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Thermal microwave emissions detected from stellar atmospheres contain information on stellar activity. However, even for the Sun, the relationship between multifrequency microwave data and other activity indices remains unclear. We investigated the relationships among the thermal microwave fluxes with 1, 2, 3.75 and 9.4 GHz, their circular polarizations, and several activity indices recorded during recent solar cycles and observed that these relationships can be categorized into two groups. In the first group, the relationship between the microwave fluxes and solar indices, which are strongly related to the active regions, can be well-fitted by using a linear function. In the second group, the fitting function is dependent on frequency. Specifically, the microwave fluxes at 1 and 2 GHz can be well-fitted to the total unsigned magnetic and extreme ultraviolet fluxes by employing a power-law function. The trend changes around 3.75 GHz, and of the trend for the 9.4 GHz fluxes can be fitted by using a linear function. For the first time, we present the relationship between circular polarization and solar indices. Moreover, we extrapolated these relationships of the solar microwave fluxes to higher values and compared them with the solar-type stars. We found that epsilon Eri, whose microwave emission originates from thermal plasma, follows the extrapolated relationship. However, to date, only one star's emission at 1--10 GHz has been confirmed as thermal emission. More solar-type stars should be observed with future radio interferometers to confirm that relationships based on solar data can be applied to stellar microwave data., Comment: 24 pages, 18 figures, accepted for publishing in Astrophysical Journal

Kepler Space Telescope and Transiting Exoplanet Survey Satellite unveiled that Sun-like stars frequently host exoplanets. These exoplanets are subject to fluxes of ionizing radiation in the form of X-ray and extreme-ultraviolet (EUV) radiation that may cause changes in their atmospheric dynamics and chemistry. While X-ray fluxes can be observed directly, EUV fluxes cannot be observed because of severe interstellar medium absorption. Here, we present a new empirical method to estimate the whole stellar XUV (X-ray plus EUV) and FUV spectra as a function of total unsigned magnetic fluxes of stars. The response of the solar XUV and FUV spectrum (0.1-180 nm) to the solar total unsigned magnetic flux is investigated by using the long-term Sun-as-a-star dataset over 10 yrs, and the power-law relation is obtained for each wavelength with a spectral resolution of 0.1-1 nm. We applied the scaling relations to active young Sun-like stars (G-dwarfs), EK Dra (G1.5V), $\pi^1$ Uma (G1.5V) and $\kappa^1$ Ceti (G5V), and found that the observed spectra (except for the unobservable longward EUV wavelength) are roughly consistent with the extension of the derived power-law relations with errors of an order of magnitude. This suggests that our model is a valuable method to derive the XUV/FUV fluxes of Sun-like stars including the EUV band mostly absorbed at wavelengths longward of 36 nm. We also discuss differences between the solar extensions and stellar observations at the wavelength in the 2-30 nm band and concluded that simultaneous observations of magnetic and XUV/FUV fluxes are necessary for further validations., Comment: 29 pages, 10 figures, 8 tables. Accepted for publication in The Astrophysical Journal

We have investigated an M1.3 limb flare, which develops as a magnetic loop/arch that fans out from an X-ray jet. Using Hinode/EIS, we found that the temperature increases with height to a value of over 10$^{7}$ K at the loop-top during the flare. The measured Doppler velocity (redshifts of 100$-$500 km s$^{-1}$) and the non-thermal velocity ($\geq$100 km s$^{-1}$) from Fe XXIV also increase with loop height. The electron density increases from $0.3\times10^{9}$ cm$^{-3}$ early in the flare rise to $1.3\times10^{9}$ cm$^{-3}$ after the flare peak. The 3-D structure of the loop derived with STEREO/EUVI indicates that the strong redshift in the loop-top region is due to upflowing plasma originating from the jet. Both hard X-ray and soft X-ray emission from RHESSI were only seen as footpoint brightenings during the impulsive phase of the flare, then, soft X-ray emission moves to the loop-top in the decay phase. Based on the temperature and density measurements and theoretical cooling models, the temperature evolution of the flare arch is consistent with impulsive heating during the jet eruption followed by conductive cooling via evaporation and minor prolonged heating in the top of the fan loop. Investigating the magnetic field topology and squashing factor map from SDO/HMI, we conclude that the observed magnetic-fan flaring arch is mostly heated from low atmospheric reconnection accompanying the jet ejection, instead of from reconnection above the arch as expected in the standard flare model., Comment: 55 pages, 21 Figures, accepted for publication in ApJ

In addition to X-rays, extreme ultraviolet (EUV) rays radiated from solar flares can cause serious problems, such as communication failures and satellite drag. Therefore, methods for forecasting EUV dynamic spectra during flares are urgently required. Recently, however, owing to the lack of instruments, EUV dynamic spectra have rarely been observed. Hence, we develop a new method that converts the soft X-ray light curve observed during large flare events into an EUV dynamic spectrum by using the Solar Dynamics Observatory / Atmospheric Imaging Assembly images, a numerical simulation, and atomic database. The simulation provides the solution for a coronal loop that is heated by a strong flare, and the atomic database calculates its dynamic spectrum, including X-ray and EUV irradiances. The coefficients needed for the conversion can be calculated by comparing the observed soft X-ray light curve with that of the simulation. We apply our new method to three flares that occurred in the active region 12673 on September 06, 2017. The results show similarities to those of the Flare Irradiance Spectral Model, and reconstruct some of the EUV peaks observed by the EUV Variability Experiment onboard the Solar Dynamics Observatory.

Recently, many superflares on solar-type stars were discovered as white-light flares (WLFs). A correlation between the energies (E) and durations (t) of superflares is derived as $t\propto E^{0.39}$, and this can be theoretically explained by magnetic reconnection ($t\propto E^{1/3}$). In this study, we carried out a statistical research on 50 solar WLFs with SDO/HMI to examine the t-E relation. As a result, the t-E relation on solar WLFs ($t\propto E^{0.38}$) is quite similar stellar superflares, but the durations of stellar superflares are much shorter than those extrapolated from solar WLFs. We present the following two interpretations; (1) in solar flares, the cooling timescale of WL emission may be longer than the reconnection one, and the decay time can be determined by the cooling timescale; (2) the distribution can be understood by applying a scaling law $t\propto E^{1/3}B^{-5/3}$ derived from the magnetic reconnection theory., Comment: 4 pages, 1 figures, paper of the Proceedings of the IAUS340, accepted

Recently, many superflares on solar-type stars have been discovered as white-light flares (WLFs). The statistical study found a correlation between their energies ($E$) and durations ($\tau$): $\tau \propto E^{0.39}$ (Maehara et al. 2017 $EP\& S$, 67, 59), similar to those of solar hard/soft X-ray flares: $\tau \propto E^{0.2-0.33}$. This indicates a universal mechanism of energy release on solar and stellar flares, i.e., magnetic reconnection. We here carried out a statistical research on 50 solar WLFs observed with \textit{SDO}/HMI and examined the correlation between the energies and durations. As a result, the $E$--$\tau$ relation on solar WLFs ($\tau \propto E^{0.38}$) is quite similar to that on stellar superflares ($\tau \propto E^{0.39}$). However, the durations of stellar superflares are one order of magnitude shorter than those expected from solar WLFs. We present the following two interpretations for the discrepancy. (1) In solar flares, the cooling timescale of WLFs may be longer than the reconnection one, and the decay time of solar WLFs can be elongated by the cooling effect. (2) The distribution can be understood by applying a scaling law ($\tau \propto E^{1/3}B^{-5/3}$) derived from the magnetic reconnection theory. In this case, the observed superflares are expected to have 2-4 times stronger magnetic field strength than solar flares., Comment: 43 pages, 15 figures, accepted for publication in ApJ

To understand the conditions that produce white-light (WL) enhancements in solar flares, a statistical analysis of visible continuum data as observed by Hinode/Solar Optical Telescope (SOT) was performed. In this study, approximately 100 flare events from M- and X-class flares were selected. The time period during which the data were recorded spans from January 2011 to February 2016. Of these events, approximately half are classified as white-light flares (WLFs), whereas the remaining events do not show any enhancements of the visible continuum (non-WLF; NWL). In order to determine the existence of WL emission, running difference images of not only the Hinode/SOT WL (G-band, blue, green, and red filter) data but also the Solar Dynamics Observatory/Helioseismic and Magnetic Imager continuum data are used. A comparison between these two groups of WL data in terms of duration, temperature, emission measure of GOES soft X-rays, distance between EUV flare ribbons, strength of hard X-rays, and photospheric magnetic field strength was undertaken. In this statistical study, WLF events are characterized by a shorter time-scale and shorter ribbon distance compared with NWL events. From the scatter plots of the duration of soft X-rays and the energy of non-thermal electrons, a clear distinction between WLF and NWL events can be made. It is found that the precipitation of large amounts of accelerated electrons within a short time period plays a key role in generating WL enhancements. Finally, it was demonstrated that the coronal magnetic field strength in the flare region is one of the most important factors that allow the individual identification of WLF events from NWL events., Comment: 17 pages, 9 figures, 3 tables, accepted for publication in ApJ

An X1.6 flare occurred in AR 12192 on 2014 October 22 at 14:02 UT and was observed by Hinode, IRIS, SDO, and RHESSI. We analyze a bright kernel which produces a white light (WL) flare with continuum enhancement and a hard X-ray (HXR) peak. Taking advantage of the spectroscopic observations of IRIS and Hinode/EIS, we measure the temporal variation of the plasma properties in the bright kernel in the chromosphere and corona. We found that explosive evaporation was observed when the WL emission occurred, even though the intensity enhancement in hotter lines is quite weak. The temporal correlation of the WL emission, HXR peak, and evaporation flows indicate that the WL emission was produced by accelerated electrons. To understand the white light emission process, we calculated the energy flux deposited by non- thermal electrons (observed by RHESSI) and compared it to the dissipated energy estimated from a chromospheric line (Mg II triplet) observed by IRIS. The deposited energy flux from the non-thermal electrons is about 3 ~ 7.7 X 10^(10) erg cm^(-2) s^(-1) for a given low energy cut-off of 30 ~ 40 keV, assuming the thick target model. The energy flux estimated from the temperature changes in the chromosphere measured using the Mg II subordinate line is about 4.6 - 6.7 X 10(9) erg cm^(-2) s^(-1): ~6-22% of the deposited energy. This comparison of estimated energy fluxes implies that the continuum enhancement was directly produced by the non-thermal electrons., Comment: 29 pages, 15 figures, 1 table, accepted for publication in ApJ

Shibata & Yokoyama (1999, 2002) proposed a method of estimating the coronal magnetic field strengths ($B$) and magnetic loop lengths ($L$) of solar and stellar flares, on the basis of magnetohydrodynamic simulations of the magnetic reconnection model. Using the scaling law provided by Shibata & Yokoyama (1999, 2002), $B$ and $L$ are obtained as functions of the emission measure ($EM=n^2L^3$) and temperature ($T$) at the flare peak. Here, $n$ is the coronal electron density of the flares. This scaling law enables the estimation of $B$ and $L$ for unresolved stellar flares from the observable physical quantities $EM$ and $T$, which is helpful for studying stellar surface activities. To apply this scaling law to stellar flares, we discuss its validity for spatially resolved solar flares. $EM$ and $T$ were calculated from GOES soft X-ray flux data, and $B$ and $L$ are theoretically estimated using the scaling law. For the same flare events, $B$ and $L$ were also observationally estimated with images taken by Solar Dynamics Observatory (SDO)/ Helioseismic and Magnetic Imager (HMI) Magnetogram and Atmospheric Imaging Assembly (AIA) 94{\AA} pass band. As expected, a positive correlation was found between the theoretically and observationally estimated values. We interpret this result as indirect evidence that flares are caused by magnetic reconnection. Moreover, this analysis makes us confident in the validity of applying this scaling law to stellar flares as well as solar flares., Comment: 17 pages, 6 figures, accepted for publication in PASJ

White-light emissions were observed from an X1.7 class solar flare on 27 January 2012, using three continuum bands (red, green, and blue) of the Solar Optical Telescope (SOT) onboard the Hinode satellite. This event occurred near the solar limb, and so differences in locations of the various emissions are consistent with differences in heights above the photosphere of the various emission sources. Under this interpretation, our observations are consistent with the white-light emissions occurring at the lowest levels of where the Ca II H emission occurs. Moreover, the centers of the source regions of the red, green, and blue wavelengths of the white-light emissions are significantly displaced from each other, suggesting that those respective emissions are emanating from progressively lower heights in the solar atmosphere. The temperature distribution was also calculated from the white-light data, and we found the lower-layer emission to have a higher temperature. This indicates that high-energy particles penetrated down to near the photosphere, and deposited heat into the ambient lower layers of the atmosphere., Comment: 25 pages, 6 figures, accepted for publication in ApJ

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 ApJ

On December 27, 2004, plasma particle detectors on the GEOTAIL spacecraft detected an extremely strong signal of hard X-ray photons from the giant flare of SGR1806-20, a magnetar candidate. While practically all gamma-ray detectors on any satellites were saturated during the first ~500 ms interval after the onset, one of the particle detectors on GEOTAIL was not saturated and provided unique measurements of the hard X-ray intensity and the profile for the first 600 ms interval with 5.48 ms time resolution. After ~50 ms from the initial rapid onset, the peak photon flux (integrated above ~50 keV) reached the order of 10^7 photons sec^{-1} cm^{-2}. Assuming a blackbody spectrum with kT=175 keV, we estimate the peak energy flux to be 21 erg sec^{-1} cm^{-2} and the fluence (for 0-600 ms) to be 2.4 erg cm^{-2}. The implied energy release comparable to the magnetic energy stored in a magnetar (~10^{47} erg) suggests an extremely efficient energy release mechanism., Comment: 6 pages, 2 color figures, submitted to Nature