On the internal structure of stars

A new model of the internal structure of certain types of celestial bodies is proposed. It is based on the concept that some neutron stars might have been formed earlier than all other type of stars, at an early stage of expansion of the universe, directly from continuous cosmic matter. Under such conditions, a neutron star after forming becomes an efficient center for the accretion of cosmic plasma. The plasma streams falling onto the neutron star carry magnetic fields with them that are created in the process (by thermoelectric currents and the dynamo process) and pack the fields tightly around the star. After a certain time, an extended and strongly magnetized plasma layer is formed around the neutron star. As a result, a stellar configuration is formed with an outer layer, mass, radius, and luminosity similar to those of an ordinary star. In the magnetized part of such a configuration, the gravitational attraction of the masses is compensated for by a magnetic pressure gradient, while the plasma is confifned by the magnetic field itself. Numerical estimates corroborate the possibility that magnetized stars exist. The radii and masses of the magnetized spheres of such stars are considerably less than the radii and masses of the corresponding configurations, so in observations they should not differ from ordinary stars: the outer layers (intermediate layer, photosphere, and chromosphere) of the magnetized configuration are the same as for an ordinary star. Structural differences may appear in the inner regions, however, involving magnetic activity and neutrino luminosity, for example.     

Possible effects of internal rotation in low-mass stars

The influence of internal rotation on the evolution of a 0.85M star is investigated by the construction of model sequences. Rotation is treated by a simple one-dimensional approximation. The calculations assume solid-body rotation on the zero-age Main Sequence, followed by conservation of angular momentum in shells. The 4 cases considered have the initial angular velocities 0,2×10^–4, 6×10^–4, and 8×10^–4/sec. All cases but the last are followed to helium ignition. Compared with the non-rotating case, the rotating models are older at Main-Sequence turnoff, develop fast-spinning central regions on the red-giant branch, and ignite helium at higher surface luminosities and at larger helium-core masses. The increases in the last two quantities are roughly proportional to the square of the initial angular velocity.The 6×10^–4 case is followed through the helium core flash to the zero-age horizontal branch. Under the assumption of spherical symmetry, the non-central ignition of helium leads to a sequence of flashes of decreasing amplitude occurring progressively closer to the center. The flashes are weaker than those encountered in previous studies and do not produce mixing.     

Effects of rotation on the colours and line indices of stars

The intrinsicuvby and HΒ indices of member stars of α-Persei, Pleiades and Scorpio-Centaurus association have been analysed in detail for rotation effects. These stars range in spectral type from B0 to F0 and the observed effects of rotation are found to be in agreement with photometric effects calculated by Collins & Sonneborn (1977) for rigidly rotating B0 to F0 stars On leave of absence from Assumption College, Changanacherry, Kerala.     

Effect of rotation and tidal distortions on the structure of polytropic stars

The averaging technique of Kippenhahn and Thomas has been used in conjunction with Kopal's method of evaluating various parameters on the Roche equipotentials, to determine the effects of rotation and tidal distortions on the shapes and structures of the polytropic models of the stars.     

Effects of rotation on colours and line indices of stars

We have analysed the broad-bandUBV colours and the intermediate banduvby colours of Persei, Pleiades, and the Scorpio-Centaurus association for rotation effects. An attempt was made to see if we can discriminate normal single stars from that of binary and peculiar stars after taking the observed rotation effects into account. It is found that the spread in the observed colours does not allow in general such a discrimination except that the objects with large reddening are double-lined binaries, peculiar stars or emission-lined objects. The few normal stars in these three clusters with such large reddening are listed as they are likely to belong to one of the above classes.On leave of absence from Assumption College, Changanacherry, Kerala.     

Equilibrium structure of stars obeying a generalized differential rotation law

In the present paper we have considered the problem of determining the equilibrium structure of differentially rotating stars in which the angular velocity of rotation varies both along the axis of rotation and in directions perpendicular to it. For this purpose, a generalized law of differential rotation of the type ² =b ₀+b ₁ s ²+b ₂ s ⁴+b ₃ z ²+b ₄ z ⁴+b ₅ z ² s ² (here is a nondimensional measure of the angular velocity of a fluid element distants from the axis of rotation andz from the plane through the centre of the star perpendicular to the axis of rotation, andb's are suitably chosen parameters) has been used. Whereas Kippenhahn and Thomas averaging approach has been used to incorporate the rotational effects in the stellar structure equations, Kopal's results on Roche equipotentials have been used to obtain the explicit form of the stellar structure equations, which incorporate the rotational effects up to second order of smallness in the distortion parameters. The method has been used to compute the equilibrium structure of certain differentially rotating polytropes. Certain differentially rotating polytropes. Certain differentially rotating models of the Sun have also been computed by using this approach.     

Differential rotation on rapidly rotating stars

Theories of meridional circulation and differential rotation in stellar convective zones predict trends in surface flow patterns on main-sequence stars that are amenable to direct observational testing. Here I summarise progress made in the last few years in determining surface differential rotation patterns on rapidly-rotating young main-sequence stars of spectral types F, G, K and M. Differential rotation increases strongly with increasing effective temperature along the main sequence. The shear rate appears to increase with depth in the sub-photospheric layers. Tidal locking in close binaries appears to suppress differential rotation, but better statistics are needed before this conclusion can be trusted. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Differential rotation of giant stars

From a set of high-resolution spectral observations of late type giant stars we used Doppler imaging to derive time-series temperature maps of the stellar surfaces. Using these temperature maps, it is possible to track the temporal changes of the spot features and derive estimates of the strength and sign of the differential surface rotation of these stars. Looking into the latitudinal changes of the surface maps, it is also possible to derive meridional flows on these stars. But due to the lower accuracy of the latitudes of the reconstructed spot features, the data requirements are higher than for the detection of differential rotation. Nevertheless, a correlation between the differential rotation and meridional flow estimates is suggested. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling the differential rotation of F stars

We model stellar differential rotation based on the mean-field theory of fluid dynamics. DR is mainly driven by Reynolds stress, which is anisotropic and has a non-diffusive component because the Coriolis force affects the convection pattern. Likewise, the convective heat transport is not strictly radial but slightly tilted towards the rotation axis, causing the polar caps to be slightly warmer than the equator. This drives a flow opposite to that caused by differential rotation and so allows the system to avoid the Taylor-Proudman state. Our model reproduces the rotation pattern in the solar convection zone and allows predictions for other stars with outer convection zones. The surface shear turns out to depend mainly on the spectral type and only weakly on the rotation rate. We present results for stars of spectral type F which show signs of very strong differential rotation in some cases. Stars just below the mass limit for outer convection zones have shallow convection zones with short convective turnover times. We find solar-type rotation and meridional flow patterns at much shorter rotation periods and horizontal shear much larger than on the solar surface, in agreement with recent observations. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effect of rotation on the luminosity of magnetic stars

The effect of rotation and a general magnetic field on the luminosity, radius, and effective temperature of the upper Main-Sequence stars has been investigated using a perturbation analysis. The magnetic field profile prevailing inside the star is assumed to have both poloidal and toroidal components. The case of constant as well as differential rotation is admitted. Model calculations indicate that these stellar parameters modify considerably as a result of coupling between rotation and the magnetic field.     

Differential rotation in F stars

Differential rotation can be detected in single line profiles of stars rotating more rapidly than about v sin i = 10km s-1 with the Fourier transform technique. This allows to search for differential rotation in large samples to look for correlations between differential rotation and other stellar parameters. I analyze the fraction of differentially rotating stars as a function of color, rotation, and activity in a large sample of F-type stars. Color and rotation exhibit a correlation with differential rotation in the sense that more stars are rotating differentially in the cooler, less rapidly rotating stars. Effects of rotation and color, however, cannot be disentangled in the underlying sample. No trend with activity is found. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Differential rotation of cool active stars

The surface differential rotation of active solar‐type stars can be investigated by means of Doppler and Zeeman‐Doppler Imaging, both techniques enabling one to estimate the short‐term temporal evolution of photospheric structures (cools spots or magnetic regions). After describing the main modeling tools recently developed to guarantee a precise analysis of differential rotation in this framework, we detail the main results obtained for a small number of active G and K fast rotating stars. We evoke in particular some preliminary trends that can be derived from this sample, bearing the promise that major advances in this field will be achieved with the new generation of spectropolarimeters (ESPaDOnS/CFHT, NARVAL/TBL). (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The rotation of 53 Be stars

Through spectral observations we obtained the rotational velocity Vsini for 53 Be stars, and estimated the values of V and i on the basis of Hutching's method. We analysed the effect of rotation on the width of emission lines and used the emission peak separation to determine the relative size of the shell and the photosphere and the dilution factor. We discuss in depth fast rotating models where stellar winds are present and their relation to the Be phenomenon.     

Effects of rotation and tidal distortions on the periods of adiabatic oscillations of composite models of stars

Mohan and Saxena's approach of using the averaging technique of Kippenhahn and Thomas in conjunction with Kopal's method of evaluating various parameters on the Roche equipotentials has been used to compute the effects of rotation and tidal distortions on the periods of small adiabatic radial and nonradial modes of oscillations of a series of composite models of stars. In these stars the density decreases slowly in the core from the centre to the interface and then falls of rapidly in the envelope from the interface to the outer surface.     

Effects of rotation on the colours and line indices of stars 1. The alpha Persei cluster

Analysis of the available observational data for the α-Persei cluster members shows that rotation effects on the intermediate-band indices c₁ and (u-b) are considerable. In c₁, rotation produces a reddening of 0.040 magnitudes per 100 km s^-1 In (u-b) the effect for B stars is found to be 0.06 magnitudes per 100 km s^-1 ofV sin i. The binaries and peculiar stars are found to behave differently in the colour excess (due to rotation) versusV sin i diagrams. These empirical effects can be utilised to recalibrate these colour indices and also to separate members that are either chemically peculiar or in binary systems.     

Effects of rotation on the colours and line indices of stars 5. The ZRMS and the ZRZAMS

The observeduvby and H_α indices of member stars of the Hyades and Praesepe clusters have been analysed in detail for rotation effects. The Alpha Persei, Pleiades and the Centaurus subgroup of the Scorpio—Centaurus association have been reanalysed using the observed indices instead of the extinction-corrected indices used earlier. The observed rotation effects from the analysis of these cluster data are found to be in excellent agreement with the theoretical predictions of Collins & Sonneborn (1977). We have also analysed the α,c and (u − b) values of the member stars of NGC 1976, 2264, 2287, 2422, 4755,1C 2391, IC 2602 and IC 4665 for rotation effects. The results are found to be consistent with the theoretical predictions. The observed slopes of the rotation effects were used to determine the zero rotation main sequence values of the intermediate band photometric indices for selected clusters. We also corrected the observed indices for each star in each cluster using the theoretical predictions of Collins and Sonneborn and derived the ZRMS values for each cluster. The agreement between the two determinations is found to be good. The various ZRMS curves were utilised to derive the ZRZAMS values. A preliminary calibration of the absolute visual magnitudes as a function of α valid for ZRZAMS has also been derived. The ZRMS values of the intermediate band photometric indices for different clusters and the ZRZAMS values are listed as a function of α. on leave from Assumption College, Changanacherry, Kerala.     

Effects of rotation and tidal distortion on the periods of small adiabatic oscillations of the polytropic models of the stars

The averaging technique of Kippenhahn and Thomas (1970) has been used in conjunction with Kopal's method of evaluating various parameters on the Roche equipotentials to determine the effects of rotation and tidal distortions on the periods of small adiabatic radial and nonradial modes of oscillations of polytropic models of the stars.     

Rapid differential rotation in intermediate mass stars

ZAMS models with internal differential rotation are computed for 6.5 M_⊙ and 10 M_⊙ models with the 2D evolution code ROTORC. Two applications of these models, their pulsational frequencies and deduced locations in the HR diagram, are discussed in order to show how the internal differential rotation could be investigated. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)