ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-Archive I-Archive I-Archive O O O O B-CelestialObject O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O
tokens: core. Figure 12 shows that such a quiescent gas environment barely affects the line ratios, as the difference in the line ratios calculated at the turbulence 0 and 150 km s −1 is very small. Figure 12. Line intensity ratio relative to w vs. log of hydrogen column density. Solid: no turbulence. Dashed: turbulence 150 km s −1 . Dotted: turbulence 500 km s −1 . We also plot the line ratios at the turbulence of 500 km s −1 . Such a high value of the turbulence is not applicable in our region of interest, but may apply for gas in other environments such as merging galaxy clusters (Cassano Brunetti 2005 ). Optical depth can be expressed as a product of column density ( N ), and absorption cross section ( α ν ):where α ν is inversely proportional to the total Doppler velocity.where is the downward transition probability, is the oscillator strength and other symbols have their usual meaning (Mihalas 1970 ). If the temperature is held constant, an increase in the turbulent velocity decreases α ν , which decreases the overall optical depth. Ideally, to achieve the same optical depth at zero and higher turbulent velocity, a higher column density should be required for the latter case. However, this outcome gets reversed due to line interlocking of x, y, and z with other ions (e.g., Fe 23+ , Cr 22+ , and Fe 22+ ; see Paper I ). The higher the turbulent velocity is, the higher the Doppler width of a line and the more pronounced the line interlocking effects will be. Total line-center optical depth will therefore increase with turbulent velocity rather than decrease, as Equation ( 3 ) suggests. 6.4. Interplay between Column Density and Metallicity Figure 13 shows the line ratios relative to w as contour plots by varying the hydrogen column density and metallicity. In the low-column-density limit, the line ratios are minimally affected by the change in metallicity. Figure 6 shows the effects of metallicity on the line ratios at the reported value of hydrogen column density by Hitomi Collaboration et al. ( 2018b ) (). The uncertainties in temperature and collision strengths from the sources mentioned previously contribute to the uncertainties in the line ratios (shown with the solid enclosed lines in Figure 6 ). At the reported hydrogen column density, x, y, and z are optically thin (Paper I ). Therefore, the line ratios are minimally affected with change in metallicity as these lines are still optically thin for the metallicity range (0 ≤ Z (solar) ≤ 5) shown in the figure. Figure 13. Left, middle, and right panels show x/w, y/w, and z/w as a function of hydrogen column density and metallicity, respectively. Hitomi Collaboration et al. ( 2018a ) use deprojected heavy element abundances relative to solar in the inner 150 kpc region from Chandra data archive for a spherically symmetric Perseus model. At a distance of 30–60 kpc from the central AGN of the Perseus core, the reported range in metallicity is ∼0.5–0.75 of solar (see Figure 7 in their paper). We