Astron. Astrophys. 319, 673-682 (1997)

6. First detection of another asymmetry

As shown in Fig. 5, rotation rates exhibit a large dispersion about the mean. The rms velocity is 3% of the mean rotation rate, and certain facular points show a deviation of more than 7% from the mean rotation rate. There are a number of reasons of instrumental and solar origin for the dispersion in the angular velocity. Instrumental errors have been discussed in Sect. 3. To address the solar causes, we subtracted the mean differential rotation (i.e. the Legendre polynomial fit) from each individual rotation rate. Then we plotted the corresponding histogram distribution in /day bins (Fig. 6). One striking result is the existence of a sharp peak in an otherwise roughly gaussian distribution (this phenomenon will be referred to hereafter as a shape-asymmetry). The histogram seems to indicate the existence of two populations: one (denoted hereafter population I) exhibiting rotation close to the mean, and another (population II) that rotates slower than average, with much smaller dispersion. As it may seem difficult at first sight to separate population II from population I, we shall attempt to identify the properties of each.

Fig. 5. Selected facular points in 1959, and polynomial fit of the average rotation (Sect. 5)

Fig. 6. Histogram for 1959 faculae (solid line) with a /day bin, a two-gaussian fit has been applied to the data (dashed line)

6.1. Histogram asymmetry

In a first step, we define a parameter r representing the proportion of points below and above the mean as

where R and L are the number of facular points having a rotation rate higher and lower, respectively, than the fit of Fig. 6, and T is the total number of points. r is of particular interest because the whole population II rotates slower than the average. Considering the uncertainty on a number of points N to be , and assuming that r is small (), the error on r is given by

The variation of r over the period [1957-1964] is given in Fig. 7. r is maximum at sunspot maximum. As shown in Table 4, no significant difference is found in the shape-asymmetry of young and old faculae.

Fig. 7. Variation of the ratio r for faculae (solid lines) between 1957 and 1964 and for sunspots (dashed line) between 1957 and 1961. Error bars are not shown for sunspots to make the graph easier to read: they are slightly smaller than the r values

Table 4. Shape-asymmetry parameter r for faculae during [1957-1964]

We also checked to see whether the shape-asymmetry is time dependent. For this purpose, we grouped the image pairs in 14-day periods (approximately half a solar rotation). The number of pairs in each period is of course not constant, because of observation gaps. Then we compute the shape-asymmetry r of the rotation rate histogram in two ways: by subtracting from the individual rotation rates (1) the polynomial fit of the corresponding 14-day period; or (2) the corresponding yearly polynomial fit. The latter means that points of the histogram are at the same position as those for the yearly histogram: zero is the same. The results are very similar, as shown in Fig. 8 for 1959. r oscillates with a period about 1.5 solar rotations throughout the year. The oscillation amplitude is hardly greater than the noise; however, if such an oscillation persisted throughout the cycle, it would hint at the existence of giant cells. This deserves further study.

Fig. 8. Variation of r for faculae versus 14-day period number in 1959, using the yearly fit (solid line) and the 14-day period fit (dashed line). Error bars are shown for only one curve, to make the graph easier to read; however, they do not differ from one curve to the other

6.2. Activity-dependence of facula shape-asymmetry

The next question to be addressed is whether the two populations differ by their activity level or size. We know that larger sunspots or sunspot groups rotate more slowly than smaller ones (Maunder & Maunder 1905; Newton & Nunn 1951; Ward 1966). One would thus expect that slowly rotating faculae (population II) would correspond to the larger faculae. The parameter r is higher in the northern hemisphere, which suggests a relation with the solar activity level. So we compare the north-south asymmetry of the shape-asymmetry with that of activity. We calculated the two north-south asymmetry parameters, each year, as follows

where and are the differences between the number of points below and above the fit, for the northern and southern hemispheres, respectively, and

where N and S are the number of active regions weighted by their activity level X, for the northern and southern hemispheres, respectively. X varies from 1 (quiet) to 10 (very active region), and reflects the size of the facula, the number of sunspots, and its lifetime. The errors on and on are, respectively,

We computed for all X, and . Results are shown in Fig. 9. No conclusion is possible as to whether or not the shape-asymmetry is due to very active regions. However the shape-asymmetry is probably related to the activity level.

Fig. 9. Variation of for all X (dashed line), (dot-dot-dot-dashed line), (dot-dashed line), and of (solid line)

6.3. Population I and II splitting

Another approach consists in selecting points from population II as follows. We know that population II facular points exhibit small rotation rate dispersion. This is particularly true for the northern hemisphere at low latitudes (see Fig. 5). We investigate the particular case of 1959, for which the shape-asymmetry is the strongest (). We select points corresponding to this concentration within the rotation range 14.25 /day and the latitude range . This restricted data set still contains points belonging to population I, but we estimate that half the sample belongs to population II (instead of the approximate 10% for the whole set of points). The results are as follows: (i) populations I and II show no significant disk longitude-dependence; (ii) both populations show two preferential longitudes (measured by Carrington longitudes); (iii) the meridional circulation of population II facular points seems negligible, in contrast to that of population I, which is one order of magnitude greater. This point will be investigated in a companion paper (Paper II).

The above procedure is rather arbitrary. However, a two-gaussian fit was also performed in each latitude bin to characterize the rotation rates precisely by two curves associated with two dispersions versus latitude, and this selection showed similar results.

6.4. Comparison with sunspots

Additional information can be obtained from sunspots during the same period. Sunspots also have a shape-asymmetry of the rotation rate distribution (Fig. 10). However, in contrast with faculae, the "peak" is broadened, suggesting that populations I and II are more mixed. The degree of asymmetry r is comparable to that of faculae (Table 5). The sunspot shape-asymmetry seems to be age-dependent, with old sunspots having a larger r than younger ones. But there is no significant difference between leaders and followers, which indicates that the whole active region contains one population or the other. There is no difference either, however complex the group might be.

Fig. 10. Sunspots histogram in [1957-1962] (solid line) with a /day bin and a two-gaussian fit (dashed line)

Table 5. Shape-asymmetry parameter r for sunspots during [1957-1962]

The comparison between sunspots and faculae is not straightforward. A facula contains many more points than a sunspot group, and its lifetime is longer. Therefore the large peak present in the facular rotation histogram might be due to a limited number of very large and long-lasting faculae.

The two-gaussian fits mentioned in Sect. 6.3 emphasize the differences between sunspot and facula shape-asymmetries. While the rms velocity of facula population II is one order of magnitude smaller than that of population I, the ratio is only of 2.4 for sunspots. Moreover, the ratio between the number of sunspots belonging to population I and II is close to 1, while it ranges from 8 to 17 for faculae. This fit also quantifies the difference of rotation rate between populations I and II: /day for faculae and /day for sunspots.

© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998
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