## 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 spectra
The 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
For the power spectrum derived from the velocity signal, there is a
break in the slope at approximately 25 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
and is dominated by shot noise for
frequencies above 11 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 nm, the scale factor included in should properly account for this variation. The scale factor changes by 30% during the year and differs between the two states of instrumental magnetic modulation by 4%. According to line contribution functions provided to us by Severino (1993), the height of formation using the Magain (1986) formulation varies between 242 and 310 km on the Vernazza et al. (1981) model C scale. These altitudes differ in density by 75% so that if the velocity scales as , the rms velocity should differ by 32% with the rms velocity being largest when the GOLF working point is closest to the line core at the most negative velocity. In addition, two states of magnetic modulation are offset from each other by an amount of 7% the orbital velocity range and should consequently show a difference in rms velocity of 2%. 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
© European Southern Observatory (ESO) 2000 Online publication: January 29, 2001 |