On the choice of parameters in solar structure inversion

The observed solar p-mode frequencies provide a powerful diagnostic of the internal structure of the Sun and permit us to test in considerable detail the physics used in the theory of stellar structure. Amongst the most commonly used techniques for inverting such helioseismic data are two implementations of the optimally localized averages (OLA) method, namely the Subtractive Optimally Localized Averages (SOLA) and Multiplicative Optimally Localized Averages (MOLA). Both are controlled by a number of parameters, the proper choice of which is very important for a reliable inference of the solar internal structure. Here we make a detailed analysis of the influence of each parameter on the solution and indicate how to arrive at an optimal set of parameters for a given data set.Comment: 14 pages, 15 figures. Accepted for publication on MNRA

A more realistic representation of overshoot at the base of the solar convective envelope as seen by helioseismology

The stratification near the base of the Sun's convective envelope is governed by processes of convective overshooting and element diffusion, and the region is widely believed to play a key role in the solar dynamo. The stratification in that region gives rise to a characteristic signal in the frequencies of solar p modes, which has been used to determine the depth of the solar convection zone and to investigate the extent of convective overshoot. Previous helioseismic investigations have shown that the Sun's spherically symmetric stratification in this region is smoother than that in a standard solar model without overshooting, and have ruled out simple models incorporating overshooting, which extend the region of adiabatic stratification and have a more-or-less abrupt transition to subadiabatic stratification at the edge of the overshoot region. In this paper we consider physically motivated models which have a smooth transition in stratification bridging the region from the lower convection zone to the radiative interior beneath. We find that such a model is in better agreement with the helioseismic data than a standard solar model.Comment: 18 pages, 4 tables, 24 figures - to appear in MNRAS (version a: equation 9 corrected

ADIPLS -- the Aarhus adiabatic oscillation package

Development of the Aarhus adiabatic pulsation code started around 1978. Although the main features have been stable for more than a decade, development of the code is continuing, concerning numerical properties and output. The code has been provided as a generally available package and has seen substantial use at a number of installations. Further development of the package, including bringing the documentation closer to being up to date, is planned as part of the HELAS Coordination Action.Comment: Astrophys. Space Sci., in the pres

On the structure of the Sun and alpha Centauri A and B in the light of seismic and non-seismic constraints

The small separation (delta nu 01, delta nu 02 and delta nu 13) between the oscillations with low degree l is dependent primarily on the sound speed profile within the stellar core, where nuclear evolution occurs. The detection of such oscillations for a star offers a very good opportunity to determine the stage of its nuclear evolution, and hence its age. In this context, we investigate the Sun and alpha Cen A and B. For alpha Cen A and B, each of the small separations delta nu 01, delta nu 02 and delta nu 13 gives a different age. Therefore, in our fitting process, we also employ the second difference, defined as nu n2 - 2 nu n1 + nu n0, which is 2 delta nu 01- delta nu 02. In addition to this, we also use frequency ratio (nu n0/ nu n2). For the Sun, these expressions areequivalent and give an age of about 4.9-5.0 Gyr. For alpha Cen A and B, however, the small separation and the second difference give very different ages. This conflict may be solved by the detection of oscillation frequencies that can be measured much more precisely than the current frequencies. When we fit the models to the observations, we find (i) Z 0=0.020, t=3.50 Gyr and M B=1.006 Msun from the small separations delta nu 01, delta nu 02 and delta nu 13 of alpha Cen B; and (ii) a variety of solutions from the non-seismic constraints and delta nu 02 of alpha Cen A and B, in which the masses of alpha Cen A and B are slightly modified and the age of the system is about 5.2-5.3 Gyr. For Z=0.025, the closest masses we find to the observed masses are M B=0.922 Msun and M A=1.115 Msun.The differences between these masses and the corresponding observed masses are about 0.01 Msun.Comment: 9 Pages and 9 Figure

Sub-Wavelength Resolution Imaging of the Solar Deep Interior

We derive expectations for signatures in the measured travel times of waves that interact with thermal anomalies and jets. A series of numerical experiments that involve the dynamic linear evolution of an acoustic wave field in a solar-like stratified spherical shell in the presence of fully 3D time-stationary perturbations are performed. The imprints of these interactions are observed as shifts in wave travel times, which are extracted from these data through methods of time-distance helioseismology \citep{duvall}. In situations where at least one of the spatial dimensions of the scatterer was smaller than a wavelength, oscillatory time shift signals were recovered from the analyses, pointing directly to a means of resolving sub-wavelength features. As evidence for this claim, we present analyses of simulations with spatially localized jets and sound-speed perturbations. We analyze 1 years' worth solar observations to estimate the noise level associated with the time differences. Based on theoretical estimates, Fresnel zone time shifts associated with the (possible) sharp rotation gradient at the base of the convection zone are of the order 0.01 - 0.1 s, well below the noise level that could be reached with the currently available amount of data ($\sim 0.15-0.2$ s with 10 yrs of data).Comment: Accepted, ApJ; 17 pages, 12 figure