Calculation of Spectral Darkening and Visibility Functions for Solar Oscillations

Calculations of spectral darkening and visibility functions for the brightness oscillations of the Sun resulting from global solar oscillations are presented. This has been done for a broad range of the visible and infrared continuum spectrum. The procedure for the calculations of these functions includes the numerical computation of depth-dependent derivatives of the opacity caused by p modes in the photosphere. A radiative-transport code was used for this purpose to get the disturbances of the opacities from temperature and density fluctuations. The visibility and darkening functions are obtained for adiabatic oscillations under the assumption that the temperature disturbances are proportional to the undisturbed temperature of the photosphere. The latter assumption is the only way to explore any opacity effects since the eigenfunctions of p-mode oscillations have not been obtained so far. This investigation reveals that opacity effects have to be taken into account because they dominate the violet and infrared part of the spectrum. Because of this dominance, the visibility functions are negative for those parts of the spectrum. Furthermore, the darkening functions show a wavelength-dependent change of sign for some wavelengths owing to these opacity effects. However, the visibility and darkening functions under the assumptions used contradict the observations of global p-mode oscillations, but it is beyond doubt that the opacity effects influence the brightness fluctuations of the Sun resulting from global oscillations

Solar-like oscillations with low amplitude in the CoRoT target HD 181906

Context: The F8 star HD 181906 (effective temperature ~6300K) was observed for 156 days by the CoRoT satellite during the first long run in the centre direction. Analysis of the data reveals a spectrum of solar-like acoustic oscillations. However, the faintness of the target (m_v=7.65) means the signal-to-noise (S/N) in the acoustic modes is quite low, and this low S/N leads to complications in the analysis. Aims: To extract global variables of the star as well as key parameters of the p modes observed in the power spectrum of the lightcurve. Methods: The power spectrum of the lightcurve, a wavelet transform and spot fitting have been used to obtain the average rotation rate of the star and its inclination angle. Then, the autocorrelation of the power spectrum and the power spectrum of the power spectrum were used to properly determine the large separation. Finally, estimations of the mode parameters have been done by maximizing the likelihood of a global fit, where several modes were fit simultaneously. Results: We have been able to infer the mean surface rotation rate of the star (~4 microHz) with indications of the presence of surface differential rotation, the large separation of the p modes (~87 microHz), and therefore also the ridges corresponding to overtones of the acoustic modes.Comment: Paper Accepted to be published in A&A. 10 Pages, 12 figure

The quest for the solar g modes

Solar gravity modes (or g modes) -- oscillations of the solar interior for which buoyancy acts as the restoring force -- have the potential to provide unprecedented inference on the structure and dynamics of the solar core, inference that is not possible with the well observed acoustic modes (or p modes). The high amplitude of the g-mode eigenfunctions in the core and the evanesence of the modes in the convection zone make the modes particularly sensitive to the physical and dynamical conditions in the core. Owing to the existence of the convection zone, the g modes have very low amplitudes at photospheric levels, which makes the modes extremely hard to detect. In this paper, we review the current state of play regarding attempts to detect g modes. We review the theory of g modes, including theoretical estimation of the g-mode frequencies, amplitudes and damping rates. Then we go on to discuss the techniques that have been used to try to detect g modes. We review results in the literature, and finish by looking to the future, and the potential advances that can be made -- from both data and data-analysis perspectives -- to give unambiguous detections of individual g modes. The review ends by concluding that, at the time of writing, there is indeed a consensus amongst the authors that there is currently no undisputed detection of solar g modes.Comment: 71 pages, 18 figures, accepted by Astronomy and Astrophysics Revie

Global asteroseismic properties of solar-like oscillations observed by Kepler : A comparison of complementary analysis methods

We present the asteroseismic analysis of 1948 F-, G- and K-type main-sequence and subgiant stars observed by the NASA {\em Kepler Mission}. We detect and characterise solar-like oscillations in 642 of these stars. This represents the largest cohort of main-sequence and subgiant solar-like oscillators observed to date. The photometric observations are analysed using the methods developed by nine independent research teams. The results are combined to validate the determined global asteroseismic parameters and calculate the relative precision by which the parameters can be obtained. We correlate the relative number of detected solar-like oscillators with stellar parameters from the {\em Kepler Input Catalog} and find a deficiency for stars with effective temperatures in the range $5300 \lesssim T_\mathrm{eff} \lesssim 5700$\,K and a drop-off in detected oscillations in stars approaching the red edge of the classical instability strip. We compare the power-law relationships between the frequency of peak power, $\nu_\mathrm{max}$, the mean large frequency separation, $\Delta\nu$, and the maximum mode amplitude, $A_\mathrm{max}$, and show that there are significant method-dependent differences in the results obtained. This illustrates the need for multiple complementary analysis methods to be used to assess the robustness and reproducibility of results derived from global asteroseismic parameters.Comment: 14 pages, 9 figures, accepted for publication in Monthly Notices of the Royal Astronomical Societ

A uniform asteroseismic analysis of 22 solar-type stars observed by Kepler

Asteroseismology with the Kepler space telescope is providing not only an improved characterization of exoplanets and their host stars, but also a new window on stellar structure and evolution for the large sample of solar-type stars in the field. We perform a uniform analysis of 22 of the brightest asteroseismic targets with the highest signal-to-noise ratio observed for 1 month each during the first year of the mission, and we quantify the precision and relative accuracy of asteroseismic determinations of the stellar radius, mass, and age that are possible using various methods. We present the properties of each star in the sample derived from an automated analysis of the individual oscillation frequencies and other observational constraints using the Asteroseismic Modeling Portal (AMP), and we compare them to the results of model-grid-based methods that fit the global oscillation properties. We find that fitting the individual frequencies typically yields asteroseismic radii and masses to \sim1% precision, and ages to \sim2.5% precision (respectively 2, 5, and 8 times better than fitting the global oscillation properties). The absolute level of agreement between the results from different approaches is also encouraging, with model-grid-based methods yielding slightly smaller estimates of the radius and mass and slightly older values for the stellar age relative to AMP, which computes a large number of dedicated models for each star. The sample of targets for which this type of analysis is possible will grow as longer data sets are obtained during the remainder of the mission.Comment: 13 pages, 5 figures in the main text, 22 figures in Appendix. Accepted for publication in Ap

Asteroseismology from multi-month Kepler photometry: the evolved Sun-like stars KIC 10273246 and KIC 10920273

The evolved main-sequence Sun-like stars KIC 10273246 (F-type) and KIC 10920273 (G-type) were observed with the NASA Kepler satellite for approximately ten months with a duty cycle in excess of 90%. Such continuous and long observations are unprecedented for solar-type stars other than the Sun. We aimed mainly at extracting estimates of p-mode frequencies - as well as of other individual mode parameters - from the power spectra of the light curves of both stars, thus providing scope for a full seismic characterization. The light curves were corrected for instrumental effects in a manner independent of the Kepler Science Pipeline. Estimation of individual mode parameters was based both on the maximization of the likelihood of a model describing the power spectrum and on a classic prewhitening method. Finally, we employed a procedure for selecting frequency lists to be used in stellar modeling. A total of 30 and 21 modes of degree l=0,1,2 - spanning at least eight radial orders - have been identified for KIC 10273246 and KIC 10920273, respectively. Two avoided crossings (l=1 ridge) have been identified for KIC 10273246, whereas one avoided crossing plus another likely one have been identified for KIC 10920273. Good agreement is found between observed and predicted mode amplitudes for the F-type star KIC 10273246, based on a revised scaling relation. Estimates are given of the rotational periods, the parameters describing stellar granulation and the global asteroseismic parameters $\Delta\nu$ and $\nu_{\rm{max}}$.Comment: 15 pages, 15 figures, to be published in Astronomy & Astrophysic

Economic growth and biological innovation : the development of the european dairy sector, 1865-1940

In this article we discuss an aspect of economic growth that has not been the subject of much consideration in economic and agrarian history to date: the effect of biological innovations on farming development between the mid nineteenth century and the 1930s. We have focused on dairy farming for two reasons. Firstly, dairy farming played a relevant economic role in a number of European regions during this period. Secondly, one of its products, liquid milk, was probably the most significant food during the early stages of the European nutrition transition. We present new statistical data for the evolution of dairy farming in different Northern European countries as well as Spain, and evaluate the impact of cattle population and milk yields in each case. We also link milk yields and the availability of fodder, but special attention is paid to the breeds kept and techniques for their improvement. The article shows that cattle improvement played a significant role in Central and Northern Europe from the mid nineteenth century, but that this was not the case in Spain. Improvement through inbreeding was soon discarded in Spain, absorbent crossbreeding failed, and the sector became dependent on foreign imports of bulls and cows, first from Switzerland and later from Holland. By taking these factors into consideration we can better understand why the dairy sector in Mediterranean Europe did not really begin until the late nineteenth century and why it stagnated in the wake of the First World War

Geochemistry of soil gas in the seismic fault zone produced by the Wenchuan Ms 8.0 earthquake, southwestern China

The spatio-temporal variations of soil gas in the seismic fault zone produced by the 12 May 2008 Wenchuan Ms 8.0 earthquake were investigated based on the field measurements of soil gas concentrations after the main shock. Concentrations of He, H2, CO2, CH4, O2, N2, Rn, and Hg in soil gas were measured in the field at eight short profiles across the seismic rupture zone in June and December 2008 and July 2009. Soil-gas concentrations of more than 800 sampling sites were obtained. The data showed that the magnitudes of the He and H2 anomalies of three surveys declined significantly with decreasing strength of the aftershocks with time. The maximum concentrations of He and H2 (40 and 279.4 ppm, respectively) were found in three replicates at the south part of the rupture zone close to the epicenter. The spatio-temporal variations of CO2, Rn, and Hg concentrations differed obviously between the north and south parts of the fault zone. The maximum He and H2 concentrations in Jun 2008 occurred near the parts of the rupture zone where vertical displacements were larger. The anomalies of He, H2, CO2, Rn, and Hg concentrations could be related to the variation in the regional stress field and the aftershock activity

Influence of Low-Degree High-Order p-Mode Splittings on the Solar Rotation Profile

The solar rotation profile is well constrained down to about 0.25 R thanks to the study of acoustic modes. Since the radius of the inner turning point of a resonant acoustic mode is inversely proportional to the ratio of its frequency to its degree, only the low-degree p modes reach the core. The higher the order of these modes, the deeper they penetrate into the Sun and thus they carry more diagnostic information on the inner regions. Unfortunately, the estimates of frequency splittings at high frequency from Sun-as-a-star measurements have higher observational errors due to mode blending, resulting in weaker constraints on the rotation profile in the inner core. Therefore inversions for the solar internal rotation use only modes below 2.4 mHz for l < 4. In the work presented here, we used an 11.5 year-long time series to compute the rotational frequency splittings for modes l < 4 using velocities measured with the GOLF instrument. We carried out a theoretical study of the influence of the low-degree modes in the region 2 to 3.5 mHz on the inferred rotation profile as a function of their error bars.Comment: Accepted for publication in Solar Physics. 17 Pages, 9 figure