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Appendix A: Resolved binaries

In our long-slit spectra, spatial information is obtained in the cross-dispersion direction. Most observations are consistent with point-source emission. The objects IRS 44, IRS 43, and SVS 20 are known binaries that were resolved in our data and are described below. Interferometry of L1551 IRS 5 at 7-mm indicates two distinct sources of dust continuum emission separated by (Looney et al. 1997; Rodriguez et al. 1998), although the two components were not resolved in high-resolution H, K, or L-band imaging by (Duchêne et al. 2007). Regardless of whether L1551 IRS 5 is a binary, the continuum has a FWHM of  in our data (either poor seeing or spatially-extended M-band continuum emission), so resolving the two components is not possible.

A.1. IRS 44

IRS 44 was definitively identified as a close binary in L-band AO imaging (Duchêne et al. 2007), which revealed two components with a flux ratio close to 1.0 and a separation of  at a PA of 87°. High-resolution K-band images also suggested that IRS 44 is a binary with a similar separation and a flux ratio of  ~5 (Ratzka et al. 2005; see also Terebey et al. 2001; Allen et al. 2002). However, the K-band imaging is somewhat less reliable than the L-band imaging because the large binary flux ratio and bright nebulosity leads to poor S/N and uncertain detections of the secondary.

Of our five CRIRES observations of IRS 44, the binary was resolved only on the nights of 6−7 Aug. 2008, when the seeing was superb (). The two components are marginally resolved with a separation of about  on the detector (see Fig. 13). This separation does not include the  ~13° offset in position angle between the slit and the binary. Assuming the binary PA from Duchêne et al. (2007), then IRS 44 E is  ~0.69  ±  0.12 mag brighter than IRS 44 W in the M-band continuum, including a 0.08 mag uncertainty attributed to uncertainty in the slit position relative to the two components. Duchêne et al. (2007) suggested based on the K- and L-band observations that IRS 44 W was more heavily reddened than IRS 44 E and is the primary in the system. This scenario predicts that the IRS 44 W would be the brighter component in the M-band, which is the opposite of what is seen.

In the CO 4.67 μm ice band, absorption reduces the continuum flux from IRS 44 E by  ~18% and from IRS 44 W by  ~22%. Some ice absorption must be local to IRS 44 W.

A.2. IRS 43

IRS 43 was resolved as a binary with an L-band flux ratio of 3.1 mag and a PA of 336° by Duchêne et al. (2007). In our M-band long-slit spectra, the continuum emission from IRS 43 is concentrated on the primary. Some extended emission is detected to the N, in the direction of the faint secondary. If this emission is attributed to the secondary component, then it is  ~1.8  ±  0.5 mag fainter than the primary in the M-band continuum.

The 4.67 μm CO ice band absorbs 80% of the photons emitted from both the continuum and from the secondary (or extended nebulosity) to the N. We infer that the ice absorption likely occurs in a cloud that envelops both objects.

A.3. SVS 20

SVS 20 is a binary with a PA of 9.9° (Eiroa et al. 1987; Haisch et al. 2002, 2006). The separation on our slit is , with an M-band continuum magnitude difference of 1.25, similar to the magnitude difference seen at other optical and IR wavelengths. The luminosity ratio of  ~500 listed in Table 2 is likely much too high.

The properties of the stellar components of SVS 20 are uncertain. SVS 20 S is considered the primary component because it is brighter in the near-IR and mid-IR. Weak K-band absorption features indicate that the primary is likely an early-G star (Doppmann et al. 2005), although as with IRS 63, this spectral type is tentative because the photospheric velocity is discrepant by 10 km s^-1 from the v_lsr of the HCO⁺ emission (Gregersen et al. 2000). Oliveira et al. (2009) found that one of the components is an M4 star with A_V = 3 mag, based on TiO features in an optical spectrum that included unresolved light from both objects. The low extinction suggests that whichever component is the M-dwarf is not embedded in the envelope and perhaps dominates the optical flux as a result. The ¹³CO absorption lines are also more optically thick to SVS 20 S than to SVS 20 N. On the other hand, the CO ice absorption has a larger opacity, τ ~ 1, to SVS 20 S than to SVS 20 N (see also Pontoppidan et al. 2003). The brightness difference between the two components,  ~1.3 mag in the near-IR and  ~1.0 mag at 10 μm (Ciardi et al. 2005; Haisch et al. 2006), also does not suggest a large difference in extinction or bolometric luminosity between the two stars. For the purposes of this paper, we assume that both objects are at a similar evolutionary state and embedded in an envelope. A third, faint component in the SVS 20 system is separated from SVS 20 S by  (Duchêne et al. 2007) and is not detected in our spectra.

Appendix B: Variable CO ice absorption from WL 6

For WL 6, the depth of CO ice absorption decreased from τ = 2.1 in the ISAAC spectrum to τ = 0.51 in the CRIRES spectrum. From Gaussian fits to the absorption band, the central wavelength and FWHM remained similar, indicating no significant change in the ice composition. No other significant changes were detectable between the two observations.

WL 6 is a point-source in K- and L-band AO imaging (Ratzka et al. 2005; Duchêne et al. 2007). Alves de Oliveira & Casali (2008) find variability of  ~0.4−0.6 mag in JHK monitoring of WL 6, which may be related to the variability in the CO ice absorption depth. If the disk is close to edge-on and occults the star only some of the time, then variability may be expected in the near-IR photometry and in the strength of the ice feature.

Appendix C: Notes on CO emission from individual targets

In Sect. 3, we discussed the CO emission from individual stars in mostly generic terms. However, the interpretation of the narrow emission component from several objects is somewhat complicated. In the following subsections, we describe details of the narrow component from three objects, GSS 30, IRS 44 W, and CrA IRS 2.

C.1. GSS 30

Our CRIRES spectrum of GSS 30 covers 4.645−4.768 μm and 5.036−5.158 μm, with a large gap that excludes ¹²CO lines with J′ = 11−34 from our spectrum. Figure C.1 compares the ¹²CO line profile for low-J lines (J′ < 10) to the scaled line profiles of ¹²CO with high-J (35 < J′ < 42), ¹³CO, C¹⁸O, and CO v = 2−1. The ¹²CO low-J lines are characterized by red- and blue-shifted emission with absorption at the cloud velocity. No absorption is detected in lines with J > 34. C¹⁷O is detected in absorption but not in emission.

The v = 2−1 lines can be described by the combination of a narrow, blueshifted Gaussian profile and a broader Gaussian profile centered at the systemic velocity. These two components roughly describe the emission profiles in lines of ¹³CO, C¹⁸O, ¹²CO with high − J, and ¹²CO with low-J, though intervening absorption complicates the analysis. The broader component¹⁰ is dominant in the high-J¹²CO lines. The Gaussian profiles compared with the other lines in Fig. C.1 are kept in the same flux ratio as measured from the v = 2−1 lines. Excluding the absorption, some minor differences can be seen between the Gaussian fits and the line emission. Very narrow emission in ¹²CO and ¹³CO transitions extends off-source in both the NE and SW within in the slit and is discussed in Sect. 3.3.

To calculate the flux in each component, an equivalent width was measured over a specific velocity range on the blue and red side of each line. The equivalent width over this velocity range was then converted to a total flux based on Gaussian fits to the v = 2−1 lines. This approach provides line fluxes measured with a consistent methodology for all lines of each isotope, despite that some model line profiles do not perfectly match the fit.

Fig. C.1 A comparison of CO line profiles from GSS 30, as extracted on-source. Two Gaussian profiles are fit to the emission in coadded v = 2−1 lines. The same two Gaussian profiles are then compared with the coadded lines of 12CO v = 1−0 with high-J, with low-J, 13CO, and C18O. The two components in the v = 2−1 lines fit the other profiles reasonably well, although in the high-J line the broader component dominates. Some narrow extended emission can also be seen as excess emission in low-J12CO and 13CO lines at −5 km s-1. Both of these Gaussian components are considered narrow, optically-thick absorption within our crude classification scheme.

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Figure 8 shows the rotational diagram for narrow CO emission from GSS 30, based on fits to the blue side of the emission line. The flux ratio of ¹²CO/¹³CO lines is  ~8, which indicates that the ¹²CO lines are optically-thick. The flux ratio of ¹³CO/C¹⁸O lines of  ~8−10 is similar to the abundance ratio of 8.1 in the local ISM (Wilson 1999) and suggests that both the ¹³CO and C¹⁸O emission are optically-thin. The measured temperatures for ¹³CO and C¹⁸O are 315 and 340 K. The ¹²CO/¹³CO line flux ratios yield a total CO column density log N(CO) = 18.6 for b ~ 2.0 km s^-1 and T = 340 K, assuming that the blueshifted ¹²CO emission is dominated by this component and not the broader emission component. At this column density, the observed ¹³CO emission lines are nearly optically-thick, but not sufficiently enough to reduce the ¹³CO/C¹⁸O flux ratio. The fluxes in C¹⁸O v = 1−0 and in ¹²CO v = 2−1 lines do not suffer from any opacity effects until log N(CO)  >  19.5. At 340 K, the v = 2−1 emission would not be detected, although a moderately higher temperature (~450 K) at this high column density would sufficiently populate the v = 2 level to detect v = 2−1 lines. The emission in high-J lines of ¹²CO and ¹³CO is also not produced at such cool temperatures. The total emitting area is roughly (22 AU)² for log N(CO)  =  18.6 + log (cosi). At a distance of 120 pc, this spatial extent should be marginally resolvable. The observed CO emission is unresolved to a FWHM  ~   (10 AU at 120 pc). The difference could be reconciled with a larger b-value or a large viewing angle for our line-of-sight to the CO slab. On the red side of the line, the column density is difficult to assess because the non-detection of ¹³CO emission is complicated by the red absorption.

When analyzing spatially-extended CO emission from GSS 30 observed with ISAAC (R = 10   000), Pontoppidan et al. (2002) found that the extraction region is much larger than the surface area implied by the line fluxes and column density. We confirm this problem with our CRIRES data. To reconcile this discrepancy, Pontoppidan et al. (2002) suggested that the extended emission is produced by material from the shock at the envelope/disk interface at 10−50 AU from the central star. This emission could then be reflected off the outflow cavity walls. This shock is expected to have a temperature plateau at  ~500 K due to reformation heating, with significant cooling in rovibrational CO and H₂O lines (Neufeld & Hollenbach 1994). In this scenario, the on-source and off-source line profiles should be similar, but Pontoppidan et al. (2002) was unable to test this prediction because the CO lines were unresolved with ISAAC. With the much higher resolution of CRIRES, we find that the off-source CO spectral line profiles are significantly narrower and have a higher peak-to-continuum ratio than the on-source CO line profiles. Although the extended nebulosity is bright in the K-band continuum, K-band pumping into v = 2 levels is ruled out by the lack of v = 2−1 emission detected off-source. An alternate but contrived explanation to reconcile the discrepancy in emission area versus extraction area is to invoke a very clumpy medium. Although the emission appears to be smoothly distributed within the slit, the spatial resolution may not be sufficient to detect many different clumps.

C.2. IRS 44W

The CO emission line profiles from IRS 44 W are similar to those from GSS 30. Figure 6 shows that ¹²CO emission is seen on both sides of the CO absorption. However, the ¹³CO and C¹⁸O emission is seen only shortwards of the CO absorption. When the ¹³CO emission line profile is scaled to the ¹²CO profile (see inset in Fig. 6), a deficit in flux is seen in the ¹³CO emission at  <−30 km s^-1, at −5 km s^-1 (between the line peak and deep absorption), and on the entire red side of the line profile.

The spatial profile of emission on the red wing of ¹²CO lines also differs from the spatial profile of the blue wing of ¹²CO lines and of the ¹³CO lines. The emission on the red wing of ¹²CO lines is consistent with the location of continuum emission from the secondary star. However, the ¹²CO emission is located  (8 AU at 120 pc) W of the continuum emission from the secondary star with a FWHM of (26 AU at 120 pc). The blueshifted component is slightly stronger on the nights with poor seeing. The unresolved line equivalent widths are stronger in the ISAAC spectrum, which used a wider aperture and was obtained in worse seeing. These results both support the presence of spatially-extended CO emission. The spectral and spatial information requires two physically distinct components for CO emission from IRS 44 W.

For the blueshifted component, fits to the ¹³CO and C¹⁸O line both yield temperatures of  ~330 K. The ¹³CO lines cannot be too optically thick, which places an upper limit on the column density of log N(CO)  ≲  19.4. The ¹²CO lines are very optically-thick, with fluxes that should be considered upper limits, which places a lower limit on the column density of log N(CO)  ≳  18.9. At this column density, the approximate emitting area is  ~6.5 AU, less than that implied by the spatial extent of the emission.

The red side of the line profile does not have reliable N(CO) and T because ¹³CO and CO v = 2−1 were not detected.

C.3. CrA IRS 2

CrA IRS 2 is classified here as an embedded object based on the SED (Nutter et al. 2005), although insufficient evidence exists in the literature to confirm the presence of an envelope.

The bright ¹²CO and ¹³CO emission lines from CrA IRS 2 have non-Gaussian profiles with centroids that are redshifted by  ~2 km s^-1 from the systemic velocity systemic and, when fit with a Gaussian profile, have FWHM of  ~26 km s^-1. The v = 1−0 lines also have a weak broad component that was discussed in Sect. 3.2.

Line fluxes are calculated by fitting a median ¹³CO line profile to every ¹²CO and ¹³CO line in the spectrum. The median ¹³CO line profile was calculated by coadding all ¹³CO lines that are not affected by absorption. The resulting fits are typically good, except that high-J¹²CO lines have broader peaks. The lack of any C¹⁸O emission, with an upper limit of 15% of the flux in ¹³CO lines, indicates that the ¹³CO lines are not optically-thick. The ¹³CO fluxes in the rotational diagram yield a best-fit temperature of T = 560 K. At this temperature, the ¹²CO/¹³CO line ratios indicate a column density log N(CO)  ~  19.1, at about the limit where C¹⁸O emission would be marginally detected. The total emitting area is (1.0 AU)².

Appendix D: Synthetic CO line fluxes

For optically-thin gas, the temperature and number of CO molecules can be directly measured from an excitation diagram. Transitions become optically thick as the column density of the medium increases, thereby changing the line flux ratios and, as a consequence, direct temperature measurements. For CO emission from disks around CTTSs and Herbig AeBe stars, CO v = 1−0 line flux ratios from disks deviate significantly from optically-thin branching ratios at a single temperature (e.g. Brittain et al. 2003; Blake & Boogert 2004; Salyk et al. 2007, 2009). When only ¹²CO lines are detected, such excitation diagrams can be explained by emission produced in optically-thick gas or in gas with a large temperature gradient. The strengths of ¹³CO and CO v = 2−1 emission, relative to v = 1−0 emission, suggests that the optically-thick interpretation is the best explanation for the curved rotational diagram obtained from our sample and from disks around CTTSs and Herbig AeBe stars.

We model the CO line fluxes by calculating the emission expected from an isothermal, 1D slab of pure CO gas. The vibrational excitation and rotational excitation of the CO gas are described by the same temperature. The molecular data was obtained from Chandra et al. (1996). Throughout the layer, absorption occurs in a Voigt profile with a Doppler broadening parameter b, which includes thermal and turbulent broadening. Emission lines have a Gaussian profile with a FWHM of 1.82  ×  b. The density is assumed to be high enough so that collisions dominate the excitation, allowing the gas to maintain local thermal equilibrium. The layer is dust-free. The fraction of photons that escape from the total layer is calculated as a function of column density in each transition.

	Fig. D.1 Synthetic CO v = 1−0 emission line fluxes for a 1D model with T = 1000 and log N(CO) = 16.0 (red circles), 17.0 (blue diamonds), 17.5 (purple asterisks), 18.0 (green triangles), and 19.5 (orange squares). At T = 1000 K, the lines with J′′ ~ 10 are the first to become optically-thick, thereby reducing the flux in mid-J lines relative to those with J < 3 and high-J lines.
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Appendix E: Additional tables

The primary benefits of an analysis of CO line opacities are measuring accurate temperatures, approximate CO column densities, and rough surface areas for the emission regions. Within this paper, the Doppler parameter is set to b = 2.0 km s^-1. A lower b parameter yields a faster increase in opacity, so resulting column densities would be smaller. The column densities in this simple 1D slab model correspond to the amount of material at a specific temperature in our line of sight. For a slab model, the vertical column density would be log N = log N_mod + log cosi, where i is the incidence angle along our line of sight into the slab and N_mod is the column density of the model Characterizing this geometrical complication is beyond the scope of the simplistic approach adopted here.

Figure D.1 shows the excitation diagram, normalized to of the R(0) line, for a range of total CO column densities, T = 1000 K, and b = 1.0 km s^-1. Each individual transition starts to become optically thick at log N_J ~ 14 and is completely opaque at log N_J > 18. At 1000 K, the rotational population peaks at J = 13, so that transitions with J′′ ~ 13 are the first to become optically thick. As a consequence, mid-J line fluxes are weaker than expected, relative to low-J and high-J lines. The opacity in the R-branch transitions increases faster than the opacity in P-branch transitions because the lower

levels of R-branch transitions are more populated than those in P-branch transitions. A more extreme example of the divergent P- and R-branch lines occurs in the Orion BN/KL region (Gonzalez-Alfonso et al. 2002).

For a slab with T = 1000 K, temperatures obtained from fits to synthetic optically-thick line ratios, either for the set of lines with J′ < 30 or the combined set of lines with J′ < 3 and 20 < J′ < 30, are  ≲200 K lower than the input model temperatures. Temperature fits to only the high-J (15 < J < 30) lines are tempting but can be misleading, with best fits as much as  ~1000 K higher than the input model temperature. Temperature fits to lines at J < 10 can yield temperatures of  <200 K and should be completely avoided.

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