ALBERT

Notes: Abstract The application of the fast-Fourier-transform (FFT) algorithm to calculating one-dimensional and bi-dimensional (temporal and spatial), power and cross-power (coherence and phase) spectra is examined for solar photospheric fluctuations. Alternative methods for smoothing raw spectra, direct averaging (employing various weights) and indirect truncation of the correlation function, are compared, and indirect smoothing is compared with spectra calculated by mean-lagged-product (MLP) methods. Besides providing the raw spectrum, FFT techniques easily allow computing a series of spectra with varying amounts of smoothing. From these spectra a range of satisfactory compromise between resolution and stability can be determined which helps in the interpretation of spectral trends, and in identifying more clearly the existence and significance of spectral features. For bi-dimensional spectra presented as contour plots, this range of satisfactory smoothing can be restricted, particularly when spectral trends must be represented by small-scale contours. Equivalent spectra (i.e. comparable equivalent degrees of freedom) computed or smoothed by different methods have minor, but not negligible, differences. Examination of these differences favors computing of FFT spectra smoothed by averaging for photospheric fluctuations.

Notes: Abstract Fluctuations measured from a time sequence of high-resolution, high-dispersion Sacramento Peak Observatory spectrograms and previously analyzed by computing one-dimensional temporal and spatial spectra (Edmonds et al., 1965), are re-analyzed using bi-dimensional (temporal and spatial) power, coherence and phase spectra computed by fast-Fourier-transform techniques. The fluctuations measured are radial velocity for the FeI 5049.83, CrI 5051.91 and CI 5052.16 spectral lines, continuum brightness, and equivalent width and central intensity of the CI line. The bidimensional spectra, particularly those of coherence and phase, allow isolating different components of the fluctuations to a degree not possible in the one-dimensional analyses. Six components of the fluctuations have been isolated (Section 5 and Figure 11); the first three components are well-known but the nature of the remaining three is less certain: (1) Supergranulation which exists only in radial-velocity fluctuations and increases in power with depth. (2) Five-minute oscillations that dominate long-wavelength radial-velocity fluctuations, which may contribute of the order of one percent to continuum brightness and equivalent width fluctuations, and are waves which can propagate across the Sun's surface and possibly travel upwards at less than 70 km s−1. (3) A long-period, convective component which extends over all but very long wavelengths, is characterized by strong correlation between the radial velocity and photometric fluctuations, and involves low power levels for the radial velocity fluctuations. Seemingly, the radial velocity fluctuations lead those of continuum brightness by roughly 20 s. (4) Low and moderate wavenumber fluctuations which seemingly extend over frequencies ≲ 6 × 10−3 Hz and are characterized by low power levels for all types of fluctuations. It is difficult to deny the physical reality and distinctness from other components of these fluctuations, but whether they constitute a single component is uncertain. The radial velocity fluctuations seem to have the same phase relations with respect to each other as the five-minute oscillations. The continuum brightness fluctuations seem to lag the equivalent width fluctuations by roughly 17 s, lead the central intensity fluctuations by roughly 10 s, and lead the radial velocity fluctuations by roughly 15 to 20 s. (5) Possible line-formation (as distinct from continuum formation) brightness fluctuations at the center of the CI 5052.16 line, which seemingly are of low frequency and long wavelength and are poorly correlated with continuum brightness and radial velocity fluctuations. (6) A low-correlation, primarily photometric component restricted to long-periods and to wavelengths only slightly less than those of super-granulation. Its existence is suggested by a phase anomaly indicating that the radial velocity fluctuations lead the photometric fluctuations by roughly 4 min.