Luca Bertello

Looking for Gravity-Mode Multiplets with the GOLF Experiment aboard SOHO

This paper is focused on the search for low-amplitude solar gravity modes between 150 and 400 � Hz, corresponding to low-degree, low-order modes. It presents results based on an original strategy that looks for multiplets instead of single peaks, taking into consideration our knowledge of the solar interior from acoustic modes. Five years of quasi-continuous measurements collected with the helioseismic GOLF experiment aboard the SOHO spacecraft are analyzed. We use different power spectrum estimators and calculate confidence levels for the most significant peaks. This approach allows us to look for signals with velocities down to 2 mm s � 1 ,n ot far from the limit of existing instruments aboard SOHO, amplitudes that have never been investigated up to now. We apply the method to series of 1290 days, beginning in 1996 April, near the solar cycle minimum. An automatic detection algorithm lists those peaks and multiplets that have a probability of more than 90% of not being pure noise. The detected patterns are then followed in time, considering also series of 1768 and 2034 days, partly covering the solar cycle maximum. In the analyzed frequency range, the probability of detection of the multiplets does not increase with time as for very long lifetime modes. This is partly due to the observational conditions after 1998 October and the degradation of these observational conditions near the solar maximum, since these modes have a ‘‘mixed’’ character and probably behave as acoustic modes. Several structures retain our attention because of the presence of persistent peaks along the whole time span. These features may support the idea of an increase of the rotation in the inner core. There are good arguments for thinking that complementary observations up to the solar activity minimum in 2007 will be decisive for drawing conclusions on the presence or absence of gravity modes detected aboard the SOHO satellite.

Global solar Doppler velocity determination with the GOLF/SoHO instrument

The Global Oscillation at Low Frequencies (GOLF) experiment is a resonant scattering spectrophotometer on board the Solar and Heliospheric Observatory (SoHO) mission, originally designed to measure the disk-integrated solar oscillations of the Sun. This instrument was designed in a relative photometric mode involving both wings of the neutral sodium doublet (D1 at λ 5896 and D2 at λ 5890 A). However, a “one-wing” photometric mode has been selected to ensure 100% continuity in the measurements after a problem in the polarization mechanisms. Thus the velocity is obtained from only two points on the same wing of the lines. This operating configuration imposes tighter constraints on the stability of the instrument with a higher sensitivity to instrumental variations. In this paper we discuss the evolution of the instrument during the last 8 years in space and the corrections applied to the measured counting rates due to known instrumental effects. We also describe a scaling procedure to obtain the variation of the Doppler velocity based on our knowledge of the sodium profile slope and we compare it to previous velocity estimations.

A search for solar g modes in the GOLF data

With over 5 years of GOLF data having some 90% continuity, a new attempt has been made to search for possible solarg modes. Statistical methods are used, based on the minimum of assumptions regarding the solar physics; namely that mode line-widths are small compared with the inverse of the observing time, and that modes are sought in the frequency interval 150 to 400Hz. A number of simulations are carried out in order to understand the expected behaviour of a system consisting principally of a solar noise continuum overlaid with some weak sharp resonances. The method adopted is based on the FFT analysis of a time series with zero-padding by a factor of 5. One prominent resonance at 284.666Hz coincides with a previous tentative assignment as one member of an n = 1, l = 1, p-mode multiplet. Components of two multiplets, previously tentatively identified as possibleg-mode candidates from the GOLF data in 1998, continue to be found, although their statistical significance is shown to be insucient, within the present assumption regarding the nature of the signal. An upper limit to the amplitude of anyg mode present is calculated using two dierent statistical approaches, according to either the assumed absence (H0 hypothesis) or the assumed presence (H1 hypothesis) of a signal. The former yields a slightly lower limit of around 6 mm/s.

Performance and Early Results from the GOLF Instrument Flown on the SOHO Mission

GOLF in-flight commissioning and calibration was carried out during the first four months, most of which represented the cruise phase of SOHO towards its final L1 orbit. The initial performance of GOLF is shown to be within the design specification, for the entire instrument as well as for the separate sub-systems. Malfunctioning of the polarising mechanisms after 3 to 4 months operation has led to the adoption of an unplanned operating sequence in which these mechanisms are no longer used. This mode, which measures only the blue wing of the solar sodium lines, detracts little from the detection and frequency measurements of global oscillations, but does make more difficult the absolute velocity calibration, which is currently of the order of 20%. Data continuity in the new mode is extremely high and the instrument is producing exceptionally noise-free p-mode spectra. The data set is particularly well suited to the study of effects due to the excitation mechanism of the modes, leading to temporal variations in their amplitudes. The g modes have not yet been detected in this limited data set. In the present mode of operation, there are no indications of any degradation which would limit the use of GOLF for up to 6 years or more.

First Results on it p Modes from GOLF Experiment

The GOLF experiment on the SOHO mission aims to study the internal structure of the Sun by measuring the spectrum of global oscillations in the frequency range 10-7 to 10-2 Hz. Here we present the results of the analysis of the first 8 months of data. Special emphasis is put into the frequency determination of the p modes, as well as the splitting in the multiplets due to rotation. For both, we show that the improvement in S/N level with respect to the ground-based networks and other experiments is essential in achieving a very low-degree frequency table with small errors ∼ 2 parts in 10-5). On the other hand, the splitting found seems to favour a solar core which does not rotate slower than its surface. The line widths do agree with theoretical expectations and other observations.

MAGNETIC FIELDS FROM SOHO MDI CONVERTED TO THE MOUNT WILSON 150 FOOT SOLAR TOWER SCALE

In order to permit the construction of long-duration time series dependent on the Suns magnetic field, this paper presents a detailed cross-correlation between sets of simultaneous magnetograms from the Mount Wilson Observatory (MWO) and the Michelson Doppler Imager (MDI) aboard the SOHO spacecraft. The MWO 150 foot (45.72 m) solar tower telescope magnetogram data are for the Fe I 525.0 nm and Ni I 676.8 nm lines, and the MDI data are level 1.8 magnetograms also for the Ni I 676.8 nm spectral line. In these comparisons, we apply a saturation correction factor to the MWO 525.0 nm fields prior to the derivation of the MDI scale factor. Data from 1997 March to 2002 August are used for this work. We have found that the ratio of MWO Fe I 525.0 nm magnetograms over MDI magnetograms is about 1.7, and it is a function of the center-to-limb angle. Moreover, there are differences between the west-side and the east-side ratios, and these differences may come from the angle dependence of the Michelson filters in the MDI instrument. The MDI tuning changes, on the other hand, are not associated with significant jumps in the derived scale factor ratio. The average scale factors should be adequate for the construction of MDI images closely comparable to those of the saturation-corrected long-duration MWO 525.0 nm sequence.

Comparison of Frequencies and Rotational Splittings of Solar Acoustic Modes of Low Angular Degree from Simultaneous MDI and GOLF Observations

During the years 1996 through 1998 the Michelson Doppler Imager (MDI) and the Global Oscillations at Low Frequency (GOLF) experiments on the Solar and Heliospheric Observatory (SOHO) mission have provided unique and nearly uninterrupted sequences of helioseismic observations. This paper describes the analysis carried out on power spectra from 759 days of calibrated disk-averaged velocity signals provided by these two experiments. The period investigated in this work is from 1996 May 25 to 1998 June 22. We report the results of frequency determination of low-degree (l ≤ 3) acoustic modes in the frequency range between 1.4 mHz and 3.7 mHz. Rotational splittings are also measured for nonradial modes up to 3.0 mHz. The power spectrum estimation of the signals is performed using classical Fourier analysis and the line-profile parameters of the modes are determined by means of a maximum likelihood method. All parameters have been estimated using both symmetrical and asymmetrical line profile-fitting formula. The line asymmetry parameter of all modes with frequency higher than 2.0 mHz is systematically negative and independent of l. This result is consistent with the fact that both MDI and GOLF data sets investigated in this paper are predominantly velocity signals, in agreement with previous results. A comparison of the results between the symmetric and asymmetric fits shows that there is a systematic shift in the frequencies for modes above 2.0 mHz. Below this frequency, the line width of the modes is very small and the time base of the data does not provide enough statistics to reveal an asymmetry. In general, the results show that frequency and rotational splitting values obtained from both the MDI and GOLF signals are in excellent agreement, and no significant differences exist between the two data sets within the accuracy of the measurements. Our results are consistent with a uniform rotation of the solar core at the rate of about 435 nHz and show only very small deviations of the core structure from the standard solar model.

Solar Radius Measurements at Mount Wilson Observatory

Possible temporal variations of the solar radius are important as an indicator of internal energy storage and as a mechanism for changes in the total solar irradiance. Variations in the total solar irradiance with an amplitude of 0.1% have been observed from space for more than two decades. Although the variability of this solar output has been definitely established, the detailed dependence of the rate of energy output on the level of solar magnetic activity has not yet been measured with enough continuity and precision to determine the correlation throughout the full solar cycle. While a large fraction of the irradiance variability can be explained by the distribution of solar magnetic activity at the surface, small changes in the solar radius (i.e., contributing to the global variability of the solar envelope) could account for a significant fraction of the remaining variations. Studies of the apparent solar radius variation have reported contradictory results, in the form of both correlations and anticorrelations between the solar radius and, for example, the cycle of sunspot numbers. We present results from more than 30 yr of solar radius measurements obtained from the Mount Wilson synoptic program of solar magnetic observations carried out at the 150 foot (45.72 m) tower. We have used an improved definition of the solar radius that also allows us to study the heliolatitude dependence of the radius measurements. We find that the variations of the average radius are not significantly correlated with the solar cycle over the last three decades. We also compare the heliolatitude dependence of these radius measurements with recent results obtained at the Pic du Midi Observatory in France.

AN INTERPRETATION OF THE DIFFERENCES IN THE SOLAR DIFFERENTIAL ROTATION DURING EVEN AND ODD SUNSPOT CYCLES

Using the data on sunspot groups during the period 1879-2004, we have found that the solar equatorial rotation rate during the odd-numbered sunspot cycles is well correlated with the equatorial rotation rate of the preceding even-numbered sunspot cycles, which is similar to the well-known Gnevyshev & Ohl rule (G-O rule) in sunspot activity. This indicates that a 22 yr cycle in the equatorial rotation rate begins in an even-numbered cycle and ends in the following odd-numbered cycle, the same as a solar magnetic cycle (Hale cycle), as inferred from the G-O rule. On the other hand, the latitudinal gradient of the solar rotation during the even-numbered cycles is found to be well correlated with that of the preceding odd-numbered cycles. This result indicates that a 22 yr cycle in the latitudinal gradient begins in an odd-numbered cycle and ends in the following even-numbered cycle. That is, the phase of the beginning of a 22 yr cycle in the latitudinal gradient is different by about 180° relative to the beginning of a 22 yr magnetic cycle.

Identification of Solar Acoustic Modes of Low Angular Degree and Low Radial Order

We present evidence for the detection of low radial order (n < 10) acoustic modes of low angular degree, l = 0-2, in the 759 day long Global Oscillations at Low Frequency and Michelson Doppler Imager time series. We used Random-Lag Singular Cross-Spectrum Analysis, which searches for simultaneous oscillatory components in two or more time series. We have determined 11 modes in the range n = 3-9, of which eight modes confirm the previous measurements by Toutain et al. and three modes of l = 0 and n = 3, 5, and 6 are reliably measured for the first time. The errors of frequency determination are also significantly reduced for several previously identified modes. New sound speed inversion results suggest that the effect of inhomogeneous initial composition of the Sun should be included in the standard solar model.