Constructing and Characterising Solar Structure Models for Computational Helioseismology

In this paper, we construct background solar models that are stable against convection, by modifying the vertical pressure gradient of Model S (Christensen-Dalsgaard et al., 1996, Science, 272, 1286) relinquishing hydrostatic equilibrium. However, the stabilisation affects the eigenmodes that we wish to remain as close to Model S as possible. In a bid to recover the Model S eigenmodes, we choose to make additional corrections to the sound speed of Model S before stabilisation. No stabilised model can be perfectly solar-like, so we present three stabilised models with slightly different eigenmodes. The models are appropriate to study the f and p1 to p4 modes with spherical harmonic degrees in the range from 400 to 900. Background model CSM has a modified pressure gradient for stabilisation and has eigenfrequencies within 2% of Model S. Model CSM_A has an additional 10% increase in sound speed in the top 1 Mm resulting in eigenfrequencies within 2% of Model S and eigenfunctions that are, in comparison with CSM, closest to those of Model S. Model CSM_B has a 3% decrease in sound speed in the top 5 Mm resulting in eigenfrequencies within 1% of Model S and eigenfunctions that are only marginally adversely affected. These models are useful to study the interaction of solar waves with embedded three-dimensional heterogeneities, such as convective flows and model sunspots. We have also calculated the response of the stabilised models to excitation by random near-surface sources, using simulations of the propagation of linear waves. We find that the simulated power spectra of wave motion are in good agreement with an observed SOHO/MDI power spectrum. Overall, our convectively stabilised background models provide a good basis for quantitative numerical local helioseismology. The models are available for download from http://www.mps.mpg.de/projects/seismo/NA4/.Comment: 35 pages, 23 figures Changed title Updated Figure 1

Bodily tides near spin-orbit resonances

Spin-orbit coupling can be described in two approaches. The method known as "the MacDonald torque" is often combined with an assumption that the quality factor Q is frequency-independent. This makes the method inconsistent, because the MacDonald theory tacitly fixes the rheology by making Q scale as the inverse tidal frequency. Spin-orbit coupling can be treated also in an approach called "the Darwin torque". While this theory is general enough to accommodate an arbitrary frequency-dependence of Q, this advantage has not yet been exploited in the literature, where Q is assumed constant or is set to scale as inverse tidal frequency, the latter assertion making the Darwin torque equivalent to a corrected version of the MacDonald torque. However neither a constant nor an inverse-frequency Q reflect the properties of realistic mantles and crusts, because the actual frequency-dependence is more complex. Hence the necessity to enrich the theory of spin-orbit interaction with the right frequency-dependence. We accomplish this programme for the Darwin-torque-based model near resonances. We derive the frequency-dependence of the tidal torque from the first principles, i.e., from the expression for the mantle's compliance in the time domain. We also explain that the tidal torque includes not only the secular part, but also an oscillating part. We demonstrate that the lmpq term of the Darwin-Kaula expansion for the tidal torque smoothly goes through zero, when the secondary traverses the lmpq resonance (e.g., the principal tidal torque smoothly goes through nil as the secondary crosses the synchronous orbit). We also offer a possible explanation for the unexpected frequency-dependence of the tidal dissipation rate in the Moon, discovered by LLR

Excitation of Jovian Seismic Waves by the Shoemaker-Levy 9 Cometary Impact

The kinetic energy released by the collision of the comet Shoemaker-Levy 9 with Jupiter is expected to be between 1020 J and 1023 J. This energy will excite seismic waves, which will propagate within Jupiter. These seismic waves are computed by summing normal modes of degree ℓ up to 1400 and frequency ν up to 10 mHz. The excitation amplitudes are obtained using a model of the blast wave induced by the explosion of the comet. Keeping in mind the possible detection of the waves with an IR camera, we examine the thermal signature of the global modes and transient waves excited by the impact. We show that the excitation of surface waves and normal modes will produce a directly observable signal for strong impacts only. An impact with an energy greater than 2.8 × 1021 J will produce a 10-mHz frequency P wave with associated peak-to-peak temperature fluctuations greater than 0.01 K at the antipode. Surface waves with frequencies less than 3 mHz will give rise to fluctuations everywhere in excess of 0.01 K for impacts greater than 9 × 1022 J. Lower energy impacts will not be directly detectable, the signal-to-noise ratio on a single pixel of the camera being too low. Stacking methods might enable the detection of P waves generated by impacts with energies as low as 7.25 × 1020 J at Δ = 90° and of surface waves generated by impacts as low as 1.4 × 1021 J. High-frequency monitoring of the temperature in the jovian troposphere daring at least 2 hr after each impact, and low-frequency monitoring during the remaining observation time may provide unique information on the inner structure of Jupiter, including the core and the discontinuity due to the possible plasma phase transition of hydrogen

Global upper-mantle structure from finite-frequency surface-wave tomography

Journal of Geophysical Research, v. 111, n. B4, p. 24 pp, 2006. http://dx.doi.org/10.1029/2005JB003677International audienceWe report global shear-wave velocity structure and radial anisotropy in the upper mantle obtained using finite-frequency surface-wave tomography, based upon complete three-dimensional Born sensitivity kernels. Because wavefront healing effects are properly taken into account, finite-frequency surface-wave tomography improves the resolution of small-scale mantle heterogeneities, especially for deep anomalies that are constrained by the longest-period surface waves. In our finite-frequency model FFSW1, the globally averaged radial anisotropy shows a transition from positive (SH > SV) to negative anisotropy (SV > SH) at about 220 km, consistent with a change in the dominant mantle circulation pattern from predominantly horizontal flow at shallow depths to vertical flow at greater depths. The radial anisotropy beneath cratons and the old Pacific plate agrees well with previous studies. However, our model exhibits a strong negative radial anisotropy at depths greater than 120 km beneath mid-ocean ridges, a feature that is not present in previous upper-mantle models. More interestingly, the depth extent of the ridge anomalies is distinctly different beneath fast- and slow-spreading centers; anomalies beneath fast-spreading centers are stronger, but the strength decreases rapidly below 250 km. In contrast, beneath slow-spreading centers such as the northern Mid-Atlantic Ridge and the Red Sea, anomalies extend down at least to the top of the transition zone. The different depth extent of the ridge anomalies suggests that the primary driving force of slow-spreading seafloor may be different from that of fast-spreading seafloor and that active upwelling beneath slow-spreading ridges may play a major role in the opening of the seafloor

Tomographic inversion with wavelets and L1-norm penalization

info:eu-repo/semantics/nonPublishe