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Shibata & Yokoyama (1999, 2002) proposed a method of estimating the coronalmagnetic field strengths ($B$) and magnetic loop lengths ($L$) of solar andstellar flares, on the basis of magnetohydrodynamic simulations of the magneticreconnection 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 coronalelectron 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. Toapply this scaling law to stellar flares, we discuss its validity for spatiallyresolved solar flares. $EM$ and $T$ were calculated from GOES soft X-ray fluxdata, and $B$ and $L$ are theoretically estimated using the scaling law. Forthe same flare events, $B$ and $L$ were also observationally estimated withimages taken by Solar Dynamics Observatory (SDO)/ Helioseismic and MagneticImager (HMI) Magnetogram and Atmospheric Imaging Assembly (AIA) 94{\AA} passband. As expected, a positive correlation was found between the theoreticallyand observationally estimated values. We interpret this result as indirectevidence that flares are caused by magnetic reconnection. Moreover, thisanalysis makes us confident in the validity of applying this scaling law tostellar flares as well as solar flares.

Validation of a Scaling Law for the Coronal Magnetic Field Strengths and Loop Lengths of Solar and Stellar Flares