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

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

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

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

Real root finding for equivariant semi-algebraic systems

Let $R$ be a real closed field. We consider basic semi-algebraic sets defined by $n$-variate equations/inequalities of $s$ symmetric polynomials and an equivariant family of polynomials, all of them of degree bounded by $2d < n$. Such a semi-algebraic set is invariant by the action of the symmetric group. We show that such a set is either empty or it contains a point with at most $2d-1$ distinct coordinates. Combining this geometric result with efficient algorithms for real root finding (based on the critical point method), one can decide the emptiness of basic semi-algebraic sets defined by $s$ polynomials of degree $d$ in time $(sn)^{O(d)}$. This improves the state-of-the-art which is exponential in $n$. When the variables $x_1, \ldots, x_n$ are quantified and the coefficients of the input system depend on parameters $y_1, \ldots, y_t$, one also demonstrates that the corresponding one-block quantifier elimination problem can be solved in time $(sn)^{O(dt)}$

Self-regulated gravitational accretion in protostellar discs

We present a numerical model for the evolution of a protostellar disc that has formed self-consistently from the collapse of a molecular cloud core. The global evolution of the disc is followed for several million years after its formation. The capture of a wide range of spatial and temporal scales is made possible by use of the thin-disc approximation. We focus on the role of gravitational torques in transporting mass inward and angular momentum outward during different evolutionary phases of a protostellar disc with disc-to-star mass ratio of order 0.1. In the early phase, when the infall of matter from the surrounding envelope is substantial, mass is transported inward by the gravitational torques from spiral arms that are a manifestation of the envelope-induced gravitational instability in the disc. In the late phase, when the gas reservoir of the envelope is depleted, the distinct spiral structure is replaced by ongoing irregular nonaxisymmetric density perturbations. The amplitude of these density perturbations decreases with time, though this process is moderated by swing amplification aided by the existence of the disc's sharp outer edge. Our global modelling of the protostellar disc reveals that there is typically a residual nonzero gravitational torque from these density perturbations, i.e. their effects do not exactly cancel out in each region. In particular, the net gravitational torque in the inner disc tends to be negative during first several million years of the evolution, while the outer disc has a net positive gravitational torque. Our global model of a self-consistently formed disc shows that it is also self-regulated in the late phase, so that it is near the Toomre stability limit, with a near-uniform Toomre parameter Q\approx 1.5-2.0. (Abstract abridged).Comment: 9 pages, 9 figures, accepted for publication in MNRA