A practical step-by-step guide to wavelet analysis is given, with examples taken from time series of the El Nino–Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finite-length time series, and the relationship between wavelet scale and Fourier frequency. New statistical significance tests for wavelet power spectra are developed by deriving theoretical wavelet spectra for white and red noise processes and using these to establish significance levels and confidence intervals. It is shown that smoothing in time or scale can be used to increase the confidence of the wavelet spectrum. Empirical formulas are given for the effect of smoothing on significance levels and confidence intervals. Extensions to wavelet analysis such as filtering, the power Hovmoller, cross-wavelet spectra, and coherence are described. The statistical significance tests are used to give a quantitative measure of change...

https://atoc.colorado.edu/research/wavelets/bams_79_01_0061.pdf

A Practical Guide to Wavelet Analysis.

Changes in Atmospheric Constituents and in Radiative Forcing

The presence of a Jupiter-mass companion to the star 51 Pegasi is inferred from observations of periodic variations in the star's radial velocity. The companion lies only about eight million kilometres from the star, which would be well inside the orbit of Mercury in our Solar System. This object might be a gas-giant planet that has migrated to this location through orbital evolution, or from the radiative stripping of a brown dwarf.

A Jupiter-Mass Companion to a Solar-Type Star

This chapter should be cited as: Myhre, G., D. Shindell, F.-M. Bréon, W. Collins, J. Fuglestvedt, J. Huang, D. Koch, J.-F. Lamarque, D. Lee, B. Mendoza, T. Nakajima, A. Robock, G. Stephens, T. Takemura and H. Zhang, 2013: Anthropogenic and Natural Radiative Forcing. In: Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change [Stocker, T.F., D. Qin, G.-K. Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex and P.M. Midgley (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA. Coordinating Lead Authors: Gunnar Myhre (Norway), Drew Shindell (USA)

Anthropogenic and Natural Radiative Forcing

We substantially update the capabilities of the open source software package Modules for Experiments in Stellar Astrophysics (MESA), and its one-dimensional stellar evolution module, MESA star. Improvements in MESA star's ability to model the evolution of giant planets now extends its applicability down to masses as low as one-tenth that of Jupiter. The dramatic improvement in asteroseismology enabled by the space-based Kepler and CoRoT missions motivates our full coupling of the ADIPLS adiabatic pulsation code with MESA star. This also motivates a numerical recasting of the Ledoux criterion that is more easily implemented when many nuclei are present at non-negligible abundances. This impacts the way in which MESA star calculates semi-convective and thermohaline mixing. We exhibit the evolution of 3-8 M ? stars through the end of core He burning, the onset of He thermal pulses, and arrival on the white dwarf cooling sequence. We implement diffusion of angular momentum and chemical abundances that enable calculations of rotating-star models, which we compare thoroughly with earlier work. We introduce a new treatment of radiation-dominated envelopes that allows the uninterrupted evolution of massive stars to core collapse. This enables the generation of new sets of supernovae, long gamma-ray burst, and pair-instability progenitor models. We substantially modify the way in which MESA star solves the fully coupled stellar structure and composition equations, and we show how this has improved the scaling of MESA's calculational speed on multi-core processors. Updates to the modules for equation of state, opacity, nuclear reaction rates, and atmospheric boundary conditions are also provided. We describe the MESA Software Development Kit that packages all the required components needed to form a unified, maintained, and well-validated build environment for MESA. We also highlight a few tools developed by the community for rapid visualization of MESA star results.

/pdf/modules-for-experiments-in-stellar-astrophysics-mesa-planets-29j324a9bq.pdf

Modules for Experiments in Stellar Astrophysics (MESA): Planets, Oscillations, Rotation, and Massive Stars

We analyze concurrent observations of Ca II H and K chromospheric emission fluxes (which are associated with the disk-averaged surface magnetic fluxes) and variability in the b and y bands of the Stromgren uvby photometric system (which are associated with the integrated total irradiance or brightness variation) in a group of stars, including the Sun. Those solar-type stars have a narrow range of mass and age, and similar observed activity variability. Their combined variability over several years reveals a range for the ratio of brightness change to chromospheric activity amplitude. We assume that the scatter in the ratios of brightness change to chromospheric activity change measured over a decade represents a distribution of variability that is intrinsic to the activity of a typical solar-type star (i.e., the Sun) over centuries. Under that assumption, we infer an empirical bound of possible solar brightness variations over centuries (Zhang et al., 1994). The estimated increase in solar brightness accompanying the net increase in average activity from the Maunder Minimum interval (ca. A.D. 1660–1710) to the decade of the 1980’s ranges from as low as 0.2 % to as high as 0.7 %; the indeterminacy of the brightness-chromospheric activity change ratio produces the large range of estimates. In addition, we estimate the timing of possible solar brightness change over the past three centuries. We also discuss the observed relation between the activity cycle amplitude and the activity cycle length, P cyc , for the Sun and solar-type stars. The activity cycle amplitude is inversely related to the parameterized quantity, (P cyc /P rot )2, where P rot is the rotation period.

A technique for estimating long-term variations of solar total irradiance: Preliminary estimates based on observations of the Sun and solar-type stars

: The authors have successfully combined photometric observations of about 30 sun-like stars from Mount Wilson, Lowell, and Fairborn Observatories to extend their joint time series from 12 to 17 years. The stability of the statistical relationships between chromospheric and brightness variability, derived previously, suggests that the full range of variation on the decadal time-scale has probably now been observed for most of their program stars. Young, active stars become fainter as their chromospheric Ca II HK emission increases, while older, less active stars, such as the Sun, become brighter as their HK emission increases. The Sun's photometric variation still appears to be somewhat small in amplitude at present, compared to other stars in this sample with similar mean chromospheric activity.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/87B842D8EC78553539AFF44512FA8895/S0074180900182221a.pdf/div-class-title-the-variability-of-sunlike-stars-on-decadal-timescales-div.pdf

The Variability of Sunlike Stars on Decadal Timescales

Modeling climatic effects of anthropogenic CO 2 emissions: Unknowns and uncertainties

/pdf/variability-in-a-large-sample-of-sun-like-stars-1vap5ndp0x.pdf

Sallie L. Baliunas

Papers

A technique for estimating long-term variations of solar total irradiance: Preliminary estimates based on observations of the Sun and solar-type stars

The Variability of Sunlike Stars on Decadal Timescales

Modeling climatic effects of anthropogenic CO 2 emissions: Unknowns and uncertainties

Variability in a Large Sample of Sun-Like Stars

Automated Precision Differential Photometry