Wavelet Analysis of solar,solar wind and geomagnetic parameters

The sunspot number, solar wind plasma, interplanetary magnetic field, and geomagnetic activity index A _p have been analyzed using a wavelet technique to look for the presence of periods and the temporal evolution of these periods. The global wavelet spectra of these parameters, which provide information about the temporal average strength of quasi periods, exhibit the presence of a variety of prominent quasi periods around 16 years, 10.6 years, 9.6 years, 5.5 years, 1.3 years, 180 days, 154 days, 27 days, and 14 days. The wavelet spectra of sunspot number during 1873–2000, geomagnetic activity index A _p during 1932–2000, and solar wind velocity and interplanetary magnetic field during 1964–2000 indicate that their spectral power evolves with time. In general, the power of the oscillations with a period of less than one year evolves rapidly with the phase of the solar cycle with their peak values changing from one cycle to the next. The temporal evolution of wavelet power in R _z, v _sw, n, B _y, B _z, |B|, and A _p for each of the prominent quasi periods is studied in detail.     

Magnetic Flux Imbalance of the Solar and Heliospheric Magnetic Fields

A comparative analysis of solar and heliospheric magnetic fields in terms of their cumulative sums reveals cyclic and long-term changes that appear as a magnetic flux imbalance and alternations of dominant magnetic polarities. The global magnetic flux imbalance of the Sun manifests itself in the solar mean magnetic field (SMMF) signal. The north – south asymmetry of solar activity and the quadrupole mode of the solar magnetic field contribute the most to the observed magnetic flux imbalance. The polarity asymmetry exhibits the Hale magnetic cycle in both the radial and azimuthal components of the interplanetary magnetic field (IMF). Analysis of the cumulative sums of the IMF components clearly reveals cyclic changes in the IMF geometry. The accumulated deviations in the IMF spiral angle from its nominal value also demonstrate long-term changes resulting from a slow increase of the solar wind speed over 1965 – 2006. A predominance of the positive IMF B _z with a significant linear trend in its cumulative signal is interpreted as a manifestation of the relic magnetic field of the Sun. Long-term changes in the IMF B _z are revealed. They demonstrate decadal changes owing to the 11/22-year solar cycle. Long-duration time intervals with a dominant negative B _z component were found in temporal patterns of the cumulative sum of the IMF B _z .     

Helical magnetorotational instability of Taylor‐Couette flows in the Rayleigh limit and for quasi‐Kepler rotation

The magnetorotational instability (MRI) of differential rotation under the simultaneous presence of axial and azimuthal components of the (current‐free) magnetic field is considered. For rotation with uniform specific angular momentum the MHD equations for axisymmetric perturbations are solved in a local short‐wave approximation. All the solutions are overstable for B_z · B_ϕ ≠ 0 with eigenfrequencies approaching the viscous frequency. For more flat rotation laws the results of the local approximation do not comply with the results of a global calculation of the MHD instability of Taylor‐Couette flows between rotating cylinders. – With B_ϕ and B_z of the same order the traveling‐mode solutions are also prefered for flat rotation laws such as the quasi‐Kepler rotation. For magnetic Prandtl number Pm → 0 they scale with the Reynolds number of rotation rather than with the magnetic Reynolds number (as for standard MRI) so that they can easily be realized in MHD laboratory experiments. – Regarding the nonaxisymmetric modes one finds a remarkable influence of the ratio B_ϕ/B_z only for the extrema. For B_ϕ ≫ B_z and for not too small Pm the nonaxisymmetric modes dominate the traveling axisymmetric modes. For standard MRI with B_z ≫ B_ϕ, however, the critical Reynolds numbers of the nonaxisymmetric modes exceed the values for the axisymmetric modes by many orders so that they are never prefered. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

p Modes in and Away from a Sunspot

A time series of GONG Dopplergrams for the period 10–14 May 1997 from Udaipur and Big Bear sites has been used to measure the velocity fluctuations in a sunspot (NOAA active region 8038) and quiet photosphere simultaneously. We observe that the power of pre-dominant p mode is reduced in the sunspot as compared to quiet photosphere by 39–52% depending on the location of the sunspot region on the solar disk. We also observe a relative peak frequency deviation of p modes in the sunspot, of the order of 80–310 Hz, which shows a linear dependence on the magnetic field gradient in the active region. The maximum frequency deviation of 310 Hz on 12 May appears to be an influence of a long-duration solar flare that occurred in this active region. We interpret this relative peak frequency deviation as either due to power re-distribution of p modes in the sunspot or a consequence of frequency modulation of these modes along the magnetic flux tubes due to rapidly varying magnetic field structure.     

160-min pulsation of the Sun: New observational results

The 1974–1988 Crimean measurements of the solar line-of-sight velocity continue to show the presence of a statistically significant periodicity P ₁ = 160.009 (±) min with an average harmonic amplitude of about 21 cm s^–1. The period is supposed to be that of the global pulsation of the Sun but with a little-known physical mechanism of excitation.The new observations give some evidence for the existence of a second periodicity, P ₁ = 160.014 (±) min. It is hypothesized that the appearance of P ₁ might be a sidelobe mode (of the P ₀-oscillation) induced by rapid rotation of the central solar core.It is also noted that the spacing, in frequency, between P ₀ and P ₁, corresponds to a beat period of 10 ± 3 yr, which happens to be in good agreement with the average duration of the 11 yr cycle of the magnetic activity of the Sun. Accordingly, we suppose that the phase shift of the P ₀-mode between the 1974–1982 and 1986–1988 time intervals reflects a remarkable change of the general magnetic field of the Sun in the course of the 22 yr solar cycle.     

On the relationship between polar faculae and large-scale magnetic field

We investigate a latitude–time distribution of polar faculae observed at Ussuriysk Observatory in years 1966–1986. The distribution is compared with the longitude-averaged (zonal) magnetic field of the Sun calculated from the data obtained at Mount Wilson Observatory in the years 1966–1976, and at Kitt Peak National Observatory during the period from 1976 to 1985. We found that slow, poleward-directed migration of the polar faculae zones occurring during the course of the solar cycle is not a continuous process, but it contains several episodes of appearance and fast poleward drift of new zones of polar faculae. At the rising phase of the solar cycle, new zones of polar faculae appear at latitudes as low as 40°, but the ones observed during the declining phase of the solar cycle originate at higher latitudes of 50–55°. Such episodes of appearance and fast migration of the polar faculae zones are associated with the poleward-directed streams of magnetic field originated at low latitudes. Moreover, we found some evidence for existence of an additional component of the polar faculae activity that reveals an equatorward migration during the course of the solar cycle. We also investigated a relationship between the number of polar faculae, n, and absolute magnetic flux _z of the zonal mode of the solar magnetic field. We found that within the polar zones of the Sun, substantial correlation between temporal variations of n and _z takes place both on the time scale of the solar cycle and on a shorter time scale of 2–4 years. The relationship between the number of polar faculae and magnetic flux may be approximated by a linear dependence n=0.12_z (where _z is expressed in 10²¹ Mx), except for time interval 1977 through 1980 for which the factor of proportionality is found to have a systematically larger value of 0.20.     

Variations of the IMF Bz component over a solar activity cycle for different regimes of solar wind formation

The behavioural features of the IMF B_z component for different solar wind velocity regimes have been studied. The study revealed a significant difference in variations of the B_z component between high-speed and low-speed regimes. Formation mechanisms for the IMF meridional component as well as the relationship of B_z with dynamical properties of the large-scale magnetic fields on the Sun are discussed.     

Towards Calibration of the Mean Magnetic Field of the sun

The 1968–2000 data on the mean magnetic field (MMF, longitudinal component) of the Sun are analysed to study long-time trends of the Sun's magnetic field and to check MMF calibration. It is found that, within the error limits, the mean intensity of photospheric magnetic field (the MMF strength, |H|), did not change over the last 33 years. It clearly shows, however, the presence of an 11-year periodicity caused by the solar activity cycle. Time variations of |H| correlate well with those of the radial component, |B _r|, of the interplanetary magnetic field (IMF). This correlation (r=0.69) appears to be significantly higher than that between |B _r| and the results of a potential source-surface extrapolation, to the Earth's orbit, of synoptic magnetic charts of the photosphere (using the so-called `saturation' factor <sup>–1</sup> for magnetograph measurements performed in the line Fei 525.0 nm; Wang and Sheeley, 1995). It seems therefore that the true source surface of IMF is the `quiet' photosphere – background fields and coronal holes, like those for MMF. The average `effective' magnetic strength of the photospheric field is determined to be about 1.9 G. It is also shown that there is an approximate linear relation between |B <sub>r</sub>| and MMF intensity |H| (in gauss)|B <sub>r</sub>|(H <sub>0</sub>)<sub>min</sub>×(1+C|H|)where =1.5×10<sup>–5</sup> normalizes the photospheric field strength to 1 AU distance from the Sun, (H <sub>0</sub>)<sub>min</sub>=1.2 G is some minimal `effective' intensity of photospheric background fields and C=1.3 G^–1 an empirical constant. It is noted that good correlation between time variations of |H| and |B _r| makes suspicious a correction of the photospheric magnetic fields with the use of saturation factor ^–1.     

Zonal structure and meridional drift of large-scale solar magnetic fields

Digitized synoptic charts of photospheric magnetic fields were analyzed for the past 4 incomplete solar activity cycles (1969–2000). The zonal structure and cyclic evolution of large-scale solar magnetic fields were investigated using the calculated values of the radial B _r, |B _r|, meridional B _θ, |B _θ|, and azimuthal B _φ, |B _φ| components of the solar magnetic field averaged over a Carrington rotation (CR). The time–latitude diagrams of all 6 parameters and their correlation analysis clearly reveal a zonal structure and two types of the meridional poleward drift of magnetic fields with the characteristic times of travel from the equator to the poles equal to ∼16–18 and ∼2–3 years. A conclusion is made that we observe two different processes of reorganization of magnetic fields in the Sun that are related to generation of magnetic fields and their subsequent redistribution in the process of emergence from the field generation region to the solar surface. Redistribution is supposed to be caused by some external forces (presumably, by sub-surface plasma flows in the convection zone).     

Large-Scale Magnetic Field and Sunspot Cycles

Hα magnetic synoptic charts of the Sun are processed for 1915–1999 and the spherical harmonics are calculated. It is shown that the polarity distribution of the magnetic field on Hα charts is similar to the polarity distribution of the Stanford magnetic field observations during 1975–1999. The index of activity of the large-scale magnetic field A(t), representing the sum of the intensities of dipole and octupole components, is introduced. It is shown that the cycle of the large-scale magnetic field of the Sun precedes on the average by 5.5 years the sunspot activity cycle, W(t). This means that the weak large-scale magnetic fields of the Sun do not result from decay and diffusion of strong fields from active regions as it is supposed in all modern theories of the solar cycle. On the basis of the new data the intensity of the current solar cycle 23 is predicted and some aspects of the theory of the solar cycle are discussed.     

Sensitivity of solar eigenfrequencies to the age of the sun

The increasing central concentration of the Sun with age modifies the acoustic eigenfrequencies. In particular, the frequency separation d _l =3(2l+3)^–1v _n,l –v _n–1,l+2 for modes with l + 1/2 n decreases as nuclear reactions augment the molecular-weight gradient in the energy-generating core. If, for example, the Sun were older than is generally believed, one might therefore expect d _l to be smaller than current theoretical predictions. On the other hand, to ensure that the luminosity is consistent with observations, the presumed initial hydrogen abundance would need to be enhanced, thereby reducing the resultant molecular-weight gradient. Thus there is some degree of cancellation of the two major factors that determine d _l .Various authors have either reported directly on the sensitivity of d _l , or have provided the information from which it can be calculated. We have added our own computations. There is broad agreement amongst the results: d _l diminishes with the presumed age of the Sun at the rate of about 1 Hz per Gy for l = 0; the magnitude of the rate appears to decline with increasing l.     

Global modes constituting the solar magnetic cycle

We show that the axisymmetric odd degree SHF modes of 21.4-yr periodicity and degrees l 29 in the solar magnetic field (as inferred from sunspot data during 1874–1976), are at least approximately stationary. Among the sine and cosine components of these SHF modes we find four groups, each defining the geometry of a coherent global oscillation characterized by a distinct power hump and its own level of variation. The first two of these geometrical eigenmodes (viz., B ₁ and B ₂), define the large-scale structure of the butterfly diagrams. Remaining SHF modes define the orderliness of the field distribution even within the wings of the butterflies down to scales l 29. These include the geometrical eigenmodes B ₃ and B ₄, which are not present in simulated data sets in which the latitudes of the sunspot groups are randomly redistributed within the wings of the butterflies.Superposition of B ₁, B ₂, B ₃, and B ₄ is necessary and sufficient to reproduce important observed properties of the latitude-time distribution of the real field, not only in the sunspot zone, but also in the middle (35°–75°) and the high (75°) latitudes, with appropriate relative orders of magnitude and phases. Thus, B ₁, B ₂, B ₃, and B ₄ seem to represent really existing global oscillations in the Sun's internal magnetic field. The geometrical form of B ₁ may also be the form of the forcing oscillation.     

Polar magnetic field reversals of the Sun in Maunder Minimum

A possible scenario of polar magnetic field reversal of the Sun during the Maunder Minimum (1645&amp;#x2013;1715) is discussed using data of magnetic field reversals of the Sun for 1880&amp;#x2013;1991 and the¹⁴ C content variations in the bi-annual rings of the pine-trees in 1600&amp;#x2013;1730 yrs.     

22-Year periodicity in the solar differential rotation

Using the data on sunspot groups compiled during 1879&amp;#x2013;1975, we determined variations in the differential rotation coefficientsA andB during the solar cycle. The variation in the equatorial rotation rateA is found to be significant only in the odd numbered cycles, with an amplitude &amp;#x223C; 0.01 &amp;#x03BC; rads^-1. There exists a good anticorrelation between the variations of the differential rotation rateB derived from the odd and even numbered cycles, suggesting existence of a &amp;#x2018;22-year&amp;#x2019; periodicity inB. The amplitude of the variation ofB is &amp;#x223C; 0.05 &amp;#x03BC; rad s^-1.     

Magnetohydrodynamic modes of a periodic magnetic medium

The oscillations of a magnetic medium periodic in the x-direction with B parallel to z, have been studied. The case with no gravity and a stepwise profile for B(x), allowing a normal mode analysis, has been examined and dispersion relations have been derived. The dispersion curves in the diagram k _z – display two types of modes, kink and sausage, like in the isolated slab, but the profiles are different and depend on Bloch's number k ₀. Moreover, modes usually absent in the isolated slab (propagating and tunelling) appear here, connecting surface- or body-wave domains. The detectability of this characteristic structure of the diagnostic diagram on the observations is discussed, and prospects for a more realistic analysis including gravity are given.     

Magnetic field of the young star RW Aur

Results of ourmeasurements of the longitudinal magnetic field B _z for the young star RWAur A are presented. B _z measured from the so-called narrow component of the He I 5876 line varies in the range from −1.47 ± 0.15 to +1.10 ± 0.15 kG. Our data are consistent with a stellar rotation period of }~5.6 days and the model of two hot spots with opposite magnetic field polarities spaced about 180° apart in longitude. Relative to the Earth, the spot with B _z < 0 lies in the hemisphere above the midplane of the accretion disk, while the spot with B _z > 0 is below the midplane. The upper limit for B _z (at the 3σ level) obtained by averaging all observations is 180 G for the photosphere and 220 and 230 G for the Hα and [OI] 6300 line formation regions, respectively. We have also failed to detect a field in the formation region of broad emission line components: the upper limit for B _z is 600 G. In two of 11 cases, we have detected a magnetic field in the formation region of the blue absorption wing of the Na I D doublet lines, i.e., in the wind from RW Aur A: B _z = −180 ± 50 and −810 ± 80 G. The radial velocity of the photospheric lines in RW Aur A averaged over all our observations is }~+10.5 km s⁻¹, i.e., a value lower than that obtained by Petrov et al. (2001) ten years earlier by 5.5 km s⁻¹. Therefore, we discuss the possibility that RW Aur is not a binary but a triple system.     

The scale and strength of the galactic magnetic field according to the pulsar data

In accordance with the data on the Faraday rotation, angular coordinates, and dispersion measurements and distances of 38 pulsars, the strengthB=2.1±1.1 G and directionl=99°±24°,b0° of the large-scale galactic magnetic field and the mean electron density in the galactic discN _e=0.03±0.01 cm^–3 are determined. A comparison with the results of a study of the measures of rotation of extragalactic radio sources enabled us to estimate the characteristic half-width of the distribution of the electron density on the Z-coordinate (h400 ps). The characteristic size of galactic magnetic field flucturations is shown to be =100–150 ps.     

HARPS spectropolarimetry of Herbig Ae/Be stars

Our knowledge of the presence and the strength of magnetic fields in intermediate‐mass pre‐main‐sequence stars remains very poor. We present new magnetic field measurements in six Herbig Ae/Be stars observed with HARPS in spectropolarimetric mode. We downloaded from the European Southern Observatory (ESO) archive the publically available HARPS spectra for six Herbig Ae/Be stars. Wavelength shifts between right‐ and left‐hand side circularly polarised spectra were interpreted in terms of a longitudinal magnetic field 〈B_z〉, using the moment technique introduced by Mathys. The application of the moment technique to the HARPS spectra allowed us in addition to study the presence of the crossover effect and quadratic magnetic fields. Our search for longitudinal magnetic fields resulted in first detections of weak magnetic fields in the Herbig Ae/Be stars HD 58647 and HD 98922. Further, we confirm the previous tentative detection of a weak magnetic field in HD 104237 by Donati et al. and confirm the previous detection of a magnetic field in the Herbig Ae star HD 190073. Surprisingly, the measured longitudinal magnetic field of HD 190073, 〈B_z〉 = 91 ± 18 G at a significance level of 5σ is not in agreement with the measurement results of Alecian et al. (2013), 〈B_z〉 = –10 ± 20 G, who applied the LSD method to exactly the same data. No crossover effect was detected for any star in the sample. Only for HD 98922 the crossover effect was found tobe close to 3σ with a measured value of –4228 ± 1443 km s^–1 G. A quadratic magnetic field of the order of 10 kG was detected in HD 98922, and of ∼3.5 kG in HD 104237. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Measurements of mean longitudinal magnetic fields in the Of?p stars HD 108 and HD 191612

Using polarimetric spectra obtained with the SOFIN spectrograph installed at the Nordic Optical Telescope, we detect a longitudinal magnetic field 〈B_z〉 = –168±35 G in the Of?p star HD 108. This result is in agreement with the longitudinal magnetic field measurement of the order of –150 G recently reported by the MiMeS team. The measurement of the longitudinal magnetic field in the Of?p star HD 191612 results in 〈B_z〉 = +450±153 G. The only previously published magnetic field measurement for this star showed a negative longitudinal magnetic field 〈B_z〉 = –220±38 G, indicating a change of polarity over ∼100 days. Further, we report the detection of distinct Zeeman features in the narrow Ca II and Na I doublet lines for both Of?p stars, hinting at the possible presence of material around these stars. The origin of these features is not yet clear and more work is needed to investigate how magnetic fields interact with stellar wind dynamics (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Duration of Polar Activity Cycles and Their Relation to Sunspot Activity

We have defined the duration of polar magnetic activity as the time interval between two successive polar reversals. The epochs of the polarity reversals of the magnetic field at the poles of the Sun have been determined (1) by the time of the final disappearance of the polar crown filaments and (2) by the time between the two neighbouring reversals of the magnetic dipole configuration (l=1) from the H synoptic charts covering the period 1870–2001. It is shown that the reversals for the magnetic dipole configuration (l=1) occur on an average 3.3±0.5 years after the sunspot minimum according to the H synoptic charts (Table I) and the Stanford magnetograms (Table III). If we set the time of the final disappearance of the polar crown filaments (determined from the latitude migration of filaments) as the criterion for deciding the epoch of the polarity reversal of the polar fields, then the reversal occurs on an average 5.8±0.6 years from sunspot minimum (last column of Table I). We consider this as the most reliable diagnostic for fixing the epoch of reversals, as the final disappearance of the polar crown filaments can be observed without ambiguity. We show that shorter the duration of the polar activity cycle (i.e., the shorter the duration between two neighbouring reversals), the more intense is the next sunspot cycle. We also notice that the duration of polar activity is always more in even solar cycles than in odd cycles whereas the maximum Wolf numbers W _\max is always higher for odd solar cycles than for even cycles. Furthermore, we assume there is a secular change in the duration of the polar cycle. It has decreased by 1.2 times during the last 120 years.