6.1  DEM

If we define, assuming that is a single-value function of the temperature, the differential emission measure DEM (T) function as

DEM (T) =  Ne NH  dh dT   [cm-5 K-1]

(13)

the intensity can be rewritten, assuming that the abundance is constant along the line of sight:

I(lij) = Ab(X) ó õ T   C(T,lij,Ne)  DEM (T)   dT    [ergs   cm-2   s-1  sr-1]

(14)

The DEM(T) gives an indication of the amount of plasma along the line of sight that is emitting the radiation observed and has a temperature between T and T+dT.

Please note that in the literature many different definitions of Differential Emission Measures, Emission Measures and approximations can be found (see Del Zanna et al., 2002 for some clarifications).

Within CHIANTI, the routine chianti_dem.pro calculates the Differential Emission Measure DEM(T) using the database, from a given set of observed lines.

Important:

• to reduce any density effects, only lines which have contribution functions independent from the density should be used to derive the DEM(T);
• only ions that have a peaked ion fraction should be used;
• ions for which an anomalous behaviour is present (see below) should be avoided;
• filling factors (see below) should be taken into account.
• appropriate values of the elemental abundances should be chosen according to the region of the Sun being observed.

The inversion problem (to obtain the DEM) is not simple nor unique. See Del Zanna (1999) for details. Fig. 14 shows the DEM of the CHIANTI test case. Once the curve is obtained, one way to present the uncertainties associated with it is to overplot for each line at its effective temperature T_eff error bars with the value DEM(T_eff) I_o / I_th where I_o is the observed intensity and I_th is the intensity calculated with the DEM(T) curve.

Figure 14: The DEM of the CHIANTI test case.