Professor Vinod Krishan-Research Profile

Modelling of Solar Coronal Loops

The solar corona is highly inhomogeneous and structures with a variety of shapes and sizes are seen to pervade it. The most ubiquitous, however, is a coronal loop which links magnetically active regions. The foot points of the loop suffer continuous turning and twistng in the convection zone. Despite such fluctuations in the velocity and magnetic fields, coronal loops exhibit a fairly stable and well configured geometry. Such a steady state is the result of various manifestations of the balance of inertial and magnetic forces. I suggested a completely different approach for the study of these loops. Applying the variational principle that the total energy of a system decays to a minimum while the magnetic helicity and cross helicity remain constant, a state with force free magnetic field and Beltrami flows results. This is, perhaps, the first time that a theoretical argument for the existence of force free magnetic fields has been given. Several papers have been published on this topic, extending the studiesto deal with time evolution of these loops. (Solar Phys. {142}, 249, 1992, Solar Phys. {157}, 121, 1995, MNRAS \underbar{249}, 596, 1991, and invited Review in Journal of Plasma Phys, 1996).. This work has become a part of the literature on Coronal loops at the text book level.

Solar Granulation

The cellular velocity patterns observed on the solar photosphere, over a variety of spatial and time scales are known as Solar Granulation and believed to be the manifestations of the convective phenomenon occuring in the sub-photospheric layers. I proposed a new model for the entire solar granulation. This model is based on the possibility of making large eddies from small eddies in a helically turbulent medium through the mechanism of inverse cascade of energy. The energy spectrum so derived consists of a Kolmogorovic branch that goes as K-5/3 and a new branch that goes as K-1. It is gratifying that the predictions of this model agree very well in the observed spectrum that has a Kolmogorov branch K-5/3 joining on to a K-0.7 branch towards large spatial scales (MNRAS), \{250}, 50, 1991, Invited articles for the books "Solar Interior and Atmosphere and IR tools for Solar Astrophysics"; also in BASI, \{24}, 1996). This model has been hailed as original and international collaborations have been initiated.
I have also participated in the interpretation of the eclipse observations of Solar Coronal Oscillations. . The results are reported in Singh et al. Solar Physics, 1997.

Extragalactic Plasmas

We initiated the investigations of the role of the nonlinear plasma processes in the generation, propagation, absorption, scattering and modulation of the nonthermal continuum of AGN and related objects. An intense radiation impinging on a plasma couples with the excitations in a plasma and produces the novelties of a nonlinear medium. As a result of which a linearly reflecting medium becomes absorbing and a linearly transparent medium becomes reflecting under the action of strong radiation. These processes known as stimulated Raman and Compton scattering and parametric decay instabillities have been shown to be of the utmost importance in the generation, absorption, modulations and extremely rapid variability of the AGN radiation. Almost the entire spectrum of a typical quasar 3C273 has been reproduced by suitably combining the stimulated Raman and Compton scattering processes. It is suggested that the break in the neighbourhood of the blue bump, may be due to the change of scattering process from Stimulated Raman to stimulated Compton (MNRAS, \{256}, 111, 1991). Through the action of the modulational instabilities of a large amplitude electromgnetic wave propagating in an electron-positron plasma, it is shown that the rapid time variability of quasar and pulsar radiation can be accounted for (MNRAS {262}, 151, 1993). A host of magnetohydrodynamic and kinetic processes have been shown to account for the quasar variability time scales ranging from years to a few minutes (Ap. J. \{423}, 172, 1994). Extremely fast variability in the polarization of quasar radiation has been shown to be caused by stimulated Raman and Comptom scattering (Ap. J. {415}, 505, 1993 and Ap. J. \{440}, 116, 1994). A few other groups e.g. at Caltech, U.S.A., Institute of Astronomy, Cambridge, England, Max Planck Institute Bonn, Nobeyama Radio Observatory, Japan, have realized the importance of these processes and are working on them. Extreme rapid variability is considered as one of the signatures of these coherent process. There is a hope that high dynamic range observations using the VLBA or conceivably QUASAT may actually be able to resolve regions where Stimulated Raman Scattering is at work (Private Communication with R.D.Blandford).

Structure Formation Through Hydrodynamics

The formation of the observed hierarchy of large scale distribution of matter and motion in the universe has remained a challenging problem and excited the imagination of many. It appears, from the literature that the role of turbulence which is omnipresent has not been taken into account while studying structure formation. It is being realized that turbulence is not only a random state of motion; it has the ability to organize itself as a result of which ordered structures appear in an otherwise disordered system. It is known that in a 3-D system withhelicity fluctuations, an inverse cascade of energy takes place whereby energy contained in small scale turbulence is transferred to large spatial scales. A structure at a given scale provides the stirring force to build up a structure at the next large spatial scale and so on and so forth. The identification of an invariant related to the square of helicity in addition to the energy invariant has opened up a possibility of an inverse cascade of energy in a 3-D system. Inverse cascade in a 2-D system is firmly established. The presence of helicity fluctuations in a 3-D system attribute it anisotropy and conditions close to a quasi-2D system obtain thus aiding inverse cascade. Using dimensional arguments of the Kolmogorovic type, an energy spectrum with branches consisting of K-5/3, K-1, K3 are derived. The requirement that a given large spatial scale cannot have more energy than contained in the small stirring scale, limits the size of the larger structure, for a given duration for which the small scale provides stirring. Thus, it was proposed that the universe is a hierarchy of eddies.. The eddies towards the small scale end can be identified with galaxies and those towards the large, the superclusters. Using the spectrum at the small scale end with K-5/3 and K-1 forms, combined with rigid rotation and Keplerian motion, rotation curves of nearly 80 galaxies have been modelled. The turbulence parameters derived from the fits have values close to those inferred from observations and other considerations. Formation of structures is also studied by solving the nonlinear Navier-Stokes equations. Here the Reynolds stresses generated by a small scale forced flow act as a source term for the generation of large scale flow. This is in the form of an instability in the linear regime. Its nonlinear evolution will determine the flow pattern. It is hoped that the Navier-Stokes study will confirm the predictions of the Kolmogorov study for a helically turbulent 3-D system. This confirmation has been achieved for a 2-D system. Helicity is zero for a 2-D system. These preliminary efforts have been reported in : MNRAS {250}, 157, 1991; MNRAS \underbar{264}, 257, 19993; Ap.J. {428}, 483, 1993, Current Science \{71}, 541, 1996; Pramana, 1997. This mechanism has raised the curiosity and interest of some astronomers. Much remains to be done, however, before this mechanism could be admitted or discarded.