Low-degree solar oscillation spectrum with wavelet decomposition

We present the technique and results of processing the observations of the solar oscillations with frequencies of 1.5–4.0 mHz. We used the time series obtained in the period 1990–1996 in the International IRIS project. The power spectrum averaged over the entire observing period was estimated from the spectra of each year preaveraged with five orthogonal tapers. The spectral profiles of the individual modes with degree l = 0 and orders n ? 12–26 were fitted using a wavelet decomposition with thresholding of the high-frequency decomposition levels. The smoothed power spectrum estimate has a considerably smaller variance, but also a lower density of reference points. The derived smoothed profiles were used to determine the eigenfrequencies by two methods: from the local peak and from the correlation between the neighboring peaks, which correspond to a nonparametric estimation procedure. For the radial modes (l = 0), there is good agreement with the independent parametric maximum likelihood frequency estimates.     

Variability of Solar Five-Minute Oscillations in the Corona as Observed by the Extreme Ultraviolet Spectrophotometer (ESP) on the Solar Dynamics Observatory/Extreme Ultraviolet Variability Experiment (SDO/EVE)

Solar five-minute oscillations have been detected in the power spectra of two six-day time intervals from soft X-ray measurements of the Sun observed as a star using the Extreme Ultraviolet Spectrophotometer (ESP) onboard the Solar Dynamics Observatory (SDO)/Extreme Ultraviolet Variability Experiment (EVE). The frequencies of the largest amplitude peaks were found to match the known low-degree (?=0?–?3) modes of global acoustic oscillations within 3.7 μHz and can be explained by a leakage of the global modes into the corona. Due to the strong variability of the solar atmosphere between the photosphere and the corona, the frequencies and amplitudes of the coronal oscillations are likely to vary with time. We investigated the variations in the power spectra for individual days and their association with changes of solar activity, e.g. with the mean level of the EUV irradiance, and its short-term variations caused by evolving active regions. Our analysis of samples of one-day oscillation power spectra for a 49-day period of low and intermediate solar activity showed little correlation with the mean EUV irradiance and the short-term variability of the irradiance. We suggest that some other changes in the solar atmosphere, e.g., magnetic fields and/or inter-network configuration may affect the mode leakage to the corona.     

The free oscillations of Jupiter

The spectrum of free oscillations of Jupiter is calculated for a set of models, each of them fitting all available observational data. Diagnostic capabilities of the spectrum are studied. They could be used, as soon as relevant observations are performed, for both the identification of the observed modes and the improvement of the models themselves. The calculations were made for five-layer models. They differ in the core mass (2–10 M_⊕) and in the molecular-metallic phase transition pressure of hydrogen (1.5–3 Mbar). The spectrum of Jupiter consists of gravitational modes related to density jumps in the planetary interiors and of acoustic modes. The periods of the acoustic modes are calculated for degree up to l=30 and overtone number up to n=20. The investigated models have a characteristic frequency of ≈152–155 μHz. Two outer gravitational modes related to density jumps in the molecular envelope and at the interface with the metallic envelope have nonzero displacements at the planetary surface. These modes have good diagnostic properties. The values of the kinetic energy averaged over the period of oscillation are calculated for a 1-m amplitude of the displacement at the planetary surface. The influence of all effects of rotation on the spectrum is discussed.     

Low-l 5-min oscillation observations

Medium resolution CCD-spectrograph observations have been obtained that are suitable for studying long spatial wavelength 5-min oscillations. We find evidence that at wavelengths of order one solar radius the oscillation field is not isotropic. It is also not well described by modes of uniform excitation. The velocity power density per spherical harmonic increases with decreasing l to 1.1 × 10³ cm² s^–2 per 3.5 × 10^–4 Hz angular frequency bandwidth at l = 4. These results are inconsistent with the data of Fossat and Ricort (1975) as analyzed by Christensen-Dalsgaard and Gough (1982), who found a substantially constant modal amplitude at intermediate l values. It is interesting that other calculations have seen a similar dependence at small l in the growth rate of p-modes due to the -mechanism.Visiting Astronomer, Sacramento Peak Observatory.     

The plasma radiation of flare kernels

We survey the mathematics of non-linear Hamiltonian oscillations with emphasis being laid on the more recently discovered Kolmogorov instability. In the context of radial adiabatic oscillations of stars this formalism predicts a Kolmogorov instability even at low oscillation energies, provided that sufficiently high linear asymptotic modes have been excited. Numerical analysis confirms the occurrence of this instability. It is found to show up already among the lowest order modes, although high surface amplitudes are then required (¦δr¦/R ～ 0.5 for an unstable fundamental mode - first harmonic coupling). On the basis of numerical evidence we conjecture that in the Kolmogorov unstable regime the enhanced coupling due to internal resonance effects leads to an equipartition of energy over all interacting degrees of freedom. We also indicate that the power spectrum of such oscillations is expected to display two components: A very broad band of overlapping pseudo-linear frequency peaks spread out over the asymptotic range, and a strictly non-linear l/f-noise type component close to the frequency origin. It is finally argued that the Kolmogorov instability is likely to occur among non-linearly coupled non-radial stellar modes at a surface amplitude much lower than in the radial case. This lends support to the view that this instability might be operative among the solar oscillations.     

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.     

Detection of solar five-minute oscillations of low degree

Solar five-minute oscillations of degree l = 3, 4, and 5 have been observed at Stanford, in the Doppler shift of the Fe 5124 line. The frequencies and amplitudes are in broad agreement with previous observations of modes with l ≤ 3, though we note that there are some systematic discrepancies between the results of different observers.     

Signatures of the Baryon acoustic oscillations on the convergence power spectrum of weak lensing by large scale structure

We employ an analytical approach to investigate the signatures of Baryon acoustic oscillations (BAOs) on the convergence power spectrum of weak lensing by large scale structure. It is shown that the BAOs wiggles can be found in both of the linear and nonlinear convergence power spectra of weak lensing at about 40 ? l ? 600, but they are weaker than that of matter power spectrum. Although the statistical error for LSST are greatly smaller than that of CFHT and SNAP survey especially at about 30 < l < 300, they are still larger than their maximum variations of BAOs wiggles. Thus, the detection of BAOs with the ongoing and upcoming surveys such as LSST, CFHT and SNAP survey confront a technical challenge.     

Helioseismology program for the PICARD satellite

The PICARD mission is a CNES micro‐satellite to be launched in 2009. Its goal is to better understand the Sun and the potential impact of its activity on earth climate by measuring simultaneously the solar total and spectral irradiance, diameter, shape and oscillations. We present the scientific objectives, instrumental requirements and data products of the helioseismology program of PICARD which aims to observe the low to medium l p‐mode oscillations in intensity and search for g‐mode oscillation signatures at the limb. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Are There Pulsationally Unstable Low-degree p1 Modes in the Sun?

By using a non-local time-dependent theory of stellar convection, the solar non-adiabatic pulsations of the low- and intermediate-degree (l < 25) modes are calculated. The results show that the non-radial p1 modes of l = 1–5 are pulsationally unstable. However, the adjacent g, f, p2-p5 modes and the p1 modes of l > 5 are stable. From the analysis of the diagram of integrated work it is discovered that the excitation of oscillations comes from the radiation zone beneath the convective region. Whether the sun possesses unstable low-degree p1 modes is of signi?cant importance for clarifying the excitation mechanism of solar ?ve-minute oscillations.     

On the excitation of free oscillations on the Moon

Since the Moon’s outer shells are very inhomogeneous, a global, spherically symmetric model of its interior structure is difficult to construct by using only seismic body-wave data. We study the diagnostic capabilities of the free-oscillation method. The sources of the largest moonquakes are located in the outer 200-km thick layer. Their seismic moments reach 10²² dyn. cm. Current seismometers are capable of detecting ground accelerations of ～10^?8 cm s^?2. Taking M ₀≈10²² dyn. cm, we show that torsional modes _n T _l with l≥7 and n=0 (l is the degree of oscillation, and n is the overtone number) can be detected. These modes contain information about the outer layers to a depth of ≈500 km and can allow a global model to be constructed for the outer, most inhomogeneous layers of the satellite. The largest moonquakes excite spheroidal modes _n S _l much worse, and it is unlikely that they can be detected with current instruments. We provide detailed information on the excitation of free oscillations for various moonquake focal mechanisms and focal depths.     

Rotational enhancement of Doppler measurements of solar and stellar hexadecapole oscillations

Rotational enhancement of the sensitivity of whole-disk Doppler observations of solar oscillations may permit the measurement of five-minute modes with l = 4. We estimate from superposed power spectra of artificial solar data that there might be identifiable power lying above the noise in the data acquired by Pallé et al. (1986), which could provide confirmation of the rotational splitting measured by Duvall and Harvey (1984).     

Variations of the low‐degree solar p‐mode frequencies for 10 years of GOLF observations

We experiment with a method of measuring the frequency of solar p modes, intended to extend the passband for the variations of the frequency spectrum as high as possible. So far this passband is limited to a fraction of μ Hz for the classical analysis based on numerical fits of a theoretical line profile to a power spectrum averaged over periods lasting at least several weeks. This limit for the present analysis can be shifted to the mHz range, corresponding to some of the “5 min” oscillations, but in this range we use a lower resolution which allows us to separate odd and even p modes. We show an example of the results for long term variations and apply this analysis to search for a modulation of the p‐mode frequency spectrum by asymptotic series of solar g modes. A faint signal is found in the analysis of 10 years of GOLF data. This very preliminary result possibly indicates the detection of a small number of g modes of degree l = 1. A tentative determination of an observational value of the parameter P₀ follows. P₀ is the scaling factor of the asymptotic series of g modes and is a key data for solar core physics. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Total Irradiance Monitor (TIM): Instrument Design

The Total Irradiance Monitor (TIM) instrument is designed to measure total solar irradiance with an absolute accuracy of 100 parts per million. Four electrical substitution radiometers behind precision apertures measure input radiant power while providing redundancy. Duty cycling the use of the radiometers tracks degradation of the nickel-phosphorous absorptive black radiometer interiors caused by solar exposure. Phase sensitive detection at the shutter frequency reduces noise and simplifies the estimate of the radiometer's equivalence ratio. An as-designed uncertainty budget estimates the instrument's accuracy goal. The TIM measurement equation defines the conversion from measured signal to solar irradiance.     

Deep versus shallow origin of gravity anomalies, topography and volcanism on Earth, Venus and Mars

The relation between gravity anomalies, topography and volcanism can yield important insights about the internal dynamics of planets. From the power spectra of gravity and topography on Earth, Venus and Mars we infer that gravity anomalies have likely predominantly sources below the lithosphere up to about spherical harmonic degree l=30 for Earth, 40 for Venus and 5 for Mars. To interpret the low-degree part of the gravity spectrum in terms of possible sublithospheric density anomalies we derive radial mantle viscosity profiles consistent with mineral physics. For these viscosity profiles we then compute gravity and topography kernels, which indicate how much gravity anomaly and how much topography is caused by a density anomaly at a given depth. With these kernels, we firstly compute an expected gravity-topography ratio. Good agreement with the observed ratio indicates that for Venus, in contrast to Earth and Mars, long-wavelength topography is largely dynamically supported from the sublithospheric mantle. Secondly, we combine an empirical power spectrum of density anomalies inferred from seismic tomography in Earth’s mantle with gravity kernels to model the gravity power spectrum. We find a good match between modeled and observed gravity power spectrum for all three planets, except for 2?l?4 on Venus. Density anomalies in the Venusian mantle for these low degrees thus appear to be very small. We combine gravity kernels and the gravity field to derive radially averaged density anomaly models for the Martian and Venusian mantles. Gravity kernels for l?5 are very small on Venus below ≈800 km depth. Thus our inferences on Venusian mantle density are basically restricted to the upper 800 km. On Mars, gravity anomalies for 2?l?5 may originate from density anomalies anywhere within its mantle. For Mars as for Earth, inferred density anomalies are dominated by l=2 structure, but we cannot infer whether there are features in the lowermost mantle of Mars that correspond to Earth’s Large Low Shear Velocity Provinces (LLSVPs). We find that volcanism on Mars tends to occur primarily in regions above inferred low mantle density, but our model cannot distinguish whether or not there is a Martian analog for the finding that Earth’s Large Igneous Provinces mainly originate above the margins of LLSVPs.     

ηBoo Inversion of simulated rotational profile

The detection of solar oscillations on ηBoo is now established. We explore here what we can expect from the inversion of similar data by COROT to recover the rotational profile of the star. We show that the observation of a few low-l mixed modes in the excited high frequency range gives access to the rotational gradient if it is large enough.     

Frequencies of low-degree solar acoustic oscillations and the phase of the solar cycle

A study of the solar total irradiance data of the Active Cavity Radiometer Irradiance Monitor (ACRIM) on the Solar Maximum Mission (SMM) satellite shows a small but formally significant shift in the frequencies of solar acoustic (p-mode) oscillations between the epochs of maximum and minimum solar activity. Specifically, the mean frequency of the strongest p-mode resonances of low spherical-harmonic degree (l = 0–2) is approximately 1.3 parts in 10⁴ higher in 1980, near the time of sunspot maximum, than in 1985, near sunspot minimum. The observed frequency shift may be an 11-yr effect but the precise mechanism is not clear.     

Internal rotation of the Sun as inferred from GONG observations

Helioseismology is a direct and most informative method of studying the structure and dynamics of the Sun. Determining the internal differential rotation of the Sun requires that the frequencies of its eigentones be estimated with a high accuracy, which is possible only on the basis of continuous long-term observations. The longest quasi-continuous series of data have been obtained by the Global Oscillation Network Group (GONG). The parameters of each individual mode of solar acoustic oscillations with low spherical degrees l=0, 1, 2, 3, 4, 5, 6 are determined by using 1260-day-long series of GONG observations. The mean frequency splitting by rotation for the modes of each radial order n is calculated by using all possible combinations between the eigenfrequencies in multiplets. As a result, it has become possible to statistically estimate the splitting and its measurement errors for the modes of each radial order. The mean splitting for each given degree l=1–6 is presented under the assumption of its independence of oscillation frequency, which holds for the achieved accuracy. The frequencies and splittings for the modes with low spherical degrees l, together with the MDI group results for higher degrees l, are used to invert the radial profile of solar angular velocity. Using the SOLA method to solve the inverse problem of restoring the rotation profile has yielded solutions sensitive to the deepest stellar interiors. Our results indicate that the solar core rotates faster than the surface, and there may be a local minimum in angular velocity at its boundary.     

Variation of the low-degree solar acoustic mode parameters over the solar cycle

VIRGO/SPM is a helioseismic sunphotometer on board SOHO that observes the disk-integrated sunlight irradiance at three different colors (red, green, and blue). The data obtained for SPM since the beginning of the SOHO mission, April 1996, to March 2001 have been used to study the differences of the p-mode parameters during the solar activity cycle. These time series have been divided in sub-series of 100 days, transformed to power spectra and averaged in sets of three to yield a total number of six averaged power spectra (around one per year). A new way of analyzing the power spectrum has been applied to the six power spectra of each color; it consists of fitting the whole p-mode spectrum at once with a unique background. The results for the frequencies, line widths, power, mode energy, energy rate fed in the mode and splittings along the activity cycle are found, compared and discussed.