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[1] It is shown that the framework of Hall magnetohydrodynamics (Hall-MHD), which can support three quadratic invariants and allows nonlinear states to depart fundamentally from the Alfvénic, is capable of reproducing in the inertial range the three branches of the observed solar wind magnetic fluctuation spectrum: the Kolmogorov branch f À5/3 , steepening to f Àa 1 , with a 1 ' 3-4 on the high-frequency side and flattening to f À1 on the low-frequency side. These fluctuations are found to be associated with the nonlinear Hall-MHD shear Alfvén waves. The spectrum of the concomitant whistler-type fluctuations is very different from the observed one. Perhaps the relatively stronger damping of the whistler fluctuations may cause their unobservability. The issue of the anisotropy of the turbulence is addressed briefly.

Received; accepted 1 sujan@iiap.ernet.in -2 - ABSTRACTTheoretical analysis and observational evidences indicate that a brown dwarf with effective temperature greater than 1300 K would have dust cloud in its atmosphere. In this letter, we show that dust scattering should yield polarized continuum radiation from the relatively warm brown dwarfs and the polarized flux profile could be a potential diagnosis tool for the optical and the physical properties of dust grains. The degree of polarization due to multiple scattering will be more in the optical region if the particle size is small while significant polarization should be detected in the infra-red region if the particle size is large. It is pointed out that the departure from sphericity in the shape of the object due to rapid rotation and due to tidal effect by the companion in a binary system ensures the disc integrated polarization to be non-zero.

The Alfvén wave is known to be an exact solution of the ideal magnetohydrodynamics (MHD), and this has found use in modelling astrophysical turbulence. In this paper we show that the Hall MHD also submits itself to an exact solution in the incompressible limit. We compare the linear and the non‐linear modes of the Hall MHD and comment on their probable role in describing turbulent fluctuations in different astrophysical situations.

A study of 90 supergranular cells obtained from SOHO Dopplergrams was undertaken in order to investigate a possible relation between the sizes and peak horizontal velocities of the cells. For the sample obtained, the two parameters are found to be correlated with a relation: horizontal velocity ∝(size)1/3. This is in agreement with the Kolmogorov theory of turbulence as applied to large‐scale solar convection.