6.2  EMs

Once the DEM(T) is known, the total emission measure EM can be calculated, integrating the DEM(T) over a suitable temperature range:

EM º ó õ h  Ne NH dh = ó õ T  DEM(T)  dT        [cm-5]

(15)

Note that sometimes the total emission measure is defined as EM = òN_e² dh = òDEM(T) dT , with the differential emission measure defined as DEM(T) = N_e² (dT / dh)^-1 .

Following Pottasch (1963), various approximations and methods have been introduced in order to simplify the inversion and to deduce elemental abundances. One method is to define for each observed line an average emission measure < EM > .

By removing an averaged value of C(T) from the integral:

Ith = Ab(Z)   < C(T) >   ó õ h   Ne NH dh

(16)

a suitably defined volume line emission measure EM_L can therefore be defined, for each observed line of intensity I_ob:

EML º  Iob Ab(Z)   < C(T) >      [cm-5]

(17)

For example, Jordan and Wilson (1971) assumed that C(T) has a constant value over a narrow temperature interval Dlog T=0.3, to calculate for each observed transition a line emission measure EM(0.3).

Another approximation is to define for each observed line an averaged < DEM > (see below).

6.2.1  The emission measure loci approach

One direct approach is to plot the ratio I_ob / G(T) for each line as a function of temperature and consider the loci of these curves to constrain the shape of the emission measure distribution. In fact, for each line and temperature T_i the value I_ob / G(T_i) represents an upper limit to the value of the line emission measure EM_L (Equation 31) at that temperature, assuming that all the observed emission I_ob is produced by plasma at temperature T_i.