Stellar Inversion Techniques

Stellar seismic inversions have proved to be a powerful technique for probing the internal structure of stars, and paving the way for a better understanding of the underlying physics by revealing some of the shortcomings in current stellar models. In this lecture, we provide an introduction to this topic by explaining kernel-based inversion techniques. Specifically, we explain how various kernels are obtained from the pulsation equations, and describe inversion techniques such as the Regularised Least-Squares (RLS) and Optimally Localised Averages (OLA) methods.Comment: 20 pages, 8 figures. Lecture presented at the IVth Azores International Advanced School in Space Sciences on "Asteroseismology and Exoplanets: Listening to the Stars and Searching for New Worlds" (arXiv:1709.00645), which took place in Horta, Azores Islands, Portugal in July 201

10,000 Standard Solar Models: a Monte Carlo Simulation

We have evolved 10,000 solar models using 21 input parameters that are randomly drawn for each model from separate probability distributions for every parameter. We use the results of these models to determine the theoretical uncertainties in the predicted surface helium abundance, the profile of the sound speed versus radius, the profile of the density versus radius, the depth of the solar convective zone, the eight principal solar neutrino fluxes, and the fractions of nuclear reactions that occur in the CNO cycle or in the three branches of the p-p chains. We also determine the correlation coefficients of the neutrino fluxes for use in analysis of solar neutrino oscillations. Our calculations include the most accurate available input parameters, including radiative opacity, equation of state, and nuclear cross sections. We incorporate both the recently determined heavy element abundances recommended by Asplund, Grevesse & Sauval (2005) and the older (higher) heavy element abundances recommended by Grevesse & Sauval (1998). We present best-estimates of many characteristics of the standard solar model for both sets of recommended heavy element compositions.Comment: ** John N. Bahcall passed away on August 17, 2005. Manuscript has 60 pages including 10 figure

Helioseismology, solar models and solar neutrinos

We review recent advances concerning helioseismology, solar models and solar neutrinos. Particularly we shall address the following points: i) helioseismic tests of recent SSMs; ii)the accuracy of the helioseismic determination of the sound speed near the solar center; iii)predictions of neutrino fluxes based on helioseismology, (almost) independent of SSMs; iv)helioseismic tests of exotic solar models.Comment: 11 pages with 6 ps figures included, procsla style, based on the talks presented at Neutrino Telescopes '99, Venice, February 1999, and at Valencia '99, Valencia, May 1999, to appear in the proceeding

A Detailed Analysis of the Dust Formation Zone of IRC+10216 Derived from Mid-IR Bands of C2H2 and HCN

A spectral survey of IRC+10216 has been carried out in the range 11 to 14 um with a spectral resolution of about 4 km s^-1. We have identified a forest of lines in six bands of C2H2 involving the vibrational states from the ground to 3nu5 and in two bands of HCN, involving the vibrational states from the ground up to 2nu2. Some of these transitions are observed also in H13CCH and H13CN. We have estimated the kinetic, vibrational, and rotational temperatures, and the abundances and column densities of C2H2 and HCN between 1 and 300 R* (1.5E16 cm) by fitting about 300 of these ro-vibrational lines. The envelope can be divided into three regions with approximate boundaries at 0.019 arcsec (the stellar photosphere), 0.1 arcsec (the inner dust formation zone), and 0.4 arcsec (outer dust formation zone). Most of the lines might require a large microturbulence broadening. The derived abundances of C2H2 and HCN increase by factors of 10 and 4, respectively, from the innermost envelope outwards. The derived column densities for both C2H2 and HCN are 1.6E19 cm^-2. Vibrational states up to 3000 K above ground are populated, suggesting pumping by near-infrared radiation from the star and innermost envelope. Low rotational levels can be considered under LTE while those with J>20-30 are not thermalized. A few lines require special analysis to deal with effects like overlap with lines of other molecules.Comment: 8 pages, 16 figures, 2 machine-readable tables, accepted in the Astrophysical Journa

Helioseismological Implications of Recent Solar Abundance Determinations

We show that standard solar models are in good agreement with the helioseismologically determined sound speed and density as a function of solar radius, the depth of the convective zone, and the surface helium abundance, as long as those models do not incorporate the most recent heavy element abundance determinations. However, sophisticated new analyses of the solar atmosphere infer lower abundances of the lighter metals (like C, N, O, Ne, and Ar) than the previously widely used surface abundances. We show that solar models that include the lower heavy element abundances disagree with the solar profiles of sound speed and density as well as the depth of the convective zone and the helium abundance. The disagreements for models with the new abundances range from factors of several to many times the quoted uncertainties in the helioseismological measurements. The disagreements are at temperatures below what is required for solar interior fusion reactions and therefore do not significantly affect solar neutrino emission. If errors in thecalculated OPAL opacities are solely responsible for the disagreements, then the corrections in the opacity must extend from 2 times 10^6 K (R = 0.7R_Sun)to 5 times 10^6 K (R = 0.4 R_Sun), with opacity increases of order 10%.Comment: ApJ in press; clarified Figure

Asteroseismology across the HR diagram

High precision spectroscopy provides essential information necessary to fully exploit the opportunity of probing the internal structure of stars using Asteroseismology. In this work we discuss how Asteroseismology combined with High Precision Spectroscopy can establish a detailed view on stellar structure and evolution of stars across the HR diagramme.Comment: 6 pages, 2 figures - to appear in Precision Spectroscopy in Astrophysics, (Eds) L. Pasquini, M. Romaniello, N.C. Santos, and A. Correia, ESO Astrophysics Symposia, 200

On the Reliability of Cross Correlation Function Lag Determinations in Active Galactic Nuclei

Many AGN exhibit a highly variable luminosity. Some AGN also show a pronounced time delay between variations seen in their optical continuum and in their emission lines. In effect, the emission lines are light echoes of the continuum. This light travel-time delay provides a characteristic radius of the region producing the emission lines. The cross correlation function (CCF) is the standard tool used to measure the time lag between the continuum and line variations. For the few well-sampled AGN, the lag ranges from 1-100 days, depending upon which line is used and the luminosity of the AGN. In the best sampled AGN, NGC 5548, the H_beta lag shows year-to-year changes, ranging from about 8.7 days to about 22.9 days over a span of 8 years. In this paper it is demonstrated that, in the context of AGN variability studies, the lag estimate using the CCF is biased too low and subject to a large variance. Thus the year-to-year changes of the measured lag in NGC 5548 do not necessarily imply changes in the AGN structure. The bias and large variance are consequences of finite duration sampling and the dominance of long timescale trends in the light curves, not due to noise or irregular sampling. Lag estimates can be substantially improved by removing low frequency power from the light curves prior to computing the CCF.Comment: To appear in the PASP, vol 111, 1999 Nov; 37 pages; 10 figure

Solar-like oscillations in the G8 V star tau Ceti

We used HARPS to measure oscillations in the low-mass star tau Cet. Although the data were compromised by instrumental noise, we have been able to extract the main features of the oscillations. We found tau Cet to oscillate with an amplitude that is about half that of the Sun, and with a mode lifetime that is slightly shorter than solar. The large frequency separation is 169 muHz, and we have identified modes with degrees 0, 1, 2, and 3. We used the frequencies to estimate the mean density of the star to an accuracy of 0.45% which, combined with the interferometric radius, gives a mass of 0.783 +/- 0.012 M_sun (1.6%).Comment: accepted for publication in A&

Numerical simulations of stellar SiO maser variability. Investigation of the effect of shocks

A stellar hydrodynamic pulsation model has been combined with a SiO maser model in an attempt to calculate the temporal variability of SiO maser emission in the circumstellar envelope (CE) of a model AGB star. This study investigates whether the variations in local physical conditions brought about by shocks are the predominant contributing factor to SiO maser variability because, in this work, the radiative part of the pump is constant. We find that some aspects of the variability are not consistent with a pump provided by shock-enhanced collisions alone. In these simulations, gas parcels of relatively enhanced SiO abundance are distributed in a model CE by a Monte Carlo method, at a single epoch of the stellar cycle. From this epoch on, Lagrangian motions of individual parcels are calculated according to the velocity fields encountered in the model CE during the stellar pulsation cycle. The potentially masing gas parcels therefore experience different densities and temperatures, and have varying line-of-sight velocity gradients throughout the stellar cycle, which may or may not be suitable to produce maser emission. At each epoch (separated by 16.6 days), emission lines from the parcels are combined to produce synthetic spectra and VLBI-type images. We report here the results for v=1, J=1-0 (43-GHz) and J=2-1 (86-GHz) masers.Comment: 16 pages, 8 figures, accepted by A&