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Astron. Astrophys. 364, 799-815 (2000) 7. ResultsWe can utilize the velocity scaling and fitting to examine the solar background velocity variations and the dependence of the rms velocity amplitude on orbital velocity. 7.1. Power spectraThe power spectra for the velocity and the difference velocity are shown in Fig. 14 and Fig. 15 respectively. Also shown on the velocity power spectrum plot is a fit to the pattern based on the formula given by Harvey (1985) which uses only three components. This fit is discussed further in the next paragraph. An alternate treatment of the GOLF data (Robillot et al. 1998) calculates a velocity from a ratio which is related to quantities used in the present approach. The numerator of their ratio is proportional to the velocity derived here. The denominator of their ration at time scales longer than one day is proportional to our difference velocity while at time scales shorter than one day the denominator is essentially constant. One might expect there to be a break in the derived power spectrum related to the denominator smoothing if the numerator and denominator are correlated at time scales shorter than one day. Consequently, it is of interest to examine the components separately. The power spectrum from the velocity signal shown in Fig. 14 is based on an approach which deals with the GOLF data without any frequency dependent factors for all time periods between the 80 day limit from the phase function detrending and the cutoff of 6000 µHz imposed for convenience in this display which emphasizes the low frequency range. It provides an estimate of the solar background spectrum free from the effects of the diurnal cycles and atmospheric transparency problems of ground-based observers and takes advantage of the long and nearly continuous GOLF sequence. As such it represents an important estimation of the solar background spectrum. Previous power spectra including this wide range of frequencies have been published by Jiménez et al. (1988) and Pallé et al. (1995). At the lowest frequencies, the darkening effects of sunspots certainly can introduce a variability which is not a true velocity signal. Indeed, the considerations by Harvey (1985) anticipated that the velocity-like signal at periods comparable to the rotation period would be due to a cross-talk between intensity and velocity. We recognize this and simply refer to the time series as velocity signals even though some of what they include comes from intensity variations.
For the power spectrum derived from the velocity signal, there is a
break in the slope at approximately 25 µHz. Below
this frequency the slope matches that of the Harvey (1985) model for
active regions with a slope of -2. The shape above the break is
steeper than would be expected from the Harvey model for granulation
alone although the break point is near where Pallé et al.
(1995) showed the granulation and active region contributions crossing
over. This change of slope suggests that the effects of active regions
should become small in the frequency range of 100 to
1000 µHz where the search for low frequency solar
modes is currently concentrated. Apparently the solar background in
this frequency range is largely due to convective effects rather than
magnetic and activity related effects. Between about
50 µHz and 250 µHz the power
spectral slope is about We caution against a physical interpretation of the power spectrum shape in terms of the processes of granulation and supergranulation. The fact that a component having a range of lifetimes near that of the granulation should be present in the power spectrum while there can be no contribution from a component having the lifetime of supergranulation is very hard to explain on the basis of a physical model. If conservation of matter can cause the contribution from supergranulation to drop out, it should apply equally well to granulation and prevent the features with that lifetime from appearing in Fig. 14. It is probable that some other process must be invoked to explain the features seen in this power spectrum. Ulrich (1999) has suggested recently that atmospheric gravity waves have a resonance at the temporal frequency shown in Fig. 14 when driven by structures having a spatial wave number appropriate for supergranulation. This resonance response can alter the balance between the intensity and velocity components of the signal. The nature of the power spectrum shown in Fig. 14 clearly deserves additional attention. The strongest peaks at the lowest frequencies correspond to 27 and
13 days and are the well-known rotational modulation associated with
the active region signal (Jiménez 1988). The power spectrum of
the difference velocity has a lower slope of
Distinct peaks or groups of peaks are found in the power spectrum of the velocity at periods of 26.9, 18.0, 9.0, 6.8 and 3.5 days. The peaks at 26.9, 18.0 and 3.5 days are distinct while those at 9.0 and 6.8 days are clusters. For the power spectrum of the difference in velocities, peaks at 27.0 and 9.0 days are clear while bands of enhanced power are seen near 13 and 7 days. 7.2. Amplitude in the 5-minute bandThe velocity scaling derived in this paper depends on the
determined line profile factors and even though the orbital velocity
moves the GOLF working point on the solar line by
In order to study the altitude dependence, the full time series was
band-pass filtered to include only variations in the five-minute band
having frequencies between 2000 µHz and
5000 µHz. The time sequence was divided into
segments of 27.28 days, a period corresponding to one synodic
Carrington rotation, and the rms variation in velocity was calculated
for each. The results are shown in Fig. 16 for both states of
magnetic modulation. One period including the time of the sodium cell
cooldown in September of 1996 is left out because the gap during the
four days of no data has been filled with a noiseless auto-recursive
representation which reduced the rms artificially for that Carrington
rotation. It is clear from Fig. 16 that the observed dependence
on altitude is much less than the estimate given here. By extracting
the lowest four harmonic components from the time series of
© European Southern Observatory (ESO) 2000 Online publication: January 29, 2001 ![]() |