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

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

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

On the notions of facets, weak facets, and extreme functions of the Gomory-Johnson infinite group problem

We investigate three competing notions that generalize the notion of a facet of finite-dimensional polyhedra to the infinite-dimensional Gomory-Johnson model. These notions were known to coincide for continuous piecewise linear functions with rational breakpoints. We show that two of the notions, extreme functions and facets, coincide for the case of continuous piecewise linear functions, removing the hypothesis regarding rational breakpoints. We then separate the three notions using discontinuous examples.Comment: 18 pages, 2 figure

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

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

Software for cut-generating functions in the Gomory--Johnson model and beyond

We present software for investigations with cut generating functions in the Gomory-Johnson model and extensions, implemented in the computer algebra system SageMath.Comment: 8 pages, 3 figures; to appear in Proc. International Congress on Mathematical Software 201

A study of possible temporal and latitudinal variations in the properties of the solar tachocline

Temporal variations of the structure and the rotation rate of the solar tachocline region are studied using helioseismic data from the Global Oscillation Network Group (GONG) and the Michelson Doppler Imager (MDI) obtained during the period 1995--2000. We do not find any significant temporal variation in the depth of the convection zone, the position of the tachocline or the extent of overshoot below the convection zone. No systematic variation in any other properties of the tachocline, like width, etc., is found either. Possibility of periodic variations in these properties is also investigated. Time-averaged results show that the tachocline is prolate with a variation by about 0.02R_sun in its position. The depth of the convection zone or the extent of overshoot does not show any significant variation with latitude.Comment: To appear in MNRA

Constraining solar abundances using helioseismology

Recent analyses of solar photospheric abundances suggest that the oxygen abundance in the solar atmosphere needs to be revised downwards. In this study we investigate the consequence of this revision on helioseismic analyses of the depth of the solar convection zone and the helium abundance in the solar envelope and find no significant effect. We also find that the revised abundances along with the current OPAL opacity tables are not consistent with seismic data. A significant upward revision of the opacity tables is required to make solar models with lower oxygen abundance consistent with seismic observations.Comment: To appear in ApJ Letters. 12 pages (that include 4 figures