this point we compute the contribution of such caustics to the probability distribution function of the filtered vorticity at large scales. We find that this contribution that this yields a negligible contribution at the 10 to 15 Mpc scales. It becomes significant only at the scales of 3 to 4 Mpc, that is, slightly above the galaxy cluster scales.
This article contains no SIMBAD objects. ## Contents- 1. Introduction
- 2. Asymmetric constrained random fields
- 2.1. The 2D field
- 2.2. The 3D field
- 3. The geometry and vorticity of large-scale caustics
- 3.1. The linear displacement field
- 3.1.1. The 2D potential
- 3.1.2. The 3D potential
- 3.2. The shape of the caustics
- 3.3. The velocity field, and the generated vorticity
- 3.3.1. The local vorticity
- 3.3.2. The integrated vorticity
- 3.3.3. Scaling laws
- 3.1. The linear displacement field
- 4. The vorticity distribution at large scales
- 5. Discussion and conclusions
- Acknowledgements
- Appendix
- Appendix A: average profile of an a-spherical constrained random field
- A.1. General formula
- A.2. The 2D profile
- A.3. The 3D profile
- Appendix B: the DF of the eigenvalues of the local deformation tensor
- Appendix C: estimation of
- C.1. The 2D statistics
- C.2. The 3D statistics
- Appendix D: asymptotic behaviour of in 3D
- Appendix E: rare event approximation
- Appendix A: average profile of an a-spherical constrained random field
- References
© European Southern Observatory (ESO) 1999 Online publication: March 1, 1999 |