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Additional acceleration of solar-wind particles in current sheets of the heliosphere  

Valentina Zharkova   Submitted: 2015-04-21 07:22

Particles of fast solar wind in the vicinity of the heliospheric current sheet (HCS) or in a front of interplanetary coronal mass ejections (ICMEs) often reveal very peculiar energy or velocity profiles, density distributions with double or triple peaks, and well-defined streams of electrons occurring around or far away from these events. In order to interpret the parameters of energetic particles (both ions and electrons) measured by the WIND spacecraft during the HCS crossings, a comparison of the data was carried out with 3-D particle-in-cell (PIC) simulations for the relevant magnetic topology (Zharkova and Khabarova, 2012). The simulations showed that all the observed particle-energy distributions, densities, ion peak velocities, electron pitch angles and directivities can be fitted with the same model if the heliospheric current sheet is in a status of continuous magnetic reconnection. In this paper we present further observations of the solar-wind particles being accelerated to rather higher energies while passing through the HCS and the evidence that this acceleration happens well before the appearance of the corotating interacting region (CIR), which passes through the spacecraft position hours later. We show that the measured particle characteristics (ion velocity, electron pitch angles and the distance at which electrons are turned from the HCS) are in agreement with the simulations of additional particle acceleration in a reconnecting HCS with a strong guiding field as measured by WIND. A few examples are also presented showing additional acceleration of solar-wind particles during their passage through current sheets formed in a front of ICMEs. This additional acceleration at the ICME current sheets can explain the anticorrelation of ion and electron fluxes frequently observed around the ICME's leading front. Furthermore, it may provide a plausible explanation of the appearance of bidirectional "strahls" (field-aligned most energetic suprathermal electrons) at the leading edge of ICMEs as energetic electrons generated during a magnetic reconnection at the ICME-front current sheet.

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

Publication Status: Ann. Geophys., 33, 457-470, 2015, published
Last Modified: 2015-04-21 10:46
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PREDICTION OF SOLAR ACTIVITY FROM SOLAR BACKGROUND MAGNETIC FIELD VARIATIONS IN CYCLES 21?23  

Valentina Zharkova   Submitted: 2014-10-22 10:24

A comprehensive spectral analysis of both the solar background magnetic field (SBMF) in cycles 21?23 and the sunspot magnetic field in cycle 23 reported in our recent paper showed the presence of two principal components (PCs) of SBMF having opposite polarity, e.g., originating in the northern and southern hemispheres, respectively. Over a duration of one solar cycle, both waves are found to travel with an increasing phase shift toward the northern hemisphere in odd cycles 21 and 23 and to the southern hemisphere in even cycle 22. These waves were linked to solar dynamo waves assumed to form in different layers of the solar interior. In this paper, for the first time, the PCs of SBMF in cycles 21?23 are analyzed with the symbolic regression technique using Hamiltonian principles, allowing us to uncover the underlying mathematical laws governing these complex waves in the SBMF presented by PCs and to extrapolate these PCs to cycles 24?26. The PCs predicted for cycle 24 very closely fit (with an accuracy better than 98%) the PCs derived from the SBMF observations in this cycle. This approach also predicts a strong reduction of the SBMF in cycles 25 and 26 and, thus, a reduction of the resulting solar activity. This decrease is accompanied by an increasing phase shift between the two predicted PCs (magnetic waves) in cycle 25 leading to their full separation into the opposite hemispheres in cycle 26. The variations of the modulus summary of the two PCs in SBMF reveals a remarkable resemblance to the average number of sunspots in cycles 21?24 and to predictions of reduced sunspot numbers compared to cycle 24: 80% in cycle 25 and 40% in cycle 26.

Authors: Simon J. Shepherd , Sergei I. Zharkov and Valentina V. Zharkova
Projects: None

Publication Status: 2014, Astrophysical Journal, 795, 46 (published)
Last Modified: 2014-10-22 12:36
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ERRATUM: "Exact Analytical Solutions of Continuity Equation for Electron Beams Precipitating in Coulomb Collisions"  

Valentina Zharkova   Submitted: 2014-08-19 03:21

In this erratum letter we correct a mistake in the characteristics for differential density N obtained in 2014ApJ...788...42D} from the updated continuity equation for electron density and compare the solutions for electron density N obtained from continuity equations (CEs) for electron flux Nv and for electron density. We show that the corrected solution for N obtained from CE for electron density still has an additional exponential term of (E2+2a\xi)-1/4 comparing to the solution found from continuity equation for electron flux. This updated solution produces power law differential spectra of beam electrons as function of E2+2a\xi having a spectral index equal to -\frac{\gamma+1}{2} and not to -\frac{\gamma+0.5}{2} as it appears from the continuity equation for electron flux Nv. This updated solution is exactly the one reported by \citet{Syrovatsky72} indicating that their solution has been derived from CE for electron density and not for electron flux as stated in their paper. The difference in the spectral indices in energy spectra is also reflected in the spectral indices for mean electron spectra with a spectral index to be equal to \gamma-2, similar to \citet{Syrovatsky72, for the solutions from CE for electron density and equal to \gamma-2.5 if continuity equation for electron flux is used.

Authors: Dobranskis R.R. and Zharkova V.V.
Projects: None

Publication Status: ApJ subm. on 26 July '14
Last Modified: 2014-08-20 09:47
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Exact Analytical Solutions of Continuity Equation for Electron Beams Precipitating in Coulomb Collisions  

Valentina Zharkova   Submitted: 2014-06-11 03:24

The original continuity equation (CE) used for the interpretation of the power law energy spectra of beam electrons in flares was written and solved for an electron beam flux while ignoring an additional free term with an electron density. In order to remedy this omission, the original CE for electron flux, considering beam's energy losses in Coulomb collisions, was first differentiated by the two independent variables: depth and energy leading to partial differential equation for an electron beam density instead of flux with the additional free term. The analytical solution of this partial differential continuity equation (PDCE) is obtained by using the method of characteristics. This solution is further used to derive analytical expressions for mean electron spectra for Coulomb collisions and to carry out numeric calculations of hard X-ray (HXR) photon spectra for beams with different parameters. The solutions revealed a significant departure of electron densities at lower energies from the original results derived from the CE for the flux obtained for Coulomb collisions. This departure is caused by the additional exponential term that appeared in the updated solutions for electron differential density leading to its faster decrease at lower energies (below 100 keV) with every precipitation depth similar to the results obtained with numerical Fokker-Planck solutions. The effects of these updated solutions for electron densities on mean electron spectra and HXR photon spectra are also discussed.

Authors: Dobranskis R.R. and Zharkova V.V.
Projects: None

Publication Status: Published in ApJ
Last Modified: 2014-06-11 09:52
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Probing latitudinal variations of the solar magnetic field in cycles 21-23 by Parker's Two-Layer Dynamo Model with meridional circulation}  

Valentina Zharkova   Submitted: 2013-11-20 12:34

Principle component analysis (PCA) of the solar background magnetic field (SBMF) measured from Wilcox Solar Observatory (WSO) magnetograms revealed the following principal components (PCs) in latitudes: two main symmetric components, which are the same for all cycles 21-23, and three pairs of asymmetric components, which are unique for each cycle. These SBMF variations are assumed to be those of poloidal magnetic field travelling slightly off-phase from pole to pole while crossing the equator. They are assumed to be caused by a joint action of dipole and quadruple magnetic sources in the Sun. In the current paper, we make the first attempt to interpret these latitudinal variations in the surface magnetic field with Parker's two-layer dynamo model. The latitudinal distributions of such waves are simulated for cycles 21-23 by the modified Parker's dynamo model taking into account both α and omega effects operating simultaneously in the two (upper and lower) layers of the solar convective zone (SCZ) and having opposite directions of meridional circulation. The simulations are carried out for both dipole and quadruple magnetic sources with the dynamo parameters specifically selected to provide the curves fitting closely the PCs derived from SBMF variations in cycles 21-23. The simulations are optimised for matching the positions of maximums in latitude, the number of equator crossings and the phase difference between the two dynamo waves operating in the two layers. The dominant pair of PCs present in each cycle is found to be fully asymmetric with respect to the magnetic poles and produced by a magnetic dipole. This pair is found to account for the two main dynamo waves operating between the two magnetic poles. There are also three further pairs of waves unique to each cycle and associated with multiple magnetic sources in the Sun. For the odd cycle 21 the simulated poloidal field fits the observed PCs, only if they are produced by magnetic sources with a quadruple symmetry in both layers, while for the even cycle 22 the fit to the observed PCs is achieved only in the case of quadruple magnetic sources in the upper layer and dipole sources in the inner layer. For the other odd cycle 23 the fit to observation is obtained for the quadruple magnetic sources in the inner layer and the dipole sources in the upper layer. The magnitudes of dynamo numbers D defining the conditions (depth and latitude) of a magnetic flux formation and the numbers N of zeros (equator crossings by the waves) are found to increase and the meridional circulation speed to decrease with a cycle number increase (D,=,-700, N,=,3 for cycle 21 and D,=,-104, N,=,9 for cycle 23). The phase delays between the waves in each unique pairs are also found to increase with the cycle number from sim,9circ in cycle 21 to sim,13circ in cycle 23

Authors: Popova E., Zharkova V. and Zharkov S.
Projects: None

Publication Status: published, Ann. Geophys., 31, 2023, 2013
Last Modified: 2013-11-21 11:50
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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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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 ofelectrons is still a great challenge for interpretation of observations in realevents. In this paper we apply the FP kinetic model of precipitation ofelectron beam with energy range from 12 keV to 1.2 MeV to the interpretation ofX-ray and microwave emissions observed in the flare of 10 March 2001. Methods.The theoretical HXR and MW emissions were calculated by using the distributionfunctions of electron beams found by solving time-dependent Fokker-Planckapproach in a converging magnetic field (Zharkova at al., 2010; Kuznetsov andZharkova, 2010) for anisotropic scattering of beam electrons on the ambientparticles in Coloumb collisions and Ohmic losses. The simultaneous observed HXRphoton spectra and frequency distribution of MW emission and polarization werefit by those simulated from FP models which include the effects of electricfield induced by beam electrons and precipitation into a converging magneticloop. Magnetic field strengths in the footpoints on the photosphere wereupdated with newly calibrated SOHO/MDI data. The observed HXR energy spectrumabove 10 keV is shown to be a double power law which was fit precisely by thephoton HXR spectrum simulated for the model including the self-induced electricfield but without magnetic convergence. The MW emission simulated for differentmodels of electron precipitation revealed a better fit to the observeddistribution at higher frequencies for the models combining collisions andelectric field effects with a moderate magnetic field convergence of 2. The MWsimulations were able to reproduce closely the main features of the MW emissionobserved 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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Subject will be restored when possible  

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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Subject will be restored when possible  

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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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 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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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 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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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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