We present the Atacama Large Millimeter/Sub-millimeter Array (ALMA) cycle-0 science verification data of the CO(1–0) line emission in the central region of NGC 4321 (also known as M100) at the distance of 17.1 Mpc and VLA, L-band data of HI of the same galaxy. We have drawn the center area of M100 in the 12CO(J = 1–0) line with the resolution of (3.87″ × 2.53″) as viewed by ALMA, along with HI and Spitzer 8 and 3.6 μm data. The relationship between the surface density of molecular gas mass ∑H2 and that of star formation rate ∑SFR has been investigated, in addition to the relationship between the surface density of the neutral atomic hydrogen mass and that of ∑SFR (Kennicutt–Schmidt law) in this galaxy with a high spatial resolution. The results indicate that a significant correlation exists between the SFR surface density and the molecular gas mass density in the ~2 kpc region. The power-law index has been determined for three regions: center, upper and lower arms. The value of this index in the center region is 1.13, which follows the traditional (K-S) law and indicates that the molecular gas is affected by star formation.

We present an extensive analysis of the relationship between star formation rate surface density (∑ SFR) and molecular gas surface density (∑ H 2 ) at sub-kpc scale in the elliptical galaxy Centaurus A (also known as NGC 5128) at the distance 3.8 Mpc.12 CO ( = 2-1) data from Atacama Large Millimetre/Sub-Millimetre Array SV data with very high resolution (2.9 , 0.84 ), as well as 24 m data from the Spitzer Space Telescope, were used. This is one of the first studies of the SF law on Centaurus A at this very high spatial resolution. The results showed a breakdown in star formation law with a 0.49 ± 0.05 index relating ∑ SFR and ∑ H 2 at 185 pc. A significant correlation exists between surface densities of molecular gas and SFR with very long depletion time (68 Gy). In addition we examined the spatially resolved relationship between velocity dispersion and star formation rate surface density for the outer disk of this galaxy and we found that the average velocity dispersion is equal to 11.78 km/s. The velocity dispersion of the molecular ISM for the outer disk is found to follow a power relation with the star formation rate surface density ∝ (∑ SFR) , where is the slope from the ordinary least square fitting. The value of is about 1/ ≈ 2.16 ± 0.40 and is the power law index of the star formation law.

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