A Hertzsprung‐Russell–like Diagram for Solar/Stellar Flares and Corona: Emission Measure versus 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 ares on the basis of the magnetic reconnection model with heat conduction and chromospheric evaporation. Here n is the electron density a n d 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 ares") with EM/ T 17=2 corresponds to the case of constant heating ux or equivalently the case of constant magnetic eld strength in the reconnection model. 2) The EM-T diagram has a forbidden region, where gas pressure of ares exceeds magnetic pressure. 3) There is a coronal branch with EM / T 15=2 for T < 10 7 K, and EM/ T 13=2 for T > 10 7 K. This branch is situated left side of the main sequence ares in the EM-T diagram. 4) There is another forbidden region determined by the length of are loop; a lower limit of are loop is 10 7 cm. Small ares near this limit correspond to nanoares observed by SOHO/EIT. 5) We can plot are evolution track o n t h e EM-T diagram. A are evolves from the coronal branch to main sequence ares, 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 ux, magnetic eld strength, total energy and so on) of ares and corona when there is no spatially resolved imaging observations.

Chandra observation of an unusually long and intense X-ray flare from a young solar-like star in M 78

“…Loops suffer magnetohydrodynamical instabilities with characteristic growth timescale, τ, corresponding to the length scale of the pre-eruption region, l, divided by the ambient Alfvèn speed (Priest & Forbes 2000), V A ∝ B n −1/2 c , with B the average magnetic field strength, and n c the pre-flare coronal density. We scale the LkHα 312 values to the solar values: l = 5 × 10 10 cm for an average CME (Gilbert et al 2001, and references therein), B ∼ 100 G (e.g., Parker 1988), and n c, ∼ 10 9 cm −3 (see Shibata & Yokoyama 2002, and references therein). We obtain:…”

“…1 of Shibata & Yokoyama 2002), no special scaling laws are required for this flare. Applying the previous set of formulae, we find:…”

Analysis of the Temperature and Emission Measure of Solar Coronal Arcades and Test of a Scaling Law of Flare/Arcade Loop Length

“…Shibata & Yokoyama (1999 presented a theory to explain this universal correlation. This theory is based on two-dimensional magnetohydrodynamic (MHD) simulations by Yokoyama & Shibata (1998) aimed to study the physics of the flare with two-dimensional MHD simulations of the reconnection including heat conduction and chromospheric evaporation and showed a simple scaling law among T, , L, and B, where T is the temperature of n 0 the flare loop, is the electron number density of the preflare n 0 corona, L is the typical loop length of solar and stellar flares, and B is the coronal magnetic field strength.…”

Evidence of thermal conduction suppression in hot coronal loops: supplementary results

“…Assuming the balance between conduction cooling and reconnection heating and the pressure balance for flare loops, Shibata & Yokoyama (2002) derived the scaling law EM ∝ B −5 T 17/2 where B is the magnetic field strength. If considering the suppressed conductivity κ S = κ 0 /S where κ 0 ≃ 10 −6 cgs is the classical Spitzer conductivity and S the suppression factor, we obtained the modified scaling law EM S ∝ S −3 B −5 T 17/2 as well as the relations T S /T = S 6/17 and B S /B = 1/S 3/5 .…”

“…The modified Spitzer cooling timescales based on the nonlocal conduction approximation are consistent with the observed, suggesting that nonlocal conduction may account for the observed conduction suppression in this event. In addition, the conduction suppression mechanism predicts that larger flares may tend to be hotter than expected by the EM-T relation derived by Shibata & Yokoyama (2002). …”