5. Power spectra
A search for possible periodicities in the fluctuations of the NBPs light curves was performed using temporal power spectra. Before computing the power spectra, the light curves were detrended using a smoothing window of 600 s. A check on this procedure showed that changing the smoothing window between 360 s and 840 s affected the power at frequencies lower than 1.2 mHz, but without changing the frequency of the peaks. The power at higher frequencies remained unaffected.
A power spectrum was computed for each light curve of the 11 NBPs and of the 11 internetwork areas. To analyze the differences between these two atmospheric components, we averaged separately the power spectra over all of the NBPs and over all of the quiet regions. In Fig. 4 we show some of these averaged curves. It must be remembered that the NSO and MDI observations have different temporal coverage (50 and 180 minutes, respectively) and temporal resolution (12 s and 60 s), so that lower temporal frequencies are better represented in the NiI series, while frequency coverage extends to higher frequencies for ground-based data. However, the power at mHz in all the ground-based signatures is due essentially to noise (Fig. 4), hence the analysis can be limited to the frequency coverage of the NiI observations, 0-8 mHz.
We describe here the power spectra characteristics from lower photospheric signatures to higher chromospheric ones. Intensity fluctuations may be plausibly interpreted as temperature fluctuations for photospheric LTE signatures such as Ni I or the H wings, formed over depths where the velocity gradient is small. In these cases, the intensity fluctuations directly reflect fluctuations of the source function (the Planck function) and hence of temperature. In the center of chromospheric lines as Na or H the NLTE effects are important and the intensity fluctuations are the response to temperature, density and even velocity changes (Cram 1978) and then are a sort of average of the variation of the state variables of the chromosphere.
5.1. Photospheric signatures
In Fig. 4a,b,d we show the power spectra of Ni I pseudo-continuum intensity, Ni I velocity and H red wing intensity. The power spectra computed for white light intensity (not shown in figure) and for the NiI pseudo-continuum are very similar, and we are confident that we can compare the two series of observations, even if their frequency resolution is different. The H blue wing spectrum (not shown in figure) has a similar behaviour but a lower amplitude with respect to the red wing (see Table 3). A value smaller than 1 for the ratio of the power in the blue and red wings of H is consistent with the observations of Bertello (1987), that found the same trend for the power of velocity oscillations in the wings of photospheric lines formed at heights lower than 150 km.
As is well known, the distribution of power for the photospheric velocity fluctuations is rather different from the one of pseudo-continuum intensity fluctuations (Fig. 4a,b). The velocity power is concentrated around the range of frequencies corresponding to the 5-minutes oscillations. The pseudo-continuum power spectrum peaks at low frequencies, around 1.5 mHz and then show a decay that might indicate the stochastic character of the granulation intensity variation, as already reported for the first time in Noyes (1967).
As a global characteristic, power spectra computed in photospheric signatures do not show any significant difference between network and internetwork structures within the 50% confidence limit (Fig. 4a,b,d). This result is consistent with previous spectral observations by several authors (Deubner & Fleck 1990; Kulaczewski 1992; Lites et al. 1993) that analyzed both intensity and velocity oscillations in the photosphere for network and internetwork features.
The power spectrum of the magnetic flux variations averaged over the NBPs is shown in Fig. 4c. Internetwork areas are not considered because the noise in the magnetic flux measure is too high for a reliable determination of fluctuations. Significant peaks are visible at low frequency (around 1.5 mHz), indicating long term evolution of the magnetic field, and around 3.5 mHz corresponding to the 5 minutes oscillations. A signal at the latter timescale might represent the magnetic response to oscillations already present in the photosphere and be of importance in the context of generation and dissipation of MHD waves in the solar atmosphere (Ulrich 1996). Observations of flux variations in small magnetic structures are scarce in the literature, but we can compare this result with those presented by Norton et al. (1999), that used a similar set of MDI data obtained in the area of a big sunspot. They found a significant peak near 5 min only for structures whose magnetic flux density exceeded 600 G, while the points we analyzed had a maximum value of about 300 G.
5.2. Chromospheric signatures
The intensity power spectra computed in chromospheric signatures display strong differences between NBPs and internetwork as shown in Fig. 4e,f. We will analyze in detail these differences, keeping in mind that the regime of oscillations changes with height in the chromosphere.
First of all we notice that the power spectrum of internetwork intensity fluctuations in NaD2 shares some characteristics with the photospheric NiI velocity power spectrum rather than with the one of Ni I intensity. In particular the strongest peak appears around 3.5 mHz, while the enhanced low frequency component, typical of photospheric intensity power spectra, is lacking. This characteristic could be explained if the intensity fluctuations in the NaD2 line center were related more to velocity than to temperature perturbations. This might be indirectly confirmed by the results of Pallé et al. (1999) in their study of the current performances of the GOLF experiment on SOHO. In determining the relative contributions of velocity and intensity signals to the intensity variations measured in the blue wings (-100 mÅ) of the sodium doublet, they conclude that the effect due to "pure" intensity changes is only 14% that of velocity changes for the p - mode frequency range. Since the width of the filter used for our observations includes that same portion of the line wing, this conclusion might apply, at least partially, also to our case.
Comparing network and internetwork power spectra for NaD2, we see that the power of the NBPs is smaller than the corresponding power for internetwork at each temporal frequency. In particular, even if both NBPs and internetwork points show a maximum around 3.5 mHz, the power at this frequency is almost an order of magnitude smaller in the NBPs. (Fig. 4d suggests that this effect might be already present in the wings of H, although its amplitude is not large enough to give an unambiguous result). This suppression of power in the NBPs indicates that the presence of the magnetic field in some way perturbs and reduces the oscillations at low chromospheric levels, especially in the p-mode range. A compression of power in magnetic structures at frequencies below 7-8 mHz, for lines formed at similar heights, has not been reported by other authors. Only Al et al. (1998) observe a similar effect, but much smaller, for the power spectrum of velocity fluctuations measured in the center of NaD2 with a narrowband filter (30 mÅ). We think that the stronger effect seen in our observations is real because our analysis selects the horizontal scale typical of chromospheric network to determine the light curves and the power spectra (see Sect. 4), and is therefore more suitable to outline characteristics and differences on the same horizontal scale for NBPs and internetwork areas.
The power spectrum computed for the intensity of H center is shown in Fig. 4f. For both NBPs and internetwork the power distribution peaks at low frequencies ( mHz), without any relevant peak at the p-mode frequencies. No enhanced power for "3-minutes" oscillations ( mHz), is detectable in the internetwork. This is consistent with observations in the H center by Cram (1978) and in the Ca II - H3 by Lites et al. 1993showing a power peak in the "3 minutes" range only for velocity power spectrum.
The spectrum of NBPs in H line has a power higher than that of the internetwork areas at each frequency, reversing the effect present in the NaD2 line, and shows three well separated peaks reminiscent of the peaks observed by Lites et al. (1993). The more relevant peak is around 2.2 mHz ("7-minutes" oscillations) and is lowered about a factor 6 in the internetwork. We cannot judge on the relevance of the peak around 1.3 mHz, since its amplitude is heavily affected by the smoothing window, as described in Sect. 5, and we cannot consider real the peak at 0.6 mHz, because it is related to the time interval of our observations. However, the increasing power at low frequencies in the spectrum of NBPs suggests that the rôle of the magnetic field in the oscillations, detectable at high chromospheric levels, is certainly different from the one at lower levels and strenghtens the hypothesis of magnetic-hydrodynamic waves present at these high levels.
Characteristics of power spectra for network and internetwork are summarized in Table 3 for the two relevant frequency windows 1.5-2.5 mHz and 3-4 mHz.
© European Southern Observatory (ESO) 2000
Online publication: June 5, 2000