tokens: the case of PRD and the dotted line that of CRD. Other input parameters are . No background continuum opacity is used. 4.2. The Case of the <inline-formula> <tex-math> </tex-math> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjaa3333ieqn70.gif"></inline-graphic> </inline-formula> Transition For the case when J a = J b = 1, even in the absence of LLP, since the upper level is polarized, a finite amount of emergent polarization is generated unlike the case of J a = 1, J b = 0. For all the computations of this particular transition ( J a = J b = 1), we again consider the hypothetical case like that described for J a = 1, J b = 0. In this case, there are four density matrix elements to be determined, namely, , , , and , when polarizability of both levels are taken into account. Figure 2 shows the emergent ( I , Q / I ) at μ = 0.11 for the transition. The solid line in Figure 2 represents the emergent profiles obtained when both the effects of PRD and LLP are considered. In order to see the importance of both effects we have overplotted the ( I , Q / I ) profiles obtained when only the effects of PRD are considered with an unpolarized lower level (ULL—dashed line); when the effects of LLP is considered in the limit of CRD (dotted line); and the case where only the CRD effects are considered with ULL (dotted–dashed line). Figure 2 clearly shows that the LLP effects appear only in the emergent polarization and the intensity profiles remain unchanged whether or not LLP is taken into account. We see that the LLP effects in the emergent Q / I are significant mainly in the core (up to ∼2 Doppler widths, see inset in the lower panel of Figure 2 ), and in the wings the effects of PRD are dominant (compare solid and dashed lines). The enhancement in the emergent polarization at the line center when LLP is included is around 5%. Figure 2. Emergent intensity and polarization for μ = 0.11 computed using the two-stage approach for the case. The different line types correspond to: solid line—PRD + LLP, dotted line—CRD + LLP, dashed line—PRD + ULL, and the dotted–dashed line—CRD + ULL. The abbreviation ULL stands for unpolarized lower level. Other input parameters are . No background continuum opacity is used. The inset in the Q / I panel shows the Q / I profiles for a shorter frequency bandwidth for the sake of clarity. In the first stage of the two-stage approach, the SEEs are solved under the approximation of CRD, and thus all the transition rates that enter into the SEEs are frequency-integrated quantities. Therefore, all the redistribution effects are integrated away. The contributions to the frequency-integrated scattering probability come almost entirely from the Doppler core. In SEEs, we compare the individual transition rates for a given radiation field. For each individual transition, the contributions of the wing photons are insignificant compared with the core photons. Since it is only the core photons that are relevant
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