The Effect of Magnetic and Density Differences on the Fast Kink Oscillations of Neighboring Coronal Loops

It is reasonable that neighboring coronal loops may obtain similar momentum during a flare. The fast kink oscillations (FKOs) between them are thus mainly influenced by their physical differences. We discuss the dependencies of FKO on the physical properties of coronal loops in a low-\(\beta \) thin-tube approximation. From the analysis, we obtain the analytic relationship between the density [\(\rho _{\mathrm{i}}\)] and magnetic field [\(B\)] of loops and the corresponding period [\(\tau \)] and amplitude [\(A\)] of FKO, which may provide us with a powerful tool to diagnose the physical differences between neighboring loops.     

GONG p-Mode Parameters Through Two Solar Cycles

We investigate the parameters of global solar p-mode oscillations, namely damping width \(\Gamma\), amplitude \(A\), mean squared velocity \(\langle v^{2}\rangle\), energy \(E\), and energy supply rate \(\mathrm{d}E/\mathrm{d}t\), derived from two solar cycles’ worth (1996?–?2018) of Global Oscillation Network Group (GONG) time series for harmonic degrees \(l=0\,\mbox{--}\,150\). We correct for the effect of fill factor, apparent solar radius, and spurious jumps in the mode amplitudes. We find that the amplitude of the activity-related changes of \(\Gamma\) and \(A\) depends on both frequency and harmonic degree of the modes, with the largest variations of \(\Gamma\) for modes with \(2400~\upmu\mbox{Hz}\le\nu\le3300~\upmu\mbox{Hz}\) and \(31\le l \le60\) with a minimum-to-maximum variation of \(26.6\pm0.3\%\) and of \(A\) for modes with \(2400~\upmu\mbox{Hz}\le\nu\le 3300~\upmu\mbox{Hz}\) and \(61\le l \le100\) with a minimum-to-maximum variation of \(27.4\pm0.4\%\). The level of correlation between the solar radio flux \(F_{10.7}\) and mode parameters also depends on mode frequency and harmonic degree. As a function of mode frequency, the mode amplitudes are found to follow an asymmetric Voigt profile with \(\nu_{\text{max}}=3073.59\pm0.18~\upmu\mbox{Hz}\). From the mode parameters, we calculate physical mode quantities and average them over specific mode frequency ranges. In this way, we find that the mean squared velocities \(\langle v^{2}\rangle\) and energies \(E\) of p modes are anticorrelated with the level of activity, varying by \(14.7\pm0.3\%\) and \(18.4\pm0.3\%\), respectively, and that the mode energy supply rates show no significant correlation with activity. With this study we expand previously published results on the temporal variation of solar p-mode parameters. Our results will be helpful to future studies of the excitation and damping of p modes, i.e., the interplay between convection, magnetic field, and resonant acoustic oscillations.     

Geomagnetic Effects of Corotating Interaction Regions

We present an analysis of the geoeffectiveness of corotating interaction regions (CIRs), employing the data recorded from 25 January to 5 May 2005 and throughout 2008. These two intervals in the declining phase of Solar Cycle 23 are characterised by a particularly low number of interplanetary coronal mass ejections (ICMEs). We study in detail how four geomagnetic-activity parameters (the Dst, Ap, and AE indices, as well as the Dst time derivative, \(\mathrm{dDst}/\mathrm{d}t\)) are related to three CIR-related solar wind parameters (flow speed, \(V\), magnetic field, \(B\), and the convective electric field based on the southward Geocentric solar magnetospheric (GSM) magnetic field component, \(\mathit{VB}_{s}\)) on a three-hour time resolution. In addition, we quantify statistical relationships between the mentioned geomagnetic indices. It is found that Dst is correlated best to \(V\), with a correlation coefficient of \(\mathrm{cc}\approx0.6\), whereas there is no correlation between \(\mathrm{dDst}/\mathrm{d}t\) and \(V\). The Ap and AE indices attain peaks about half a day before the maximum of \(V\), with correlation coefficients ranging from \(\mathrm{cc}\approx0.6\) to \(\mathrm{cc}\approx0.7\), depending on the sample used. The best correlations of Ap and AE are found with \(\mathit{VB}_{s}\) with a delay of 3 h, being characterised by \(\mathrm{cc}\gtrsim 0.6\). The Dst derivative \(\mathrm{dDst}/\mathrm{d}t\) is also correlated with \(\mathit{VB}_{s}\), but the correlation is significantly weaker \(\mathrm{cc}\approx 0.4\)?–?0.5, with a delay of 0?–?3 h, depending on the employed sample. Such low values of correlation coefficients indicate that there are other significant effects that influence the relationship between the considered parameters. The correlation of all studied geomagnetic parameters with \(B\) are characterised by considerably lower correlation coefficients, ranging from \(\mathrm{cc}=0.3\) in the case of \(\mathrm{dDst}/\mathrm{d}t\) up to \(\mathrm{cc}=0.56\) in the case of Ap. It is also shown that peak values of geomagnetic indices depend on the duration of the CIR-related structures. The Dst is closely correlated with Ap and AE (\(\mathrm{cc}=0.7\)), Dst being delayed for about 3 h. On the other hand, \(\mathrm{dDst}/\mathrm{d}t\) peaks simultaneously with Ap and AE, with correlation coefficients of 0.48 and 0.56, respectively. The highest correlation (\(\mathrm{cc}=0.81\)) is found for the relationship between Ap and AE.     

STEREO observations of hybrid stars V775 Tau and V483 Tau

In this study, pulsational and physical characteristics of two \(\delta\) Scuti stars, V775?Tau and V483?Tau, are analysed by using four-year high-precision photometric data of the STEREO satellite. Thus, it is aimed to gain new insights into behaviours of these pulsators and evolution of \(\delta\) Scuti, \(\gamma\) Dor and Am type stars. The data are taken between 2007–2011 and examined with the help of the Lomb–Scargle method. The detection precision in the four-year combined data is around \(10^{-5}\) cd^?1 in frequency and \(10^{-5}\) mag in amplitude. It is revealed that V775?Tau exhibits weak pulsation characteristic which is interpreted as the existence of the interaction between the helium loss in the partial ionization zone and pulsation intensities. It is also considered that the absence of strong pulsations is also related to the evolution status of the star. Further, its periodogram shows low-frequency peaks. If these oscillations are g-modes, V775?Tau can be thought to be one of the rare stars that show all \(\gamma\) Dor, \(\delta\) Scuti and Am type variations. V483?Tau is comparatively more luminous, hotter and has higher rotational velocity. Therefore, although it shares the same region with V775?Tau in the H–R diagram, it is not considered to be an Am star. Yet, it exactly overlaps with the \(\gamma\) Dor stars. These clues as well as g-modes detected in its periodogram indicate that V483?Tau is a hybrid star. Finally, both V775?Tau and V483?Tau display period changes whose rates are between \(10^{-3}\) and \(10^{-4}\) yr^?1. Considering the \(\delta\) Scuti nature, it may be speculated that these changes are non-evolutionary.     

Fourier Power Spectra of Solar Noise Storms

We analyzed three noise storms recorded on 200?–?400 MHz Trieste Callisto radio spectra on 2 July 2012, 8 July 2012, and 16 July 2012 by the Fourier method. We divided intervals of the noise storms into five-minute intervals, and in these intervals we computed the mean Fourier spectra as a function of the wave numbers in the frequency and height-scale spaces. We found that these Fourier spectra, where the spectrum from the quiet-activity interval was subtracted, are power-law spectra. The mean power-law index of these spectra in the range \(\ln(k_{z}) = [1.8, 2.9]\) (where \(k_{z}\) is the wave number in the height-scale space) is \(-1.7\pm0.14\), \(-1.6\pm0.14\), and \(-1.5 \pm0.12\) for the 2 July 2012, the 8 July 2012, and the 16 July 2012 noise storms, respectively. It appears that as the number of Type-I bursts in the studied interval increases, the power-law index becomes closer to \(-5/3\); this is known as the Kolmogorov spectral index. The power-law index of the noise storms is very similar to that of the narrowband dm-spikes found in our previous studies. Furthermore, we found a break in the power spectra at \(\ln(k_{z}) \approx2.9\), and the mean power-law index values above this break are \(-2.9\pm0.46\), \(-3.1\pm0.65\), and \(-3.4\pm0.98\), respectively.     

Correlation Between the Magnetic Field and Plasma Parameters at 1 AU

The physical parameters of the solar wind observed in-situ near 1 AU have been studied for several decades, and relationships between them, such as the positive correlation between the solar wind plasma temperature, \(T\), and velocity, \(V\), and the negative correlation between density, \(N\), and velocity, \(V\), are well known. However, the magnetic field intensity, \(B\), does not appear to be well correlated with any individual plasma parameter. In this article, we discuss previously under-reported correlations between \(B\) and the combined plasma parameters \(\sqrt{N V^{2}} \) as well as between \(B\) and \(\sqrt{NT}\). These two correlations are strong during periods of corotating interaction regions and high-speed streams, and moderate during intervals of slow solar wind. The results indicate that the magnetic pressure in the solar wind is well correlated both with the plasma dynamic pressure and the thermal pressure.     

Density variation effect on multi-ions with kinetic Alfven wave around cusp region—a kinetic approach

The kinetic Alfven waves in the presence of homogeneous magnetic field plasma with multi-ions effect are investigated. The dispersion relation and normalised damping rate are derived for low-\(\beta\) plasma using kinetic theory. The effect of density variation of \(\text{H}^{+}\), \(\text{He}^{+}\) and \(\text{O}^{+}\) ions is observed on frequency and damping rate of the wave. The variation of frequency (\(\omega\)) and normalised damping rate (\(\gamma / \varOmega_{H^{ +}} \)) of the wave are studied with respect to \(k_{ \bot} \rho_{j}\), where \(k_{ \bot} \) is the perpendicular wave number, \(\rho_{j}\) is the ion gyroradius and \(j \) denotes \(\text{H}^{+}\), \(\text{He}^{+}\) and \(\text{O}^{+}\) ions. The variation with \(k_{ \bot} \rho_{j}\) is considered over wide range. The parameters appropriate to cusp region are used for the explanation of results. It is found that with hydrogen and helium ions gyration, the frequency of wave is influenced by the density variation of \(\text{H}^{+}\) and \(\text{He}^{+}\) ions but remains insensitive to the change in density of \(\text{O}^{+}\) ions. For oxygen ion gyration, the frequency of wave varies over a short range only for \(\text{O}^{+}\) ion density variation. The wave shows damping at lower altitude due to variation in density of lighter \(\text{H}^{+}\) and \(\text{He}^{+}\) ions whereas at higher altitude only heavy \(\text{O}^{+}\) ions contribute in wave damping. The damping of wave may be due to landau damping or energy transfer from wave to particles. The present study signifies that the both lighter and heavier ions dominate differently to change the characteristics of kinetic Alfven wave and density variation is also an important parameter to understand wave phenomena in cusp region.     

Role of primordial black holes in the direct collapse scenario of supermassive black hole formation at high redshifts

In this paper, we explore the possibility of accreting primordial black holes as the source of heating for the collapsing gas in the context of the direct collapse black hole scenario for the formation of super-massive black holes (SMBHs) at high redshifts, \(z\sim \) 6–7. One of the essential requirements for the direct collapse model to work is to maintain the temperature of the in-falling gas at \(\approx \)10\(^4\) K. We show that even under the existing abundance limits, the primordial black holes of masses \(\gtrsim \)10\(^{-2}M_\odot \), can heat the collapsing gas to an extent that the \(\mathrm{H}_2\) formation is inhibited. The collapsing gas can maintain its temperature at \(10^4\) K till the gas reaches a critical density \(n_{{c}} \,{\approx }\, 10^3~\hbox {cm}^{-3}\), at which the roto-vibrational states of \(\mathrm{H}_2\) approaches local thermodynamic equilibrium and \(\mathrm{H}_2\) cooling becomes inefficient. In the absence of \(\mathrm{H}_2\) cooling, the temperature of the collapsing gas stays at \(\approx \)10\(^4\) K even as it collapses further. We discuss scenarios of subsequent angular momentum removal and the route to find collapse through either a supermassive star or a supermassive disk.     

Ratio of the Core to the Extended Emissions in the Comoving Frame for Blazars

In a two-component jet model, the emissions are the sum of the core and extended emissions: \(S^{\mathrm{ob}}=S_{\mathrm{core}}^{\mathrm{ob}}+S_{\mathrm{ext}}^{\mathrm{ob}}\), with the core emissions, \(S_{\mathrm{core}}^{\mathrm{ob}}= f S_{\mathrm{ext}}^{\mathrm{ob}}\delta ^{q}\) being a function of the Doppler factor \(\delta \), the extended emission \(S_{\mathrm{ext}}^{\mathrm{ob}}\), the jet type dependent factor q, and the ratio of the core to the extended emissions in the comoving frame, f. The f is an unobservable but important parameter. Following our previous work, we collect 65 blazars with available Doppler factor \(\delta \), superluminal velocity \(\beta _{\mathrm{app}}\), and core-dominance parameter, R, and calculated the ratio, f, and performed statistical analyses. We found that the ratio, f, in BL Lacs is on average larger than that in FSRQs. We suggest that the difference of the ratio f between FSRQs and BL Lacs is one of the possible reasons that cause the difference of other observed properties between them. We also find some significant correlations between \(\log f\) and other parameters, including intrinsic (de-beamed) peak frequency, \(\log \nu _{\mathrm{p}}^{\mathrm{in}}\), intrinsic polarization, \(\log P^{\mathrm{in}}\), and core-dominance parameter, \(\log R\), for the whole sample. In addition, we show that the ratio, f, can be estimated by R.     

Relating Solar Energetic Particle Event Fluences to Peak Intensities

Recently we (Kahler and Ling, Solar Phys.292, 59, 2017: KL) have shown that time–intensity profiles [\(I(t)\)] of 14 large solar energetic particle (SEP) events can be fitted with a simple two-parameter fit, the modified Weibull function, which is characterized by shape and scaling parameters [\(\alpha\) and \(\beta\)]. We now look for a simple correlation between an event peak energy intensity [\(I_{\mathrm{p}}\)] and the time integral of \(I(t)\) over the event duration: the fluence [\(F\)]. We first ask how the ratio of \(F/I_{\mathrm{p}}\) varies for the fits of the 14 KL events and then examine that ratio for three separate published statistical studies of SEP events in which both \(F\) and \(I_{\mathrm{p}}\) were measured for comparisons of those parameters with various solar-flare and coronal mass ejection (CME) parameters. The three studies included SEP energies from a 4?–?13 MeV band to \(E > 100~\mbox{MeV}\). Within each group of SEP events, we find a very robust correlation (\(\mathrm{CC} > 0.90\)) in log–log plots of \(F\)versus\(I_{\mathrm{p}}\) over four decades of \(I_{\mathrm{p}}\). The ratio increases from western to eastern longitudes. From the value of \(I_{\mathrm{p}}\) for a given event, \(F\) can be estimated to within a standard deviation of a factor of \({\leq}\,2\). Log–log plots of two studies are consistent with slopes of unity, but the third study shows plot slopes of \({<}\,1\) and decreasing with increasing energy for their four energy ranges from \(E > 10~\mbox{MeV}\) to \({>}\,100~\mbox{MeV}\). This difference is not explained.     

Advective accretion flow properties around rotating black holes – application to GRO J1655-40

We examine the properties of the viscous dissipative accretion flow around rotating black holes in the presence of mass loss. Considering the thin disc approximation, we self-consistently calculate the inflow-outflow solutions and observe that the mass outflow rates decrease with the increase in viscosity parameter (\(\alpha \)). Further, we carry out the model calculation of quasi-periodic oscillation frequency (\(\nu _{\mathrm{QPO}}\)) that is frequently observed in black hole sources and observe that \(\nu ^\mathrm{max}_{\mathrm{QPO}}\) increases with the increase of black hole spin (\(a_k\)). Then, we employ our model in order to explain the High Frequency Quasi-Periodic Oscillations (HFQPOs) observed in black hole source GRO J1655-40. While doing this, we attempt to constrain the range of \(a_k\) based on observed HFQPOs (\(\sim \)300 Hz and \(\sim \)450 Hz) for the black hole source GRO J1655-40.     

Measurement of coronal properties of Seyfert galaxies from NuSTAR’s hard X-ray spectrum

Precise measurement of the coronal properties of Active Galactic Nuclei (AGN) requires the availability of high signal-to-noise ratio data covering a wide range of X-ray energies. The Nuclear Spectroscopic Telescope Array (NuSTAR) which is highly sensitive to earlier missions in its operational energy range of 3–79 keV, allows us to arrive at precise estimates of the coronal parameters such as cut-off energy (\(E_\mathrm{cut}\)), coronal temperature (\(\textit{kT}_e\)) and geometry of the corona at least for sources that have \(E_\mathrm{cut}\) within the energy range of NuSTAR. In this paper, we present our preliminary results on the spectral analysis of two Seyfert galaxies namely 3C 120 and NGC 4151 using NuSTAR observations in the 3–79 keV band. We investigated the continuum and coronal parameters, the photon index \(\Gamma \), \(E_\mathrm{cut}\) and \(\textit{kT}_{e}\). By fitting the X-ray spectrum of 3C 120 and NGC 4151 with a simple phenomenological model, we found that both the sources showed a clear cut-off in their spectrum.     

Spectroscopic Variability of Supergiant Star HD14134, B3Ia

Profile variations in the \(\hbox {H}\alpha \) and \(\hbox {H}\beta \) lines in the spectra of the star HD14134 are investigated using observations carried out in 2013–2014 and 2016 with the 2-m telescope at the Shamakhy Astrophysical Observatory. The absorption and emission components of the \(\hbox {H}\alpha \) line are found to disappear on some observational days, and two of the spectrograms exhibit inverse P-Cyg profile of \(\hbox {H}\alpha \). It was revealed that when the \(\hbox {H}\alpha \) line disappeared or an inversion of the P-Cyg-type profile is observed in the spectra, the \(\hbox {H}\beta \) line is displaced to the longer wavelengths, but no synchronous variabilities were observed in other spectral lines (CII \( \lambda \) 6578.05 Å, \( \lambda \) 6582.88 Å  and HeI \( \lambda \) 5875.72 Å) formed in deeper layers of the stellar atmosphere. In addition, the profiles of the \(\hbox {H}\alpha \) and \(\hbox {H}\beta \) lines have been analysed, as well as their relations with possible expansion, contraction and mixed conditions of the atmosphere of HD14134. We suggest that the observational evidence for the non-stationary atmosphere of HD14134 can be associated in part with the non-spherical stellar wind.     

A Solar Stationary Type IV Radio Burst and Its Radiation Mechanism

A stationary Type IV (IVs) radio burst was observed on September 24, 2011. Observations from the Nançay RadioHeliograph (NRH) show that the brightness temperature (\(T_{\mathrm{B}}\)) of this burst is extremely high, over \(10^{11}\) K at 150 MHz and over \(10^{8}\) K in general. The degree of circular polarization (\(q\)) is between \(-60\% \sim -100\%\), which means that it is highly left-handed circularly polarized. The flux–frequency spectrum follows a power-law distribution, and the spectral index is considered to be roughly \(-3 \sim -4\) throughout the IVs. Radio sources of this event are located in the wake of the coronal mass ejection and are spatially dispersed. They line up to present a formation in which lower-frequency sources are higher. Based on these observations, it is suggested that the IVs was generated through electron cyclotron maser emission.     

Average Magnetic Field Magnitude Profiles of <Emphasis Type="Italic">Wind</Emphasis> Magnetic Clouds as a Function of Closest Approach to the Clouds’ Axes and Comparison to Model

We examine the average magnetic field magnitude (\(| \boldsymbol{B} | \equiv B\)) within magnetic clouds (MCs) observed by the Wind spacecraft from 1995 to July 2015 to understand the difference between this \(B\) and the ideal \(B\)-profiles expected from using the static, constant-\(\alpha\), force-free, cylindrically symmetric model for MCs of Lepping, Jones, and Burlaga (J. Geophys. Res. 95, 11957, 1990, denoted here as the LJB model). We classify all MCs according to an assigned quality, \(Q_{0}\) (\(= 1, 2, 3\), for excellent, good, and poor). There are a total of 209 MCs and 124 when only \(Q_{0} = 1\), 2 cases are considered. The average normalized field with respect to the closest approach (\(\mathit{CA}\)) is stressed, where we separate cases into four \(\mathit{CA}\) sets centered at 12.5 %, 37.5 %, 62.5 %, and 87.5 % of the average radius; the averaging is done on a percentage-duration basis to treat all cases the same. Normalized \(B\) means that before averaging, the \(B\) for each MC at each point is divided by the LJB model-estimated \(B\) for the MC axis, \(B_{0}\). The actual averages for the 209 and 124 MC sets are compared to the LJB model, after an adjustment for MC expansion (e.g. Lepping et al. in Ann. Geophys. 26, 1919, 2008). This provides four separate difference-relationships, each fitted with a quadratic (Quad) curve of very small \(\sigma\). Interpreting these Quad formulae should provide a comprehensive view of the variation in normalized \(B\) throughout the average MC, where we expect external front and rear compression to be part of its explanation. These formulae are also being considered for modifying the LJB model. This modification will be used in a scheme for forecasting the timing and magnitude of magnetic storms caused by MCs. Extensive testing of the Quad formulae shows that the formulae are quite useful in correcting individual MC \(B\)-profiles, especially for the first \({\approx\,}1/3\) of these MCs. However, the use of this type of \(B\) correction constitutes a (slight) violation of the force-free assumption used in the original LJB MC model.     

The Na <Emphasis Type="SmallCaps">i</Emphasis> and Sr <Emphasis Type="SmallCaps">ii</Emphasis> Resonance Lines in Solar Prominences

We estimate the electron density, \(n_{\mathrm{e}}\), and its spatial variation in quiescent prominences from the observed emission ratio of the resonance lines Na?i?5890 Å (D₂) and Sr?ii?4078 Å. For a bright prominence (\(\tau_{\alpha}\approx25\)) we obtain a mean \(n_{\mathrm{e}}\approx2\times10^{10}~\mbox{cm}^{-3}\); for a faint one (\(\tau _{\alpha }\approx4\)) \(n_{\mathrm{e}}\approx4\times10^{10}~\mbox{cm}^{-3}\) on two consecutive days with moderate internal fluctuation and no systematic variation with height above the solar limb. The thermal and non-thermal contributions to the line broadening, \(T_{\mathrm{kin}}\) and \(V_{\mathrm{nth}}\), required to deduce \(n_{\mathrm{e}}\) from the emission ratio Na?i/Sr?ii cannot be unambiguously determined from observed widths of lines from atoms of different mass. The reduced widths, \(\Delta\lambda_{\mathrm{D}}/\lambda_{0}\), of Sr?ii?4078 Å show an excess over those from Na?D₂ and \(\mbox{H}\delta\,4101\) Å, assuming the same \(T_{\mathrm{kin}}\) and \(V_{\mathrm{nth}}\). We attribute this excess broadening to higher non-thermal broadening induced by interaction of ions with the prominence magnetic field. This is suggested by the finding of higher macro-shifts of Sr?ii?4078 Å as compared to those from Na?D₂.     

Dynamics of Large-Scale Solar-Wind Streams Obtained by the Double Superposed Epoch Analysis: 3. Deflection of the Velocity Vector

This work is a continuation of our previous articles (Yermolaev et al. in J. Geophys. Res.120, 7094, 2015 and Yermolaev et al. in Solar Phys.292, 193, 2017), which describe the average temporal profiles of interplanetary plasma and field parameters in large-scale solar-wind (SW) streams: corotating interaction regions (CIRs), interplanetary coronal mass ejections (ICMEs, including both magnetic clouds (MCs) and ejecta), and sheaths as well as interplanetary shocks (ISs). Changes in the longitude angle, \(\varphi\), in CIRs from ?2 to \(2^{\circ}\) agree with earlier results (e.g. Gosling and Pizzo, 1999). We have also analyzed the average temporal profiles of the bulk velocity angles in sheaths and ICMEs. We have found that the angle \(\varphi\) in ICMEs changes from 2 to \(-2^{\circ}\), while in sheaths it changes from ?2 to \(2^{\circ}\) (similar to the change in CIRs), i.e. the angle in CIRs and sheaths deflects in the opposite sense to ICMEs. When averaging the latitude angle \(\vartheta\) on all the intervals of the chosen SW types, the angle \(\vartheta\) is almost constant at \({\sim}\,1^{\circ}\). We made for the first time a selection of SW events with increasing and decreasing \(\vartheta\) and found that the average \(\vartheta\) temporal profiles in the selected events have the same “integral-like” shape as for \(\varphi\). The difference in \(\varphi\) and \(\vartheta\) average profiles is explained by the fact that most events have increasing profiles for the angle in the ecliptic plane as a result of solar rotation, while for the angle in the meridional plane, the numbers of events with increasing and decreasing profiles are equal.     

Nowcasting Solar Energetic Particle Events Using Principal Component Analysis

We perform a principal component analysis (PCA) on a set of six solar variables (i.e. width/size (\(s\)) and velocity (\(u\)) of a coronal mass ejection, logarithm of the solar flare (SF) magnitude (\(\log\mathit{SXRs}\)), SF longitude (\(\mathit{lon}\)), duration (\(\mathit{DT}\)), and rise time (\(\mathit{RT}\))). We classify the solar energetic particle (SEP) event radiation impact (in terms of the National Oceanic and Atmospheric Administration scales) with respect to the characteristics of their parent solar events. We further attempt to infer the possible prediction of SEP events. In our analysis, we use 126 SEP events with complete solar information, from 1997 to 2013. Each SEP event is a vector in six dimensions (corresponding to the six solar variables used in this work). The PCA transforms the input vectors into a set of orthogonal components. By mapping the characteristics of the parent solar events, a new base defined by these components led to the classification of the SEP events. We furthermore applied logistic regression analysis with single, as well as multiple explanatory variables, in order to develop a new index (\(I\)) for the nowcasting (short-term forecasting) of SEP events. We tested several different schemes for \(I\) and validated our findings with the implementation of categorical scores (probability of detection (POD) and false-alarm rate (FAR)). We present and interpret the obtained scores, and discuss the strengths and weaknesses of the different implementations. We show that \(I\) holds prognosis potential for SEP events. The maximum POD achieved is 77.78% and the relative FAR is 40.96%.     

Addendum to: Strength of the Solar Coronal Magnetic Field – A Comparison of Independent Estimates Using Contemporaneous Radio and White-Light Observations

This addendum uses an alternate fit for the electron density distribution \(N(r)\) (see Figure 1) and estimates the coronal magnetic field using the new model. We find that the estimates of the magnetic field are in close agreement using both the models.

We have fit the \(N(r)\) distribution obtained from STEREO-A/COR1 and SOHO/LASCO-C2 using a fifth-order polynomial (see Figure 1). The expression can be written as

$$\begin{aligned} N_{\text{cor}}(r) &= 1.43 \times 10^{9} r^{-5} - 1.91 \times 10^{9} r^{-4} + 1.07 \times 10^{9} r^{-3} - 2.87 \times 10^{8} r^{-2} \\ &\quad {} + 3.76 \times 10^{7} r^{-1} - 1.91 \times 10^{6} , \end{aligned}$$

(1)

where \(N_{\text{cor}}(r)\) is in units of cm^?3 and \(r\) is in units of \(\mathrm{R}_{\odot}\). The background coronal electron density is enhanced by a factor of 5.5 at 2.63 \(\mathrm{R}_{\odot}\) during the coronal mass ejection (CME). The estimated coronal magnetic field strength (\(B\)) using radio data indicates that \(B(r) \approx(0.51\text{\,--\,}0.48) \pm 0.02\ \mathrm{G}\) in the range \(r \approx2.65\text{\, --\,}2.82\ \mathrm{R}_{\odot}\). The field strengths for STEREO-A/COR1 and SOHO/LASCO-C2 are ≈?0.32 G at \(r \approx 3.11\ \mathrm{R}_{\odot}\) and ≈?0.12 G at \(r \approx 4.40\ \mathrm{R}_{\odot}\), respectively.

     

Intermittency of the Solar Magnetic Field and Solar Magnetic Activity Cycle

Small-scale solar magnetic fields demonstrate features of fractal intermittent behavior, which requires quantification. For this purpose we investigate how the observational estimate of the solar magnetic flux density \(B\) depends on resolution \(D\) in order to obtain the scaling \(\ln B_{D} = - k \ln D +a\) in a reasonably wide range. The quantity \(k\) demonstrates cyclic variations typical of a solar activity cycle. In addition, \(k\) depends on the magnetic flux density, i.e. the ratio of the magnetic flux to the area over which the flux is calculated, at a given instant. The quantity \(a\) demonstrates some cyclic variation, but it is much weaker than in the case of \(k\). The scaling obtained generalizes previous scalings found for the particular cycle phases. The scaling is typical of fractal structures. In our opinion, the results obtained trace small-scale action in the solar convective zone and its coexistence with the conventional large-scale solar dynamo based on differential rotation and mirror-asymmetric convection.