We present a revised method for simultaneous determination of the pattern speed (Ω P ) and star formation timescale (t SF ) of spiral galaxies, which is originally proposed in our previous work. As this method utilizes offsets between molecular and young-stellar arms, we refer to it as the "Offset Method". Details of the method, its application, and results for CO and Hα images of 13 nearby spiral galaxies are described here. CO data are from our observations with the Nobeyama Millimeter Array for 2 galaxies, and from the BIMA SONG for the rest. Out of 13 galaxies, we were able to derive Ω P and t SF for 5 galaxies. We categorize them as "C" galaxies as their offsets are clear. Our findings from these galaxies are as follows. (1) The corotation radius calculated by the derived Ω P is close to the edge of the CO data, and is about half of the optical radius for 3 galaxies.(2) The derived t SF is roughly consistent with the free-fall time of typical molecular clouds, which indicates that the gravitational instability is the dominant mechanism triggering star formation in spiral arms. (3) The t SF is found to be almost independent of surface density of molecular gas, metallicity, or spiral arm strengths. The number of "C" galaxies and the quality of CO data, however, are not enough to confirm these relationships. We also find that 2 other galaxies show no offsets between CO and Hα, although their arms are clearly traced, and categorize them as "N" galaxies. The presence of a bar could account for this feature, since these 2 galaxies are both barred. With one galaxy excluded from our analysis due to its poor rotation curve, offsets of the remaining 5 galaxies are found to be ambiguous. Either their dependence on the rotational frequency cannot be explained by our picture, or the number or quality of data -2is not sufficient for the analysis. We categorize them as "A" galaxies. The possible reasons for this ambiguity are (1) the density wave is weaker, and/or (2) observational resolution and sensitivity are not enough to detect the spiral arms and their offsets clearly. The former is supported by our finding that the arm strengths of "A" galaxies are slightly weaker than that of "C" galaxies.
We report systematic variations in the emission line ratio of the CO J = 2 − 1 and J = 1 − 0 transitions (R 2−1/1−0 ) in the grand-design spiral galaxy M51. The R 2−1/1−0 ratio shows clear evidence for the evolution of molecular gas from the upstream interarm regions, passage into the spiral arms and back into the downstream interarm regions. In the interarm regions, R 2−1/1−0 is typically < 0.7 (and often 0.4-0.6); this is similar to the ratios observed in Galactic giant molecular clouds (GMCs) with low far infrared luminosities. However, the ratio rises to > 0.7 (often 0.8-1.0) in the spiral arms, particularly at the leading (downstream) edge of the molecular arms. These trends are similar to those seen in Galactic GMCs with OB star formation (presumably in the Galactic spiral arms). R 2−1/1−0 is also high, ∼ 0.8 − 1.0, in the central region of M51. Analysis of the molecular excitation using a Large Velocity Gradient radiative transfer calculation provides insight into the changes in the physical conditions of molecular gas between the arm and interarm regions: cold and low density gas ( 10 K, 300 cm −3 ) is required for the interarm GMCs but this gas must become warmer and/or denser in the more active star forming spiral arms. The ratio R 2−1/1−0 is higher in areas of high 24µm dust surface brightness (which is an approximate tracer of star formation rate surface density) and high CO(1-0) integrated intensity (i.e., a well-calibrated tracer of total molecular gas surface density). The systematic enhancement of the CO(2-1) line relative to CO(1-0) in luminous star forming regions suggests that some caution is needed when using CO(2-1) as a tracer of bulk molecular gas mass, especially when galactic structures are resolved.
We report the CO(J = 1-0) observations of the Whirlpool Galaxy M51 using both the Combined Array for Research in Millimeter Astronomy (CARMA) and the Nobeyama 45 m telescope (NRO45). We describe a procedure for the combination of interferometer and single-dish data. In particular, we discuss (1) the joint imaging and deconvolution of heterogeneous data, (2) the weighting scheme based on the root-mean-square (rms) noise in the maps, (3) the sensitivity and uv coverage requirements, and (4) the flux recovery of a combined map. We generate visibilities from the single-dish map and calculate the noise of each visibility based on the rms noise. Our weighting scheme, though it is applied to discrete visibilities in this paper, should be applicable to grids in uv space, and this scheme may advance in future software development. For a realistic amount of observing time, the sensitivities of the NRO45 and CARMA visibility data sets are best matched by using the single-dish baselines only up to 4-6 kλ (about 1/4-1/3 of the dish diameter). The synthesized beam size is determined to conserve the flux between the synthesized beam and convolution beam. The superior uv coverage provided by the combination of CARMA long baseline data with 15 antennas and NRO45 short spacing data results in the high image fidelity, which is evidenced by the excellent overlap between even the faint CO emission and dust lanes in an optical Hubble Space Telescope image and polycyclic aromatic hydrocarbon emission in a Spitzer 8 μm image. The total molecular gas masses of NGC 5194 and 5195 (d = 8.2 Mpc) are 4.9 × 10 9 M and 7.8 × 10 7 M , respectively, assuming the CO-to-H 2 conversion factor of X CO = 1.8 × 10 20 cm −2 (K km s −1 ) −1 . The presented images are an indication of the millimeter-wave images that will become standard in the next decade with CARMA and NRO45, and the Atacama Large Millimeter/Submillimeter Array.
We report a super-linear correlation for the star formation law based on new CO(J=1-0) data from the CARMA and NOBEYAMA Nearby-galaxies (CANON) CO survey. The sample includes 10 nearby spiral galaxies, in which structures at sub-kpc scales are spatially resolved. Combined with the star formation rate surface density traced by Hα and 24 µm images, CO(J=1-0) data provide a super-linear slope of N = 1.3. The slope becomes even steeper (N = 1.8) when the diffuse stellar and dust background emission is subtracted from the Hα and 24 µm images. In contrast to the recent results with CO(J=2-1) that found a constant star formation efficiency (SFE) in many spiral galaxies, these results suggest that the SFE is not independent of environment, but increases with molecular gas surface density. We suggest that the excitation of CO(J=2-1) is likely enhanced in the regions with higher star formation and does not linearly trace the molecular gas mass. In addition, the diffuse emission contaminates the SFE measurement most in regions where star formation rate is law. These two effects can flatten the power law correlation and produce the apparent linear slope. The super linear slope from the CO(J=1-0) analysis indicates that star formation is enhanced by non-linear processes in regions of high gas density, e.g., gravitational collapse and cloud-cloud collisions.
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