Does solar structure vary with solar magnetic activity?

We present evidence that solar structure changes with changes in solar activity. We find that the adiabatic index, Gamma_1, changes near the second helium ionization, i.e., at a depth of about 0.98 R_sun. We believe that this change is a result of the change in the effective equation of state caused by magnetic fields. Inversions should be able to detect the changes in Gamma_1 if mode sets with reliable and precise high-degree modes are available.Comment: To appear in ApJ Letter

The discrepancy between solar abundances and helioseismology

There have been recent downward revisions of the solar photospheric abundances of Oxygen and other heavy elements. These revised abundances along with OPAL opacities are not consistent with seismic constraints. In this work we show that the recently released OP opacity tables cannot resolve this discrepancy either. While the revision in opacities does not seem to resolve this conflict, an upward revision of Neon abundance in solar photosphere offers a possible solution to this problem.Comment: To appear in ApJ Letter

Determining solar abundances using helioseismology

The recent downward revision of solar photospheric abundances of Oxygen and other heavy elements has resulted in serious discrepancies between solar models and solar structure as determined through helioseismology. In this work we investigate the possibility of determining the solar heavy-element abundance without reference to spectroscopy by using helioseismic data. Using the dimensionless sound-speed derivative in the solar convection zone, we find that the heavy element abundance, Z, of 0.0172 +/- 0.002, which is closer to the older, higher value of the abundances.Comment: To appear in Ap

Temporal variations of the rotation rate in the solar interior

The temporal variations of the rotation rate in the solar interior are studied using frequency splittings from Global Oscillations Network Group (GONG) data obtained during the period 1995-99. We find alternating latitudinal bands of faster and slower rotation which appear to move towards the equator with time - similar to the torsional oscillations seen at the solar surface. This flow pattern appears to persist to a depth of about 0.1R_sun and in this region its magnitude is well correlated with solar activity indices. We do not find any periodic or systematic changes in the rotation rate near the base of the convection zone.Comment: To appear in Ap

Solar Models with Revised Abundances and Opacities

Using reconstructed opacities, we construct solar models with low heavy-element abundance. Rotational mixing and enhanced diffusion of helium and heavy elements are used to reconcile the recently observed abundances with helioseismology. The sound speed and density of models where the relative and absolute diffusion coefficients for helium and heavy elements have been increased agree with seismically inferred values at better than the 0.005 and 0.02 fractional level respectively. However, the surface helium abundance of the enhanced diffusion model is too low. The low helium problem in the enhanced diffusion model can be solved to a great extent by rotational mixing. The surface helium and the convection zone depth of rotating model M04R3, which has a surface Z of 0.0154, agree with the seismic results at the levels of 1 $\sigma$ and 3 $\sigma$ respectively. M04R3 is almost as good as the standard model M98. Some discrepancies between the models constructed in accord with the new element abundances and seismic constraints can be solved individually, but it seems difficult to resolve them as a whole scenario.Comment: 10 pages, 1 figur

GRB011211: An alternative interpretation of the optical and X-ray spectra in terms of blueshifts

The redshifts of the gamma ray burst (GRB) GRB 011211 has been determined as 2.14 from several absorption lines seen in the spectrum of its optical afterglow. The spectrum of its X-ray afterglow exhibited several emission lines,and their identification led to a mean redshift 1.862. A supernova model has been proposed based on the redshift of the GRB as 2.141. It is shown here that the redshift interpretation cannot explain the observed spectra, as some serious inconsistencies exist in the process of redshift determinations in spectra of both optical and X-ray afterglows. In view of that, an alternative interpretation of the spectra is presented in terms of blueshifts. Ejection mechanism is proposed as a possible scenario to explain the blueshifted spectrum.Comment: 26 pages, one table; in Canadian Journal of Physics, June 200

Solar internal rotation rate and the latitudinal variation of the tachocline

A new set of accurately measured frequencies of solar oscillations are used to infer the rotation rate inside the Sun, as a function of radial distance as well as latitude. We have adopted a regularized least squares technique with iterative refinement for both 1.5D inversion using the splitting coefficients and 2D inversion using individual m splittings. The inferred rotation rate agrees well with earlier estimates showing a shear layer just below the surface and another one around the base of the convection zone. The tachocline or the transition layer where the rotation rate changes from differential rotation in the convection zone to almost latitudinally independent rotation rate in the radiative interior is studied in detail. No compelling evidence for any latitudinal variation in position and width of tachocline is found though it appears that the tachocline probably shifts to slightly larger radial distance at higher latitudes and possibly becomes thicker also. However, these variations are within the estimated errors and more accurate data would be needed to make a definitive statement about latitudinal variations.Comment: 15 pages, MNRAS-TeX, 15 figure

Ring diagram analysis of near-surface flows in the Sun

Ring diagram analysis of solar oscillation power spectra obtained from MDI data is carried out to study the velocity fields in the outer part of the solar convection zone. The three dimensional power spectra are fitted to a model which has a Lorentzian profile in frequency and which includes the advection of the wave front by horizontal flows, to obtain the two components of the sub-surface flows as a function of the horizontal wave number and radial order of the oscillation modes. This information is then inverted using OLA and RLS methods to infer the variation in horizontal flow velocity with depth. The average rotation velocity at different latitudes obtained by this technique agrees reasonably with helioseismic estimates made using frequency splitting data. The shear layer just below the solar surface appears to consist of two parts with the outer part up to a depth of 4 Mm, where the velocity gradient does not show any reversal up to a latitude of 60 degrees. In the deeper part the velocity gradient shows reversal in sign around a latitude of 55 degrees. The zonal flow velocities inferred in the outermost layers appears to be similar to those obtained by other measurements. A meridional flow from equator polewards is found. It has a maximum amplitude of about 30 m/s near the surface and the amplitude is nearly constant in the outer shear layer.Comment: aastex, 12 figures, to appear in Ap.

The structure of the infinite models in integer programming

The infinite models in integer programming can be described as the convex hull of some points or as the intersection of halfspaces derived from valid functions. In this paper we study the relationships between these two descriptions. Our results have implications for corner polyhedra. One consequence is that nonnegative, continuous valid functions suffice to describe corner polyhedra (with or without rational data)