Determining the Mass of Molecular Gas in Galaxies: A ¹³CO Survey
Paglione, T.A.D. (FCRAO/INAOE), Wall, W.F. (INAOE) & Heyer, M.H. (FCRAO)

Abstract
We propose using the unique mapping capability and sensitivity of SEQUOIA to survey the CO and ¹³CO J=1-0 emission in the disks of galaxies. Our goal is to determine if the ¹²CO/¹³CO ratio varies with galactocentric radius, galaxy type, star formation, etc. Assuming both lines trace the total molecular content of a source, but the ¹³CO emission is optically thin, variations in this ratio from galaxy to galaxy, and within galaxies, indicates a change in the conversion factor relating CO intensity and \htwo\ mass. Previous surveys were very small and yielded contradictory results. As an array, SEQUOIA can detect such changes with negligible uncertainties in relative calibration and pointing. A better understanding of the CO-to-H₂ conversion factor in galaxies will yield more accurate mass determinations critical for understanding important galactic problems such as dynamics, structure and star formation, to name but a few. This project should span roughly 3 observing seasons and takes advantage of the most undersubscribed LST range of the telescope. We intend for undergraduates to take the majority of the observations.

Introduction
Knowing the distribution of molecular mass in a galaxy is fundamental to understanding its evolution, structure, kinematics and star formation. Unfortunately, H₂ is not visible in typical cloud regions. CO, the most abundant interstellar molecule next to H₂, is relatively easy to excite, and its J=1-0 emission is readily observable with ground-based telescopes. Therefore, CO is detectable in nearly all molecular regions, and the integrated CO J=1-0 intensity is commonly used to measure molecular gas column density. However, because CO J=1-0 emission is often optically thick and arises in nearly all parts of every molecular cloud, using a ``standard'' CO-to-H₂ conversion factor everywhere may be inappropriate, especially if it depends on the physical conditions of the gas (e.g., Sakamoto 1996). This problem may worsen when studying the unresolved, overlapping clouds of external galaxies. Further, it is unclear whether X(CO), the empirical conversion factor derived from Galactic disk clouds, is valid in other galaxies, or in the dense, metal-rich clouds of our own Galactic center (Maloney & Black 1988; Sodroski et al. 1995; Paglione et al. 1998).

One way to test for variations in X(CO) in galaxies is to observe optically thin ¹³CO emission. If the CO/¹³CO ratio varies with position or velocity, then the (most likely saturated) CO line is not a constant measure of gas mass. A few such studies have been done (Rickard & Blitz 1985; Young & Sanders 1986; Sage & Isbell 1991). The basic results of these small surveys were the following:

• There was no systematic change in CO/¹³CO with radius. In direct conflict with the later surveys, Rickard & Blitz found low values of CO/¹³CO in galactic disks. However, just 13 of the combined sample of only 19 galaxies were observed at more than one position.
• No significant correlations were seen between CO/¹³CO and many galactic parameters except dust color temperature. The relation to temperature is expected assuming LTE. With CO optically thick, ¹³CO optically thin, and both lines thermalized, then T_B(CO) is roughly T_gas, and T_B(¹³CO) is roughly 1/T_gas. However, even this one correlation relied mostly on only two data points.
• The average CO/¹³CO ratio in galaxies was higher than in the Milky Way. They concluded the higher ratio was due to a different value of X(CO). However, the large beams may simply be sensitive to a more prevalent diffuse component visible mostly in CO (Polk et al. 1988).

With the sensitivity and mapping ability of SEQUOIA, we will be able to find unambiguously any variations with position because uncertainties in relative pointing and calibration are minimized with an array. A comprehensive survey of many galaxy types will bring out any relations between CO/¹³CO and galactic parameters if they exist. Measuring CO/¹³CO in a large, representative sample of galaxies will indicate any deviation of the mean X(CO) from the Galactic value. Large-scale surveys of CO and ¹³CO in the Milky Way are also available for comparison if indeed CO/¹³CO depends on the spatial scale of the observations.

Time Request and Justification
We propose mapping the CO and ¹³CO emission in 54 galaxies. We will take advantage of the undersubscribed LST range of the FCRAO covering roughly 9 to 16 hours, given the available manpower to take the observations. Observing remotely with the FCRAO makes manpower a smaller issue than in the past, though we intend for undergraduates to contribute to this effort significantly, including trips to Quabbin, data reduction and analysis.

The project is split into 3 observing seasons, each to stand alone in its own right as well as to contribute to the comprehensive survey:

• Map 16 of the galaxies with previous ¹³CO detections. A single deep SEQUOIA observation will yield sensitive detections at many positions for each galaxy. (We do not include M31 in this proposal. Only two previously mapped galaxies fall outside the undersubscribed LST range: NGC 253 and NGC 1068. We ask to map them when the schedule permits - ``filler time.'')
• Complete the survey by mapping each of the remaining galaxies with at least one SEQUOIA pointing. The candidates are taken from the FCRAO extragalactic CO survey of Young et al. (1995).
• Conduct further observations on objects of certain interest. For example, we will map galaxies with very extended emission more thoroughly. We will also integrate more deeply on galaxies where the CO/¹³CO ratio in the nucleus is large (>20), which indicates a ¹²C/¹³C abundance ratio very different from the Galactic center. We will also integrate more on any source where the CO and ¹³CO peaks are shifted spatially and/or in velocity, which may indicate large gradients in abundances or cloud properties. Many of these galaxies have been observed in CO J=2-1 (Braine et al. 1993), which allows an estimation of excitation conditions.

Depending on the weather, manpower, telescope schedule, and how extended the emission is, we will map one galaxy every 1 to 3 days (5 to 20 hours). The same regions will be mapped in both lines in a single observing session to avoid calibration offsets. The array will be oriented along the major axis of each galaxy. A 7 hour session will yield good sensitivity for both lines. The r.m.s. antenna temperature should be better than 2 mK for ¹³CO after 6 hours, given T_sys<500 K and a 5 MHz channel width. For CO, with T_sys<1000 K, we should achieve better than 10 mK r.m.s. after 1 hour. These estimates are very conservative since the system temperatures are usually much better, and we can smooth the data in velocity for more sensitivity.

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