THE EGNoG SURVEY: GAS EXCITATION IN NORMAL GALAXIES AT z ≈ 0.3

The galaxies of EGNoG bin C are drawn from the main spectroscopic sample of the Sloan Digital Sky Survey (SDSS) Data Release 7 (York et al. 2000; Strauss et al. 2002; Abazajian et al. 2009). The galaxies were selected from the parent sample to be as representative as possible of the MS of star-forming galaxies. The MS is the tight correlation between M_* and SFR that has been observed over a large range of redshifts, e.g., z ∼ 0 (Brinchmann et al. 2004), z ∼ 0.2–1 (Noeske et al. 2007), z ∼ 1–2 (Elbaz et al. 2007; Daddi et al. 2007; Pannella et al. 2009), (see also the summary of recent results in Dutton et al. 2010). Building on these observations, a few authors have attempted to describe the MS relation at 0 ⩽ z ≲ 2.5 with one equation (Bouché et al. 2010; Karim et al. 2011; Elbaz et al. 2011). In order to classify the EGNoG galaxies, we adopt a relation which roughly agrees with the relations from Bouché et al. (2010), Karim et al. (2011), and Elbaz et al. (2011) (see Bauermeister et al. 2012, for a complete description):

$$\begin{equation} {\rm sSFR}_\mathrm{MS}(\mathrm{Gyr}^{-1}) = 0.07 (1+z)^{3.2} \left(\frac{M_*}{10^{11}\ {M}_\odot }\right)^{-0.2}, \end{equation} \tag{ 1 }$$

where sSFR_MS is the specific star formation rate (sSFR=SFR/M_*) of the MS of star-forming galaxies. We differentiate "SB" from "normal" galaxies according the criteria of Rodighiero et al. (2011): sSFR_SB > 4 × sSFR_MS. Therefore, SFGs (normal star-forming galaxies) lie roughly within a factor of four of the MS sSFR (which is a function of M_* and z) and SBs lie at sSFR values larger than four times the MS sSFR.

In the selection of the EGNoG sample, we apply the following criteria in each redshift bin in order to identify non-interacting, star-forming galaxies lying as close to the MS as possible. Star-forming galaxies are selected using the BPT diagram (Baldwin et al. 1981) criteria from Kauffmann et al. (2003) (rejecting sources with active galactic nuclei). Obviously interacting galaxies were excluded via visual inspection of the SDSS optical images. However, some interacting galaxies may be in the sample due to the difficulty of identification at the modest resolution of the SDSS images. Practical considerations imposed the following further constraints. We required a spectroscopic redshift so that the error in the redshift is small enough to ensure that CO emission would be captured within the observed bandwidth. We excluded galaxies with SFRs below a minimum value estimated from the instrument sensitivity.

The result of the sample selection is illustrated in Figure 1, which shows stellar mass versus SFR of the EGNoG bin C galaxies (red points). The blue shading indicates the (logarithm of the) density of points in the M_*–SFR plane for all star-forming galaxies (spectroscopic targets only; ≈1300 galaxies) at z = 0.25–0.35. We plot galaxies in a slightly larger redshift range than the bin C specification in order to better capture the behavior of the MS. The MS of star-forming galaxies at z = 0.3 is indicated by the solid black line, with the SB cutoff indicated by the dashed black line. In this plot, the low-mass, low-SFR end of the MS is sparsely sampled due to the limited number of spectroscopically targeted, low-SFR, star-forming galaxies in the SDSS at z ≈ 0.3. While the EGNoG bin C galaxies are high-M_*, high-SFR galaxies, they lie within the expected scatter of the MS (as defined in Equation (1)), and are not classified as SB galaxies according to the prescription from Rodighiero et al. (2011) (presented above).

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Spectroscopic redshifts are from David Schlegel's spZbest files produced by the Princeton-1D code, specBS.⁶ The stellar masses and SFRs of galaxies in the SDSS DR7 are provided by the Max-Planck-Institute for Astrophysics–John Hopkins University (MPA–JHU) group (http://www.mpa-garching.mpg.de/SDSS). Stellar masses are derived by fitting SDSS ugriz photometry to a grid of models spanning a wide range of star formation histories. This method is found to compare quite well with the Kauffmann et al. (2003) methodology using spectral features (more detail on this comparison is found on the Web site above). SFRs are derived by fitting the fluxes of no less than five emission lines using the method described in Brinchmann et al. (2004). Both stellar masses and SFRs are derived using a Bayesian analysis, producing probability distributions of each quantity for each galaxy. These distributions for the four bin C galaxies are shown in Figure 2. We take the median of the distribution, with errors indicated by the 16th and 84th percentile points. In the case where a duplicate SDSS source exists (as a result of SDSS automated source-finding), we take the average of the two median values and use the lowest(highest) 16th(84th) percentile value to indicate the negative(positive) error. The redshifts, stellar masses, and SFRs (with errors) are given in Table 1.

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The CO(J = 1 → 0) transition for the galaxies presented here lies in the 3 mm band of CARMA (single-polarization, linearly polarized feeds). The wide bandwidth of the CARMA correlator allowed us to observe both the ¹²CO(J = 1 → 0) and the ¹³CO(J = 1 → 0) lines simultaneously. The ¹²CO (¹³CO) line was observed with five (three) overlapping 500 MHz bands, covering ≈7000 (5000) km s⁻¹ total, at 42 km s⁻¹ resolution, with 3-bit sampling. These observations were carried out from 2011 August to November in CARMA's D configuration, with 11–150 m baselines yielding a typical synthesized beam of 48 × 39 at 88 GHz. Each galaxy was observed for 20–30 hr (time on-source) in moderate to good weather conditions for 3 mm observation, yielding final images with rms noise of ≈1.2 mJy beam⁻¹ in a 42 km s⁻¹ channel. The flux scale in each data set is set by the flux of the phase calibrator, which is determined from the flux calibrator. For these data, we use phase calibrators 0854+201 (4 Jy, 9% linearly polarized), 1357+193 (0.8 Jy), and 1310+323 (1.7 Jy).

All four galaxies were clearly detected in the CO(J = 1 → 0) line, as shown in Figure 3. The top panels show the vector-averaged Real and Imaginary amplitudes and phase of the calibrated uv data versus velocity for the CO(J = 1 → 0) line. For a compact source at the center of the field of view, the Real part shows the signal without a noise bias, and the Imaginary part shows the noise. In all four cases, we see coherent emission (larger Real amplitudes coincident with noise-like Imaginary amplitudes and phases of ≈0) over multiple velocity channels, indicative of a detection. We report no detection of the ¹³CO(J = 1 → 0) line, which is expected to be weaker than the ¹²CO(J = 1 → 0) line by a factor of 7–17 (Rickard & Blitz 1985).

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The CO(J = 3 → 2) transition at the redshift of the galaxies discussed here lies in the CARMA 1 mm band (dual-polarization, circularly polarized feeds). We again observed both the ¹²CO(J = 3 → 2) and the ¹³CO(J = 3 → 2) lines simultaneously. The ¹²CO (¹³CO) line was observed with three (one) overlapping 500 MHz bands, covering ≈1500 (550) km s⁻¹ total, at 14 km s⁻¹ resolution, with three-bit sampling. These observations were carried out in CARMA's E and D configuration during 2011 August and 2012 April, respectively. Source C4 was observed entirely in E configuration, while the other three sources were observed mostly in D configuration. The E configuration has 8–66 m baselines yielding a typical synthesized beam of 32 × 25 at 266 GHz. The D configuration has 11–150 m baselines yielding a typical synthesized beam of 17 × 15 at 266 GHz. Each galaxy was observed for 2–6.5 hr (time on-source) in good weather conditions for 1 mm observation, yielding final images with rms noise of 5–10 mJy beam⁻¹ in a 42 km s⁻¹ channel. For these data, we use phase calibrators 0854+201 (2 Jy in 2011 August, 4 Jy in 2012 April), 1224+213 (0.6 Jy), and 1310+323 (0.6 Jy).

Sources C2, C3, and C4 were detected at the ≈5σ level in the CO(J = 3 → 2) line. However, C1, with its wide velocity profile (observed in the CO(J = 1 → 0) line), was only marginally detected and we give only an upper limit on the CO(J = 3 → 2) flux. The vector-averaged Real and Imaginary amplitudes and phase of the calibrated uv data versus velocity for the CO(J = 3 → 2) line are shown in the bottom panels of Figure 3. The peak of the CO(J = 3 → 2) emission in galaxies C1 and C2 is offset from the nominal center of each galaxy, so the uv spectra are calculated at this slightly offset (<15 ∼ 6 kpc) position. We report no detection in the ¹³CO(J = 3 → 2) line for any galaxy.

3.2.1. Source C1 Upper Limit

Table 2 presents the quantities we derive from the CO emission images. The CO line luminosity is calculated from the line flux (S_CO in Jy km s⁻¹, calculated as described in Section A.2) following:

$$\begin{equation} L_\mathrm{CO}^{\prime } = 3.25 \times 10^7 \ S_\mathrm{CO} \ \nu _\mathrm{obs}^{-2} \ r_\mathrm{com}^2 (1+z)^{-1} \end{equation} \tag{ 2 }$$

(see the review by Solomon & Vanden Bout 2005), where ν_obs is in GHz and r_com is the comoving distance in Mpc. The units of L'_CO are K km s⁻¹ pc². We report the measurement error for S_CO. The error reported for L'_CO includes both the measurement error of S_CO and a 30% systematic error, added in quadrature (see Section A.2 for more details).

The center velocity, v_center, is the flux-weighted average velocity of the galaxy-integrated spectrum (v = 0 at the redshift in Table 1). The error reported is the standard deviation of the v_center values found with the three flux measurement methods and different channel averaging described in Section A.2. The reported velocity width (ΔV) is the full width of the emission, where "source" velocity channels are selected by eye. We give the velocity width of a single channel as the error. The line ratio r₃₁ is given by

$$\begin{equation} r_{31} = L_\mathrm{CO(3-2)}^{\prime } / L_\mathrm{CO(1-0)}^{\prime } \end{equation} \tag{ 3 }$$

and the error is calculated by propagating the errors of the individual line luminosities.

Moment maps (discussed in Section 4.2 and displayed in Appendix B) are created from the 2σ clip smooth mask (see Section A.2). Moment 0 (total intensity) maps are a simple sum of the masked images in the "source" velocity channels. Moment 1 (intensity-weighted mean velocity) maps are produced by summing the masked image multiplied by the velocity in each channel then normalizing by the moment 0 value.

As a first step, we calculate r₃₁ in the simplest way possible, taking the ratio of the total line luminosities. Of the four galaxies observed, we detect three in both lines, yielding r₃₁ values (see Table 2) of 0.34–0.44 with an average value of 0.39. For source C1 we derive an upper limit on r₃₁ of 0.49, which is consistent with the other values.

These r₃₁ values carry the caveat that they are determined from line luminosities that are calculated independently of one another. The "source" velocity channels for each line are selected by eye for the most convincing detection. Further, the CO(J = 1 → 0) and CO(J = 3 → 2) lines are observed at different frequencies in the same configuration (except source C4). This yields different sampling of the uv-plane, which means that the two maps are sensitive to slightly different spatial scales. We recalculate r₃₁ more carefully for C2, C3, and C4 in the following sections.

In this section, we attempt to standardize the flux calculated for each line as much as possible by matching both spatial and spectral resolution. First, we use the same spectral resolution in both the CO(J = 1 → 0) and CO(J = 3 → 2) data, selecting the starting channel so that the image velocity channels line up exactly.

Next, to investigate the effect of the different uv sampling of the two lines, we recreate the images using only data at uv-distances present in both the 1 and 3 mm data (matched uv data): 8–44 kλ, which corresponds to spatial scales of ≈25–13''. Further, we force all the images to have a standard pixel size (099 for all except the CO(J = 3 → 2) line for C2 and C3 using all uv data, for which we use 033 pixels since these images have higher resolution). Figures 8–10 in Appendix B show images and spectra calculated within the standard source regions (discussed in Section A.2) using all uv data (top panel) and using matched uv data (bottom panel).

This uv-distance restriction makes the beam sizes more similar, but not necessarily the same due to different sampling within the allowed uv-distance range. Table 3 compares the measured fluxes and beam sizes using all uv data and matched uv data. The change in the measured flux is ≲ 6% for sources C2 and C4, which is less than the expected measurement error in the total flux. However, the change in flux is more significant for source C3 in both lines. For the CO(J = 1 → 0) line, the matched uv coverage excludes the short uv spacings, which are sensitive to large-scale structure. Therefore, the presence of extended emission in source C3 would explain the decrease in flux in the matched uv data. This is supported by the radial profile of the CO(J = 1 → 0) cumulative flux in Figure 6 in Appendix A, which shows the matched uv data agreeing with the all uv data at small radii and diverging at larger radii. The CO(J = 3 → 2) line, on the other hand, loses long uv spacings (sensitive to small-scale structure) in the matched uv data. However, the uv-distance restriction excludes a sizable fraction of the uv data, which decreases the signal to noise in the image so that less flux is recovered using the masking technique. A comparison of the unmasked CO(J = 3 → 2) line fluxes in the all uv and matched uv data sets for source C3 shows a drop of only 7.2%, which is within the expected measurement error.

Table 3. Comparison of uv Data Selections

Name,	All uv Data		Matched uv Data		Flux
Trans.	SCO	Beam	SCO	Beam	% Diff.
C2 1–0	2.30	490 × 408	2.15	454 × 375	−6.5%
3–2	7.06	170 × 156	7.00	320 × 284	−0.8%
C3 1–0	4.29	497 × 406	3.71	462 × 377	−13.5%
3–2	13.75	171 × 146	11.61	312 × 302	−15.6%
C4 1–0	2.95	499 × 402	2.76	462 × 383	−6.4%
3–2	12.79	333 × 241	12.01	355 × 308	−6.1%

Notes. Measured CO line fluxes (S_CO in Jy km s⁻¹) and beam sizes for images made using all uv data and matched uv data. The fluxes reported here are calculated using the 2σ smooth masking technique discussed in Section A.2. The percent difference in the measured flux is defined as 100(S_{CO, match} − S_{CO, all})/S_{CO, all}.

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In the rest of our analysis, we consider the emission measured in both cases of uv coverage.

We now make a more careful measurement of r₃₁, with the CO(J = 1 → 0) and CO(J = 3 → 2) flux measurements as well matched to one another as possible. For each uv data selection (all uv, matched uv), we calculate r₃₁ in each channel where flux is measured in both lines.

Figure 4 shows the integrated L'_CO and r₃₁ velocity profiles for each of the three significantly detected galaxies. L'_CO as a function of velocity is plotted in the top panels for each transition (CO(J = 1 → 0) in red, CO(J = 3 → 2) in blue), for all uv data (solid lines) and matched uv data (dashed lines). Source velocity channels for each line (chosen by eye) are indicated by shading in the corresponding color. The bottom panels show the r₃₁ profiles for all uv data (solid black line, with the average value indicated by the horizontal black dotted line) and the matched uv data (dashed magenta line, with average value shown by the horizontal magenta dash-dotted line). For galaxy C2, we have excluded the velocity channels at ±86 km s⁻¹ from this analysis. At −86 km s⁻¹, we do not detect the CO(J = 3 → 2) line despite a 3σ detection in the CO(J = 1 → 0) line. At +86 km s⁻¹, the CO(J = 3 → 2) image suggests a weak (2σ) detection at the center, but the measured flux is dominated by a 3σ noise spike close to this emission. Therefore, we use only the central three velocity channels in the CO(J = 3 → 2) transition.

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In galaxies C2 and C3, the r₃₁ profiles appear well behaved, remaining roughly constant in all velocity channels. On the other hand, galaxy C4 shows significant deviations from a flat profile, with a very low r₃₁ at ≈0 km s⁻¹ and a very high value at ≈40 km s⁻¹. Due to the modest signal to noise ratio at which the CO(J = 3 → 2) line is detected in each channel, we cannot draw any definitive conclusions, but note that if the enhanced r₃₁ is real, it may indicate a region of enhanced gas excitation (at a velocity close to 0, it is likely to be physically near the center of the galaxy), such as a starbursting clump, in which a higher r₃₁ would be expected.

For each galaxy, Table 4 gives the number of velocity channels in which r₃₁ is calculated, the mean and standard deviation (σ) of r₃₁ for each uv data selection and the average r₃₁ value for the two uv data selections (galaxy mean), with the expected measurement error (meas. error). We expect a 20% measurement error in the flux of each line, in each channel (Section A.2), which gives a 30% error in r₃₁ in each channel, and a 30%(N_ch)^−1/2 error in the average r₃₁. This value is reported in the last column of Table 4 for each galaxy. The bottom rows give the mean and standard deviation of the average r₃₁ values for the three sample galaxies. In this paper, the standard deviation given is the square root of the unbiased sample variance.

The average values for each uv selection are consistent with each other within each galaxy and roughly consistent across the three galaxies. While the uv selection appears to have a small effect on the average r₃₁ value, it is not in a systematic direction. The standard deviation of r₃₁ we observe in galaxies C2 and C3 is consistent with the expected 30% measurement errors in each channel. The standard deviation for galaxy C4 is roughly twice the expected 30% error due to the two outlier channels discussed above. Overall, in the three EGNoG galaxies discussed here, we find a mean r₃₁ of 0.46 with a standard deviation of 0.07. Since we estimate each line flux has systematic errors of up to ≈30% (see Section A.2), the systematic errors in the ratio r₃₁ will be ≲ 40%.

Since r₃₁ traces the local excitation conditions of the molecular gas of a galaxy, it is expected to vary within the disk of the galaxy. In fact, Dumke et al. (2001) found CO(J = 3 → 2) emission to be more centrally concentrated than CO(J = 1 → 0) emission in nearby galaxies, so that r₃₁ decreased with radius. To look for radial variation in r₃₁ in the EGNoG data, we cannot compare the emission maps directly due to the marginal resolution of the galaxies and the different uv coverage of the two transitions. In order to disentangle the true emission distribution from the uv sampling, we fit a two-dimensional Gaussian to the total intensity (moment 0) map of each CO transition using the MIRIAD program imfit. This analysis is presented in detail in Appendix C.

While the error bars are large, we do find the ratio of the deconvolved peak intensities (representative of the conditions in the central region of the galaxy) to be systematically higher than the ratio of the total fluxes. In our sample, we find r₃₁(peak) = 0.73 ± 0.31, with a standard deviation across the three galaxies of 0.04. We compare this to the ratio calculated from the fit total fluxes: 0.42 ± 0.11, with a standard deviation of 0.04. While the small standard deviations in our r₃₁ values show consistency between the three galaxies, these results are plagued by sizable uncertainties as a result of fitting data with only modest signal to noise (note that our error estimates are conservative and may in fact be overestimating the true error). Therefore, we conclude (but not robustly) that r₃₁ is higher in the center of the EGNoG galaxies than in the molecular disk as a whole (consistent with Dumke et al. 2001).

To date, the study of CO line ratios in intermediate- and high-redshift galaxies has been dominated by work on extreme starbursting systems: SMGs and quasars. The CO lines from (J = 1 → 0) up to (J = 9 → 8) in quasars at z ≈ 2–4 are well fit by a single component of highly excited gas (Riechers et al. 2006; Weiß et al. 2007; Riechers 2011). In contrast, while the high-J CO transitions in z ≈ 2–4 SMGs are fit by similar highly excited gas, recent observations of the CO(J = 1 → 0) line in these systems reveal a diffuse, low-excitation component in addition to the highly excited component (Carilli et al. 2010; Riechers et al. 2011), similar to what has been observed in local ULIRGs (Papadopoulos et al. 2007; Greve et al. 2009). In contrast, the limited work on z ≈ 1–2 SFGs suggests low-excitation gas similar to the Milky Way (Dannerbauer et al. 2009; Aravena et al. 2010). Since the EGNoG galaxies are SFGs (lying on the MS), we restrict the rest of this discussion to SFGs (normal star-forming galaxies) at low and high redshifts.

To place the r₃₁ values we measure at z ≈ 0.3 in the context of previous work on normal SFGs, Figure 5 shows r₃₁ versus approximate SFR for the EGNoG galaxies (red diamonds) and a compilation of literature data, which includes three large surveys of r₃₁ in nearby galaxies (Yao et al. 2003; Mao et al. 2010; Papadopoulos et al. 2012) as well as the study at z = 1.5 (Aravena et al. 2010). We plot r₃₁ from our matched analysis (Section 4.3) for sources C2, C3, and C4 (values from Table 4, with 40% error bars to indicate potential systematic errors) and the upper limit for source C1 derived from the total line luminosities (Section 4.1, Table 2). While SFRs are available for the present survey and Aravena et al. (2010), the other three surveys only provide total infrared luminosities (L_IR) or far infrared luminosities (L_FIR) calculated from Infrared Astronomical Satellite fluxes. We use approximate SFRs of 1.7 × 10⁻¹⁰ L_FIR M_☉ yr⁻¹ (L_FIR in L_☉; Kennicutt 1998) and LIR/L_FIR = 1.3 (Graciá-Carpio et al. 2008) in Figure 5. Values for the Milky Way are plotted as well: the Galactic center (MW GC), inner disk (MWinner), and outer disk (MWouter) values, all in black, are taken from Fixsen et al. (1999) and plotted (slightly offset from one another) for illustrative purposes at the left side of the plot. The average r₃₁ values of the Yao et al. (2003), Mao et al. (2010), and Papadopoulos et al. (2012) data sets are indicated by the horizontal lines of the corresponding color, with the corresponding shaded rectangles indicating the standard deviation around the average values. To guide the eye, the dashed black line shows r₃₁ = 1.

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Despite the large range of values observed, we find general agreement between our values, that of Aravena et al. (2010) and the average values of the local surveys, with the EGNoG galaxies showing slightly lower r₃₁ values than the other studies. Note that the Mao et al. (2010) survey found an average value of 0.81 for the entire sample, but a lower average of 0.61 for galaxies classified as "normal," based on SFR surface density as indicated by the far infrared luminosity and optical diameter. Further, the CO(J = 3 → 2) survey of local, low-SFR spirals by Wilson et al. (2012) find a lower value (using CO(J = 1 → 0) luminosities from Kuno et al. 2007) of r₃₁ ≈ 0.2, but note that the authors have not made any correction for differences in the fraction of each galaxy mapped by the two surveys. Their r₃₁ value is at the low end of the spread of values plotted in Figure 5. The range and average r₃₁ values for the points plotted (including number of galaxies, redshift, and SFR ranges) are given in Table 5.

In order to compare our values to the literature data, we first discuss the nature of the observations presented. Yao et al. (2003) observe 60 IR-luminous galaxies (most sources have L_FIR > 10¹⁰ L_☉) selected from the SCUBA Local Universe Galaxy Survey. Each line is measured with a single pointing of a single-dish telescope: CO(J = 1 → 0) at the Nobeyama Radio Observatory, CO(J = 3 → 2) at the James Clerk Maxwell Telescope (JCMT). For both measurements, the beam size is ≈15'', corresponding to physical sizes of ≈0.5–13 kpc for their sample galaxies (≈0.5–5 kpc for most of the sample).

Mao et al. (2010) measure the CO(J = 3 → 2) line for 125 nearby galaxies of various types (e.g., normal, SB, LIRG, ULIRG) using the Heinrich Hertz Telescope (HHT; beam size ≈22''). This beam size corresponds to a physical size of ≈0.25–17 kpc for the sample galaxies (1.7 kpc on average). The CO(J = 1 → 0) data for their sample were taken from the literature and therefore the beam size depends on the telescope used. In their analysis, Mao et al. (2010) only use those galaxies for which they found IRAM 30 m CO(J = 1 → 0) data (61), which have a beam size matching the HHT CO(J = 3 → 2) data. These measurements are plotted with error bars in Figure 5. Galaxies with CO(J = 1 → 0) data from other sources are reported as upper or lower limits.

Papadopoulos et al. (2012) examine a composite sample of 70 LIRGs in the nearby universe (z ⩽ 0.1) spanning a wide range of morphologies. They present new measurements of 36 galaxies and data from the literature for 34 more. The new measurements use the IRAM 30 m telescope for CO(J = 1 → 0) (beam size ≈22'') and the JCMT for CO(J = 3 → 2) (beam size ≈14''), and therefore are not observed with the same beam size. The authors do not comment on matching beam sizes in the new measurements or those from the literature.

The galaxy in which Aravena et al. (2010) measure r₃₁, BzK-21000 at z = 1.5, was observed in the CO(J = 3 → 2) line with the Plateau de Bure Interferometer by Dannerbauer et al. (2009) and in the CO(J = 1 → 0) line with the Very Large Array in C and D configurations (Aravena et al. 2010). In both cases, the source is unresolved or marginally resolved, so the measured fluxes should represent the total emission of the galaxy.

The three samples of nearby galaxies are observed with single-dish instruments, typically sampling the inner portion of the molecular gas disk of the observed galaxies. This is different from the r₃₁ measurements for the EGNoG galaxies (Table 4) and the galaxy at z = 1.5 (Aravena et al. 2010), for which the emission from the entire gas disk is observed. We note that a gradient in r₃₁ has been observed in nearby galaxies (Dumke et al. 2001), with higher values measured in the centers. This can be inferred from the Milky Way measurements (Fixsen et al. 1999) as well. This effect may well account for the EGNoG and Aravena et al. (2010) measurements appearing systematically lower than the average values reported by the surveys observing the central regions of nearby galaxies. Supporting this explanation, our analysis in Section 4.4 suggests that r₃₁ is higher in the centers of the EGNoG galaxies (more in line with the average values of the local surveys) compared to r₃₁ averaged over the entire disk. However, with such a large spread in values and inhomogeneous data sets, it is difficult to draw any robust conclusions on this point.

We have measured r₃₁ = 0.46 ± 0.07 (with systematic errors of up to 40%) in three galaxies at z ≈ 0.3, suggestive of optically thick, sub-thermal gas. Despite being massive and highly star-forming (with SFRs of 50–65 M_☉ yr⁻¹ and stellar masses of ≈2 × 10¹¹ M_☉), the excitation of the gas in these galaxies is consistent with SFGs like local spirals, not starbursting systems like ULIRGS, SMGs, and quasars. Since the EGNoG galaxies have been selected from the MS of star-forming galaxies at z = 0.3, our findings suggest that galaxies on the MS, over a range of star formation activity, harbor sub-thermally excited gas. Therefore, we suggest that CO line ratios similar to those observed in local spiral galaxies are appropriate for MS star-forming galaxies.

The extension of the EGNoG results to MS star-forming galaxies means that sub-thermal line ratios are appropriate for the z ∼ 1–2 SFGs in which Tacconi et al. (2010) and Daddi et al. (2010) report high molecular gas fractions (20%–80%). Tacconi et al. and Daddi et al. estimated the molecular gas mass associated with the observed J_upper > 1 CO luminosity assuming sub-thermal r_J1 line ratios and a Milky-Way-like α_CO (Daddi et al. 2010 used a slightly smaller value for α_CO). As the conversion factor is a complex problem, expected to vary as a function of gas excitation, density, metallicity and radiation field (Shetty et al. 2011; Leroy et al. 2011), the results of this work do not directly inform the choice of conversion factor. However, the r₃₁ line ratios of the EGNoG gas excitation sample support the assumption of a sub-thermal line ratio in these studies. Specifically, Tacconi et al. (2010) use r₃₁ = 0.5 to calculate molecular gas masses, which is consistent with our results (Daddi et al. 2010 observed the CO(J = 2 → 1) line and assume a sub-thermal r₂₁).

Each data set is reduced and calibrated as follows. The data are flagged for antenna–antenna shadowing as well as any other issues during the observation. The instrument bandpass is calibrated with mfcal on a bright passband calibrator. The time-dependent antenna gains (from atmospheric variation) are derived by performing a selfcal on the phase calibrator with an averaging interval of 18 minutes (the timescale of switching between the source and phase calibrator). For sources C1 and C2, the phase calibrator, 0854+201, is ≈10% polarized, which required additional steps in the reduction of the 3 mm data (observed with linearly polarized feeds). This is described in more detail in the full survey paper (Bauermeister et al. 2012).

For each data set, the flux of the phase calibrator is set during the antenna gain calibration in order to properly set the flux scale of the data. The flux of each phase calibrator is assumed to be constant over timescales of weeks, and is therefore determined from the best data sets of the survey using bootflux on bandpass-calibrated, phase-only gain-calibrated data with Mars or MWC349 as a primary flux calibrator. The brightness temperature of Mars is set by the CARMA system using the Caltech thermal model of Mars (courtesy of Mark Gurwell), which includes seasonal variations in temperature and can be accessed in MIRIAD using marstb. This model gives brightness temperatures ≈218 K at 266 GHz and ≈208–200 K at 88 GHz for 2011 August–November observations, and ≈201 K at 266 GHz for 2012 April observations. For MWC349 we set the flux to 1.2 Jy at 88 GHz, the typical value from historical flux monitoring at CARMA. The fluxes used for each phase calibrator are as follows: for the 3 mm data (≈89 GHz, 2010 August–November), the flux of 0854+201 is set to 4 Jy (9% linearly polarized), 1357+193 0.8 Jy, and 1310+323 1.7 Jy. For the 1 mm data (≈265 GHz, 2011 August and 2012 April) the flux of 0854+201 is set to 2 Jy in 2011 August and 4 Jy in 2012 April, 1224+213 0.6 Jy in 2012 April and 1310+323 0.6 Jy in 2011 August.

Images are produced combining all fully calibrated data sets for each source. We used invert, weighting the visibilities by the system temperature as well as using a Briggs' visibility weighting robustness parameter (Briggs 1995) of 0.5. Since CARMA is an inhomogeneous array (these data use both the 10 m and 6 m dishes), we also use options=mosaic in the invert step in order to properly handle the three different primary beams patterns (10–10 m, 10–6 m and 6–6 m). All observations are single pointing. The resulting images are primary-beam-corrected. In most of the sources discussed here, we map the 3 mm data (CO(J = 1 → 0) line) channel by channel, using the full spectral resolution of 42 km s⁻¹. We match this resolution in the 1 mm data (CO(J = 3 → 2) line) by averaging channels in sets of three. The exception to this scheme is source C1, which has emission spread over a very wide velocity range, requiring more channel averaging to increase the signal to noise.

We deconvolve each image with mossdi (the mosaic version of clean), cleaning down to the rms noise within a single channel, within a cleaning box selected by eye to include only source emission. We clean only channels which contain visible source emission. Cleaning down to a specified noise level is preferred to using a set number of clean iterations due to the nature of the spectral line emission: some channels will contain more flux and therefore require more clean iterations. In tests using a model source of known flux inserted into real data (emission-free channels), we found a 1σ cutoff to best extract the true source emission without overestimating the flux over a range of detection significance levels, with a 10%–30% uncertainty in the recovered flux (depending on the significance of the signal). The final clean images are produced by restor, which convolves the clean component image with the clean beam (calculated by fitting a Gaussian to the combined mosaic beam given by mospsf), and adds the residuals from the cleaning process.

Total source fluxes in the CO lines are calculated by summing "source" pixels in each "source" velocity plane of the image. The source velocity planes are selected by eye. The source pixels are those within the "source" region which are not masked by our smooth mask (adapted from Dame 2011). The smooth mask is created by applying a 2σ clip to a smoothed version of the image: Hanning smoothing is done along the velocity axis, and each velocity plane is convolved with a Gaussian beam twice the size of the original synthesized beam. This smoothed mask is used in order to exclude noise pixels but still capture low-level emission that a simple clip would miss. In our own testing (using a model source of known flux inserted into real data), we found a 2σ clip to best reproduce the true flux over a range of detection significance levels.

The appropriate source region size is selected to recover all of the flux without including the negative bowl. Since we do not have single-dish data to complement the interferometric data presented here, our data sets are missing the shortest uv spacings. As a result, the emission in the clean images sits in a negative bowl, which will affect the measured flux (calculated by summing pixels within a given radius). In order to accurately estimate the flux, we use the radius at which the radial profile of the enclosed flux first peaks, thereby excluding the negative bowl. The radial profiles of the enclosed flux for sources C2, C3, and C4 are shown in Figure 6: CO(J = 1 → 0) in red in the top panels and CO(J = 3 → 2) in blue in the bottom panels. The profiles for both uv selections (all and matched), unmasked and masked are shown for each transition. The negative bowl is most evident in the unmasked profiles (dotted and dash-dotted lines), in which the enclosed flux peaks and then decreases with radius. The radius of the first peak of the enclosed flux distribution is 65 for the CO(J = 1 → 0) data and 45 for the CO(J = 3 → 2) data (shown by the vertical dotted black lines). These radii are used in the calculation of total fluxes throughout this work.

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The error in the flux measurement is estimated from the standard deviation of the measured fluxes using different velocity channel averaging and starting channel, using three different methods of calculating the flux in each case. The three methods are: the 2σ masking technique described above, the same masking technique with a 3σ clip, and the simple addition of all pixels (no mask) within the source region.

We performed extensive testing of our analysis technique in order to choose the parameters of the reduction to eliminate systematic offsets and minimize the uncertainty due to noise (as described above). We find a 10%–30% error in the flux measurement coming from noise in the data reduction and analysis steps. From this, we take an average uncertainty of 20% in the flux estimated in each channel, which results in a uncertainty in the total flux of 20%(N_ch)^−0.5 (N_ch is the number of velocity channels in which the flux is summed). For the total flux values reported in Table 2, we estimate the error from the variation in the flux calculated using different channel averaging, flux measurement method, etc. (described above), which is consistent with the 20%(N_ch)^−0.5 we expect. In our analysis of the integrated flux velocity profiles (Section 4.3), we assume errors of 20% in the flux in each channel.

Further, these data suffer from systematic errors due to absolute flux calibration and primary beam correction. We set the flux scale in our data set based on a primary flux calibrator (Mars or MWC349), the flux of which is only known to ≈20%. In the primary beam correction of the data set, pointing and focus errors at the time of the observations as well as errors in the primary beam model can significantly reduce image fidelity, leading to errors in the measured fluxes of ≈20% (see SKA Memo 103, Wright & Corder 2008). Combining these systematic errors in quadrature, we estimate that our flux measurements suffer from systematic uncertainties of up to ≈30%. We consider all these factors in the presentation of our data in Table 2: for the line flux (S_CO), we report the measured error; for L'_CO, we include a 30% systematic error (added in quadrature to the measured error in S_CO).