A HR-like Diagram for Solar/Stellar Flares and Corona -- Emission Measure vs Temperature Diagram

Abstract

In our previous paper, we have presented a theory to explain the observed universal correlation between the emission measure ($EM=n^2 V$) and temperature (T) for solar/stellar flares on the basis of the magnetic reconnection model with heat conduction and chromospheric evaporation. Here n is the electron density and V is the volume. By extending our theory to general situations, we examined the EM-T diagram in detail, and found the following properties: 1) The universal correlation sequence (``main sequence flares'') with $EM \propto T^{17/2}$ corresponds to the case of constant heating flux or equivalently the case of constant magnetic field strength in the reconnection model. 2) The EM-T diagram has a forbidden region, where gas pressure of flares exceeds magnetic pressure. 3) There is a coronal branch with $EM \propto T^{15/2}$ for $T< 10^7$ K, and $EM \propto T^{13/2}$ for $T> 10^7$ K. This branch is situated left side of the main sequence flares in the EM-T diagram. 4) There is another forbidden region determined by the length of flare loop; a lower limit of flare loop is $10^7$ cm. Small flares near this limit correspond to nanoflares observed by SOHO/EIT. 5) We can plot flare evolution track on the EM-T diagram. A flare evolves from the coronal branch to main sequence flares, then returns to the coronal branch eventually. These properties of the EM-T diagram are similar to those of the HR diagram for stars, and thus we propose that the EM-T diagram is quite useful to estimate the physical quantities (loop length, heating flux, magnetic field strength, total energy and so on) of flares and corona when there is no spatially resolved imaging observations.