A statistical study of giant molecular clouds traced by ¹³CO, C¹⁸O, CS, and CH₃OH in the disk of NGC 1068 based on ALMA observations

We present 1″.4 (98 pc) resolution ALMA observations of ¹³CO(J = 1-0), C¹⁸O(J = 1-0), CS(J = 2-1), and CH₃OH(J_K = 2_K-1_K) molecular rotational lines in the central 1′ (4.2 kpc) diameter region of NGC 1068 to study the physical and chemical properties of giant molecular clouds (GMCs) and to test whether these GMC-scale properties are linked to the larger-scale galactic environment. Using the derived ¹³CO cube, we have identified 187 high-significance (>8σ) GMCs by employing the CLUMPFIND algorithm. The molecular gas masses of GMCs (M_13CO), derived from the ¹³CO data, range from 1.8 × 10⁴ M_⊙ to 4.2 × 10⁷ M_⊙. A mass function of GMCs in NGC 1068 has been obtained for the first time at ∼100 pc resolution. We find the slope of the mass function γ = -1.25 ± 0.07 for a mass range of M_13CO ≥ 10⁵ M_⊙. This is shallower than the GMCs in the disk regions of the Milky Way, M 51, and NGC 300. Further, we find that the high mass cut-off of the GMC mass function occurs at M_13CO ∼ 6 × 10⁷ M_⊙, which is an order of magnitude larger than that in the nuclear bar region of M 51, indicating that the more massive clouds dominate the mass budget in NGC 1068. The observed C¹⁸O(J = 1-0)/¹³CO(J = 1-0) intensity ratios are found to be fairly uniform (0.27 ± 0.05) among the identified GMCs. In contrast, the CH3OH(J_K = 2_K-1_K)/¹³CO(J = 1-0) ratios exhibit striking spatial variation across the disk, with the smallest values around the bar-end (<0.03), and larger ratios along the spiral arms (∼0.1-0.2). We find that GMCs with detectable methanol emission tend to have systematically larger velocity widths than those without methanol emission, suggesting that (relatively weak) shocks are responsible for the enhancement of the CH₃OH/¹³CO ratios of GMCs in the disk of NGC 1068.