Kennicutt-Schmidt Law in the Central Region of NGC 4321 as Seen by ALMA

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.


Results and Discussion
Line Emission Distribution. CO . Figure 1 shows the CO(1-0) integrated intensity map. Where the CO emission trace clearly the two arms that are highly contrasted with spiral pattern. The two arms emerge from the end of a huge gaseous bar, which corresponds to the stellar bar observed in the infrared images of the galaxy. Arm 1 (lower arm) emerges from the east part and gradually extends towards the south, which is stronger on average, and it can be tracked more continuously than arm 2 (upper arm). The later emerges from the west and it splits up into two armlets that meet at approximately r = 6″, then disappear and finally show up in the north.
HI. Figure 2 shows the velocity-channel map of the neutral atomic hydrogen gas (HI) in the central region of the spiral galaxy NGC 4321 at the resolution of 52.98″ × 47.5″. The HI emission is detected in 27 of the channel maps of the 10 km s −1 velocity width. The rms noise in the channel map is 0.99 mJy beam −1 , and the beak emission is 58.8 mJy beam −1 in the channel 1450 km s −1 . The total HI flux detected in the beam is 47.3 Jy km s −1 . No HI bridge is visible in the data either in the channel maps or in the intensity map. Figure 3 shows the intensity map of the HI gas (zeroth map), which is derived from the Briggs weighted channel map without Hanning smoothing. A relative deficiency of HI is observed in the center, although the gas is detected over almost the entire disk. The HI gas distribution is extended toward the upper and lower arms. The disk of NGC 4321 is symmetrical. The spiral arm could not be detected because of poor resolution of these data. Based on the CO(1-0) data of the same galaxy that show a peak in the center region and decline in the disk, it is clear that the lack in the center of the galaxy does not imply a lack of gas there. . The molecular gas bulk is traced by CO(1-0) 29 . Accordingly, the CO(1-0) integrated intensity map can be used to calculate the molecular gas mass and surface density. The mass of the molecular gas in the integrated intensity map can be estimated by the CO flux using the CO-to-H 2 conversion factor. If the conversion factor is assumed to be X = 2.3 × 10 20 cm −2 (K km s −1 ) −1 (see Burillo et al. 30 ), the CO flux can be converted into the mass of the molecular hydrogen using the following formula (assuming the distance D = 17.1 Mpc):

Gas Mass and Surface Density. Molecular Gas CO
Scientific RepoRts | 6:26896 | DOI: 10.1038/srep26896 The total molecular gas mass M(H 2 ) within the total area ∆x × ∆y = 200″ × 200″ (as shown in Fig. 1) is equal to 0.9 × 10 10 M ⊙ at D = 17.1 Mpc. The molecular gas mass in the center region at r = 30″ is equal to 3.1 × 10 9 M ⊙ , which is close to the result of M(H 2 ) = 2.8 × 10 9 M ⊙ at r = 30″ from the IRAM single dish observation 31 and similar to the result of M(H 2 ) = 3.1 × 10 9 M ⊙ from the JCMT 32 . This result indicates that no missing flux exists in the central region at r = 30″. A direct measurement is unavailable for the conversion factor in M100. Thus, an error of the mass of the molecular gas estimated using the galactic conversion factor is possible. The central 14.5 kpc region of the NGC 4321 galaxy is divided into 174 regions covering the nucleus (black boxes), lower arm (red boxes) and upper arm (yellow boxes), as shown in Fig. 1. The size of each box is 4″ × 4″, which corresponds to 331.6 pc × 331.6 pc. The molecular hydrogen mass and density for each region are obtained and listed in Table 2.
The surface density values are in terms of hydrogen alone, i.e. the contribution of Helium hasn't been included. A strong concentration of molecular gas mass is observed toward the nucleus (black boxes region) that contains ~20.5% of the total H 2 content in the sample region ∆x × ∆y = 200″ × 200″.
Neutral Atomic Gas HI. The intensity map is divided into 61 regions (see Fig. 3), and each region is 55″ × 55″ (4560 pc × 4560 pc). The values of the HI surface density, HI mass, SFR and SFR surface density are derived for each region, and the results are summarized in Table 3. The total mass of the atomic hydrogen gas can then be calculated, using the following equation 16 :

Relationship between Gas Mass Density and Star Formation.
The surface density of the molecular gas and SFR is calculated in the nuclear disk region and along the upper and lower arms and then compared with neutral atomic gas. The infrared data are used as star formation tracers. The infrared data are obtained from the Spitzer Space Telescope Infrared Array Camera (IRAC) 3.6 and 8 μm images (http://ssc.spitzer.caltech.edu/ archanaly/archive.html). These data are background-subtracted images. Wu 35 showed that the dust emission at 8 μm can be used as a star formation indicator. The dust emission in the central and spiral arms of the NGC 4321 is estimated using the observed Spitzer IRAC 8 and 3.6 μm fluxes applying the following equation 29 : where Lv is the 8 μm dust luminosity. The derived values are shown in Tables 2 and 3. The relationship between the SFR and molecular gas surface densities is drawn for NGC 4321 with the spatial resolution of 4″ × 4″ as shown in Fig. 4a. The data are colorized by region, namely, center region (black circle), upper arm (yellow circle) and lower arm (red circle) to distinguish these regions. Numerous differences are observed between the SFR surface density and the distribution of the molecular gas mass density in each region. For each region ordinary least square fitting was used. The uncertainties for the slope and the intercept for each region are calculated using python, they refer to the fitting error. For the center region (black box), the derived power-law index of ∑gas − ∑SFR relation is equal to 1.13 ± 0.20 with intercept −3.71 ± 0.53. This value is within the range of the traditional K-S law, which is around 1-2.0. This linear relation is interpreted as star formation efficiency (SFE, the SFR divided by M(H 2 )) is constant. This result can be interpreted as an indication that external processes or feedback mechanisms that control the gas supply are important for regulating star formation in massive galaxies 37 . The constant star formation efficiency (SFE) has been found in many spiral galaxies as shown in 38 . In addition to that Wilson 32 has found a uniform depletion time (SFE) −1 for the central region of M100 spiral galaxy. However they found that the CO J = 3-2 line may represent more reliable tracer of the dense molecular gas than is the CO J = 1-0. For the lower arm (red boxes), the index of K-S is 0.8 ± 0.14 with intercept −2.86 ± 0.3. Although this value is smaller than the traditional K-S law. It's common for K-S law to relate the observed CO luminosity to the number of star   forming clouds, assuming these clouds to have isotropic properties such as volume density, SFR and efficiency of cloud. However for the observations at resolution >100 pc, instead of resolving the individual clouds, the CO flux is rather dispersed throughout the beam. In such case, regions with abundant clouds will emit more CO directly proportional to the number of these clouds. These conclusions are clearly supported by the studies [39][40][41][42] specially for the N values ~0.6-0.8, which are close to our results. The sub-linear K-S relationship indicates that     . Relation between the surface density of molecular gas and ∑SFR for normal galaxies (blue squares), starburst galaxies (green triangle), and NGC 4321 (red circles). The gas surface density is derived from CO(1-0) emission. The normal and star burst galaxy samples are obtained from.
between SFR surface density and molecular gas mass surface density in the ~2 kpc region (black boxes). The correlation coefficient r = 0.69 with 99.9% probability.
To study the K-S law behavior at different regions as in Fig. 5, which shows the relationship between the neutral atomic hydrogen and SFR surface densities. The physical interpretation of the SFR versus the HI K-S law is not obvious. However, HI may trace the physical influences of atomic gas density on the SFR, or the density of HI could be regulated through the SFR, by the dissociation of molecular gas by a hot star 2,45,46 . The relationship between the surface ∑gas and ∑SFR is shown in Fig. 6. The star formation rate surface density of the center and spiral arm regions of NGC 4321 are similar to those of starburst galaxies and considerably higher than those of normal galaxies 2,47 . However, they all appear to follow the same star formation law 2 . This result supports the idea that the spiral arms and the center in the inner region are suffering from a starburst.

Summary and Conclusion.
We have drawn the galaxy M100 in 12 CO(J = 1-0) line with ALMA and compared the emission with the HI 21-cm line from VLA. We have tested the relationship between the surface density of molecular gas and the SFR in an external galaxy with high resolution for three regions, namely, center, upper arm and lower arm. We have concluded that the center region is composed of relatively high density gases that have sufficient intensity to undergo the star formation process. By contrast, the emerged gases for the lower arm region have higher intensity (energy) and more density than the upper arm. Hence, the power law index in the lower arm region is higher than that in upper arm, but still lower than that in the traditional K-S law. The value of the power-law index in the upper arm is significantly low, which is based on the distribution of gases as they emerge from the east bar of the nucleus region and split into two armlets. This split may induce dissipation in the gas energy and reduce the collisions between these gases, which may result in the gas being under the sub-thermal condition. This condition can be observed by the disappearance of gas emission slightly after the two armlets meet in the north.