Charles L. Wolff

A spectrum of the four-decade solar irradiance record has a prominent cluster of power for periodicities near 1 yr. Correlating irradiance with a bandpass filter showed that periodicity values were not constant, but varied sinusoidally with each cycle lasting 14 ± 1 yr. The large modulation amplitude makes solar frequencies ≥1 yr⁻¹ hard to detect at the solar surface. After removing the modulation, a Lomb–Scargle spectrum exposed two true periodicities: 1.006 and 0.920 yr. They are interpreted as the synodic rotation periods of r modes of lowest angular degree (ℓ = 1). The first propagates in the stable interior and the second in the convective envelope perturbed by its several flow fields. The rotational beat period of the two modes is about 10.9 yr. This is close to the average length of a solar cycle and possibly controls this average. The 1.006 yr periodicity dominates most of the filtered irradiance record but an abrupt change to about 0.8 yr occurs in mid-2010. Also found was evidence for higher-degree r modes (ℓ = 2 to 8) and a curious sawtooth modulation with a recurrence period of 2.6 yr.

In several papers, the solar cycle (SC) effect in the lower atmosphere has been linked observationally to the Quasi-biennial Oscillation (QBO) of the zonal circulation. Salby and Callaghan (2000) in particular analyzed the QBO wind measurements, covering more than 40 years, and discovered that they contain a large SC signature at 20 km. We present here the results from a study with our 3-D Numerical Spectral Model (NSM), which relies primarily on parameterized gravity waves (GW) to describe the QBO. In our model, the period of the SC is taken to be 10 years, and the relative amplitude of radiative forcing varies exponentially with height, i.e., 0.2% at the surface, 2% at 50 km, and 20% at 100 km and above. Applying spectral analysis to identify the SC signature, the model generates a relatively large modulation of the QBO, which reproduces the observations qualitatively. The numerical results demonstrate that the QBO modulation, closely tracking the phase of the SC, is robust and persists at least for 70 years. The question is what causes the SC effect, and our analysis shows that four interlocking processes are involved: (1) In the mesosphere at around 60 km, the solar UV variations generate in the zonal winds a SC modulation of the 12-month annual oscillation, which is hemispherically symmetric and confined to equatorial latitudes like the QBO. (2) Although the amplitude of this equatorial annual oscillation (EAO) is relatively small, its SC modulation is large and extends into the lower stratosphere under the influence of, and amplified by, wave forcing. (3) The amplitude modulations of both EAO and QBO are essentially in phase with the imposed SC heating for the entire time span of the model simulation. This indicates that, due to positive feedback in the wave mechanism, the EAO apparently provides the pathway and pacemaker for the SC modulation of the QBO. (4) Our analysis demonstrates that the SC modulations of the QBO and EAO are amplified by tapping the momentum from the upward propagating gravity waves. Influenced and amplified by wave processes, the QBO thus acts as conduit to transfer to lower altitudes the larger SC variations in the UV absorbed in the mesosphere. Our model produces in the temperature variations of the QBO and EAO measurable SC modulations at polar latitudes near the tropopause. The effects are apparently generated by the meridional circulation, and planetary waves presumably, which redistribute the energy from the equatorial region where the waves are very effective in amplifying the SC influence.

Groupsof linear g-modescansumtocreatenonlinear motioninsmall''hotvolumes''(diameter � 10Mm)nearthe solarcenterthathelpdrivethemodes.Weexploretheconsequencesof couplingonlyinthehotvolumeswherethetime- averagedrateof 3Heburningcandoubleiftemperatureoscillationsexceed10%.Anticipatinglargelocal motionsinthe core, we impose a mixed shell r ¼ (0:10 � 0:03) Ron an otherwise standard solar model before computing g-mode solutions. Mixing is rapid (T106 yr) in this shell, with slower mixing somewhat beyond. Ifl is the principal spherical harmonic index, a set of g-modes for any singlel � 5 with six consecutive radial harmonics can be excited with nearly linear thermal amplitudesAT � 0:05 throughout the star. But far smaller thresholds for excitationare actually expected when sets for many values of l can be computed simultaneously. This is a new kind of stellar instability whose effectivenessriseswiththenumberof activemodes.Eachsetrotatesrigidlyandmaximizesthereleaseof nuclearenergy from its hot volumes. There is some evidence for their rotation rates in the long solar activity record. The upward wave fluxpoweredbythehotvolumeshasalsobeensuggestedtoexplainthe1.3yrreversingflowstentativelydetectedbelow the Sun's convective envelope. An analog using uncoupled modes is also investigated based on an observation that indicates g-mode activity up to l � 20. If all modes in that range had linear amplitudes of only AT � 0:0015, their combined effect would give positive growth rates to dozens of low harmonic g-modes. Subject headinggs: stars: oscillations — Sun: interior — Sun: oscillations

The solar cycle (SC) effect in the lower atmosphere has been linked observationally to the quasi‐biennial oscillation (QBO) of the zonal circulation. Salby and Callaghan (2000) in particular analyzed the QBO covering more than 40 years and found that it contains a large SC signature at 20 km. We discuss a 3D study in which we simulate the QBO under the influence of the SC. For a SC period of 10 years, the relative amplitude of radiative forcing is taken to vary with height: 0.2% (surface), 2% (50 km), 20% (100 km and above). This model produces in the lower stratosphere a relatively large modulation of the QBO, which appears to come from the SC and qualitatively agrees with the observations. The modulation of the QBO, with constant phase relative to the SC, is shown to persist at least for 50 years, and it is induced by a SC modulated annual oscillation that is hemispherically symmetric and confined to low latitudes (Mayr et al., 2005).