Non-potential field formation in the X-shaped quadrupole magnetic field configuration

Some types of solar flares are observed in X-shaped quadrupolar field configuration. To understand the magnetic energy storage in such a region, we studied non-potential field formation in an X-shaped quadrupolar field region formed in the active region NOAA 11967, which produced three X-shaped M-class flares on February 2, 2014. Nonlinear force-free field modeling was applied to a time series of vector magnetic field maps from the Solar Optical Telescope on board Hinode and Helioseismic and Magnetic Imager on board Solar Dynamics Observatory. Our analysis of the temporal three-dimensional magnetic field evolution shows that the sufficient free energy had already been stored more than 10 hours before the occurrence of the first M-class flare and that the storage was observed in a localized region. In this localized region, quasi-separatrix layers (QSLs) started to develop gradually from 9 hours before the first M-class flare. One of the flare ribbons that appeared in the first M-class flare was co-spatial with the location of the QSLs, suggesting that the formation of the QSLs is important in the process of energy release. These QSLs do not appear in the potential field calculation, indicating that they were created by the non-potential field. The formation of the QSLs was associated with the transverse photospheric motion of the pre-emerged flux and the emergence of a new flux. This observation indicates that the occurrence of the flares requires the formation of QSLs in the non-potential field in which free magnetic energy is stored in advance.Comment: Accepted for publication in Ap

A4×U(1)PQA_4 \times U(1)_{PQ} Model for the Lepton Flavor Structure and the Strong CPCP Problem

We present a model with $A_4 \times U(1)_{PQ}$ lepton flavor symmetry which explains the origin of the lepton flavor structure and also solves the strong $CP$ problem. Standard model gauge singlet fields, so-called "flavons", charged under the $A_4 \times U(1)_{PQ}$ symmetry are introduced and are coupled with the lepton and the Higgs sectors. The flavon vacuum expectation values (VEVs) trigger spontaneous breaking of the $A_4 \times U(1)_{PQ}$ symmetry. The breaking pattern of the $A_4$ accounts for the tri-bimaximal neutrino mixing and the deviation from it due to the non-zero $\theta_{13}$ angle, and the breaking of the $U(1)_{PQ}$ gives rise to a pseudo-Nambu-Goldstone boson, axion, whose VEV cancels the QCD $\theta$ term. We investigate the breaking of the $A_4 \times U(1)_{PQ}$ symmetry through an analysis on the scalar potential and further discuss the properties of the axion in the model, including its decay constant, mass and coupling with photons. It is shown that the axion decay constant is related with the right-handed neutrino mass through the flavon VEVs. Experimental constraints on the axion and their implications are also studied.Comment: 13 pages, final version, minor modification

Which Component of Solar Magnetic Field Drives the Evolution of Interplanetary Magnetic Field over Solar Cycle?

The solar magnetic structure changes over the solar cycle. It has a dipole structure during solar minimum, where the open flux extends mainly from the polar regions into the interplanetary space. During maximum, a complex structure is formed with low-latitude active regions and weakened polar fields, resulting in spread open field regions. However, the components of the solar magnetic field that is responsible for long-term variations in the interplanetary magnetic field (IMF) are not clear, and the IMF strength estimated based on the solar magnetic field is known to be underestimated by a factor of 3 to 4 against the actual in-situ observations (the open flux problem). To this end, we decomposed the coronal magnetic field into the components of the spherical harmonic function of degree and order $(\ell, m)$ using the potential field source surface model with synoptic maps from SDO/HMI for 2010 to 2021. As a result, we found that the IMF rapidly increased in December 2014 (seven months after the solar maximum), which coincided with the increase in the equatorial dipole, $(\ell, m)=(1, \pm1)$, corresponding to the diffusion of active regions toward the poles and in the longitudinal direction. The IMF gradually decreased until December 2019 (solar minimum) and its variation corresponded to that of the non-dipole component $\ell\geq2$. Our results suggest that the understanding of the open flux problem may be improved by focusing on the equatorial dipole and the non-dipole component and that the influence of the polar magnetic field is less significant.Comment: 19 pages, 9 figures, accepted for publication in Ap

Neutrino Mass in Non-Supersymmetric SO(10)SO(10) GUT

We study a prediction on neutrino observables in a non-supersymmetric renormalizable $SO(10)$ GUT model that contains a ${\bf 10}$ complex scalar field and a ${\bf 126}$ scalar field whose Yukawa couplings with ${\bf 16}$ matter fields provide the quark and charged lepton Yukawa couplings, neutrino Dirac Yukawa coupling and Majorana mass for the singlet neutrinos. The $SO(10)$ breaking is achieved in two steps by a ${\cal O}(10^{15})$ GeV VEV of a ${\bf 54}$ real scalar field and a ${\cal O}(10^{14})$ GeV VEV of the ${\bf 126}$ field. First, we analyze the gauge coupling unification conditions and determine the VEV of the ${\bf 126}$ field. Next, we constrain the Yukawa couplings of the ${\bf 10}$ and ${\bf 126}$ fields at the scale of the ${\bf 126}$ field's VEV from experimental data on quark and charged lepton masses and quark flavor mixings. Then we express the active neutrino mass with the above Yukawa couplings and the ${\bf 126}$ field's VEV based on the Type-1 seesaw mechanism, and fit neutrino oscillation data, thereby deriving a prediction on poorly or not measured neutrino observables. What distinguishes our work from previous studies is that we do not assign Peccei-Quinn charges on visible sector fields so that the ${\bf 10}$ scalar field and its complex conjugate both have Yukawa couplings with ${\bf 16}$ matter fields. From the fitting of neutrino oscillation data, we find that not only the normal neutrino mass hierarchy, but also the inverted hierarchy can be realized. We also reveal that in the normal hierarchy case, the Dirac CP phase of the neutrino mixing matrix $\delta_{CP}$ is likely in the ranges of $-2.4<\delta_{\rm CP}<-1.2$ and $1.2<\delta_{\rm CP}<2.4$, and not in the region with $\delta_{\rm CP}\sim\pi$, and that in the normal hierarchy case, $\theta_{23}$ is likely in the upper octant and in the range of $0.50\lesssim\sin^2\theta_{23}\lesssim0.55$.Comment: 22 pages, 3 figure

Higgs Portal Majorana Fermionic Dark Matter with the Freeze-in Mechanism

We consider a minimal model of fermionic dark matter, in which the Majorana fermion dark matter (DM) $\chi$ couples with the Standard Model (SM) Higgs field $H$ through a higher-dimensional term $-{\cal L}\supset H^\dagger H \bar{\chi}\chi/\Lambda$, where $\Lambda$ is the cutoff scale. We assume that $\Lambda$ is sufficiently large that DM particles are not in thermal equilibrium with the SM Particles throughout the history of the Universe. Hence, DM particles are produced only by the freeze-in mechanism. Through a numerical analysis of the freeze-in mechanism, we show contour plots of the DM relic abundance for various values of the DM mass, reheating temperature and the cutoff scale. We obtain an upper bound of the DM mass and cutoff scale from contour plots on ($m_\chi, \Lambda$)-plane. We also consider the direct DM detection for the parameter regions where the DM relic abundance is consistent with the experimental values. We find that the spin-independent cross section for the elastic scattering with a nucleon is below the current experimental upper bound.Comment: 11 pages, 10 figure

G-band and Hard X-ray Emissions of the 2006 December 14 flare observed by Hinode/SOT and RHESSI

We report on G-band emission observed by the Solar Optical Telescope onboard the Hinode satellite in association with the X1.5-class flare on 2006 December 14. The G-band enhancements originate from the footpoints of flaring coronal magnetic loops, coinciding with non-thermal hard X-ray bremsstrahlung sources observed by the Reuven Ramaty High Energy Solar Spectroscopic Imager. At the available 2 minute cadence, the G-band and hard X-ray intensities are furthermore well correlated in time. Assuming that the G-band enhancements are continuum emission from a blackbody, we derived the total radiative losses of the white-light flare (white-light power). If the G-band enhancements additionally have a contribution from lines, the derived values are overestimates. We compare the white-light power with the power in hard X-ray producing electrons using the thick target assumption. Independent of the cutoff energy of the accelerated electron spectrum, the white-light power and the power of accelerated electrons are roughly proportional. Using the observed upper limit of ~30 keV for the cutoff energy, the hard X-ray producing electrons provide at least a factor of 2 more power than needed to produce the white-light emission. For electrons above 40 keV, the powers roughly match for all four of the time intervals available during the impulsive phase. Hence, the flare-accelerated electrons contain enough energy to produce the white-light flare emissions. The observed correlation in time, space, and power strongly suggests that electron acceleration and white-light production in solar flares are closely related. However, the results also call attention to the inconsistency in apparent source heights of the hard X-ray (chromosphere) and white-light (upper photosphere) sources.Comment: 15 pages, 7 figures, accepted for publication in Ap