The RMS survey: near-IR spectroscopy of massive young stellar objects

Abstract

1 INTRODUCTION

Massive stars (>8 M_⊙, i.e. >5 × 10³ L_⊙) have a profound influence on their surroundings due to their intense ionizing radiation, strong stellar winds and powerful outflows. However, despite the fact that low-mass star formation is broadly understood (Shu, Adams & Lizano 1987), relatively little is known about the conditions and processes that influence high-mass star formation. The study of massive star formation is hindered by the rarity of massive stars, their short evolutionary time-scales and the dust extinction which renders the stars invisible at short wavelengths for most of their formation.

The massive young stellar object (MYSO) phase is of particular interest for the study of massive star formation. In this relatively brief phase (10^4–5 yr; Davies et al. 2011; Mottram et al. 2011a), fusion has begun in the central star, but it has not yet ionized its surroundings to form an H ii region. Accretion may be disrupted or completely halted, in which case the final mass of the star would be set in this phase. MYSOs typically have strong, ionized stellar winds (Bunn, Hoare & Drew 1995) and bipolar molecular outflows (Shepherd & Churchwell 1996), both of which have an important feedback effect on the surrounding molecular cloud.

Whilst these properties mean that the MYSO stage is crucial to the understanding of massive star formation, their observation is not without difficulties. Dust extinction hinders optical and infrared (IR) studies, their lack of H ii regions means that radio emission is either weak or non-existent, and although MYSOs are often associated with masers, no single maser transition can be guaranteed to be present (Beuther et al. 2002).

Most of the bolometric luminosity of MYSOs is found in the thermal IR, so that is where they are most easily observed. Previous attempts to produce a large sample of MYSOs have been made using IRAS (e.g. Molinari et al. 1996; Sridharan et al. 2002). The low spatial resolution of IRAS (3 arcmin × 5 arcmin at 100 μm) meant that in star clusters and in the dense environment of the Galactic plane sources were often confused. Since most massive stars form in clusters and exist within the Galactic plane, the MYSOs in these studies may not be representative of all massive stars. The small number of MYSOs that have been identified so far means that there is a lack of statistical evidence with which to improve our understanding of high-mass star formation.

The Red MSX Source survey (RMS; Hoare et al. 2005; Urquhart et al. 2008a) is a valuable tool with which to address these issues, having taken both imaging and spectroscopic data from near-IR to radio wavelengths on a comprehensive, uniformly selected sample of MYSOs. The MSX point source catalogue (Egan et al. 2003) and near-IR 2 Micron All Sky Survey (2MASS; Skrutskie et al. 2006) data were used to find sources with IR excess. The MSX survey has a much better spatial resolution than IRAS, thus eliminating the bias against dense environments (Hoare et al. 2004). The reddest, most embedded objects were selected as targets using colour cuts defined by Lumsden et al. (2002). However, ultra-compact H ii (UCHII) regions, planetary nebulae (PN) and dusty evolved stars also have similar colours to MYSOs, so classification of the sources has been a major part of the project. A campaign of follow-up observations has been undertaken to achieve this (see Urquhart et al. 2008a). We combined radio, mid-IR and near-IR images with kinematic distances and far-IR data to characterize our sources (Mottram et al. 2007, 2010, 2011a; Urquhart et al. 2007a,b, 2008b, 2009a,b, 2011a,b, 2012). The full classification criteria are discussed in Lumsden et al. (in preparation).

Near-IR spectroscopy is the final classification stage, separating the MYSOs from the remaining sources. To date, ∼90 per cent of the ∼2000 objects from the original survey have been classified, identifying ∼600 MYSOs and ∼500 UCHII regions.¹ In total, we have spectroscopic observations of ∼450 objects. The data for the ∼200 objects observed in the Southern hemisphere are still in the analysis process, and will be presented in a future paper. In this paper, we present near-IR spectra and classifications of 247 objects observed in the Northern hemisphere, i.e. ∼12 per cent of the objects in the survey.

2 OBSERVATIONS

Spectroscopic observations of the YSO candidates were made using the UIST instrument at the United Kingdom Infra-Red Telescope (UKIRT) observatory from 2002 to 2008. 247 objects were successfully observed over 84 nights. Sources were selected from the ∼2000 candidate MYSOs found using the MSX catalogue in the preceding stages of the RMS survey. Initially, no radio or luminosity data were available, so the criteria for the spectroscopic observations were that the objects satisfy the colour cuts laid out in Lumsden et al. (2002), and that they were bright enough to be seen at the K band in 2MASS to enable correct identification of the counterpart. Once luminosity estimates were available, a loose luminosity cut of L_21 μm ≥ 500 L_⊙ (which corresponds to L_BOL ≥ 10 000 L_⊙, see Mottram et al. 2011a) was imposed. Therefore fewer low-luminosity sources were observed in the later runs. We targeted our source selection to observe all objects we believed to be YSOs with the appropriate luminosity, plus the 10 per cent of the ∼2000 candidates whose classifications were ambiguous. A full list of observational parameters for each individual object is shown in Tables A1 and A2 (see Appendix A).

UIST is a 1–5 μm imager spectrometer with a 1024 × 1024 InSb array and a camera with 0.12 arcsec/pixel resolution in spectroscopy mode. The HK grism (1.395–2.506 μm) was used, with a 0.48 arcsec × 120 arcsec long slit. This produces a fairly low spectral resolution of λ/Δλ ∼ 500, but meant that in ideal conditions a high signal-to-noise ratio could be achieved with relatively short exposure time. This allowed identification of faint lines whilst maximizing the number of objects that could be observed in the time awarded. In practice, a large number of the observations were done in poor weather conditions and with typical seeing of 1 arcsec, so the signal-to-noise ratio was not always very high, and flux calibration was unreliable on some nights. Exposure times for each object are shown in Table A1.

Many of the observations were taken before the near-IR counterparts had been accurately identified. As a result, finding charts was frequently done at the telescope using UIST in imaging mode so that the counterpart could be identified prior to taking the spectrum. In a few instances, such spectra were repeated later if subsequent high spatial resolution thermal IR images suggested that a different source was the correct counterpart. The position angle for the slit (also shown in Table A1) was derived from such images, as well as from 2MASS images for brighter, isolated sources, or GLIMPSE² for complex embedded sources. The aim was to avoid very bright, unrelated stars nearby, and if possible to align the slit on other interesting objects and extended emission nearby. This proved a useful technique as several fields of view had more than one MYSO within the field, and many have extended emission. In the tables, multiple objects within the same field of view are denoted by G*** – 1, G*** – 2, etc.

Standard stars with spectral types ranging from A0 to B9.5 were observed before each object for flux calibration, and the objects were nodded along the slit to minimize the effect of bad pixels and aid sky subtraction. The spectrum of an argon lamp was taken each night for wavelength calibration.

The standard star and object spectra were all reduced using the UKIRT pipeline Orac-Dr and the Starlink package figaro. To prevent confusion between emission lines in the object spectra and the H i absorption lines in the standard star spectra, the lines in the standards were fitted with Gaussian functions and removed before flux calibrating the object spectra. Flux calibration was done using the figaro routine irflux. This routine uses a blackbody model for the standard star, normalized to the star's flux at K. The K-band magnitudes and spectral types of the standard stars were taken from the SIMBAD data base. The temperatures corresponding to the spectral types were taken from Schmidt-Kaler (1982).

3 PHOTOMETRY

We compared our magnitude data with the 2MASS Point Source Catalogue (2MASS PSC; Skrutskie et al. 2006) and UKIDSS Galactic Plane Survey (GPS) data base release 8.³ The choice of catalogue used for analysis was decided on an object-by-object basis. Some objects are listed in both catalogues, others in only one and some do not have any near-IR magnitude data available. Where available, UKIDSS GPS magnitudes were preferred due to their improved sensitivity and resolution. However, due to its incomplete status, not all the objects we observed were covered by UKIDSS, and those that were do not always have data for all of J, H and K bands. In addition, the UKIDSS camera, Wide Field Camera (WFCAM; Casali et al. 2007) tends to saturate for the brighter objects. For objects with incomplete, low quality or saturated WFCAM data, 2MASS was used. Overall, from our 247 sources, 125 were compared to 2MASS photometry, 108 to UKIDSS and 14 had no magnitude data available in either catalogue. The data for each object are found in Table A2.

The magnitudes were also measured from the spectra using the figaro function istat, which gives the mean and total flux and the rms. (σ) across a user-defined wavelength range. The ranges used to measure the total flux were 1.5365–1.7875 μm and 2.028–2.290 μm for H and K, respectively. These correspond to the wavelength ranges for the 2MASS magnitude measurements, as described in Cohen, Wheaton & Megeath (2003). UKIDSS magnitudes are calibrated to 2MASS (Hodgkin et al. 2009), so the same ranges were used to measure the spectral magnitude regardless of which catalogue magnitudes were used for comparison. The continuum noise (σ) was measured using 0.01 μm ranges around 1.6 μm and 2.2 μm for H and K, respectively. These ranges are clear of emission lines and of distortion from atmospheric features, both of which can cause an overestimation of σ. The fluxes were then converted into magnitudes, using the H and K zero-points 1.133 × 10⁻⁹ and 4.283 × 10⁻¹⁰ W m⁻² μm⁻¹ for 2MASS sources (Cohen et al. 2003), and 1.131 × 10⁻⁹ and 4.271 × 10⁻¹⁰ W m⁻² μm⁻¹ for UKIDSS sources (Hodgkin et al. 2009). The errors on the magnitudes given in Table A2 are 3σ errors. Some of the sources were not detected at H, in which case their H-band magnitudes could not be calculated. However, most spectra were bright enough at H that their magnitudes could be measured, and all were bright enough at K.

Fig. 1 shows a comparison of catalogue with measured magnitudes, for both H and K bands. The dotted lines represent Akritas–Thiel–Sen (ATS) regressions. The ATS regression and Kendall's τ were calculated using the cenken (Akritas, Murphy & LaValley 1995) function in the NADA library (Helsel 2005) from the R-project statistics package, and compared with other regression methods and correlation tests performed using the asurv statistics package (Isobe, Feigelson & Nelson 1986; Isobe & Feigelson 1990; Lavalley, Isobe & Feigelson 1992). These statistical methods were used to take account of the many censored data present (see also Section 6.5). Based on a y = a + bx fit, the ATS fit coefficients for H are a_H = 0.96 and b_H = 0.92. For K, the coefficients are a_K = −0.08 and b_K = 1.02. Kendall's τ values for H and K are 0.48 and 0.70, respectively, both with p-values ≃ 0; i.e. there is essentially no possibility that a correlation does not exist.

Figure 1.

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Measured versus catalogue magnitudes for both H and K bands. The catalogue magnitudes were taken from either UKIDSS or 2MASS depending on the object and the quality of the catalogue data. The detections are denoted by black diamonds and limits by green arrows. The dotted lines represent the ATS regressions. As expected, a strong correlation was found between the measured and catalogue magnitudes (see the text for more details).

The lower τ and greater deviation in the fit from m_obs = m_cat for H-band magnitudes are primarily due to the fact that many of the fainter objects have very noisy H-band spectra, and some were not detected at shorter wavelengths. This means that there are more limits, and the errors at the high end of the magnitude range are larger, both of which decrease the measured correlation coefficient and pull the regression line away from m_obs = m_cat. Nevertheless, the correlation is clearly there for both H and K bands, and the regression coefficients for the K band are very close to m_obs = m_cat. This shows that, for most objects, the photometry measured from the spectra is good despite the frequently poor weather conditions.

Those objects that deviate strongly from the m_obs = m_cat were all taken in very poor weather conditions and/or with poor seeing. The conditions were highly time-variable for these badly affected observations. The much longer exposure times for the objects average out such variations whereas the shorter exposure times for the standards do not. The raw standard star data counts were noticeably very low for these observations in particular. The ratio of object to standard then becomes exaggerated. Since there is only one standard star spectrum per object, there was no way to mitigate against this. For consistency, all the fluxes were normalized to the catalogue magnitudes. The correction factor, |$f_{\rm obs}/f_{\rm corr}=10^{(m_{\rm obs}-m_{\rm cat})/-2.5}$|⁠, was calculated using the standard equation for apparent magnitude, and is shown in Table A3.

4 CLASSIFICATION

The objects were primarily classified using the RMS follow-up observations. These criteria are described in detail in Lumsden et al. (in preparation). In summary, MYSOs conform to the colour cuts defined in Lumsden et al. (2002), are radio-quiet due to insufficient ionized gas, show strong millimetre CO emission as expected in a star formation region and appear as point sources in mid-IR images at 1 arcsec resolution. They show clustering in near-IR images in contrast to more evolved stars, which appear as isolated point sources. This left a sample of predominantly MYSOs, but also of some H ii regions, proto-planetary nebulae (PPN), compact PN and embedded evolved stars. Near-IR spectroscopy was necessary to distinguish between the MYSOs and contaminants.

The spectra were classified according to the shape of their continuum and the presence or absence of emission and/or absorption features. All the spectra show telluric water absorption in the 1.8–2.0 μm range. Consequently, this range could not be used in the analysis and was taken out of the figures. The example spectra of the contaminants are shown in Fig. 2. Fig. 3 shows the example spectra of MYSOs. Each major emission line is present in at least one of the MYSO spectra shown in the example figures. The spectra of all objects observed will be available on the RMS data base.⁴

Figure 2.

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Example spectra of each class of contaminants found within the sample, i.e. the non-YSOs. From top-left to bottom-right: the H ii region G019.7540−00.1279; the evolved star G049.5373−00.3929; the PPN G026.4897−00.5455; the PN G030.2340−00.1392; the M-Giant G025.4018+00.0198A and finally the hot star G026.3050+00.1162, labelled as ‘Other’ in the data base and tables. Note the similarity of the PN spectrum to that of the H ii region. This object required the RMS follow-up campaign's mid-IR imaging data in order to be correctly classified.

Figure 3.

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Example spectra of the MYSOs. All have the steep rising continuum and some emission lines; however, there is variation in which lines are present. This figure shows all the major emission lines seen in MYSOs, but is not intended to be representative in terms of the proportion of MYSOs that show each emission line.

MYSOs are still embedded in their natal clouds, so their spectra show strong dust extinction in the form of a steep rising continuum, and occasionally excess dust emission at λ ≳ 2.3 μm. Almost all have emission lines, the most common being Brγ and H₂. Some also have H-band Brackett series, shocked [Fe ii], fluorescent Fe ii or CO bandhead emission. Both Brγ and He i can be seen in emission, absorption, or with a P-Cygni-type profile, though at this low resolution it was not possible to obtain expansion velocities for such profiles.

Massive YSOs were differentiated from low-mass YSOs by their luminosity; a loose cut of L > 10³ L_⊙ was applied. Most of the RMS YSOs have luminosities characteristic of massive stars; 131/195 (∼70 per cent) of the RMS YSOs in this paper have L > 5 × 10³ L_⊙, which corresponds to M > 8 M_⊙ (Mottram et al. 2011b). However, their spectral properties are very different from those of typical main sequence stars (Hanson et al. 2005).

H ii regions have comparatively flat continua, strong H i emission, and, often, He i emission. The H i emission conforms to case B of Baker & Menzel (1938) since it originates in an optically thin ionized region. It is worth noting that it was occasionally difficult to distinguish between MYSOs with strong H i emission and H ii regions by their spectra alone. Generally, this was achieved using other data from the RMS survey follow-up or in the literature. In particular, radio observations and GLIMPSE images were used. In most cases, H ii regions produce free–free radio emission owing to the large amount of ionized gas, whereas H i emission in MYSOs does not produce bright free–free emission. In addition, H ii regions appear diffuse in mid-IR GLIMPSE images, so even radio-quiet ‘weak’ H ii regions can usually be distinguished from MYSOs. Sometimes the suspected central star of an H ii region has characteristics of a YSO. These were classified as ‘YSO/HIIR’.

Evolved stars have much less dust extinction and therefore have comparatively blue continua, or continua that peak in the middle of the 1.5–2.5 μm range. They occasionally have the Brackett series in emission or absorption, and frequently have CO bandhead absorption. PPN are very red and can have strong CO absorption. Some of the PPN spectra closely resemble those of FU-Ori type objects, so it is possible that some of the objects we have classified as PPN are in fact FU-Ori type objects. The spectra of PN are flat or red and are often very similar to YSO or H ii region spectra. In these cases, other data from the RMS survey follow-up and the literature were used to classify the object. The final class found within our sample were M-Giants. These have continua that peak in the middle of the 1.5–2.5 μm region, show molecular absorption lines owing to their cool atmospheres and have strong H₂O absorption.

Of the 247 objects whose spectra were taken, there were 180 YSOs, 15 YSOs within H ii regions, 26 H ii regions, 7 evolved stars, 5 PPN, 4 PN, 5 M-type supergiants and 5 evolved hot stars labelled as ‘Other’ in the table and on the RMS data base website due to unusual characteristics in their data. Spectra were found to be a valuable confirmation of classification in addition to our imaging data in 45 per cent of cases, and the only means of classifying the source in 5 per cent of cases.

5 EXTINCTION

Figure 4.

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Left: comparison of extinction calculated using J- and H-band magnitudes (A_V (JH)) and H- and K-band magnitudes (A_V (HK)), for the YSOs. The detections are denoted by black diamonds and limits by green arrows. The solid line represents A_V (HK) = A_V (JH), and the dotted line is the ATS regression line. Right: number distribution of A_V for the YSOs, using A_V (HK) where available, or otherwise using A_V (JH).

Fig. 5 shows a colour–colour diagram demonstrating this point. Some of the objects do fall very close to the extinction line, i.e. the line that runs parallel to the extinction vector and starts at the intrinsic J − H and H − K colours. However, most fall above this line, showing evidence of the dust excess emission and/or scattering described above.

Figure 5.

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Colour–colour diagram showing YSO J − H and H − K colours for the RMS objects. The detections are denoted by black diamonds and limits by green arrows. The black arrow shows the extinction vector, of length A_V = 10, calculated using the Draine (1989) extinction law. The blue triangle shows the intrinsic colours of a B0 star, taken from Koornneef (1983): J − H = −0.12 and H − K = −0.05.

Figure 6.

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The K-band section of the spectrum of the YSO G033.3891+00.1989. This shows a very clear example of the saw-tooth profile of the CO bandhead. It also has Brγ emission.

Figure 7.

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The H-band section of the spectrum of the YSO G019.8922+00.1023. This object has both the Brackett series and the [Fe ii] 1.64402 μm line, as well as the fluorescent Fe ii 1.6878 μm line. Note that the Br 12/[Fe ii] line at ∼ 1.64 μm is much stronger than the other Brackett series lines.

For extinction correction, A_V (HK) was used where available, or A_V (JH) when A_V (HK) was not available, or was a lower limit. The number distribution of these extinctions is shown in the right-hand panel of Fig. 4. The median is A_V = 42, and the extinctions range from A_V = 2.7 to A_V = 114, demonstrating that this study covers the minimally obscured objects right through to very red, dusty sources.

6 YOUNG STELLAR OBJECTS

6.1 Spectral features

In addition to the strong dust extinction and corresponding steep rising continuum, most YSOs have emission lines in their spectra. However, not all of them show the same lines. One of the objectives of the RMS survey is to identify why there are differences. The main emission lines observed in YSOs in our sample were Brγ, Br 10, Br 11, Br 12, [Fe ii] 1.64 μm line, H₂ 2.1218 μm, H₂ 2.2477 μm, fluorescent Fe ii 1.6878 μm and CO bandhead. Some objects also exhibited the Pfund series, or other molecular H₂ lines. He i 2.0587 μm was seen in both emission and absorption. Both Brγ and He i were occasionally seen with P-Cygni-type profiles: 13 MYSOs had Brγ with a P-Cygni profile and 15 had He i with a P-Cygni profile, of which 8 had P-Cygni profiles for both Brγ and He i. These objects are listed in Table B3 However, the He i 2.11 μm doublet was not seen in the YSOs, only in H ii regions. Detection frequencies are shown in Table 1.

6.2 Emission and absorption line fluxes

The fluxes of the YSO emission and absorption lines were measured using the Starlink package dipso. The continuum was fitted by a third-order polynomial function, and then subtracted. In many cases, the steepness of the continuum obscured the presence of emission lines that became visible when the continuum was subtracted. For all spectral features except the CO 2–0 bandhead, the line profiles were fitted with a Gaussian function, which dipso then integrated to find the total flux of the line. The majority of the spectral lines are unresolved so a Gaussian function is a good assumption.

The continuum rms noise was measured using figaro’s istat function, taking wavelength ranges with no spectral lines, close enough to the pertinent spectral line that extinction would not distort the result. The rms noise was measured for two ranges per line, one either side of the line, and the mean value of these was taken. The upper limits for non-detections were calculated using the same equation, with h = 3 × continuum rms.

The CO bandhead has a saw-tooth shaped profile (see Fig. 6), so different treatment was required. The equivalent width (EW) was measured from 2.289–2.313 μm, again using dipso. The mean continuum flux density was measured across the 2.2825–2.2875 μm range just to the blue end of the bandhead, using figaro’s istat function. The EWs were then converted into fluxes. This is consistent with the method used by Ishii et al. (2001). Detections were again defined as EW > 3 δEW, where δEW is the error given by dipso. Limits were taken as EW_limit = 3 δEW.

The fluxes of the Brγ, Br 10, Br 11, Br 12/[Fe ii] 1.64 μm line, H₂ 2.1218 μm, H₂ 2.2477 μm, fluorescent Fe ii 1.6878 μm and He i 2.0587 μm lines are listed in Table B1, with the presence of the Pfund series denoted by ‘P’ in the final column. The EWs of the CO 2–0 bandhead are listed in Table B2. The errors in the tables are at the 1σ level. The fluxes and EWs in the tables are the raw values as measured directly from the spectra, and are not corrected for extinction or normalized to the catalogue magnitude (see Section 3).

Br 12 and [Fe ii] 1.64402 μm are close to each other and form a blend when both are present (see Fig. 7). To determine whether the line seen at 1.64 μm is Br 12, [Fe ii], or a blend, one has to compare this line with the rest of the Brackett series. For this reason, the fluxes of Br 12 and [Fe ii] are listed in Table B1 in the same column. Unblended [Fe ii] corresponds to the presence of a line at 1.64 μm when Br 10 and Br 11 are absent. When the rest of the Brackett series is present, the presence of [Fe ii] can only be inferred if the relative strength of the 1.64 μm line compared to Br 11 is higher than expected. Assuming Baker & Menzel (1938) case-B recombination with the Storey & Hummer (1995) line ratios for T_e = 7500 K and N_e = 10⁶ cm⁻³, the 1.64 μm line was defined as a blend if f(1.64 μm) > 0.788 × f(Br 11). See Section 6.3 for a full discussion of the properties of H i lines.

This cut relies on the emission lines being optically thin. If the lines are not optically thin, the flux of the Br 12 line may fall above this limit but not have a contribution from [Fe ii]. This means that there are probably some objects that are considered to have a blend of Br 12 and [Fe ii] under this definition that actually only have Br 12. However, the low resolution of the spectra meant that deconvolving the lines was not possible, so this was considered to be the best available separation method for the purposes of this paper.

In nine of the YSO spectra, dust extinction rendered part or all of the H band too noisy to identify emission lines in this region with any confidence. This caused difficulties in the analysis of these spectra. However, given that there are 195 objects classified as YSO or YSO/HIIR, this represents only ∼5 per cent of the objects. Excluding these objects from the H band data analysis still leaves a large enough sample to make statistically sound conclusions.

6.3 H i emission

The detection rate of Brγ emission amongst the YSOs is 75 per cent, and many of these also have other H i lines. This detection frequency is lower than the 97 per cent found by Ishii et al. (2001) for intermediate-mass YSOs and Herbig Ae/Be stars, but comparable with the 71 per cent found by Carr (1990) for low-mass YSOs. Brγ was also seen with a P-Cygni profile in the spectra of 13 objects (see Table B3), indicating that for those objects, Brγ originated in an outflowing wind.

Figure 8.

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Left: Brγ luminosity against bolometric luminosity for RMS sources. The detections are denoted by black diamonds and limits by green arrows. The errors on detections are shown, but are frequently too small to be easily distinguishable on this scale. The dotted line represents the ATS regression. Right: comparison of RMS data (diamonds) with those of Carr (1990) (circles) and Ishii et al. (2001) (triangles). Only detections above the 3σ limit are shown. The solid lines represent the loci of L_ACC = L_BOL, L_ACC = 0.1 L_BOL and L_ACC = 0.01 L_BOL using the Calvet et al. (2004) relationship between L_ACC and L_Brγ. In both plots, all the line luminosities have been corrected for extinction, and the RMS data have been corrected for the difference between measured and catalogue magnitudes.

One of the considerations when distinguishing MYSOs with Brackett series emission from H ii regions is whether the recombination conforms to case B of Baker & Menzel (1938); recombination emission in typical compact H ii regions conforms to case B, whereas this is not always true for MYSOs. Storey & Hummer (1995) tabulated the case-B line ratios for a range of temperatures and densities.