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Principal Component Analysis of Background and Sunspot Magnetic Field Variations During Solar Cycles 21-23  

Valentina Zharkova   Submitted: 2012-07-05 06:42

The aim of this paper is to derive principal components (PCs) in variations of (a) the solar background magnetic field (SBMF) measured by the Wilcox Solar Observatory with low spatial resolution for solar cycles 21-23, and, (b) the sunspot magnetic field (SMF) in cycle 23 obtained by SOHO/MDI. For reduction of the component dimensions, the Principal Component Analysis (PCA) is carried out to identify global patterns in the data and to detect the pairs of principal components and corresponding empirical orthogonal functions (EOFs). PCA analysis reveals two main temporal PCs in SBMF of opposite polarities originating in the opposite hemispheres and running noticeably off-phase (with about a two and half year delay), with their maximums overlapping in the most active hemisphere for a given cycle. Their maximum magnitudes are reduced by factor 3 from cycle 21 to 23 overlapping in the Northern hemisphere for cycle 21, the Southern one in cycle 22 and in the Northern again in cycle 23. The reduction of magnitudes and slopes of the maximums of the SBMF waves from cycle 21 towards cycle 23 leads us to expect lower magnitudes of the SBMF wave in cycle 24. Also PCA allowed us to detect 4 pairs of EOFs in the SBMF latitudinal components: the two main latitudinal EOFs attributed to symmetric and another three pairs of EOFs assigned to asymmetric types of meridional flows. The results allow us to postulate the existence of dipole and quadruple (or triple dipole) magnetic structures in the SBMF, which varies from cycle to cycle and takes the form of two waves travelling off phase, with a phase shift of one quarter of the 11 year period. Similar PC and EOF components were found in temporal and latitudinal distributions of the sunspot magnetic field for cycle 23 revealing the polarities opposite to the SBMF polarities and double maximum in time or maximums in latitude corresponding to the maximums of the SBMF PC residuals or minimums in SBMF EOFs, respectively. This allows to suggest that the SBMF waves also modulate the occurrence and magnitudes of sunspot magnetic field in time and latitude.

Authors: Zharkova V.V., Shepperd, S.J. and Zharkov S.I.
Projects: SoHO-MDI

Publication Status: 2012, MNRAS, in press
Last Modified: 2012-07-05 07:17
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Particle dynamics in the reconnecting heliospheric current sheet: solar wind data versus 3D PIC simulations  

Valentina Zharkova   Submitted: 2012-04-20 11:07

In this paper we apply an assumption of the reconnecting heliospheric current sheet (HCS) for explanation of some contradictory results in the experimental detection of the sector boundaries (SBs) from the interplanetary magnetic field (IMF) and electron pitch angle measurements. Trajectories, densities, velocity and pitch angle distributions of particles accelerated by a super-Dreicer electric field are investigated with 2.5D full kinetic particle-in-cell (PIC) approach in the heliospheric current sheet (HCS) assumed to undergo a slow magnetic reconnection process with magnetic field configurations deduced from the solar wind observations. This approach reveals that during motion in a current sheet both kinds of particles, electrons and protons, are to be separated, either fully or partially, with respect to its midplane that can lead to their ejection to the opposite semiplanes that was also observed during the HCS crossings. This separation is found to form Hall's currents and polarisation electric field across the current sheet, which distribution over the current sheets allows to reproduce the magnitudes and temporal profiles of proton and ion velocities measured across the sector boundary (current sheet midplane). This separation process, in turn, divides both kinds of particles on 'transit' and 'bounced' ones depending on a side of the current sheet where they enter it and where they are supposed to be ejected. The transit and bounced protons reproduce rather closely the measured distributions of proton/ion densities about the current sheet midplane with a larger maximum occurring at the heliospheric sector boundary to be formed by the bounced protons and the other two smaller maximums on both sides from the central one to be formed by 'transit' protons. The observed electron distributions of density and energy before and after SBCs are found to fit the simulated ones for electrons accelerated in a current sheet revealing a sharp increase of density from one side from the HCS boundary and a depression from the other side. The transit electrons are shown to gain energies up to ten of keVs while the bounced ones gain only a few tens eVs as often measured in the HCS with a single crossing that results in the bump-in-tail electron distributions leading to Langmuir turbulence. The bounced electrons are shown to be responsible for the increased density of electrons detected at some distance from the HCS boundary (midplane) with the horse shoe-like or medallion- (or locket)-type distributions in pitch angles with the distance, at which electrons turn away from the HCS, being dependent on a magnitude of the guiding magnetic field.

Authors: Zharkova V.V. and Khabarova O.V.
Projects: None

Publication Status: Astrophysical Journal, 2012, 750/1, in press
Last Modified: 2012-04-25 12:45
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Diagnostics of electron beam properties from the simultaneous hard X-ray and microwave emission in the 10 March 2001 flare  

Valentina Zharkova   Submitted: 2011-05-23 08:56

Simultaneous simulation of HXR and MW emission with the same populations of electrons is still a great challenge for interpretation of observations in real events. In this paper we apply the FP kinetic model of precipitation of electron beam with energy range from 12 keV to 1.2 MeV to the interpretation of X-ray and microwave emissions observed in the flare of 10 March 2001. Methods. The theoretical HXR and MW emissions were calculated by using the distribution functions of electron beams found by solving time-dependent Fokker-Planck approach in a converging magnetic field (Zharkova at al., 2010; Kuznetsov and Zharkova, 2010) for anisotropic scattering of beam electrons on the ambient particles in Coloumb collisions and Ohmic losses. The simultaneous observed HXR photon spectra and frequency distribution of MW emission and polarization were fit by those simulated from FP models which include the effects of electric field induced by beam electrons and precipitation into a converging magnetic loop. Magnetic field strengths in the footpoints on the photosphere were updated with newly calibrated SOHO/MDI data. The observed HXR energy spectrum above 10 keV is shown to be a double power law which was fit precisely by the photon HXR spectrum simulated for the model including the self-induced electric field but without magnetic convergence. The MW emission simulated for different models of electron precipitation revealed a better fit to the observed distribution at higher frequencies for the models combining collisions and electric field effects with a moderate magnetic field convergence of 2. The MW simulations were able to reproduce closely the main features of the MW emission observed at higher frequencies.

Authors: Zharkova, V.V., Meshalkina, N.S., Kashapova, L.K., Kuznetsov, A.A. and Altyntsev A.T.
Projects: RHESSI

Publication Status: Astronomy and Astrophysics, in press
Last Modified: 2011-05-24 09:44
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The effects of electron beam induced electric field on the generation of Langmuir turbulence in flaring atmospheres  

Valentina Zharkova   Submitted: 2011-03-16 08:15

The precipitation of an electron beam injected into the solar atmosphere is studied for generation of Langmuir wave turbulence in the presence of collisional and Ohmic losses. The system of quasi-linear time-dependent kinetic equations describing the evolution of beams and Langmuir waves is solved by using the summary approximation method. It is found that at upper atmospheric levels the self-induced electric field suppresses the generation of Langmuir turbulence to very small regions below injection. With further precipitation into deeper atmo- sphere the initial single power law distributions of beam electrons are transformed into energy distributions with maxima at lower energies formed by collisional and Ohmic energy depletion. The electrons with lower energies (<20 keV) generateon large spatial scales intense low-hybrid and high-hybrid Langmuir waves with well defined patterns in the corona while higher energy electrons generate moderate low hybrid waves in the chromosphere. The maximum wave density appears at the maximum of the ambient density. The self-induced electric field reduces the level and makes narrower the regions with low-hybrid Langmuir turbulence in the corona and upper chromosphere. The higher the beam energy flux, or its self-induced electric field, the narrower the regions with Langmuir turbulence. High hybrid Langmuir turbulence generated in a form of regular patterns in depth and electron energies is also reduced by electric field to smaller number of patterns shifted to smaller region in the upper corona.

Authors: Zharkova V.V. and Siversky T.V.
Projects: None

Publication Status: Astrophysical Journal, in press
Last Modified: 2011-03-16 15:12
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Valentina Zharkova   Submitted: 2008-02-07 08:11

The Solar Feature Catalogues for sunspots and active regions measured with SOHO/MDI instrument and Ca II K3 spectroheliograph of the Paris-Meudon Obser- vatory are analyzed with the automated classification technique for sunspot groups and active region polarities. We report the first classification results for daily vari- ations of tilt angles (normal and trigonometric ones) in sunspot groups (SG) and active (AR) regions in the cycle 23. The average normal tilts are presented for every year at the ascending and descending phases of the cycle 23 which are similar to those deduced by other authors for the cycles 19-22. The normal tilts of both the sunspot groups and active regions are shown to increase in the ascending phase and a decrease in the descending phase. Similar to SG and AR areas, the trigonometric tilts are shown to have the noticeable North-South asymmetry with the Southern hemisphere dominant in the selected ascending and descending periods. The nor- mal tilt variations with latitude follow Joy?s law revealing a periodicity along the meridian of about 10 and reaching the maximum of 14 at the latitude of about 32 corresponding to the top of the ?royal zone? where the sunspots appear. The variations of polarity separation with a latitude are in an anti-phase with those of the tilts reaching a maximum at the latitude of 35 and showing a small positive separation for the groups/active regions in a vicinity of the average tilts ?40. The ratio R of the polarity separation to the trigonometric tilt fits the linear function of a latitude ' as R = −0.0213' − 0.1245 confirming positive separation for the polarities of active regions with the average tilts, or the dominance of activity in the Southern hemisphere activity, for the selected period of observations.

Authors: Zharkova V.V. and Zharkov S.I.
Projects: SoHO-MDI

Publication Status: Adv.Space Res., 2008 in press
Last Modified: 2008-02-07 09:22
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Valentina Zharkova   Submitted: 2008-02-07 08:11

The Solar Feature Catalogues for sunspots and active regions measured with SOHO/MDI instrument and Ca II K3 spectroheliograph of the Paris-Meudon Observatory are analyzed with the automated classification technique for sunspot groups and active region polarities. We report the first classification results for daily variations of tilt angles (normal and trigonometric ones) in sunspot groups (SG) and active (AR) regions in the cycle 23. The average normal tilts are presented for every year at the ascending and descending phases of the cycle 23 which are similar to those deduced by other authors for the cycles 19-22. The normal tilts of both the sunspot groups and active regions are shown to increase in the ascending phase and a decrease in the descending phase. Similar to SG and AR areas, the trigonometric tilts are shown to have the noticeable North-South asymmetry with the Southern hemisphere dominant in the selected ascending and descending periods. The normal tilt variations with latitude follow Joy's law revealing a periodicity along the meridian of about 10° and reaching the maximum of 14° at the latitude of about 32° corresponding to the top of the ''royal zone'' where the sunspots appear. The variations of polarity separation with a latitude are in an anti-phase with those of the tilts reaching a maximum at the latitude of 35°and showing a small positive separation for the groups/active regions in a vicinity of the average tilts ±40°. The ratio R of the polarity separation to the trigonometric tilt fits the linear function of a latitude φ as R = −0.0213φ − 0.1245 confirming positive separation for the polarities of active regions with the average tilts, or the dominance of activity in the Southern hemisphere activity, for the selected period of observations.

Authors: Zharkova V.V. and Zharkov S.I.
Projects: SoHO-MDI

Publication Status: Adv.Space Res., 2008 in press
Last Modified: 2008-02-07 12:43
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Valentina Zharkova   Submitted: 2008-02-07 07:59

The observed phase relations between the weak background solar magnetic (poloidal) field and strong magnetic field assocciated wtih sunspots (toroidal field) measured at different latitudes are presented. For measurements of the solar magnetic field (SMF) the low-resolution images obtained from Wilcox Solar Observatory (WSO) are used while sunspot magnetic field was taken from the Solar Feature Catalogues utilizing the SOHO/MDI fulldisk magnetograms. The quasi-3D latitudinal distributions of sunspot areas and magnetic elds obtained for 30 latitudinal bands (15 in the northern and 15 in the southern hemispheres) within the whole mu-hemispheres in longitudes are correlated with those of the background SMF. The sunspot areas in all latitudinal zones (averaged with a sliding one-year filter) reveal a strong positive correlation with the absolute SMF in the same zone appearing rst with a zero timelag and repeating with a two  three year time lag through the whole period of observations. The residuals of the sunspot areas averaged by one year and those by four years are also shown to have a well defined periodic structure visible in every two - three years close to pi/4 with the maxima occurring at -40 and +40 degrees in latitude and the drifts during this period either towards the Equator or the Poles depending on the latitude of sunspot occurrence. This phase relation between poloidal and toroidal field throughout the whole cycle is discussed in association with both the symmetric and asymmetric components of the background SMF and relevant predictions by the solar dynamo models.

Authors: Zharkov S.I., Gavryuseva,E. and Zharkova V.V
Projects: SoHO-MDI

Publication Status: Solar Physics, in press
Last Modified: 2008-02-07 09:22
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Valentina Zharkova   Submitted: 2008-02-07 07:59

The observed phase relations between the weak background solar magnetic (poloidal) field and strong magnetic field assocciated wtih sunspots (toroidal field) measured at different latitudes are presented. For measurements of the solar magnetic field (SMF) the low-resolution images obtained from Wilcox Solar Observatory (WSO) are used while sunspot magnetic field was taken from the Solar Feature Catalogues utilizing the SOHO/MDI full disk magnetograms. The quasi-3D latitudinal distributions of sunspot areas and magnetic fields obtained for 30 latitudinal bands (15 in the northern and 15 in the southern hemispheres) within the whole mu-hemispheres in longitudes are correlated with those of the background SMF. The sunspot areas in all latitudinal zones (averaged with a sliding one-year filter) reveal a strong positive correlation with the absolute SMF in the same zone appearing first with a zero timelag and repeating with a two-three year time lag through the whole period of observations. The residuals of the sunspot areas averaged by one year and those by four years are also shown to have a well defined periodic structure visible in every two-three years close to π/4 with the maxima occurring at -40 and +40 degrees in latitude and the drifts during this period either towards the Equator or the Poles depending on the latitude of sunspot occurrence. This phase relation between poloidal and toroidal field throughout the whole cycle is discussed in association with both the symmetric and asymmetric components of the background SMF and relevant predictions by the solar dynamo models.

Authors: Zharkov S.I., Gavryuseva,E. and Zharkova V.V
Projects: SoHO-MDI

Publication Status: Solar Physics, in press
Last Modified: 2008-02-07 09:45
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Subject will be restored when possible  

Valentina Zharkova   Submitted: 2008-02-07 07:59

The observed phase relations between the weak background solar magnetic (poloidal) field and strong magnetic field associated with sunspots (toroidal field) measured at different latitudes are presented. For measurements of the solar magnetic field (SMF) the low-resolution images obtained from Wilcox Solar Observatory (WSO) are used while sunspot magnetic field was taken from the Solar Feature Catalogues utilizing the SOHO/MDI full disk magnetograms. The quasi-3D latitudinal distributions of sunspot areas and magnetic fields obtained for 30 latitudinal bands (15 in the northern and 15 in the southern hemispheres) within the whole µ-hemispheres in longitudes are correlated with those of the background SMF. The sunspot areas in all latitudinal zones (averaged with a sliding one-year filter) reveal a strong positive correlation with the absolute SMF in the same zone appearing first with a zero timelag and repeating with a two-three year time lag through the whole period of observations. The residuals of the sunspot areas averaged by one year and those by four years are also shown to have a well defined periodic structure visible in every two-three years close to π/4 with the maxima occurring at -40 and +40 degrees in latitude and the drifts during this period either towards the Equator or the Poles depending on the latitude of sunspot occurrence. This phase relation between poloidal and toroidal field throughout the whole cycle is discussed in association with both the symmetric and asymmetric components of the background SMF and relevant predictions by the solar dynamo models.

Authors: Zharkov S.I., Gavryuseva,E. and Zharkova V.V
Projects: SoHO-MDI

Publication Status: Solar Physics, in press
Last Modified: 2008-02-07 09:47
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Valentina Zharkova   Submitted: 2008-02-07 07:55

The observed phase relations between the weak background solar magnetic (poloidal) eld and strong magnetic eld associated with sunspots (toroidal eld) measured at dierent latitudes are presented. For measurements of the solar magnetic eld (SMF) the low-resolution images obtained from Wilcox Solar Observatory (WSO) are used while sunspot magnetic eld was taken from the Solar Feature Catalogues utilizing the SOHO/MDI fulldisk magnetograms. The quasi- 3D latitudinal distributions of sunspot areas and magnetic elds obtained for 30 latitudinal bands (15 in the northern and 15 in the southern hemispheres) within the whole -hemispheres in longitudes are correlated with those of the background SMF. The sunspot areas in all latitudinal zones (averaged with a sliding one-year lter) reveal a strong positive correlation with the absolute SMF in the same zone appearing rst with a zero timelag and repeating with a two  three year time lag through the whole period of observations. The residuals of the sunspot areas averaged by one year and those by four years are also shown to have a well dened periodic structure visible in every two  three years close to =4 with the maxima occurring at

Authors: Zharkov S.I., Gavryuseva,E. and Zharkova V.V
Projects: SoHO-MDI

Publication Status: Solar Physics, in press
Last Modified: 2008-02-07 07:55
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Abstracts by Author
Principal Component Analysis of Background and Sunspot Magnetic Field Variations During Solar Cycles 21-23
Particle dynamics in the reconnecting heliospheric current sheet: solar wind data versus 3D PIC simulations
Diagnostics of electron beam properties from the simultaneous hard X-ray and microwave emission in the 10 March 2001 flare
The effects of electron beam induced electric field on the generation of Langmuir turbulence in flaring atmospheres
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