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Reply to comment by Usoskin (2017) on the paper  

Valentina Zharkova   Submitted: 2017-10-10 05:25

In this communication we provide our answers to the comments by Usoskin (2017) on our recent paper (Popova et al, 2017a). We show that Principal Component Analysis (PCA) allows us to derive eigen vectors with eigen values assigned to variance of solar magnetic field waves from full disk solar magnetograms obtained in cycles 21-23 which came in pairs. The current paper (Popova et al, 2017a) adds the second pair of magnetic waves generated by quadruple magnetic sources. This allows us to recover a centennial cycle, in addition to the grand cycle, and to produce a closer fit to the solar and terrestrial activity features in the past millennium.

Authors: Zharkova V.V., Popova E., Shepherd S.J. and Zharkov S.
Projects:

Publication Status: accepted
Last Modified: 2017-10-12 16:26
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Non-thermal hydrogen Balmer and Paschen emission in solar flares generated by electron beams  

Valentina Zharkova   Submitted: 2017-10-10 05:22

Sharp rises of hard X-ray (HXR) emission accompanied by Hα line profiles with strong red shifts up to 4 Å from the central wavelength, often observed at the onset of flares with the Specola Solare Ticinese Telescope (STT) and the Swedish Solar Telescope (SST), are not fully explained by existing radiative models. Moreover, the observations of white light (WL) and Balmer contin- uum emission with the Interface Region Imaging Spectrograph (IRIS) reveal strong co-temporal enhancements and often nearly co-spatial with HXR emission. These effects indicate a fast ef- fective source of excitation and ionisation of hydrogen atoms in flaring atmospheres associated with HXR emission. In this paper we investigate electron beams as the agents accounting for the observed hydrogen line and continuum emission. Flaring atmospheres are considered to be produced by a 1D hydrodynamic response to the injection of an electron beam defining their kinetic temperatures, densities and macrovelocities. A radiative response in these atmospheres is simulated using a fully non-local ther- modynamic equilibrium (NLTE) approach for a 5 levels plus continuum hydrogen atom model, considering its excitation and ionisation by spontaneous, external and internal diffusive radiation and by inelastic collisions with thermal and beam electrons. Resulting intensities of hydrogen line and continuum emission were also calculated for Balmer and Paschen series. We find that inelastic collisions with beam electrons strongly increase excitation and ionisation of hydrogen atoms from the chromosphere to photosphere. This leads to an increase in Lyman continuum radiation, which has high optical thickness, and after the beam is off it governs hydrogen ionisation and leads to the long lasting order of magnitude enhancement of emission in Balmer and Paschen continua. The ratio of Balmer-to-other-continuum head intensities are found correlated with the beams's initial flux. The height distribution of contribution functions for Paschen continuum emission indicate a close correlation with the observations of heights of WL and HXR emission reported for limb flares. This process also leads to a strong increase of wing emission (Stark's wings) in Balmer and Paschen lines, that is superimposed on large red-shifted enhancements of Hα-Hγ line emission resulting from a downward motion by hydrodynamic shocks. The simulated line profiles are shown to closely fit the observations for different flaring events.

Authors: Druett M. and Zharkova V.V.
Projects: None

Publication Status: Accepted
Last Modified: 2017-10-11 06:21
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Beam electrons as a source of Hα flare ribbons  

Valentina Zharkova   Submitted: 2017-06-27 07:18

The observations of solar flare onsets show rapid increase of hard and soft X-rays, ultra-violet emission with large Doppler blue shifts associated with plasma upflows, and Hα hydrogen emission with red shifts up to 1-4 Å. Modern radiative hydrodynamic models account well for blue-shifted emission, but struggle to reproduce closely the red-shifted Hα lines. Here we present a joint hydrodynamic and radiative model showing that during the first seconds of beam injection the effects caused by beam electrons can reproduce Hα line profiles with large red-shifts closely matching those observed in a C1.5 flare by the Swedish Solar Telescope. The model also accounts closely for timing and magnitude of upward motion to the corona observed 29 s after the event onset in 171 Å by the Atmospheric Imaging Assembly/Solar Dynamics Observatory.

Authors: Malcolm Druett, Eamon Scullion, Valentina Zharkova, Sarah Matthews, Sergei Zharkov & Luc Rouppe Van der Voort
Projects: None

Publication Status: published in Nature Communications
Last Modified: 2017-06-28 08:41
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On a role of quadruple component of magnetic field in defining solar activity in grand cycles  

Valentina Zharkova   Submitted: 2017-05-16 06:03

In this paper we revise our prediction of solar activity using a solar background magnetic field as a proxy by the inclusion of eigen vectors of solar magnetic waves produced by quadruple magnetic sources, in addition to the principal eigen modes generated by two-layer dipole sources (Zharkova et al., 2015). By considering the interference of two dipole and one quadruple waves we produce the revised summary curve for the last 400 years accounting for the additional minima of solar activity occurred at the beginning of 19th (Dalton minimum) and 20th centuries. Using the dynamo model with meridional circulation and selecting the directions of circulation for quadruple waves, we estimate the parameters of quadrupole waves best fitting the observations in the past grand cycle. The comparison shows that the quadruple wave has to be generated in the inner layer of the solar convective zone, in order to provide the additional minima observed in 19 and 20 centuries, thus, naturally accounting for Gleissberg centennial cycle. The dynamo wave simulated for the dipole and quadruple sources reveals much closer correspondence of the resulting summary curve derived from the principal components of magnetic field variations to the solar activity oscillations derived from the average sunspot numbers in the current grand cycle.

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

Publication Status: Journal of Atmospheric and Solar-Terrestrial Physics, http://dx.doi.org/10.1016/j.jastp.2017.05.006 in press
Last Modified: 2017-05-18 11:32
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Analytical solutions of continuity equation for joint collisional and Ohmic energy losses and their effects on hard X-ray emission.II. Mixed energy losses  

Valentina Zharkova   Submitted: 2016-03-08 04:49

In this paper we consider simultaneous analytical solutions of continuity equations for electron beam precipitation a) in collisional losses and b) in Ohmic losses, or mixed energy losses (MEL), by applying the iterative method to calculate the resulting differential densities at given precipitation depth. The differential densities of precipitating electrons derived from the analytical solutions for mixed energy losses reveal increased flattening at energies below 10-30 keV compared to a pure collisional case. This flattening becomes stronger with an increasing precipitation depth turning into a positive slope at greater precipitation depths in the chromosphere resulting in a differential density distribution with maximum that shifts towards higher energies with increase of a column depth. While the differential densities combining precipitating and returning electrons are higher at lower energies than those for a pure collisional case. The resulting hard X-ray (HXR) emission produced by the beams with different initial energy fluxes and spectral indices is calculated using the MEL approach for different ratios between the differential densities of precipitating and returning electrons. The number of returning electrons can be even further enhanced by a magnetic mirroring, not considered in the present model, while dominating at lower atmospheric depths where the magnetic convergence and magnitude are the highest. The proposed MEL approach provides an opportunity to account simultaneously for both collisional and ohmic losses in flaring events, which can be used for a quick spectral fitting of HXR spectra and evaluation of a fraction of returning electrons versus precipitating ones. The semi-analytical MEL approach is used for spectral fitting to RHESSI observations of nine C, M and X class flares revealing a close fit to the observations and good resemblance to numerical FP solutions.

Authors: Zharkova V.V. and Dobranskis R.R.
Projects: RHESSI

Publication Status: MNRAS, in press
Last Modified: 2016-03-08 12:17
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On the Generation of Hydrodynamic Shocks by Mixed Beams and Occurrence of Sunquakes in Flares  

Valentina Zharkova   Submitted: 2015-11-19 07:38

Observations of solar flares with sunquakes by space- and ground-based instruments reveal essentially different dynamics of seismic events in different flares. Some sunquakes are found to be closely associated with the locations of hard X-ray (HXR) and whitelight (WL) emission, while others are located outside either of them. In this article we investigate possible sources causing a seismic response in a form of hydrodynamic shocks produced by the injection of mixed (electron plus proton) beams, discuss the velocities of these shocks, and the depths where they deposit the bulk of their energy and momentum. The simulation of hydrodynamic shocks in flaring atmospheres induced by electron-rich and proton-rich beams reveals that the linear depth of the shock termination is shifted beneath the level of the quiet solar photosphere on a distance from 200 to 5000 km. The parameters of these atmospheric hydrodynamic shocks are used as initial condition for another hydrodynamic model developed for acoustic-wave propagation in the solar interior (Zharkov, Mon. Not. Roy. Astron. Soc. 431, 3414, 2013). The model reveals that the depth of energy and momentum deposition by the atmospheric shocks strongly affects the propagation velocity of the acoustic-wave packet in the interior. The locations of the first bounces from the photosphere of acoustic waves generated in the vicinity of a flare are seen as ripples on the solar surface, or sunquakes. Mixed proton-dominated beams are found to produce a strong supersonic shock at depths 200 ? 300 km under the level of the quiet-Sun photosphere and in this way produce well-observable acoustic waves, while electron-dominated beams create a slightly supersonic shock propagating down to 5000 km under the photosphere. This shock can only generate acoustic waves at the top layers beneath the photosphere since the shock velocity very quickly drops below the local sound speed. The distance 'delta' of the first bounce of the generated acoustic waves is discussed in relation to the minimal phase velocities of wave packets defined by the acoustic cutoff frequency and the parameters of atmospheric shock termination beneath the photosphere.

Authors: Zharkova V.V. and Zharkov S.I.
Projects: None

Publication Status: published, Solar Physics journal
Last Modified: 2015-11-20 15:38
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Heartbeat of the Sun from Principal Component Analysis and prediction of solar activity on a millennium timescale  

Valentina Zharkova   Submitted: 2015-11-01 10:33

We derive two principal components (PCs) of temporal magnetic field variations over the solar cycles 21?24 from full disk magnetograms covering about 39% of data variance, with σ = 0.67. These PCs are attributed to two main magnetic waves travelling from the opposite hemispheres with close frequencies and increasing phase shift. Using symbolic regeression analysis we also derive mathematical formulae for these waves and calculate their summary curve which we show is linked to solar activity index. Extrapolation of the PCs backward for 800 years reveals the two 350-year grand cycles superimposed on 22 year-cycles with the features showing a remarkable resemblance to sunspot activity reported in the past including the Maunder and Dalton minimum. The summary curve calculated for the next millennium predicts further three grand cycles with the closest grand minimum occurring in the forthcoming cycles 26?27 with the two magnetic field waves separating into the opposite hemispheres leading to strongly reduced solar activity. These grand cycle variations are probed by α - Ω dynamo model with meridional circulation. Dynamo waves are found generated with close frequencies whose interaction leads to beating effects responsible for the grand cycles (350?400 years) superimposed on a standard 22 year cycle. This approach opens a new era in investigation and confident prediction of solar activity on a millenium timescale.

Authors: Zharkova V.V., Shepherd S.J., Popova E., Zharkov S.I.
Projects: None

Publication Status: Nature Scientific Reports 5, 15689 (2015) doi:10.1038/srep15689
Last Modified: 2015-11-02 10:52
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Dynamical small-scale magnetic islands as a source of local acceleration of particles in the solar wind  

Valentina Zharkova   Submitted: 2015-11-01 10:31

We present observations of energetic particle flux increases up to 1 MeV at 1 AU, which cannot be associated with ordinary mechanisms of particle acceleration, such as acceleration at shocks or at the Sun. Such unusual energetic particle events very likely have a local origin. Multi-spacecraft observations show that numerous cases of energetic particle flux enhancements and spikes correspond to passages of spacecraft through areas filled with magnetic islands with a typical width ~0.010.001AU that experience dynamical merging or/and contraction. The presence of magnetic islands inside magnetically confined cavities in the solar wind may lead to local particle energization, especially in the case when the particles have already been pre-accelerated to keV energies, for example, at shocks or due to magnetic reconnection at the heliospheric current sheet. We consider different magnetic configurations that provide favourable conditions for both the appearance of small-scale magnetic islands and their confinement.

Authors: O. V. Khabarova, G. P. Zank, G. Li, J. A. le Roux, G. M.Webb, A. Dosch, O. E. Malandraki, Zharkova V.V.
Projects: None

Publication Status: Journal of Physics: Conference Series (JPCS), 642, 012033
Last Modified: 2015-11-02 10:52
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Particle acceleration in 3D single current sheets formed in the solar corona and heliosphere: PIC approach  

Valentina Zharkova   Submitted: 2015-11-01 10:28

Acceleration of protons and electrons in a reconnecting current sheet (RCS) is investigated with the test particle and particle-in-cell (PIC) approaches in a 3D magnetic topology. PIC simulations confirm a spatial separation of electrons and protons with respect to the midplane depending on the guiding field. Simulation reveals that the separation occurs in magnetic topologies with strong guiding fields and lasts as long as the particles are kept dragged into a current sheet. This separation produces a polarisation electric field induced by the plasma feedback to a presence of accelerated particles, which shape can change from symmetric towards the midplane (for weak guiding field) to fully asymmetric (for strong guiding field). Particles are found accelerated at a midplane of any current sheets present in the heliosphere to the energies up to hundred keV for electrons and hundred MeV for protons. The maximum energy gained by particles during their motion inside the current sheet is defined by its magnetic field topology (the ratio of magnetic field components), the side and location from the X-nullpoint, where the particles enter a current sheet. In strong magnetic fields of the solar corona with weaker guiding fields, electrons are found circulating about the midplane to large distances where proton are getting accelerated, creating about the current sheet midplane clouds of high energy electrons, which can be the source of hard X-ray emission in the coronal sources of flares. These electrons are ejected into the same footpoint as protons after the latter reach the energy sufficient to break from a current sheet. In a weaker magnetic field of the heliosphere the bounced electrons with lower energies cannot reach the midplane turning instead at some distance D before the current sheet midplane by 180 degrees from their initial motion. Also the beams of accelerated transit and bounced particles are found to generate turbulent electric fields in a form of Langmuir waves (electrons) or ion-acoustic waves (protons).

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

Publication Status: Journal of Physics, Conference Series (JPCS), 2015, 642, 012032
Last Modified: 2015-11-02 10:52
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Updated analytical solutions of continuity equation for electron beams precipitation. I. Pure collisional and pure ohmic energy losses  

Valentina Zharkova   Submitted: 2015-08-14 10:35

We present updated analytical solutions of continuity equations for power-law beam electrons precipitating in (a) purely collisional losses and (b) purely ohmic losses. The solutions of continuity equation (CE) normalized on electron density presented in Dobranskis & Zharkova are found by method of characteristics eliminating a mistake in the density characteristic pointed out by Emslie et al. The corrected electron beam differential densities (DD) for collisions are shown to have energy spectra with the index of -(γ + 1)/2, coinciding with the one derived from the inverse problem solution by Brown, while being lower by 1/2 than the index of -γ/2 obtained from CE for electron flux. This leads to a decrease of the index of mean electron spectra from -(γ - 2.5) (CE for flux) to -(γ - 2.0) (CE for electron density). The similar method is applied to CE for electrons precipitating in electric field induced by the beam itself. For the first time, the electron energy spectra are calculated for both constant and variable electric fields by using CE for electron density. We derive electron DD for precipitating electrons (moving towards the photosphere, μ = +1) and 'returning' electrons (moving towards the corona, μ = -1). The indices of DD energy spectra are reduced from -γ - 1 (CE for flux) to -γ (CE for electron density). While the index of mean electron spectra is increased by 0.5, from -γ + 0.5 (CE for flux) to -γ + 1(CE for electron density). Hard X-ray intensities are also calculated for relativistic cross-section for the updated differential spectra revealing closer resemblance to numerical Fokker-Planck (FP) solutions.

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

Publication Status: published: MNRAS, 2015,453 (1): 229-241
Last Modified: 2015-08-17 15:12
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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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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 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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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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Abstracts by Author
Reply to comment by Usoskin (2017) on the paper
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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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Subject will be restored when possible
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