The prediction of solar activity is important for advanced technologies and space activities. The peak sunspot number (SSN), which can represent the solar activity, has declined continuously in the past four solar cycles (21$-$24), and the Sun would
experience a Dalton-like minimum, or even the Maunder-like minimum, if the declining trend continues in the following several cycles, so that the predictions of solar activity for cycles 25 and 26 are crucial. In Qin & Wu, 2018, ApJ, we established an SSN prediction model denoted as two-parameter modified logistic prediction (TMLP) model, which can predict the variation of SSNs in a solar cycle if the start time of the cycle has been determined. In this work, we obtain a new model denoted as TMLP-extension (TMLP-E). If the start time of a cycle $n$ is already known, TMLP-E can predict the variation of SSNs in the cycle $n+1$. Cycle 25 is believed to start in December 2019, so that the predictions of cycles 25 and 26 can be made with our models. It is found that the predicted solar maximum, ascent time, and cycle length are 115.1, 4.84 yr, and 11.06 yr, respectively, for cycle 25, and 107.3, 4.80 yr, and 10.97 yr, respectively, for cycle 26. The solar activities of cycles 25 and 26 are predicted to be at the same level as that of cycle 24, but will not decrease further. We therefore suggest that the cycles 24$-$26 are at a minimum of Gleissberg cycle.
We present a study of the acceleration efficiency of suprathermal electrons at collisionless shock waves driven by interplanetary coronal mass ejections (ICMEs), with the data analysis from both the spacecraft observations and test-particle simulatio
ns. The observations are from the 3DP/EESA instrument onboard emph{Wind} during the 74 shock events listed in Yang et al. 2019, ApJ, and the test-particle simulations are carried out through 315 cases with different shock parameters. It is shown that a large shock-normal angle, upstream Alfv$acute{text e}$n Mach number, and shock compression ratio would enhance the shock acceleration efficiency. In addition, we develop a theoretical model of the critical shock normal angle for efficient shock acceleration by assuming the shock drift acceleration to be efficient. We also obtain models for the critical values of Mach number and compression ratio with efficient shock acceleration, based on the suggestion of Drury 1983 about the average momentum change of particle crossing of shock. It is shown that the theories have similar trends of the observations and simulations. Therefore, our results suggest that the shock drift acceleration is efficient in the electron acceleration by ICME-driven shocks, which confirms the findings of Yang et al.
Forbush decreases (Fds) in galactic cosmic ray intensity are related to interplanetary coronal mass ejections (ICMEs). The parallel diffusion of particles is reduced because the magnetic turbulence level in sheath region bounded by ICMEs leading edge
and shock is high. Besides, in sheath and magnetic cloud (MC) energetic particles would feel enhanced magnetic focusing effect caused by the strong inhomogeneity of the background magnetic field. Therefore, particles would be partially blocked in sheath-MC structure. Here, we study two-step Fds by considering the magnetic turbulence and background magnetic field in sheath-MC structure with diffusion coefficients calculated with theoretical models, to reproduce the Fd associated with the ground-level enhancement event on 2000 July 14 by solving the focused transport equation. The sheath and MC are set to spherical caps that are portions of spherical shells with enhanced background magnetic field. Besides, the magnetic turbulence levels in sheath and MC are set to higher and lower than that in ambient solar wind, respectively. In general, the simulation result conforms to the main characteristics of the Fd observation, such as the pre-increase precursor, amplitude, total recovery time, and the two-step decrease of the flux at the arrival of sheath and MC. It is suggested that sheath played an important role in the amplitude of Fd while MC contributed to the formation of the second step decrease and prolonged the recovery time. It is also inferred that both magnetic turbulence and background magnetic field in sheath-MC structure are important for reproducing the observed two-step Fd.
Ground-level enhancements (GLEs) generally accompany with fast interplanetary coronal mass ejections (ICMEs), the shocks driven by which are the effective source of solar energetic particles (SEPs). In the GLE event of 2000 July 14, observations show
that a very fast and strong magnetic cloud (MC) is behind the ICME shock and the proton intensity-time profiles observed at 1 au had a rapid two-step decrease near the sheath and MC. Therefore, we study the effect of sheath and MC on SEPs accelerated by an ICME shock through numerically solving the focused transport equation. The shock is regarded as a moving source of SEPs with an assumed particle distribution function. The sheath and MC are set to thick spherical caps with enhanced magnetic field, and the turbulence levels in sheath and MC are set to be higher and lower than that of the ambient solar wind, respectively. The simulation results of proton intensity-time profiles agree well with the observations in energies ranging from $sim$1 to $sim$100 MeV, and the two-step decrease is reproduced when the sheath and MC arrived at the Earth. The simulation results show that the sheath-MC structure reduced the proton intensities for about 2 days after shock passing through the Earth. It is found that the sheath contributed most of the decrease while the MC facilitated the formation of the second step decrease. The simulation also infers that the coordination of magnetic field and turbulence in sheath-MC structure can produce a stronger effect of reducing SEP intensities.
The Spatial Parallel Diffusion Coefficient (SPDC) is one of the important quantities describing energetic charged particle transport. There are three different definitions for the SPDC, i.e., the Displacement Variance definition $kappa_{zz}^{DV}=lim_
{trightarrow t_{infty}}dsigma^2/(2dt)$, the Ficks Law definition $kappa_{zz}^{FL}=J/X$ with $X=partial{F}/partial{z}$, and the TGK formula definition $kappa_{zz}^{TGK}=int_0^{infty}dt langle v_z(t)v_z(0) rangle$. For constant mean magnetic field, the three different definitions of the SPDC give the same result. However, for focusing field it is demonstrated that the results of the different definitions are not the same. In this paper, from the Fokker-Planck equation we find that different methods, e.g., the general Fourier expansion and perturbation theory, can give the different Equations of the Isotropic Distribution Function (EIDFs). But it is shown that one EIDF can be transformed into another by some Derivative Iterative Operations (DIOs). If one definition of the SPDC is invariant for the DIOs, it is clear that the definition is also an invariance for different EIDFs, therewith it is an invariant quantity for the different Derivation Methods of EIDF (DMEs). For the focusing field we suggest that the TGK definition $kappa_{zz}^{TGK}$ is only the approximate formula, and the Ficks Law definition $kappa_{zz}^{FL}$ is not invariant to some DIOs. However, at least for the special condition, in this paper we show that the definition $kappa_{zz}^{DV}$ is the invariant quantity to the kinds of the DIOs. Therefore, for spatially varying field the displacement variance definition $kappa_{zz}^{DV}$, rather than the Ficks law definition $kappa_{zz}^{FL}$ and TGK formula definition $kappa_{zz}^{TGK}$, is the most appropriate definition of the SPDCs.
We investigated Sr$_3$Ru$_2$O$_7$, a quantum critical metal that shows a metamagnetic quantum phase transition and electronic nematicity, through density functional calculations. These predict a ferromagnetic ground state in contrast to the experimen
tally observed paramagnetism, raising the question of competing magnetic states and associated fluctuations that may suppress magnetic order. We did a search to identify such low energy antiferromagnetically ordered metastable states. We find that the lowest energy antiferromagnetic state has a striped order. This corresponds to the E-type order that has been shown to be induced by Mn alloying. We also note significant transport anisotropy in this E-type ordered state. These results are discussed in relation to experimental observations.
The acceleration of suprathermal electrons in the solar wind is mainly associated with shocks driven by interplanetary coronal mass ejections (ICMEs). It is well known that the acceleration of electrons is much more efficient at quasi-perpendicular s
hocks than at quasi-parallel ones. Yang et al. (2018, ApJ, 853, 89) (hereafter YEA2018) studied the acceleration of suprathermal electrons at a quasi-perpendicular ICME-driven shock event to claim the important role of shock drift acceleration (SDA). Here, we perform test-particle simulations to study the acceleration of electrons in this event, by calculating the downstream electron intensity distribution for all energy channels assuming an initial distribution based on the averaged upstream intensities. We obtain simulation results similar to the observations from YEA2018 as follows. It is shown that the ratio of downstream to upstream intensities peaks at about 90$^circ$ pitch angle. In addition, in each pitch angle direction the downstream electron energy spectral index is much larger than the theoretical index of diffusive shock acceleration. Furthermore, considering SDA, the estimated drift length is proportional to the electron energy but the drift time is almost energy independent. Finally, we use a theoretical model based on SDA to describe the drift length and time, especially, to explain their energy dependence. These results indicate the importance of SDA in the acceleration of electrons by quasi-perpendicular shocks.
Solar cycles are studied with the Version 2 monthly smoothed international sunspot number, the variations of which are found to be well represented by the modified logistic differential equation with four parameters: maximum cumulative sunspot number
or total sunspot number $x_m$, initial cumulative sunspot number $x_0$, maximum emergence rate $r_0$, and asymmetry $alpha$. A two-parameter function is obtained by taking $alpha$ and $r_0$ as fixed value. In addition, it is found that $x_m$ and $x_0$ can be well determined at the start of a cycle. Therefore, a prediction model of sunspot number is established based on the two-parameter function. The prediction for cycles $4-23$ shows that the solar maximum can be predicted with average relative error being 8.8% and maximum relative error being 22% in cycle 15 at the start of solar cycles if solar minima are already known. The quasi-online method for determining solar minimum moment shows that we can obtain the solar minimum 14 months after the start of a cycle. Besides, our model can predict the cycle length with the average relative error being 9.5% and maximum relative error being 22% in cycle 4. Furthermore, we predict the sunspot number variations of cycle 24 with the relative errors of the solar maximum and ascent time being 1.4% and 12%, respectively, and the predicted cycle length is 11.0 (95% confidence interval is 8.3$-$12.9) years. The comparison to the observation of cycle 24 shows that our prediction model has good effectiveness.
The 11-year and 22-year modulation of galactic cosmic rays (GCRs) in the inner heliosphere are studied using a numerical model developed by Qin and Shen in 2017. Based on the numerical solutions of Parkers transport equations, the model incorporates
a modified Parker heliospheric magnetic field, a locally static time delayed heliosphere, and a time-dependent diffusion coefficients model in which an analytical expression of the variation of magnetic turbulence magnitude throughout the inner heliosphere is applied. Furthermore, during solar maximum, the solar magnetic polarity is determined randomly with the possibility of $A>0$ decided by the percentage of the north solar polar magnetic field being outward and the south solar polar magnetic field being inward. The computed results are compared with several GCR observations, e.g., IMP 8, SOHO/EPHIN, Ulysses, Voyager 1 & 2, at various energies and show good agreement. It is shown that our model has successfully reproduced the 11-year and 22-year modulation cycles.
Mewaldt et al. 2012 fitted the observations of the ground level enhancement (GLE) events during solar cycle 23 to the double power-law equation to obtain the four energy spectra parameters, the normalization parameter $C$, low-energy power-law slope
$gamma_1$, high-energy power-law slope $gamma_2$, and break energy $E_0$. There are 16 GLEs from which we select $13$ for study by excluding some events with complicated situation. We analyze the four parameters with conditions of the corresponding solar events. According to solar event conditions we divide the GLEs into two groups, one with strong acceleration by interplanetary (IP) shocks and another one without strong acceleration. By fitting the four parameters with solar event conditions we obtain models of the parameters for the two groups of GLEs separately. Therefore, we establish a model of energy spectrum of solar cycle 23 GLEs which may be used in prediction in the future.
