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Structure and rotation of the large scale solar magnetic field observed at the Wilcox Solar Observatory
Physics and Chemistry of the Earth 31 (2006) 68–76 www.elsevier.com/locate/pce
Structure and rotation of the large scale solar magnetic field observed at the Wilcox Solar Observatory E. Gavryuseva *, G. Godoli Department of Astronomy and Space Science, Florence University, Florence, Italy Received 21 December 2004; accepted 18 March 2005
Abstract Line of sight component of the photospheric large scale magnetic field has been analyzed using the observations made at the Wilcox Solar Observatory since 1976 up to 2004. Magnetic field structure in latitude and in longitude and differential rotation and their variations in time have been studied. A four zones latitudinal structure has been evidenced with boundaries around +25, 0 and 25 and with a period of polarity change of 22 years about. Quasi-stable over several years longitudinal structure has been revealed in the coordinate system differentially rotating together with the photosphere. An 11-year periodicity has been found in the rotational rate. Additionally in the equatorial zone 4–5-year periodicity has been revealed. 2006 Elsevier Ltd. All rights reserved. Keywords: Sun: large scale magnetic field, rotation
1. Introduction Information on solar magnetic field can be acquired using several angular resolution scales. Since the beginning of observation of intense magnetic field in sunspots, through the measurement of the Zeeman line splitting by Hale in 1908 and since the introduction of the magnetograph (Babcock, 1953) the highest angular resolution possible has been pursued. Subsequently the introduction of research on stellar activity of solar type (Godoli, 1967, 1968; IAU, 1970) and the exigence of analyzing correlations between solar and interplanetary magnetic field (see e.g. Scherrer et al., 1977a,b) suggested to observe the mean solar magnetic field (MSMF) in integrated light without any resolution (i.e. to observe the Sun as a star). MSMF has been observed at the Crimean Astrophysical Observatory since 1968 (Severny, 1969, 1970); at the Mt. Wilson 46-m Tower *
Corresponding author. E-mail address: [email protected] (E. Gavryuseva).
1474-7065/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.pce.2005.03.008
Telescope since 1970 (Howard, 1974); at the Wilcox Solar Observatory of the Stanford University (WSO) since 1975. In the mean time to observe the large scale solar magnetic field (LSSMF) intermediate angular resolutions have been employed at the Mt. Wilson Observatory for the years 1959–1978; at the Kitt Peak National Observatory for the years 1975–1984 and at the WSO since 1976 to the present. Observation and analysis of LSSMF are fundamental for the understanding the solar structure (see e.g. Delache et al., 1993; Gavryuseva et al., 1994; Gavryuseva and Gavryusev, 2000) and the solar cycle and for improving our knowledge of the relationship between photospheric field and coronal structures (see e.g. Mogilevsky et al., 1997; Rusin and Rybansky, 2002) and between coronal structures and properties of the solar wind (see e.g. Gibson, 2001; Gavryuseva, 2005, 2006; Gavryuseva et al., 2005) and between solar wind properties and geomagnetic activity. In this work we would like to analyze the WSO data in order to describe the LSSMF latitudinal and longitudinal structure, differential rotation and their dynamics through
E. Gavryuseva, G. Godoli / Physics and Chemistry of the Earth 31 (2006) 68–76
solar cycles (Gavryuseva and Kroussanova, 2003). The WSO observations provide us the longest continuous data sets of LSSMF available on line. 2. Data The Wilcox Solar Observatory (WSO) large scale magnetic data were used (Scherrer et al., 1977a,b; http:// wso.stanford.edu/synoptic.html). WSOs Babcock solar magnetograph measures the line of sight component of the photospheric magnetic field, using the Zeeman splitting of the 525.0 nm Fe I spectral line, since May 1976. The noise level of each measurement is less than 10 lT (100 lT = 1 G). Magnetograms with three arcminute resolution (about 10 heliographic degrees at the center of the solar disc) are taken every day. Data now span the two 11-year solar activity cycles 21 and 22, beginning with solar minimum in 1976, and a large part of cycle 23. Because of the saturation of the magnetic signal in the magnetograph, the measured values reported are assumed to be smaller than the actual field strength by about a factor of two. Because of the large size of the aperture the regions from 70 to the poles lie entirely within the last aperture and are not resolved. Additionally we should remember that during the course of a year the solar rotation axis tips away and towards the Earth by 7.25. The original data are not cor-
69
rected for this effect of the orbital motion of the Earth (Hoeksema, 1985). Magnetograms taken over a solar rotation are combined to give a complete picture of the solar field over any one Carrington Rotation (CR). The magnetic field for the Carrington Rotations since CR1642 have been used. Carrington Rotations are a convenient coordinate system for locating positions on the Sun. The first Carrington Rotation was in 1853. CR 1642 begins 1976:05:27. We remember that Lord Carrington determined the solar rotation rate by watching low-latitude sunspots in the 1850s. He defined a rigid solar coordinate system that rotates in a sidereal frame exactly once every 25.38 days. The synodic rotational rate varies a little during the year because of the eccentricity of the Earth’s orbit: its mean value is about 27.2753 days (Carrington, 1863, http:// sun.stanford.edu/wso/words/Coordinates.html). Steps in longitude are of 5. The grid in latitude contains the 30 data in equal steps of the latitude sine given by the formula sinh = (14.5 i)/15.0 where i = 0, 1,. . . , 29 and h = ±75.2, ±64.2, ±56.4, ±50.1, ±44.4, ±39.3, ±34.5, ±30.0, ±25.7, ±21.5, ±17.5, ±13.5, ±9.6, ±5.7, ±1.9. 3. Latitudinal zonal structure of the solar magnetic field The latitudinal structure of the solar magnetic field is presented in Fig. 1. On the upper plot the mean LSSMF
Fig. 1. Distribution of the magnetic field in latitude and in time averaged over 1 CR (upper plot) and over 1 year (bottom plot) with 1 CR step. Yellow and red (blue and green) colors indicate positive (negative) polarities. The contours correspond to the levels of 50, 0, 50 lT. (For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
70
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over 1 CR is shown and on the bottom plot the annual mean is shown. The existence of a global zonal structure clearly appears. Four zones can be single out: two equatorial and two subpolar. The equatorial zones are located between the equator and ±25 of heliographic latitude. The polarity is opposite in the two hemispheres; it is constant during one 11-year solar cycle and reverses from one cycles to the next. The subpolar zones span from about ±25 to ±75. Their polarity is opposite in the two hemispheres; it reverses with the period of 11 years but there is a delay of 3–5 years between the inversion of the polarity in the subpolar zones and the inversion in the equatorial ones; moreover there is some small shift between the time of the polarity inversions in the two hemispheres. We notice that the latitudinal distribution of the LSSMF is almost antisymmetric from the northern to the southern solar hemisphere and from one cycle to the next. In the upper plot of Fig. 1 the yearly period of LSSMF at the highest latitudes is due to the yearly cycle of the heliographic latitude of the Earth. 4. Differential rotation of the solar magnetic field We have used two independent methods to evaluate the differential rotational rate of magnetic field.
4.1. First method Using spectral analysis (FFT) the mean periods of rotation for each latitude were deduced for the whole data set and for the subsets of 6, 13, 40, 67 CR (i.e. about half a year, 1, 3, 5 years) with steps of 1 CR. Additionally the first five harmonics were calculated too and the mean between them was found. 4.2. Second method Rotation of the solar LSSMF was analyzed for each latitude using the auto correlation method too. This method was applied to the sets of 28 years and to the shorter subsets as well. The mean rotational rate was also estimated as a mean in time of the rotational rates calculated for the short series and for each latitude. The results obtained by the first method for subsets of 13 CR are presented in Fig. 2. On the upper plot the period of the magnetic field rotation as a function of time and latitude is shown. On the bottom plot the mean North–South deviation of the periods averaged over 13 CR from the period averaged over 28 years is shown as a function of time and latitude. The rotation of the subpolar zones is slower than that of the low latitude zones. Additionally there is a clearly visible increase of the rotational rate after the polarity inversion
Fig. 2. On the upper plot the period of the magnetic field differential rotation rate averaged over 3 years with 1 CR step is shown as a function of time and latitude. Blue color corresponds to the shorter periods of rotation. Yellow color corresponds to the longer ones. On the bottom the mean North–South deviation of the rotation rate period averaged over 3 years from the differential rotation rate averaged over 28 years is plotted as a function of time and latitude. (For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
E. Gavryuseva, G. Godoli / Physics and Chemistry of the Earth 31 (2006) 68–76
approximately in 1980 and 1991. This happens with 11-year periodicity. The rotational rate of the equatorial zones varies in time with a periodicity of 55–60 CR about (4.2–4.5 years) and may be with its first harmonic as well. This is clarified by Fig. 3 where the correlation between the deviations on the different latitudes on the northern and on the southern hemispheres from the mean rotational rate corresponding to each latitude is represented. This result confirms the increase of the rotational rate during the periods and in the latitude zones of the weak magnetic field and demonstrates the variability of the rotational rate in the equatorial zones with the period of 4–5 years about. Results obtained with the second method entirely confirmed the preceding conclusions. 5. Longitudinal structure of the solar magnetic field To analyze the longitudinal structure of the magnetic field it is necessary to take into account the differential characteristic of the solar rotation and to assume the coordinate system rotating with the rate corresponding to each latitude. But since we saw that rotational rate is changing in time the coordinate system should follow this variation too. In this way it is possible to reconstruct the longitudinal structure in the system rotating together with the photospheric field. Fist of all, after we performed such a reconstruction we have found that in the equatorial and in the subpolar zones
71
the influence of the latitudinal structure of the LSSMF is so strong that a possible longitudinal dependence is hardly detectable. In Figs. 4–6 the time dependences, for each longitudinal step, of LSSMF averaged for 6 latitudinal belts have been plotted. On the left sections of the figures time resolution is of 1 CR; on the right section time resolution is of 1 year. From these figures it appears evident that some longitudinal structure can be distinguished only in the belts between 22 and 35 about to the North and to the South of the equator, out of subpolar and equatorial zones. We had to subtract the latitude distribution to reveal the possible longitude structure. On the plots of Figs. 7–9 are presented the same data of Figs. 4–6 from which latitudinal distribution of LSSMF has been substructed. In Fig. 10 longitudinal distribution of LSSMF from which latitudinal distribution has been substructed averaged over all latitudes and rotations is plotted. The longitudinal activity is characterized by the amplitude of the magnetic field and not only by its polarity which is changing in time: to prevent the reduction (or even annihilation) of the mean magnetic field over 28-year analyzed interval due to the various inversions of polarity, the longitudinal distribution of the absolute value of the LSSMF averaged over all latitudes and over all rotations have been computed and plotted in Fig. 11. In Figs. 7–11 quasi-stable over several years longitudinal distribution with evidence of a sector structure is present in the coordinate system differentially rotating together with the photosphere. This result excludes the possibility of
Fig. 3. Correlation between the deviation of the rotational period from the mean one for each latitude on the North and on the South as a function of time shift expressed in the Carrington rotation number.
72
E. Gavryuseva, G. Godoli / Physics and Chemistry of the Earth 31 (2006) 68–76
Fig. 4. Time dependence for each longitudinal steps of magnetic field averaged over all the latitudes between 39 and 75 in the northern (upper plot) and southern (bottom plot) solar hemispheres. On the left (right) section time resolution is of 1CR (1 year). Yellow (blue) color indicates positive (negative) magnetic field. (For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. Time dependence for each longitudinal steps of magnetic field averaged over all latitudes between 34.5 and 21.5 in the northern (upper plot) and southern (bottom plot) solar hemispheres. On the left (right) section time resolution is of 1CR (1 year). Yellow (blue) color indicates positive (negative) magnetic field. (For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
E. Gavryuseva, G. Godoli / Physics and Chemistry of the Earth 31 (2006) 68–76
73
Fig. 6. Time dependence for each longitudinal steps of magnetic field averaged over all latitudes between 17.5 and 1.9 in the northern (upper plot) and southern (bottom plot) solar hemispheres. On the left (right) section time resolution is of 1CR (1 year). Yellow (blue) color indicates positive (negative) magnetic field. (For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
Fig. 7. The same distribution as in Fig. 4 from which the latitudinal distribution of the magnetic field has been substructed.
74
E. Gavryuseva, G. Godoli / Physics and Chemistry of the Earth 31 (2006) 68–76
Fig. 8. The same distribution as in Fig. 5 from which the latitudinal distribution of the magnetic field has been substructed.
Fig. 9. The same distribution as in Fig. 6 from which the latitudinal distribution of the magnetic field has been substructed.
the interpretation of the longitudinal distribution of the photospheric magnetic field by the models of fully random
perturbations or, that is more interesting, by the models of fully stochastic excitation.
E. Gavryuseva, G. Godoli / Physics and Chemistry of the Earth 31 (2006) 68–76
75
Fig. 10. Averaged longitudinal distribution of the solar magnetic field over the 28-year analyzed interval (1976–2004).
Fig. 11. Averaged longitudinal distribution of the absolute value of the solar magnetic field over 1976–2004 interval, as in Fig. 10.
6. Conclusions and discussions • Latitudinal structure with a period of polarity change of 22 years has been evidenced. Four zones: two subpolar and two equatorial with boundaries around +25, 0 and 25 are clearly shown.
• Differential rotational rate of the magnetic field and its temporal dependence has been evidenced. The 11-year periodicity has been found in the rotational rate on high latitudes. The 11-year and 4–5-year periodicity has been found in the equatorial zone rotational rate.
76
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• Quasi-stable over several years longitude structure has been revealed. There is an evidence of sectoral structures in longitude in the coordinate system differentially rotating together with the photosphere. The polarity of the two equatorial zones is in phase with the solar activity, but the boundaries of zonal structure (where the value of the magnetic field averaged over one or several rotations is minimal or close to zero) are located on about ±25 of latitude where the absolute value of the local magnetic field is maximal. The polarity inversion of the LSSMF in the subpolar zones takes place around the maximum of the solar activity cycle, often with some shift in the northern and southern hemispheres. This inversion was observed since cycle 19 (Babcock, 1959). According to Snodgrass et al. (2000) the time of reversal in cycle 22 occurred earlier (November 1989) in the northern hemisphere than in the southern (May 1991). In the cycle 19 the inversion in each hemisphere was in phase with the activity maximum of spots (Waldmeier, 1960) and of calcium plages (Godoli, 1964). In agreement with our results Erofeev (1998) analyzing data of Mount Wilson Observatory from 1963 to 1976 and of Kitt Peak National Observatory since 1976 has found that the LSSMF rotates differentially at latitude of up to 55 and do not exhibit the ‘quasi-rigid’ rotation that is assumed to be characteristic of long living magnetic features. Lots of work has been dedicated to the study of the longitudinal activity (see e.g. Bumba et al., 2000), but the direct comparison with the results presented in this paper is rather difficult due to our reconstruction of the longitudinal distribution in the system rotating with the photosphere. As it was noticed in the introduction these results are fundamental for the understanding of the heliospheric structure and for the prediction of the magnetospheric perturbations.
References Babcock, H.W., 1953. ApJ 118, 387. Babcock, H.W., 1959. ApJ 130, 364. Bumba, V., Garcia, A., Klvana, M., 2000. Sol. Phys. 196, 403. Carrington, R.C., 1863. Observations of the Spots on the Sun, pp. 221– 244. Delache, Ph., Gavryusev, V., Gavryuseva, E., Laclare, F., Regulo, C., Roca Cortes, T., 1993. ApJ 407, 801. Erofeev, D.V., 1998. Sol. Phys. 182, 21. Gavryuseva, E., Gavryusev, V., 2000. In: Schroder, W. (Ed.), Long and Short Term Variability in Sun’s History and Global Change, Science ed. Bremen, Germany, p. 89. Gavryuseva, E., Gavryusev, V., Laclare, F., 1994. A&A 286, 305. Gavryuseva, E., Kroussanova, N., 2003. Topology and dynamic of solar magnetic field. In: Proc. Solar Wind-10 Conference, 2003. Gavryuseva, E., 2005. Latitudinal streams of solar magnetic field. In: Proc. Eleventh International Scientific Conference ‘‘Solar-Terrestrial influences’’. Sofia, 2005. Reports of BAS,. Howard, R., 1974. Sol. Phys. 38, 283. IAU, 1970. Trans. XIVA, 262. Mogilevsky, E.I., Obridko, V.N., Shilova, N.S., 1997. Sol. Phys. 176, 107. Rusin, V., Rybansky, M., 2002. Sol. Phys. 207, 47. Scherrer, P.H. et al., 1977a. Sol. Phys. 52, 3. Scherrer, P.H. et al., 1977b. Sol. Phys. 54, 353. Severny, A., 1969. Nature 224, 53. Severny, A., Wilcox, J.M., Scherrer, P.H., Coleman, D.S., 1970. Sol. Phys. 15, 3. Snodgrass, B., Kress, J.M., Wilson, P.R., 2000. Sol. Phys. 191, 1. Waldmeier, M., 1960. ZfA 49, 176.
Structure and rotation of the large scale solar magnetic field observed at the Wilcox Solar Observatory E. Gavryuseva *, G. Godoli Department of Astronomy and Space Science, Florence University, Florence, Italy Received 21 December 2004; accepted 18 March 2005
Abstract Line of sight component of the photospheric large scale magnetic field has been analyzed using the observations made at the Wilcox Solar Observatory since 1976 up to 2004. Magnetic field structure in latitude and in longitude and differential rotation and their variations in time have been studied. A four zones latitudinal structure has been evidenced with boundaries around +25, 0 and 25 and with a period of polarity change of 22 years about. Quasi-stable over several years longitudinal structure has been revealed in the coordinate system differentially rotating together with the photosphere. An 11-year periodicity has been found in the rotational rate. Additionally in the equatorial zone 4–5-year periodicity has been revealed. 2006 Elsevier Ltd. All rights reserved. Keywords: Sun: large scale magnetic field, rotation
1. Introduction Information on solar magnetic field can be acquired using several angular resolution scales. Since the beginning of observation of intense magnetic field in sunspots, through the measurement of the Zeeman line splitting by Hale in 1908 and since the introduction of the magnetograph (Babcock, 1953) the highest angular resolution possible has been pursued. Subsequently the introduction of research on stellar activity of solar type (Godoli, 1967, 1968; IAU, 1970) and the exigence of analyzing correlations between solar and interplanetary magnetic field (see e.g. Scherrer et al., 1977a,b) suggested to observe the mean solar magnetic field (MSMF) in integrated light without any resolution (i.e. to observe the Sun as a star). MSMF has been observed at the Crimean Astrophysical Observatory since 1968 (Severny, 1969, 1970); at the Mt. Wilson 46-m Tower *
Corresponding author. E-mail address: [email protected] (E. Gavryuseva).
1474-7065/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.pce.2005.03.008
Telescope since 1970 (Howard, 1974); at the Wilcox Solar Observatory of the Stanford University (WSO) since 1975. In the mean time to observe the large scale solar magnetic field (LSSMF) intermediate angular resolutions have been employed at the Mt. Wilson Observatory for the years 1959–1978; at the Kitt Peak National Observatory for the years 1975–1984 and at the WSO since 1976 to the present. Observation and analysis of LSSMF are fundamental for the understanding the solar structure (see e.g. Delache et al., 1993; Gavryuseva et al., 1994; Gavryuseva and Gavryusev, 2000) and the solar cycle and for improving our knowledge of the relationship between photospheric field and coronal structures (see e.g. Mogilevsky et al., 1997; Rusin and Rybansky, 2002) and between coronal structures and properties of the solar wind (see e.g. Gibson, 2001; Gavryuseva, 2005, 2006; Gavryuseva et al., 2005) and between solar wind properties and geomagnetic activity. In this work we would like to analyze the WSO data in order to describe the LSSMF latitudinal and longitudinal structure, differential rotation and their dynamics through
E. Gavryuseva, G. Godoli / Physics and Chemistry of the Earth 31 (2006) 68–76
solar cycles (Gavryuseva and Kroussanova, 2003). The WSO observations provide us the longest continuous data sets of LSSMF available on line. 2. Data The Wilcox Solar Observatory (WSO) large scale magnetic data were used (Scherrer et al., 1977a,b; http:// wso.stanford.edu/synoptic.html). WSOs Babcock solar magnetograph measures the line of sight component of the photospheric magnetic field, using the Zeeman splitting of the 525.0 nm Fe I spectral line, since May 1976. The noise level of each measurement is less than 10 lT (100 lT = 1 G). Magnetograms with three arcminute resolution (about 10 heliographic degrees at the center of the solar disc) are taken every day. Data now span the two 11-year solar activity cycles 21 and 22, beginning with solar minimum in 1976, and a large part of cycle 23. Because of the saturation of the magnetic signal in the magnetograph, the measured values reported are assumed to be smaller than the actual field strength by about a factor of two. Because of the large size of the aperture the regions from 70 to the poles lie entirely within the last aperture and are not resolved. Additionally we should remember that during the course of a year the solar rotation axis tips away and towards the Earth by 7.25. The original data are not cor-
69
rected for this effect of the orbital motion of the Earth (Hoeksema, 1985). Magnetograms taken over a solar rotation are combined to give a complete picture of the solar field over any one Carrington Rotation (CR). The magnetic field for the Carrington Rotations since CR1642 have been used. Carrington Rotations are a convenient coordinate system for locating positions on the Sun. The first Carrington Rotation was in 1853. CR 1642 begins 1976:05:27. We remember that Lord Carrington determined the solar rotation rate by watching low-latitude sunspots in the 1850s. He defined a rigid solar coordinate system that rotates in a sidereal frame exactly once every 25.38 days. The synodic rotational rate varies a little during the year because of the eccentricity of the Earth’s orbit: its mean value is about 27.2753 days (Carrington, 1863, http:// sun.stanford.edu/wso/words/Coordinates.html). Steps in longitude are of 5. The grid in latitude contains the 30 data in equal steps of the latitude sine given by the formula sinh = (14.5 i)/15.0 where i = 0, 1,. . . , 29 and h = ±75.2, ±64.2, ±56.4, ±50.1, ±44.4, ±39.3, ±34.5, ±30.0, ±25.7, ±21.5, ±17.5, ±13.5, ±9.6, ±5.7, ±1.9. 3. Latitudinal zonal structure of the solar magnetic field The latitudinal structure of the solar magnetic field is presented in Fig. 1. On the upper plot the mean LSSMF
Fig. 1. Distribution of the magnetic field in latitude and in time averaged over 1 CR (upper plot) and over 1 year (bottom plot) with 1 CR step. Yellow and red (blue and green) colors indicate positive (negative) polarities. The contours correspond to the levels of 50, 0, 50 lT. (For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
70
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over 1 CR is shown and on the bottom plot the annual mean is shown. The existence of a global zonal structure clearly appears. Four zones can be single out: two equatorial and two subpolar. The equatorial zones are located between the equator and ±25 of heliographic latitude. The polarity is opposite in the two hemispheres; it is constant during one 11-year solar cycle and reverses from one cycles to the next. The subpolar zones span from about ±25 to ±75. Their polarity is opposite in the two hemispheres; it reverses with the period of 11 years but there is a delay of 3–5 years between the inversion of the polarity in the subpolar zones and the inversion in the equatorial ones; moreover there is some small shift between the time of the polarity inversions in the two hemispheres. We notice that the latitudinal distribution of the LSSMF is almost antisymmetric from the northern to the southern solar hemisphere and from one cycle to the next. In the upper plot of Fig. 1 the yearly period of LSSMF at the highest latitudes is due to the yearly cycle of the heliographic latitude of the Earth. 4. Differential rotation of the solar magnetic field We have used two independent methods to evaluate the differential rotational rate of magnetic field.
4.1. First method Using spectral analysis (FFT) the mean periods of rotation for each latitude were deduced for the whole data set and for the subsets of 6, 13, 40, 67 CR (i.e. about half a year, 1, 3, 5 years) with steps of 1 CR. Additionally the first five harmonics were calculated too and the mean between them was found. 4.2. Second method Rotation of the solar LSSMF was analyzed for each latitude using the auto correlation method too. This method was applied to the sets of 28 years and to the shorter subsets as well. The mean rotational rate was also estimated as a mean in time of the rotational rates calculated for the short series and for each latitude. The results obtained by the first method for subsets of 13 CR are presented in Fig. 2. On the upper plot the period of the magnetic field rotation as a function of time and latitude is shown. On the bottom plot the mean North–South deviation of the periods averaged over 13 CR from the period averaged over 28 years is shown as a function of time and latitude. The rotation of the subpolar zones is slower than that of the low latitude zones. Additionally there is a clearly visible increase of the rotational rate after the polarity inversion
Fig. 2. On the upper plot the period of the magnetic field differential rotation rate averaged over 3 years with 1 CR step is shown as a function of time and latitude. Blue color corresponds to the shorter periods of rotation. Yellow color corresponds to the longer ones. On the bottom the mean North–South deviation of the rotation rate period averaged over 3 years from the differential rotation rate averaged over 28 years is plotted as a function of time and latitude. (For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
E. Gavryuseva, G. Godoli / Physics and Chemistry of the Earth 31 (2006) 68–76
approximately in 1980 and 1991. This happens with 11-year periodicity. The rotational rate of the equatorial zones varies in time with a periodicity of 55–60 CR about (4.2–4.5 years) and may be with its first harmonic as well. This is clarified by Fig. 3 where the correlation between the deviations on the different latitudes on the northern and on the southern hemispheres from the mean rotational rate corresponding to each latitude is represented. This result confirms the increase of the rotational rate during the periods and in the latitude zones of the weak magnetic field and demonstrates the variability of the rotational rate in the equatorial zones with the period of 4–5 years about. Results obtained with the second method entirely confirmed the preceding conclusions. 5. Longitudinal structure of the solar magnetic field To analyze the longitudinal structure of the magnetic field it is necessary to take into account the differential characteristic of the solar rotation and to assume the coordinate system rotating with the rate corresponding to each latitude. But since we saw that rotational rate is changing in time the coordinate system should follow this variation too. In this way it is possible to reconstruct the longitudinal structure in the system rotating together with the photospheric field. Fist of all, after we performed such a reconstruction we have found that in the equatorial and in the subpolar zones
71
the influence of the latitudinal structure of the LSSMF is so strong that a possible longitudinal dependence is hardly detectable. In Figs. 4–6 the time dependences, for each longitudinal step, of LSSMF averaged for 6 latitudinal belts have been plotted. On the left sections of the figures time resolution is of 1 CR; on the right section time resolution is of 1 year. From these figures it appears evident that some longitudinal structure can be distinguished only in the belts between 22 and 35 about to the North and to the South of the equator, out of subpolar and equatorial zones. We had to subtract the latitude distribution to reveal the possible longitude structure. On the plots of Figs. 7–9 are presented the same data of Figs. 4–6 from which latitudinal distribution of LSSMF has been substructed. In Fig. 10 longitudinal distribution of LSSMF from which latitudinal distribution has been substructed averaged over all latitudes and rotations is plotted. The longitudinal activity is characterized by the amplitude of the magnetic field and not only by its polarity which is changing in time: to prevent the reduction (or even annihilation) of the mean magnetic field over 28-year analyzed interval due to the various inversions of polarity, the longitudinal distribution of the absolute value of the LSSMF averaged over all latitudes and over all rotations have been computed and plotted in Fig. 11. In Figs. 7–11 quasi-stable over several years longitudinal distribution with evidence of a sector structure is present in the coordinate system differentially rotating together with the photosphere. This result excludes the possibility of
Fig. 3. Correlation between the deviation of the rotational period from the mean one for each latitude on the North and on the South as a function of time shift expressed in the Carrington rotation number.
72
E. Gavryuseva, G. Godoli / Physics and Chemistry of the Earth 31 (2006) 68–76
Fig. 4. Time dependence for each longitudinal steps of magnetic field averaged over all the latitudes between 39 and 75 in the northern (upper plot) and southern (bottom plot) solar hemispheres. On the left (right) section time resolution is of 1CR (1 year). Yellow (blue) color indicates positive (negative) magnetic field. (For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. Time dependence for each longitudinal steps of magnetic field averaged over all latitudes between 34.5 and 21.5 in the northern (upper plot) and southern (bottom plot) solar hemispheres. On the left (right) section time resolution is of 1CR (1 year). Yellow (blue) color indicates positive (negative) magnetic field. (For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
E. Gavryuseva, G. Godoli / Physics and Chemistry of the Earth 31 (2006) 68–76
73
Fig. 6. Time dependence for each longitudinal steps of magnetic field averaged over all latitudes between 17.5 and 1.9 in the northern (upper plot) and southern (bottom plot) solar hemispheres. On the left (right) section time resolution is of 1CR (1 year). Yellow (blue) color indicates positive (negative) magnetic field. (For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
Fig. 7. The same distribution as in Fig. 4 from which the latitudinal distribution of the magnetic field has been substructed.
74
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Fig. 8. The same distribution as in Fig. 5 from which the latitudinal distribution of the magnetic field has been substructed.
Fig. 9. The same distribution as in Fig. 6 from which the latitudinal distribution of the magnetic field has been substructed.
the interpretation of the longitudinal distribution of the photospheric magnetic field by the models of fully random
perturbations or, that is more interesting, by the models of fully stochastic excitation.
E. Gavryuseva, G. Godoli / Physics and Chemistry of the Earth 31 (2006) 68–76
75
Fig. 10. Averaged longitudinal distribution of the solar magnetic field over the 28-year analyzed interval (1976–2004).
Fig. 11. Averaged longitudinal distribution of the absolute value of the solar magnetic field over 1976–2004 interval, as in Fig. 10.
6. Conclusions and discussions • Latitudinal structure with a period of polarity change of 22 years has been evidenced. Four zones: two subpolar and two equatorial with boundaries around +25, 0 and 25 are clearly shown.
• Differential rotational rate of the magnetic field and its temporal dependence has been evidenced. The 11-year periodicity has been found in the rotational rate on high latitudes. The 11-year and 4–5-year periodicity has been found in the equatorial zone rotational rate.
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• Quasi-stable over several years longitude structure has been revealed. There is an evidence of sectoral structures in longitude in the coordinate system differentially rotating together with the photosphere. The polarity of the two equatorial zones is in phase with the solar activity, but the boundaries of zonal structure (where the value of the magnetic field averaged over one or several rotations is minimal or close to zero) are located on about ±25 of latitude where the absolute value of the local magnetic field is maximal. The polarity inversion of the LSSMF in the subpolar zones takes place around the maximum of the solar activity cycle, often with some shift in the northern and southern hemispheres. This inversion was observed since cycle 19 (Babcock, 1959). According to Snodgrass et al. (2000) the time of reversal in cycle 22 occurred earlier (November 1989) in the northern hemisphere than in the southern (May 1991). In the cycle 19 the inversion in each hemisphere was in phase with the activity maximum of spots (Waldmeier, 1960) and of calcium plages (Godoli, 1964). In agreement with our results Erofeev (1998) analyzing data of Mount Wilson Observatory from 1963 to 1976 and of Kitt Peak National Observatory since 1976 has found that the LSSMF rotates differentially at latitude of up to 55 and do not exhibit the ‘quasi-rigid’ rotation that is assumed to be characteristic of long living magnetic features. Lots of work has been dedicated to the study of the longitudinal activity (see e.g. Bumba et al., 2000), but the direct comparison with the results presented in this paper is rather difficult due to our reconstruction of the longitudinal distribution in the system rotating with the photosphere. As it was noticed in the introduction these results are fundamental for the understanding of the heliospheric structure and for the prediction of the magnetospheric perturbations.
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