Steady models for the hard X-ray loops in the solar corona

In some gradual hard X-ray bursts with high intensity, hard X-ray source (15–40 keV) is steadily located in the corona along with softer X-ray source (5–10 keV).Two stationary models, high density and high temperature models, are proposed to solve the difficult problem of confinement of hot (or nonthermal) plasma in the direction of the magnetic field along the loops in the corona. In both models, an essential point is that the effective X-ray source is composed of fine dense filamentary loops imbeded in a larger rarefied coronal loop, and the electron number density in the filaments is so high as 10¹¹–10¹² cm^-3. If the density is so high heat conduction can be as reasonably small as of the order of 10²⁷ erg s ^-1 for the given emission measures of observed X-rays, since the required cross-sectional area is small and also classical conduction is valid. Collisional confinement of thermal tail, and nonthermal electrons if any, up to 50–60 keV in the filaments is also possible, so that the hard X-ray images can be loop like structure instead of double source (foot points).High density model is applicable to the coronal filamentary loops with temperature T_m < 5 × 10⁷ K at the loop summit. The heat flow from the summit downwards is lost almost completely by the radiation from the loop during the conduction to the foot points. A continuous energy release is assumed near the summit to maintain the stationary temperature T_m, and pressure balance is maintained along the loop. In this model, the number density at the summit is given by n_m - 10⁶T_m²/s_m, where s_m is the length of the loop from the summit to the foot point, and the distribution of temperature and density along the loop are given by T = T_m(s/s_m)^1/3 and n = n_m(s/s_m)^-1/3, respectively.High temperature model is applicable to the filamentary loops with higher temperature up to about 10^8.5 K and comparatively lower number density as 10¹¹ cm^-3 for the requirement of magnetic confinement of the hot plasma in radial direction. The radiation from the loop is negligibly small in this model so that the heat flux is nearly conserved down to the foot points. In this case, temperature gradient is smaller than that of the high density model, depending on the tapering of the magnetic bottle.In both models, the differential emission measure is maximum at the highest temperature T_m and the brightness distribution along the loop shows a maximum around the summit of the loop if some magnetic tapering is taken into account.