MOLECULAR GAS EVOLUTION ACROSS A SPIRAL ARM IN M51

In order to identify each molecular cloud structure, the clumpfind method provided by Williams et al. (1994) has been applied to the CLEANed ¹²CO(1–0) data cube with the lowest level and contouring step of 1σ. Both of these two parameters are constant within the FOV. We have then defined detections as clumps (1) within the FOV, (2) with the peak flux whose local signal-to-noise ratio (S/N) ⩾ 4, and (3) with the FWHM in velocity larger than 0.5 pixel (or 2.54 km s⁻¹). We have calculated this local S/N, considering the variable sensitivity within the FOV.

The 34 selected clumps are indicated by circles in the left panel of Figure 1 superimposed on the moment 0 map. The line width and color represents the local S/N of each clump; thin blue is for 5> S/N ⩾4, while thick red is for S/N ⩾5. The radius measured by the clumpfind is 05–14 or 10–60 pc, corresponding to the radius of the circles in the figure. The FWHM in R.A. and decl. also fall in the same range with the radius and about one-third of the selected clumps are resolved. While most of the clumps are found in the arm, larger and more massive clumps are located only on the west side of the spiral arm. Assuming a trailing arm, this corresponds to the downstream side. On the other hand, some of the smaller clumps are found in the upstream interarm region (east side of the FOV). In Section 3.2, we discuss it in more detail by comparison with the K09 data.

From Figure 1, we have noticed that there are several emission peaks not selected as clumps. Most of them are close to the edge of the FOV and thus are presumably elevated noise, while some appear sequentially on the upstream side of the spiral arm. We have examined all the clumps with S/N ⩾3 and found that they are superpositions of several weak- and narrow-line clumps at different velocities. As some of them seem to be associated with H ii regions (see Figure 5), they perhaps are real molecular clouds, but we need a higher sensitivity to confirm that and do not include them in further discussion.

For the ¹³CO(1–0) line in the LSB data, the same procedures as the ¹²CO(1–0) data have been applied and three clumps with S/N ⩾4 have been detected. None of them, however, are found to be associated with the ¹²CO(1–0) clumps. Lowering the S/N cutoff to 3.0, we have detected 162 clumps and found two clumps with S/N ≃3.6 located near ¹²CO(1–0) clumps; one is located close to the pointing center and coincides with the largest and most massive ¹²CO(1–0) clump (marked as "d" in Figure 2), while the other is located close to the two ¹²CO(1–0) clumps ∼10'' north of the pointing center ("b" and "c" in Figure 2). The ratio of the peak temperatures of the corresponding clumps is T_peak(¹³CO)/T_peak(¹²CO) ∼ 0.4, while the ratio of the total flux is F_tot(¹³CO)/F_tot(¹²CO) ∼ 0.2. The average integrated intensity ratio for the Galaxy is 1/5.5 (Solomon et al. 1979b), implying that these massive clumps detected in M51 are in similar condition to GMCs in the Galaxy. As these ¹³CO(1–0) structures do not meet the S/N criterion for the clump selection, we discuss only the ¹²CO(1–0) results hereafter.

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The conversion factor from the ¹²CO(1–0) integrated intensity to the H₂ column density (N(H₂) = X_COI_CO) has been measured in a number of ways. For the Galaxy, X_CO ≃ 3 × 10²⁰ cm⁻² (K km s⁻¹)⁻¹ was derived by comparing the virial mass and the ¹²CO(1–0) flux of GMCs (e.g., Solomon et al. 1987; Young & Scoville 1991). More recently, smaller values (∼1.8 × 10²⁰ cm⁻² (K km s⁻¹)⁻¹) have been reported by comparison with the γ-ray or far infrared data (Strong & Mattox 1996; Dame et al. 2001; Grenier et al. 2005). Heyer et al. (2009) derived GMC masses from the ¹³CO(1–0) emission lines under the local thermodynamic equilibrium (LTE) assumption and found that the LTE masses are factor of ∼5 smaller than the virial masses. The inconsistencies in the X_CO values are due to the combination of uncertainties and/or invalidities of the models and assumptions introduced and imply difficulties in the X_CO determination.

As for the Galaxy, the derived X_CO values for M51 depend largely on data and methods. While the virial masses of GMAs derived by Rand & Kulkarni (1990) agree with X_CO = 3 × 10²⁰ cm⁻² (K km s⁻¹)⁻¹, those derived by Adler et al. (1992) based on a different CO data set suggest X_CO = 1.2 × 10²⁰ cm⁻² (K km s⁻¹)⁻¹. Even smaller values have been suggested (Garcia-Burillo et al. 1993; Rand 1993; Nakai & Kuno 1995). More recently, Schinnerer et al. (2010) applied the large velocity gradient (LVG) modeling to 2'' resolution multi-transition CO data and derived X_CO = (1.3–1.9) × 10²⁰ cm⁻² (K km s⁻¹)⁻¹. In this paper, we adopt X_CO = 1.5 × 10²⁰ cm⁻² (K km s⁻¹)⁻¹. The variations of X_CO within the FOV as a function of galactocentric radius should be small enough to be neglected, as the data only cover 53'' or 2.2 kpc.

The noise rms (1σ) in the ¹²CO(1–0) data thus corresponds to $M_{\rm H_2}=2.5\times 10^4$ M_☉ within the synthesized beam (∼30 pc) and one velocity channel (5.08 km s⁻¹). Though the absolute mass of molecular gas could be changed by a factor of two or more according to adopted X_CO values, the sensitivity in mass is still smaller than typical GMCs in any case. Furthermore, the conclusion of this paper does not depend on the X_CO value, since we only focus on the spatial and kinematical information and discuss relative values of mass from the B-array and K09 data.

In the left panel of Figure 2, contours from the K09 I_CO map are overlaid on the B-array I_CO image. We have applied the clumpfind algorithm to the K09 data cube and defined GMAs as clumps with M>10⁷ M_☉. Following the selection criteria for the B-array data, clumps on the data edge have been excluded. These selected GMAs are shown as open black circles in the right panel of Figure 2 together with the detected clumps in the B-array data in the same manner as Figure 1. The background image is the K09 moment 0 map. From this figure, we find that GMAs are not filled with the GMC-scale clumps. As the 1σ sensitivity of the B-array data is about 10 times smaller than the typical mass of GMCs, we should have detected tens or more of them if GMAs were confused with GMCs. This result strongly indicates that GMAs are not confusions nor overlappings of GMCs.

The total flux within the FOV of the B-array data has been measured to be 67 Jy km s⁻¹ and 1.1 × 10³ Jy km s⁻¹ for the B-array and K09 data, respectively. As the K09 data include the single-dish observations with the Nobeyama 45 m telescope, it should represent the total ¹²CO(1–0) flux. The missing flux in the B-array data is thus 94%, suggesting that most of the CO flux in the spiral arm of M51 should come from either extended structures or molecular clouds smaller than GMCs and supporting the aforementioned indication that GMAs are not collections of GMCs.

Another important clue from comparison of the two I_CO maps is that their peak positions do not coincide; massive clumps detected in the B-array data are shifted a few arcseconds toward the downstream side of the global spiral arm seen in the K09 map. To investigate this difference further with the velocity information, we have made spectra of B-array and K09 data at the positions of the selected clumps. The box size for the average spectra was set to be the same as the diameter of each clump derived by clumpfind. In Figure 3, the sample spectra for massive clumps are displayed. The flux difference mentioned above is also clearly seen in the spectra. From these spectra, we have found that massive clumps have offsets in peak velocity between the two data sets. We have defined the velocity offset as

$$\begin{equation} V_{\rm ofs}=V_{\rm cl}({\rm B})-V_{\rm peak}({\rm K09}), \end{equation} \tag{ 1 }$$

where V_cl(B) is the peak velocity for clumps measured by the clumpfind and V_peak(K09) is the peak velocity in the K09 spectra. The V_ofs is plotted against the mass of each clump in Figure 4. It is clear from this plot that almost all of the clumps with $M_{\rm H_2} > 5\times 10^5$ M_☉ have negative V_ofs. Considering the galactic rotation, negative velocities correspond to the downstream side. Therefore, massive clumps are kinematically as well as spatially located downstream of the spiral arm. This difference indicates that the massive clumps are in a later evolutionary stage compared to the larger scale structures or GMAs. We refer to these massive clumps as GMA cores hereafter.

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Smaller clumps on the other hand are located preferentially on upstream of the spiral arm, and little emission is found in the interarm region on downstream. This distribution of small clumps indicates that they are somehow destroyed through the evolution across the spiral arm. Before forming stars, the small clumps (M ∼ 10⁵ M_☉) could collide with each other to form larger clouds such as GMAs. Meanwhile, they would be dissociated into atomic gas or broken up to even smaller clouds (M < 10⁵ M_☉) after forming stars.

As already mentioned in Section 1, star-forming regions are located on the downstream side of the spiral arms. Since we have found that GMA cores are also on downstream, it is worth comparing these two components.

The Hα data taken under the HST program (ID: 10452, PI: S. Beckwith) were obtained from the HST Web site⁴ and cover ∼7' × 10', including the entire galactic disk and the companion galaxy (Mutchler et al. 2005). The Paα image taken for another HST program (ID: 7237, PI: N. Scoville) was presented by Scoville et al. (2001) and covers the central 3' of the disk. The astrometry of the Paα image was found to be slightly off compared to the Hα image. In order to match their coordinates, we measured the peak position of bright H ii regions seen in both Hα and Paα images and adjusted the coordinates of the Paα image through the use of the task ccmap of the Image Reduction and Analysis Facility (IRAF).⁵ Although the fitting rms from ccmap is as small as 017 and 013 for R.A. and decl., respectively, the errors in the coordinates could be larger as H ii regions are extended especially in the Hα image and extinction gradients might affect the flux distribution and thus the peak positions. We estimate the effective uncertainty in the coordinates to be about 40 pc or 1'', which is the typical size of GMCs and H ii regions. In Figure 5, circles indicating the selected clumps are superimposed on the Hα and Paα images.

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As expected, bright H ii regions are located on the downstream side of the CO spiral arm seen in the lower resolution K09 data. GMA cores found in the high resolution B-array data, on the other hand, coincide with the H ii regions. This correlation indicates that GMA cores are the site of massive star formation, which is consistent with the result in the previous subsection that they are in a later stage of the molecular gas evolution. Meanwhile, we have found that not all the H ii regions are accompanied by the cores, which implies that GMA cores are short-lived or are not prerequisites for massive star formation.

Given that only the ¹²CO(1–0) data are available at this resolution, physical conditions such as density and temperature of GMA cores cannot be determined uniquely; high density and high temperature can both produce high I_CO. The largest core close to the pointing center (marked as "d" in Figure 2) gives a clue to this issue. From Figure 5, we have found that it does not have a counterpart in Hα but in Paα, indicating high extinction and thus a high column density. From the mass (2.5 × 10⁶ M_☉) and radius (55 pc) measured by clumpfind, the average H₂ column density is derived to be N(H₂) = 1.6 × 10²² cm⁻² for this core. Assuming A_V/N_H = 5.3 × 10⁻²² mag cm² (Bohlin et al. 1978), the estimated extinction is as high as A_V = 17 mag. The most plausible detection of ¹³CO(1–0) at this location is also consistent with the high density. Therefore, at least for this core, we conclude that the high I_CO represents high column density of molecular gas. This agreement in high extinction and density also confirms that the coordinate adjustment for the Paα image is correct within the core size or ∼1''.

Additionally, it is clear from Figure 5 that the distribution of H ii regions is quite similar in the Hα and Paα images, indicating that only a few regions (such as the most massive core mentioned above) are significantly affected by extinction. This means that Hα is a good tracer of the locations of current star formation in most cases and is preferable over extinction-free 24 μm for measuring offsets between molecular arm and young stellar arm (Egusa et al. 2009) as it generally provides higher angular resolution.

The results presented above reveal the structure and distribution of molecular clouds at 30 pc scale for the first time in grand-design spiral galaxies. Based on their properties and relationship to the global (kpc) spiral structure, we here propose a scenario for the ISM evolution across the spiral arm. We should note here that smaller spatial scale across the arm corresponds to shorter timescale, which enables us to describe the scenario in unprecedented detail.

On the upstream side of the spiral arm, molecular clouds of $M_{\rm H_2} \sim 10^5$ M_☉ collide with each other and probably with smaller clouds to grow into GMAs ($M_{\rm H_2} \gtrsim 10^7$ M_☉). GMAs are presumably distinct and smooth structures and a few GMC-scale cores (∼10⁶ M_☉) are formed within each GMA, which turn out to be the site of OB star formation as they evolve. If not all the gas in cores would turn into stars, the remaining gas in the core should break up to smaller molecular clouds (<10⁵ M_☉) or become dissociated into atomic hydrogen by strong radiation from young stars. From the star formation law presented by Kennicutt et al. (2007) for M51, the gas consumption timescale measured as the ratio of the total gas mass to the star formation rate is ∼10⁹ yr. Since the star formation timescale is much shorter (∼10⁷ yr; Egusa et al. 2009) than this timescale, most of the gas in GMAs is not used by the star formation activity. Such gas remains molecular through the evolutionary sequence, considering that the molecular fraction to the total hydrogen has been estimated as 70%–80% even in the interarm regions (K09).