![Left-hand panel: luminosity line ratios (in units of L⊙) from 12CO, [C i] and [C ii] as a function of density and far-UV flux (G0 in units of Habing field), from the PDR models of Kaufman et al. (1999). Tracks are drawn for the measured ratios in solid lines with the 1σ errors as dotted lines. The line ratios within SMM J2135 intercept at n∼ 104.1 cm−3 and G0∼ 103.6 Habing fields and n∼ 104.3 cm−3 and G0∼ 103.3 Habing fields for the Kaufman et al. (1999) and Meijerink et al. (2007) models, respectively. To better display the preferred regions of parameter space we combine the probability distributions from all of these lines [excluding L[C I](2-1)/L[C I](1-0) for reasons explained in Section 3.2] to derive a peak likelihood solution for each model. Right-hand panel: the same parameter space for the models, now comparing the peak likelihood solutions from the model grids to the derived values of G0 and density (n) for various low- and high-redshift galaxies and molecular clouds. We also indicate the regions of parameter space which are typically encompassed by Galactic OB star formation regions, starburst galaxies and non-starburst and Galactic molecular clouds from Stacey et al. (1991). This shows that the line ratios for SMM J2135 are consistent with those typically found in local starbursts or ULIRGs. The local galaxy that lies within the contours of the peak likelihood for the Kaufman models is NGC 253, a spiral starburst galaxy (Negishi et al. 2001). We also show the peak likelihood solution derived from the PDR models of Meijerink et al. (2007), which provide a concomitant solution. The contours represent the 1σ and 2σ limits compared to the best-fitting solution. The peak likelihood solutions are derived without including the L[C I](2-1)/L[C I](1-0) track, which we plot on both panels to show its discrepancy from the general solution from the other lines (see Section 3.2).](https://oup.silverchair-cdn.com/oup/backfile/Content_public/Journal/mnras/410/3/10.1111/j.1365-2966.2010.17549.x/2/mnras0410-1687-f4.jpeg?Expires=1750594881&Signature=G5dRapbsmMlNQL8z0YO0yO6QSRz5D1GFxYadL3LNvVvxkrJrB1geCAH5graia2e~JUdWKotD06BOi2FNXm5fmE9J0iAi9qJbnTOpV~9u4fipYwfFgT4TNYtz-CjoY-43QK-mGdUFdIpX9te2HGxos2lzmCnrc6~wk1FeqzFmDQY8VrKiG-p9Kg4B6KAAH1uBCZaeYJny~jLG6me4s0Fi4R0HSjD2qB2173yza2tBch-UPDLJ8lKYT7skr3b2gBuAdVVmgH2KV~bJicKsx0Dq3eDKMSovGtLQY1g8lhQgUoht2D-b2tZfgH1aaxqTY600rXPV0xIMpXUyOXQqrSd6sg__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Left-hand panel: luminosity line ratios (in units of L⊙) from 12CO, [C i] and [C ii] as a function of density and far-UV flux (G0 in units of Habing field), from the PDR models of Kaufman et al. (1999). Tracks are drawn for the measured ratios in solid lines with the 1σ errors as dotted lines. The line ratios within SMM J2135 intercept at n∼ 104.1 cm−3 and G0∼ 103.6 Habing fields and n∼ 104.3 cm−3 and G0∼ 103.3 Habing fields for the Kaufman et al. (1999) and Meijerink et al. (2007) models, respectively. To better display the preferred regions of parameter space we combine the probability distributions from all of these lines [excluding L[C I](2-1)/L[C I](1-0) for reasons explained in Section 3.2] to derive a peak likelihood solution for each model. Right-hand panel: the same parameter space for the models, now comparing the peak likelihood solutions from the model grids to the derived values of G0 and density (n) for various low- and high-redshift galaxies and molecular clouds. We also indicate the regions of parameter space which are typically encompassed by Galactic OB star formation regions, starburst galaxies and non-starburst and Galactic molecular clouds from Stacey et al. (1991). This shows that the line ratios for SMM J2135 are consistent with those typically found in local starbursts or ULIRGs. The local galaxy that lies within the contours of the peak likelihood for the Kaufman models is NGC 253, a spiral starburst galaxy (Negishi et al. 2001). We also show the peak likelihood solution derived from the PDR models of Meijerink et al. (2007), which provide a concomitant solution. The contours represent the 1σ and 2σ limits compared to the best-fitting solution. The peak likelihood solutions are derived without including the L[C I](2-1)/L[C I](1-0) track, which we plot on both panels to show its discrepancy from the general solution from the other lines (see Section 3.2).
