Line luminosity ratios of Hα, Pβ, and Pα with respect to Hβ of red quasars. The Pβ/Hβ luminosity ratios of eight red quasars are indicated by the open triangles, and the yellow stars are the Hα/Hβ luminosity ratios of the local red AGNs from Rose et al. (2013). The green arrows indicate the lower limits. Thedotted line is the line luminosity ratio reproduced by the CLOUDY code with a set of parameters (α = −1.0, U = 10^−1.5, and n_H= 10⁹ cm⁻³), which is consistent with the line luminosity ratios of unobscured type 1 quasars from Hβ to Pα (Kim et al. 2010). Panel A: the five colored solid lines represent the line luminosity ratios from the CLOUDY code with n_H = 10¹⁰ cm⁻³, U = 10⁰, and various α from − 2 to 2. The various α is represented by color, i.e., the purple, blue, green, yellow, and red lines indicate α is − 2, − 1, 0, 1, and 2, respectively. Panel B: the meanings of the symbols and lines are identical to panel A, but the five colored lines are the line luminosity ratios with n_H = 10¹⁰ cm⁻³, α = 0, and various U from 10⁻⁵ to 10³. Panel C: the meanings of the symbols and lines are identical to panel A, but the five colored lines are the line luminosity ratios with α = 0, U = 10⁰, and various n_H from 10⁷ to 10¹⁴ cm⁻³. Panel D: the meanings of the symbols and the dotted line are identical to panel A, and the gray lines represent the line luminosity ratios computed from the CLOUDY code with various physical conditions, within α = −2 to 2, n_H = 10⁷−10¹⁴ cm⁻³, and U = 10⁻⁵−10⁵.