Fig. 1. Reduced fit for He-triplets with a three-Gaussian model, taking Si xiii of Vela X-1 with  as an example. Best fitting result and its error range are shown in red thick line and red shadow, respectively. The observed spectrum and its error bars are shown in black steps.

Fig. 2. The best model-predicted continuum shown in red thick lines for three phases. The scatter and direct components are shown separately. Shadows are the 68.3% errors in the recovered value of parameters. The observed spectrum and its error bars are shown in black steps and gray shadow. The large residual values are caused by emission lines.

Fig. 3. The best model-predicted He-like Mg xi shown in red thick line for both (a) the Eclipse phase and (b) . Red shadows are the 68.3% errors in the recovered value of parameters list in Table 4. The observed spectrum and its error bars are shown in black steps.

Fig. 4. The best model-predicted He-like Si XIII shown in red thick line for both (a) the Eclipse phase and (b) . Red shadows are the 68.3% errors in the recovered value of parameters list in Table 4. The observed spectrum and its error bars are shown in black steps.

Fig. 5. Comparisons with previous works. Red thick lines and their shadows are our present best-fit results. Aqua, blue, and purple dash lines are the results with parameters determined by S99, G04, and W06, respectively.

Fig. 6. Posterior PDFs of parameters and their correlations. Using the parameters of continuum for  as an example. Red lines represent values used in best-fit for , and dashed lines correspond to 1- error. The plot is made by a Python module corner^[30].