An Introduction to Data Analysis in Asteroseismology

A practical guide is presented to some of the main data analysis concepts and techniques employed contemporarily in the asteroseismic study of stars exhibiting solar-like oscillations. The subjects of digital signal processing and spectral analysis are introduced first. These concern the acquisition of continuous physical signals to be subsequently digitally analyzed. A number of specific concepts and techniques relevant to asteroseismology are then presented as we follow the typical workflow of the data analysis process, namely, the extraction of global asteroseismic parameters and individual mode parameters (also known as peak-bagging) from the oscillation spectrum.Comment: 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

Impact of magnetic activity on inferred stellar properties of main-sequence Sun-like stars

The oscillation frequencies observed in Sun-like stars are susceptible to being shifted by magnetic activity effects. The measured shifts depend on a complex relationship involving the mode type, the field strength, and spatial distribution of activity, as well as the inclination angle of the star. Evidence of these shifts is also present in frequency separation ratios that are often used when inferring global properties of stars in order to avoid surface effects. However, one assumption when using frequency ratios for this purpose is that there are no near-surface perturbations that are non-spherically symmetric. In this work, we studied the impact on inferred stellar properties when using frequency ratios that are influenced by non-homogeneous activity distributions. We generate several sets of artificial oscillation frequencies with various amounts of shift and determine stellar properties using two separate pipelines. We find that for asteroseismic observations of Sun-like targets we can expect magnetic activity to affect mode frequencies that will bias the results from stellar modelling analysis. Although for most stellar properties this offset should be small, typically less than 0.5 per cent in mass, estimates of age and central hydrogen content can have an error of up to 5 per cent and 3 per cent, respectively. We expect a larger frequency shift and therefore larger bias for more active stars. We also warn that for stars with very high or low inclination angles, the response of modes to activity is more easily observable in the separation ratios and hence will incur a larger bias

Neutrino fluxes from CNO cycle in the Sun in the non stationary case with mixing

The computational analyses is presented of the non stationary case with mixing of the solar model when the neutrino flux $F_{13}$ from the decay of $^{13}N$ is higher than a standard solar model predictsComment: 6 pages, 3figure

Central pain mechanisms predict physical inactivity at 1-year in individuals with knee pain

Purpose: Pain is the primary clinical manifestation in individuals with osteoarthritis (OA). It is an unpleasant and distressing experience, particularly during weight-bearing activities, inhibiting activity, and reducing quality of life. Two groups of mechanisms cause OA pain: peripheral (local joint pain from joint pathology) and central (severely worsened pain due to brain and spinal cord processing of peripheral nociceptive inputs). Each contributes to varying extents at different times to an individual’s OA pain. Pain and physical inactivity are often treated by discrete interventions, but in reality are tightly integrated. Several traits linked to central pain processing, such as catastrophising, depression and fatigue, have been independently linked to physical inactivity. This study aimed to explore cross sectional and longitudinal associations between central pain mechanisms and physical inactivity in individuals with knee pain.Methods: This study is an analysis of the first 5,000 participants with validated questionnaire data, aged ≥40 who completed FRAIL in the Investigating Musculoskeletal Health and Wellbeing (IMH&W) cohort (n= >8,570), based in the East Midlands region of the UK. Participants completed a questionnaire at baseline and 1-year later, including participant characteristics and 0 to 10 numerical rating scale (NRS) of pain in the most troublesome joint in the past 4-weeks. Central pain Mechanisms Trait (CMT) was measured using the Central Aspects of Pain in the Knee (CAP-Knee) questionnaire, comprising 8-items addressing anxiety, depression, catastrophising, neuropathic-like pain, fatigue, sleep disturbance, pain distribution and cognitive impact, giving a maximum total score of 16. Self-reported physical activity was measured using the FiND questionnaire item, through which participants report their level of physical activity as either regular (at least 2-4 hours a week) or none/mainly sedentary. Associations were explored using logistic regression models. Data are presented as median (interquartile range), odds ratios (OR), and 95% confidence intervals.Results: 2473 participants completed the FRAIL, of whom 722 participants reported knee as their most troublesome joint and an NRS pain ≥1, of whom 407 participants had self-reported physical activity data also at 1-year. The 722 participants had a median (IQR) age 72 (65-77), with a BMI of 28.08 (24.82-31.64), 55% were female, and 70% reported being regularly physically active at baseline. Median (IQR) CAP-Knee was 8 (5-11) and NRS pain was 6 (4-8). Individuals who did not complete follow-up data had significantly higher baseline NRS pain, CAP-Knee, lower BMI, and were more sedentary. For each unit increase in NRS pain or CAP-Knee at baseline, participants were more likely to be sedentary at baseline (NRS OR=1.25 (95%CI 1.16, 1.36), P<0.001; CAP-Knee OR=1.20 (95%CI 1.14, 1.26), P<0.001) and follow-up (NRS OR=1.17 (95%CI 1.05, 1.30), P=0.004; CAP-Knee OR=1.15 (95%CI 1.08, 0.93), P<0.001). When adjusted for potential confounders age, sex, BMI, knee replacement the association between baseline CAP-Knee and baseline physical activity remained significant (aOR=1.19 (95%CI 1.13, 1.25) P<0.001, Table 1), and significantly predicted 1-year physical inactivity (aOR=1.13, (95%CI 1.06, 1.21) P<0.001, Table 2). The depression item was the only CAP-Knee item significantly associated with physical activity levels in both cross-sectional and longitudinal analyses. Baseline fatigue was significantly associated with baseline physical activity.Conclusions: Higher scores for baseline central pain mechanisms were associated with lower baseline physical activity and predicted 1-year physical inactivity. Our data highlight the integration between pain and physical activity. The observed associations between central pain mechanisms and physical activity might indicate shared neurological mechanisms, and central pain mechanisms might also act as barriers to increasing activity. Specific central mechanisms, particularly depression and fatigue, might be important targets to help improve physical activity in people with knee pain

Further Evidence Suggestive of a Solar Influence on Nuclear Decay Rates

Recent analyses of nuclear decay data show evidence of variations suggestive of a solar influence. Analyses of datasets acquired at the Brookhaven National Laboratory (BNL) and at the Physikalisch-Technische Bundesanstalt (PTB) both show evidence of an annual periodicity and of periodicities with sidereal frequencies in the neighborhood of 12.25 year^{-1} (at a significance level that we have estimated to be 10^{-17}). It is notable that this implied rotation rate is lower than that attributed to the solar radiative zone, suggestive of a slowly rotating solar core. This leads us to hypothesize that there may be an "inner tachocline" separating the core from the radiative zone, analogous to the "outer tachocline" that separates the radiative zone from the convection zone. The Rieger periodicity (which has a period of about 154 days, corresponding to a frequency of 2.37 year^{-1}) may be attributed to an r-mode oscillation with spherical-harmonic indices l=3, m=1, located in the outer tachocline. This suggests that we may test the hypothesis of a solar influence on nuclear decay rates by searching BNL and PTB data for evidence of a "Rieger-like" r-mode oscillation, with l=3, m=1, in the inner tachocline. The appropriate search band for such an oscillation is estimated to be 2.00-2.28 year^{-1}. We find, in both datasets, strong evidence of a periodicity at 2.11 year^{-1}. We estimate that the probability of obtaining these results by chance is 10^{-12}.Comment: 12 pages, 6 figures, v2 has a color corrected Fig 6, a corrected reference, and a corrected typ

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

Sensitivity of the g-mode frequencies to pulsation codes and their parameters

From the recent work of the Evolution and Seismic Tools Activity (ESTA, Lebreton et al. 2006; Monteiro et al. 2008), whose Task 2 is devoted to compare pulsational frequencies computed using most of the pulsational codes available in the asteroseismic community, the dependence of the theoretical frequencies with non-physical choices is now quite well fixed. To ensure that the accuracy of the computed frequencies is of the same order of magnitude or better than the observational errors, some requirements in the equilibrium models and the numerical resolutions of the pulsational equations must be followed. In particular, we have verified the numerical accuracy obtained with the Saclay seismic model, which is used to study the solar g-mode region (60 to 140$\mu$Hz). We have compared the results coming from the Aarhus adiabatic pulsation code (ADIPLS), with the frequencies computed with the Granada Code (GraCo) taking into account several possible choices. We have concluded that the present equilibrium models and the use of the Richardson extrapolation ensure an accuracy of the order of $0.01 \mu Hz$ in the determination of the frequencies, which is quite enough for our purposes.Comment: 10 pages, 5 figures, accepted in Solar Physic

Asteroseismology of Eclipsing Binary Stars in the Kepler Era

Eclipsing binary stars have long served as benchmark systems to measure fundamental stellar properties. In the past few decades, asteroseismology - the study of stellar pulsations - has emerged as a new powerful tool to study the structure and evolution of stars across the HR diagram. Pulsating stars in eclipsing binary systems are particularly valuable since fundamental properties (such as radii and masses) can determined using two independent techniques. Furthermore, independently measured properties from binary orbits can be used to improve asteroseismic modeling for pulsating stars in which mode identifications are not straightforward. This contribution provides a review of asteroseismic detections in eclipsing binary stars, with a focus on space-based missions such as CoRoT and Kepler, and empirical tests of asteroseismic scaling relations for stochastic ("solar-like") oscillations.Comment: 28 pages, 12 figures, 2 tables; Proceedings of the AAS topical conference "Giants of Eclipse" (AASTCS-3), July 28 - August 2 2013, Monterey, C