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Physical and chemical conditions in methanol maser selected hot-cores and UCHII regions

We present the results of a targeted 3-mm spectral line survey towards the eighty-three 6.67 GHz methanol maser selected star forming clumps observed by Purcell et al. 2006. In addition to the previously reported measurements of HCO+ (1 - 0), H13CO+ (1 - 0), and CH3CN (5 - 4)&(6 -5), we used the Mopra antenna to detect emission lines of N2H+ (1 - 0), HCN (1 - 0) and HNC (1 - 0) towards 82/83 clumps (99 per cent), and CH3OH (2 - 1) towards 78/83 clumps (94 per cent). The molecular line data have been used to derive virial and LTE masses, rotational temperatures and chemical abundances in the clumps, and these properties have been compared between sub-samples associated with different indicators of evolution. The greatest differences are found between clumps associated with 8.6 GHz radio emission, indicating the presence of an Ultra-Compact HII region, and `isolated' masers (without associated radio emission), and between clumps exhibiting CH3CN emission and those without. In particular, thermal CH3OH is found to be brighter and more abundant in Ultra-Compact HII (UCHII) regions and in sources with detected CH3CN, and may constitute a crude molecular clock in single dish observations. Clumps associated with 8.6 GHz radio emission tend to be more massive and more luminous than clumps without radio emission. This is likely because the most massive clumps evolve so rapidly that a Hyper-Compact HII or UCHII region is the first visible tracer of star-formation. The gas-mass to sub-mm/IR luminosity relation for the combined sample was found to be L proportional to M**0.68, considerably shallower than expected for massive main-sequence stars.


INTRODUCTION
Molecular emission is a powerful tool when used to investigate the physical and chemical conditions in hot cores. Transitions requiring different temperatures and densities for excitation constitute an excellent probe of physical structure. Because the chemical proper-ties of hot cores vary with time, the relative molecular abundances can also be used as indicators of evolution.
Chemical models, including both gas-phase and grain-surface reactions have been developed for specific objects whose physical structure and conditions are well known, e.g. G34.3+0.15 (Millar et al. 1997; Thompson et al. 1999), as well as for general cases, e.g. Rodgers & Charnley (2003). These and earlier models are limited by the computational power available at the time and consider either time-dependent chemistry at a test position, or a 'snapshot' of spatial abundances at a single time. Advances in computational power have recently allowed the development of models which consider both time-and space-dependent chemistry simultaneously, e.g., the model of AFGL 2591 by Doty et al. (2002). Today it is the lack of observational constraints which restrict our understanding of chemistry in young massive stellar objects. The priority in the coming years must be to assemble a large sample of molecular abundance measurements towards a broad range of massive star forming regions, at different stages of evolution and with luminosities and masses from B3 to O5 type massive stars.
In this paper we present the remaining results of the Mopra 'Hot Molecular Cores' (HMC) survey towards 6.67 GHz methanol (CH3OH) maser selected targets. The initial results were presented in Purcell (2006) (hereafter Paper 1), wherein we reported the detection of the hot-core species methyl-cyanide (CH3CN) and the observations of the formyl ion (HCO + ), and its isotopomer (H 13 CO + ). Here we expand the analysis to cover thermal transitions of methanol (CH3OH), carbon-monoxide ( 13 CO), diazenylium (N2H + ), hydrocyanic acid (HCN) and hydroisocyanic acid (HNC). We analyse the full complement of molecules for evidence of evolution.
Note: Tables 3-9 are available in electronic form only along with additional supporting text and figures.

OBSERVATIONS
Observations were conducted on the Mopra millimetre wave telescope over five years 2000 -2004 during the winter observing season, June -September. We observed the transitions CH3OH (2 -1), 13 CO (1 -0), N2H + (1 -0), HCN (1 -0) and HNC (1 -0) as single pointings, targeted at the maser sites. Electronic properties of the molecules and transitions are presented in Table 1. Five sources do not contain methanol masers but were detected as discrete clumps at 1.2 mm, adjacent to clumps containing CH3OH masers (Hill et al. 2005). These 'mm-only' sources were observed as potential precursors to the hot-core phase of massive starformation. In each case we targeted the peak of the 450 µm continuum emission later detected by Walsh et al. (2003). The signal from the receiver was processed in an autocorrelator backend configured to have a bandwidth of 64 MHz, split into 1024 channels. At 3-mm wavelengths this delivers a velocity resolution of ∼0.2 km s −1 over a usable velocity interval of ∼130 km s −1 .
All observations were performed in position switching mode by integrating for equal times on the science object and an emission-free reference position. Initial reduction of the raw data was performed using the SPC 1 package. Polynomial baselines were The vertical dashed line marks the systemic velocity of the source, measured from the peak of the optically thin H 13 CO + line profile (see Purcell 2006). Vertical dotted lines mark the expected velocity of other transitions of the same molecule. Individual Gaussian fits to the line profiles are plotted by a dotted grey line and the cumulative fit by a solid grey line. We did not attempt to fit Gaussians to HCN lines as the majority of profiles have complex shapes. subtracted from the line-free channels using the XS 2 software package. The CLASS 3 spectral line analysis software was used for all further processing and analysis, including baseline subtraction and fitting Gaussian line profiles. For further details on the observing setup and data analysis please refer to Section 3 of Paper 1.

RESULTS
Thermal molecular emission was detected in 82/83 targets, with the exception being the source G10.10−0.72. In the interim period this source has been reobserved at 6.67 GHz using the 30 m Ceduna radio telescope (University of Tasmania) and no CH3OH maser was detected (S. Ellingsen, private communication). This source is thus most likely a noise artifact in the Walsh et al. (1998) survey and is discounted in the remainder of this work. Emission from 13 CO(1 -0), N2H + (1 -0), HNC (1 -0) and HCN (1 -0) was detected towards the remaining 82 sources, while CH3OH (2 -1) emission was detected towards 79/82 sources (96 per cent). The 3-σ noise limit on the spectra where no lines were detected is recorded in Table 2. Figure 1 presents sample spectra for the source G323.74−0.26. The vertical dashed line marks the systemic velocity of the gas, measured from the optically thin H 13 CO + line (Paper 1). In the case of CH3OH, the rest-frame is centred on the A+ transition, and for N2H + and HCN the rest-frame is centred on the JF = 12 → 01 E transition. Plots of all molecular spectra for all 83 observed sources (including G10.10−0.72) are available as additional online material.

Line profile parameters
As with CH3CN in Paper 1, we fit the multiple transitions of CH3OH (2 -1) simultaneously with four Gaussian lines having equal full-width half-maximum (FWHM) linewidths and whose line-centre separations were fixed to the theoretical values. The weakest component in the spectrum, the J K,K ′ = 21,1 → 11,0 E line, was detected towards 50 per cent of sources. Individual line profiles are generally well fit by single Gaussians, and the average linewidth is 4.7 km s −1 . The CH3OH line profiles of five sources (G0.21+0.00, G0.26+0.01, G6.54−0.11, G10.30−0.15, and G15.03−0.71) were too confused or too weak to be successfully fit with Gaussians. The parameters of the Gaussian fits to the remaining 74 spectra are presented in Table 3.
The N2H + (1 -0) transition is split into seven hyperfine lines, as illustrated in Figure 2 (adapted from Caselli et al. 1995). The relatively broad linewidths (> 2 km s −1 ) observed towards massive star forming regions result in the seven components blending into three groups with roughly Gaussian shapes. Consequently, we have characterised the profiles using two analysis schemes. In the first instance we used the hyperfine structure fitting (HFS) routine in the CLASS software to simultaneously fit the N2H + profiles with seven Gaussians. Free parameters were the velocity (VLSR), common linewidth, excitation temperature, and optical depth. In the case of severely blended lines (as presented in this work) the fits are not well constrained and values for the optical depth and excitation temperature contain substantial uncertainties. Using this method we find the mean N2H + linewidth of the sample is 3.0 km s −1 . Because of the uncertainty introduced by the blending, CLASS assigned an erroneous value of τ = 0.1 to all sources, rendering the resultant excitation temperatures meaningless. As an alternative measure of optical depth and integrated intensity, we also fit the three blended groups individually with single Gaussians. In total we successfully fit Gaussians to 79 spectra. The N2H + emission in the source G0.26+0.01, G6.54−0.11 and G6.61−0.8 was too weak or two confused to achieve a reliable fit. We discuss the optical depth and column densities derived from the N2H + spectra in Section 4.4. The results of the CLASS HFS fits and the parameters of the Gaussian fits are presented in Table 4.
Line profiles of HNC are observed to be similar to HCO + . The critical densities of the two molecules are approximately the same at ∼ 3 × 10 5 cm −3 (Schilke et al. 1992) and it is likely that they trace the same gas. Both molecules exhibit high velocity linewings. Self-absorbed HNC line profiles are common in the sample and we referred to the low optical depth H 13 CO + and N2H + line profiles when attempting to distinguish between self-absorption and multiple clouds along the line of sight. We fit self-absorbed profiles with a single Gaussian by masking off the absorption dip (see Paper 1, Figure 3). We also measured the line intensity by integrating under the line between velocity limits bracketing the pos-  (Caselli et al. 1995). Linewidths towards massive star-forming regions are 4 -5 times greater, resulting in the hyperfine components blending into three groups, designated 1 -3 in this work (dashed lines).
itive line emission and we calculated an equivalent linewidth from ∆Vequiv = In Equation 1 R T mb dv is the integrated intensity and T mb is the peak main-beam brightness temperature. HNC emission from the sources G0.21+0.00 and G0.26+0.01 was not measured as the line profiles were too confused. In total 79 spectra were successfully fit with Gaussians, while 80 were measured by integrating under the line profile. The results of the fits and integrated intensity measurements are presented in Table 5.
The 13 CO line profiles often exhibit multiple components spread over the 64 MHz bandpass. Usually a single bright component is present at the systemic velocity of the source, which is easily fit with a single Gaussian. Occasionally several smaller components are crowded around the main line and these are fit as blended Gaussian lines. In general, the 13 CO profiles appear moderately optically thick but exhibit less self-absorption than HNC or HCO + . We again measure the integrated intensity and peak brightness temperature directly from the raw spectrum. The parameters of the fits and integrated intensity measurement of all 82 spectra are presented in Table 6.
HCN exhibited highly confused line profiles, with few sources exhibiting the expected 3-component hyperfine structure. We attribute the complex profiles to a combination of high optical depths, multiple clouds along the line of sight and low level emission from broad line-wings tracing outflows. It is possible that some spectra may be contaminated by emission from the reference position, as HCN appears to be ubiquitous near the Galactic plane.
Like HCO + , high velocity outflows wings are common in the spectra of HNC and, to a lesser extent, 13 CO. We fit broad Gaussians to these wings simultaneously with the main component, and their parameters are presented in Tables 5 and 6 marked with a 'w'. Distributions of full-width half-maximum linewidths from the Gaussian fits to the spectra. The HNC and 13 CO line profiles were fit with single Gaussian components. CH 3 OH was fit with multiple Gaussians, where the linewidths were constrained to have the same value. The N 2 H + spectrum was fit using the HFS method in CLASS. Seven Gaussian components with a common linewidth were fit to the three groups of blended lines. The value plotted here is the linewidth of an individual component. The mean CH 3 OH, HNC and 13 CO linewidth are all at approximately 4.5 km s −1 , while the mean N 2 H + linewidth is at 3.0 km s −1 .
The Gaussian parameters for blended lines are marked with a 'b' in the same tables. Figure 3 shows the distributions of full-width half-maximum linewidths for the four molecules which were fit with Gaussians. The median CH3OH, HNC and 13 CO linewidths are all at approximately 4.5 km s −1 , while the median N2H + linewidth is uniformly lower at 3.0 km s −1 . Kolmogorov-Smirnov (KS) tests yield probabilities above 50 per cent that the CH3OH, HNC and 13 CO linewidth distributions are similar, implying that these lines are emitted from gas with similar dynamics. In contrast, the N2H + distribution is signifficantly different, yielding probabilities of less than 0.0001 per cent in each case.

Linewidths
For a temperature of 58 K (see Section 4.1) the median intrinsic thermal linewidths for the molecules are as follows: CH3OH: 0.29 km s −1 , 13 CO: 0.31 km s −1 , HNC: 0.32 km s −1 and N2H + : 0.31 km s −1 . These values represent only 7 to 10 per cent of the measured linewidths. Non-thermal line broadening may arise from bulk motions, rotation or turbulence, which are difficult to distinguise at the resolutions of these observations. We can conclude that the N2H + emission emanates from a more quiescent region than the other molecules.

DERIVED PARAMETERS
We present the general physical parameters of the sources and the excitation temperatures, column densities and optical depths derived from the line profiles. The frequencies and electronic constants used in the calculations are collected in Table 1.

Gas mass and virial mass
Gas masses have been calculated from the 1.2-mm continuum flux density, taken from the work of Hill et al. (2005). For a 1.2-mm integrated continuum flux density Sν the mass of gas is given by Hildebrand (1983) where D is the distance to the source in metres, κ d is the mass absorption coefficient per unit mass of dust, Bν is the Planck function for a blackbody of temperature T dust , and R d is the dust to gas mass ratio. We have adopted a value of 0.1 m 2 kg −1 for κ d at 1.2-mm and have assumed a dust to gas mass ratio of 0.01 (Ossenkopf & Henning 1994). The distance has been estimated from the VLSR of the source using the Galactic rotation curve of Brand & Blitz (1993) (see Paper 1). Values for T dust were taken from the cold component of the greybody-fit to the spectral energy distribution (SED) presented in Paper 1. For sources where we had insufficient data to perform a fit we adopted the average value of T dust = 58 K, determined from 65 good fits. We note that these temperatures are not well constrained by the sparsely sampled SED and are generally higher than the values of 20 -30 K adopted in the literature. For dust temperatures of 20 K and 30 K the gas-mass derived here will be under-estimated on average by factors of 3.6 and 2.1, respectively. Values for Mgas were derived for 66 sources and are recorded in column six of Table 7. We estimated virial masses from the CH3OH, N2H + , 13 CO and HNC line-profiles following the approach by MacLaren et al. (1988). In the simplest case, neglecting support by magnetic fields or internal heating sources, the total mass of a simple spherical system is given by where σ is the full 3-dimensional velocity dispersion, r is the dust-radius of the cloud in pc, ∆v is the FWHM linewidth of the molecular line in km s −1 and G is the gravitational constant in N m 2 kg −2 . The virial mass is the minimum mass required in order for a cloud to be gravitationally bound, i.e. the cloud is bound if Mgas/Mvir > 1. If magnetic field support is important the virial mass may be overestimated by up to a factor of two (MacLaren et al. 1988). Observationally, the linewidths may be artificially broadened due to blending of multiple components along the line of sight, or in optically thick lines, due to radiative transfer effects. Enhanced linewidths will cause us to overestimate the virial mass by an unknown amount and the values quoted here should be considered upper limits. Columns 7 -10 of Table 7 present the virial masses derived from the four molecules. The distributions of Mgas and Mvir are illustrated in Figure 4. Optically thin N2H + and H 13 CO + produce similar estimates of the mean virial mass at 573 M⊙ and 905 M⊙, respectively. 13 CO and CH3OH have the broadest linewidths, most likely due to optical depth effects or low velocity outflows, leading to mean mass estimates of 1293 M⊙ and 1305 M⊙, respectively. The values derived for Mgas and Mvir are consistent with having the same magnitude in the majority of clumps. The large uncertainties associated with the calculations prevent the interpretation of individual objects as gravitationally bound.

H2 column and volume density
We estimated the H2 column density, NH 2 , from the gas-mass using the following relation: where Mp = 1.673 × 10 −27 kg is the mass of a proton, fHe = 1.36 is a correction factor to account for Helium present in the interstellar medium (Allen 1973) and A is the projected surface area of the mm-continuum emission. Assuming a cylindrical source with uniform density, the projected area is given by where r is the angular radius of the source in radians and D is the distance to the source in metres (1 pc = 3.08568×10 16 m). In a similar manner the volume density nH 2 can be estimated by replacing A in Equation 4 by V the projected volume of emitting gas Equation 6 assumes emission from a uniformly dense sphere of angular radius r. The radius of the dust continuum emission was measured directly from the 1.2-mm continuum images (provided courtesy of Hill et al. 2005) by fitting a Gaussian to the azimuthally averaged source profiles. We find values for the full-width halfmaximum vary between 99 ′′ and 24 ′′ (the limiting resolution of the SIMBA bolometer), and have a mean value of 34 ′′ . Derived values of NH 2 and nH 2 are presented in columns four and five of Table 7 and have means of 6.1× 10 22 cm −2 and 4.8× 10 4 cm −3 , respectively. We urge caution in interpreting any value of the H2 column density derived in this manner as the assumptions introduce large unknown errors. Firstly, the mass absorption coefficient and dust to gas ratio used to calculate Mgas in Equation 2 may vary considerably from source to source, leading to a corresponding error in the H2 column density. The spatial distribution of H2 is a further unknown and additional errors are introduced by assuming a uniform column density over a spherical projected volume. For the six sources at the limit of SIMBA resolution (24 ′′ ) derived values should be considered beam averaged lower limits. Also see Section 6.3 for a discussion on beam dilution.

CH3OH rotational temperature and column density
CH3OH is a slightly asymmetric rotor, resembling a symmetric top except for the O-H group, which is angled with respect to the principal axis. Internal hindered motion coupled with the rotation of the molecule results in a complicated rotational spectrum, organised into non-degenerate A and two-fold degenerate E levels, corresponding to different torsional symmetry. The A and E states have nuclear statistical weights of 2 and 1, respectively, thus their overall degeneracy is the same (Bockelee- Morvan et al. 1994).
A rotational temperature Trot and column density N may be estimated from the ratios of the thermal CH3OH lines based on the assumptions of low optical depths and that the background temperature (T b ≈ 2.7 K) is small compared to the brightness temperature of the line. Under conditions of Local Thermodynamic Equilibrium all the observed energy levels can be described by a single excitation temperature Tex, defined by the Boltzmann relation. Using the relation for rotational temperature (Goldsmith & Langer 1999), a rotation diagram may be drawn by plotting ln (Nu/gu) versus Eu/k. The rotation temperature and column density in the upper level Nu are found from the slope and y-axis intercept, respectively, of a straight line fit to the data. The total column density N may then be found assuming local thermal equilibrium and a partition function Q(Trot), which for CH3OH is given by (Townes & Schawlow 1955) In Equation 8 we have approximated the partition function by a fit to the discrete values in the Pickett et al. (1998) spectral line catalogue. Note that values for Eu are referenced to different ground state energy levels in A and E-type CH3OH. The ground state for A-type is the JK = 0 0 level, while for E-type CH3OH is the JK = 1 −1 level (Menten et al. 1988). This is commonly overlooked in the literature as all values quoted in Pickett et al. (1998) are referenced to the JK = 0 0 level, resulting in incorrect rotation diagrams. The correct values of Eu/k are cited in Table 1. An example of a CH3OH rotation diagram is shown in Figure 5 (left). The data point at Eu/k ≈ 7 K corresponds to the A+ line, while the other three points correspond to E transitions. In general, where we detect three E-type lines, they are well fit with a straight line, implying that our assumption of optically thin conditions is valid.
A and E type methanol are oblate and prolate forms, respectively, of the assymetric top and only inter-convert on timescales of ∼10,000 years. It is not clear that the A/E ratio can be assumed equal to one and a rotation diagram including both A and E type transitions may not be valid. In Figure 5 (left) the solid line indicates a fit to the E-type transitions only, while the dotted line is a fit to both the A and E-type. Rotation temperatures derived from only the E-transitions have a mean value of 6.67 K, similar to the mean temperature derived from all four transitions, which is 6.8 K. Rotational temperatures and column densities derived using both fitting   Table 8 and the distributions of rotational temperatures are illustrated in Figure 5 (right).
Column densities are averaged over the telescope beam and are likely underestimated. If the bulk of the CH3OH emission stems from within a hot core then the typical size of the emitting region will be ∼0.1 pc (≈ 20, 000 AU, Kurtz et al. 2000). Columns three and four of Table 8 present the angular size and beam dilution factor calculated using this assumption. Columns seven and ten present the column densities corrected for this assumed dilution factor.
On inspection of the bulk of the rotation diagrams (available as an online supplement) we see a pattern emerge. The A-type transition has a consistently higher Nu/gu compared to a straight line fit through the E-type transitions. This indicates a greater abundance of A-type CH3OH and an A/E ratio > 1. Considering only sources in which all three E-type lines were detected (36 sources), and assuming equal excitation temperatures in A and E lines, we derive A/E abundance ratios ranging from 0.47 to 1.80, with a mean of 1.30. These values are comparable to values previously derived in the literature, e.g., Menten et al. (1988) who calculated A/E ratios between 1.3 and 2.0, using the same transitions, towards warm clumps in Orion KL.

N2H + optical depth and column density
Optical depths were derived from the blended hyperfine components of N2H + , which assume set ratios under optically thin conditions (see Section 3.1). Assuming the linewidths of the individual hyperfine components are all equal, the integrated intensities of the three blended groups should be in the ratio of 1 : 5 : 2 under optically thin conditions. The optical depth is calculated from the ratio of integrated intensities ( R TB dv) of any two groups using the following equation: where 'a' is the expected ratio of τ 2/τ 1 under optically thin conditions. Caselli et al. (1995) report anomalous excitation of the F1, F = 1, 0 → 1, 1 and 1, 2 → 1, 2 components (in our group-3), so we determine the optical depth solely from the intensity ratio of group-1/group-2. We find that 97 percent of sources have optical depths below 1. Figure 6 plots the distribution of the derived optical depths, which range from 0.035 to 2.43, with a mean of 0.35 and a standard-deviation of 0.42. Values for the optical depth towards individual sources are presented in column two of Table 9. Column densities of N2H + can be found from the following standard formula (Rohlfs & Wilson 2004), where Q(Tex) is the partition function, extrapolated from a fit to the values given by the (Pickett et al. 1998) spectral line catalogue: Equation 10 requires an estimate of the excitation temperature Tex.
Unfortunately, under optically thin conditions, the excitation temperature cannot be determined from the N2H + line profiles, so we assume a constant value of 10 K. For excitation temperatures of 5 K and 20 K the total column density should be multiplied by 0.8 and 1.6, respectively. Beam averaged column densities derived using Equation 10 are presented in column five of Table 9. In the literature, high-resolution maps show that N2H + traces the spatial extent of the dust closely (e.g. Pirogov et al. 2003). We have estimated the average FWHM of the dust emission for all sources observed by Hill et al. (2005) (see section 4.2) and use these values to correct for beam dilution. Total column densities corrected by a factor (θ dust /θ beam ) 2 are presented in column six of Table 9.

13 CO, HNC and HCN column density
The HNC, HCN and 13 CO profiles frequently display asymmetries which may indicate that they are optically thick in general. Lacking an estimate for both the excitation temperature and the optical depth we are unable to calculate reliable column densities.

Abundances
The relative abundance X between two species may be found directly from the ratio of their volume densities. Assuming both molecules occupy the same volume of space, this is simply equivalent to the ratio of their column densities.
If, however, one or both species subtend angles smaller than the beam, we must correct for their relative volume filling factor and Equation 12 becomes assuming spherically symmetric emission with characteristic sizes θ1 and θ2. For the single-position observations presented here, the volume filling factors are complete unknowns and constitute the greatest source of errors in the abundance. Additional errors stem from calibration of the brightness scale (∼ 30 per cent) and the pointing accuracy of the telescope (∼ 20 per cent). Abundances relative to H2 depend also on the assumptions made in calculating the gas mass from the 1.2-mm continuum emission and cannot be determined reliably.

LUMINOSITIES AND MASSES
The relationship between mass and luminosity provides clues to the star formation efficiency, stellar content and evolutionary state of the clumps. gas mass for the 55 clumps whose properties could be determined. The luminosity has been measured from a two-component greybody fit to the spectral energy distribution and is directly related to the stellar content of the clump. Sub-millimetre emission from assumed optically thin dust (Hill et al. 2005) has been used to derive the total gas-mass of the clumps. In the plot, the thick line marks the expected luminosity from a minimum number of stars of mass M * 100 M ⊙ , assuming Mgas ≡ Mstars. Cesaroni (2005) divide a sample of 21 known hot cores 4 into 'light' and 'heavy' categories, based on their position above or below this division. 'Light' cores have gas masses below ∼100 M ⊙ and fall above the thick line. Their high luminosity-to-mass ratio implies that the mass of their stellar content is greater than that of the gas. 'Heavy' cores have gas masses above ∼100 M ⊙ and fall below the thick line. The mass of their stellar content is comparable to, or less than, the mass of the gas. Cesaroni (2005) have interpreted the Lstars/Mgas ratio in the 'light' cores as suggesting only a single embedded massive star exists in these clumps. Conversely the 'heavy' clumps are likely to contain multiple massive stars which have formed in clustered mode. We do not find any 'light' cores in our sample. An alternative explanation for high Lstars/Mgas ratios in the 'light' sources might derive from the age of the star forming regions. A massive young stellar object at a late stage of evolution could be expected to have dispersed a large fraction of its molecular gas, through the action of stellar winds, intense UV-radiation and outflows from young OB stars. This would result in a decrease in the measured gas-mass without a corresponding decrease in the luminosity. In Figure 7 the points would move horizontally into the 'light' portion of the plot. We note that Cesaroni's light cores include Orion-KL, and IRAS 20126+4014, neither of which are believed to be at a late stage of evolution. Orion is the closest massive star forming region and is not clear if it is representative of massive star-forming regions in general. The mass of IRAS 20126+4014 (7 ± 3M⊙) has been measured assuming Keplerian rotation of a molecular disk ) and relates to the inner object only. On larger scales the gas-mass has been measured to be several hundred solar masses (e.g. Estalella et al. 1993), putting IRAS 20126+4014 in the 'heavy' category. We find that all of our maser selected sample have gas masses above ∼30 M ⊙ and all fall into the 'heavy' category. If the division between 'light' and 'heavy' cores is an indication of age, then all of our sample are at a relatively early stage of evolution, i.e., the powering massive young stellar objects have not yet dispersed their natal molecular clouds.
In Figure 7 the shaded region between the dashed lines represents the range of luminosities expected from the most massive star in a cluster where Mstars = Mgas, if the initial mass function (IMF) follows a Salpeter power law (α = 2.35) and assuming a fundamental upper stellar mass limit of M * = 150 M ⊙ (Weidner & Kroupa 2004). The luminosity of the cluster will be dominated by the most massive star so this is a good approximation to the expected total luminosity. The range in expected luminosities derives from the uncertainty in the mass-luminosity relation for massive young stellar objects. This may be represented by a power law of the form L * ∝ M γ * , where γ ranges between 3 and 4 in the literature for OB-stars (e.g., Lada 1999;Churchwell 2002). Our maser selected sample exhibit a rough correlation between mass and luminosity, which may be fit with a single power law with index γ = 0.68 ± 0.08. This is a much shallower rise than observed in evolved stars, however, the luminosities of the most massive clusters are consistent with the 150 M ⊙ stellar cutoff (Weidner & Kroupa 2004), even in the more conservative limit of L * ∝ M 3 * . The derived gas-mass is highly dependent on the temperature in Equation 2. The shallow power law might be explained if the average dust temperature increases with luminosity and this change is not reflected in the sparsely sampled greybody fits to the SED, from  which we take our temperature estimates. If we assume the mass estimates are correct to within a factor of a few, then the main result is that the lower mass clumps are over-luminous and the higher mass clumps are under-luminous.

UCHII regions: Luminosity or Age?
UCHII regions (triangles) are in general more luminous and more massive than the isolated masers (crosses) in the sample. Individual power law fits to the isolated masers and UCHII sub-samples yield mass-luminosity relations of L bol | masers ∝ M 0.59±0.13 and L bol | UCHII ∝ M 0.64±0.18 , respectively. These fits are consistent with the fit to the combined sample, within the errors, and a single power law can describe both distributions. Figure 7 (right) is a histogram of the Mgas/Lstars ratio for UCHII regions (top) and isolated masers (bottom). As expected from the mass-luminosity plot, the distributions are similar and a KS-test cannot distinguish between them, yielding a 76 per cent probability of the two sub-samples being drawn from the same population. This result implies that for the same masses, the two samples have the same luminosities. Early in the evolution of a massive young stellar object we would expect its luminosity to increase as it accretes matter and more mass is transfered from the envelope to the star. At the same time the overall mass of gas and dust in the clump is expected to remain relatively constant, or indeed decrease, as winds from the young OB-cluster break up the cloud. By this rationale, if our sample of UCHII regions are older and more evolved, we would expect them to have a lower Mgas/Lstars ratio than the isolated masers. There are several possible reasons why we do not see a difference between the mass-luminosity distributions. It is possible that systematic errors (which we discuss below) associated with our assumptions cause us to overestimate the mass of the clouds hosting the UCHII regions relative to the clouds hosting the isolated masers. For there to be no difference between the mean masses of the sub-samples, the isolated masers would need to have a dust temperature on average 36 K lower than the UCHII regions. Figure 8 (left) illustrates the distributions of T cold from the SED fits, for UCHII regions (top) and isolated masers (bottom). While the UCHII regions clearly have temperatures which are skewed to the high end, the difference in the means is only 4.3 K. The rotational temperatures calculated from CH3CN are likewise similar, however, we cannot rule out different average dust temperatures on the basis that CH3CN emission likely probes only the embedded 'hot core' and does not reflect the conditions in the extended clump. Thermal CH3OH emission is thought to derive from a more extended envelope and rotational temperatures calculated from this molecule appear to support very different temperatures in the two groups. Figure 8 (right) shows histograms of the CH3OH rotational temperature for the UCHII regions (top) and isolated masers (bottom). A KS-test returns a probability of 0.002 per cent of the distributions deriving from the same parent. We note that the mean values of 9.9 K for the UCHII regions and 6.1 K for the isolated masers do not reflect the kinetic temperature as the CH3OH is likely sub-thermally excited (see Goldsmith & Langer 1999).
As an alternate estimate of the mass we derived a 'LTE-mass' from the column density of N2H + . In our calculations we assume (i) the N2H + emission closely traces the 1.2-mm dust continuum and has a flat density distribution within the FWHM of the clump, (ii) a fixed [H2] / [N2H + ] abundance ratio of 1.7 × 10 −10 (Pirogov et al. 2003). The mass of gas may then be estimated from the column density using Equation 4. Figure 9 (left) is is a massluminosity plot similar to Figure 7, except that the mass plotted on the x-axis is the LTE-mass calculated from N2H + . Although the scatter is greater, we clearly see the masses of the UCHII regions and isolated masers are still weakly offset, with the UCHII regions having greater masses on average, as in Figure 7. The distributions of the Mgas/Lstars ratios are illustrated in Figure 9 (right). A KStest returns a probability of 50 per cent that both distributions are derived from the same parent, confirming the original result.
Another explanation for the offset in the masses derives from the sensitivity limit on the radio-survey. In the preceeding paper we assumed the UCHII regions were older and more evolved than the isolated masers. We argued that the original radio continuum survey was sensitive enough to detect UCHII regions associated with the less luminous isolated masers (see Paper 1). However, if a sensativity bias existed it would manifest as a mass and luminosity offset between the radio-loud and radio-quiet, i.e, the UCHII regions  Figure 7, except in this case the mass is the LTE-mass derived from the column density of N 2 H + assuming a fixed abundance ratio of 1.7 × 10 −10 and that the N 2 H + emission closely follows the spacial distribution of the 1.2-mm continuum emission.
would be more massive and more luminous than isolated masers. In other words, some of the lower Lstars isolated masers may indeed be associated with UCHII regions which fall below our detection limit. In Paper 1 we showed that most sources are luminous enough to have detectable UCHII regions, assuming up to 90 per cent of the Lyman continuum photons are absorbed by dust (Kurtz et al. 1994). If the disparity in luminosity is due to a real sensitivity limit, this would imply that, on average, at least 99 per cent of the ionising photons are absorbed by dust before contributing to the creation of a UCHII region. We believe this is unlikely in the majority of cases.
Some of the isolated maser sites may also be associated with hyper-compact HII (HCHII) regions. This recently discovered class of HII region is typically less than 0.01 pc across (Avalos et al. 2006) and exhibits a free-free emission spectrum with a turnover at higher frequencies than UCHII regions, typically 20 GHz. HCHII regions are expected to be optically thick at 8.6 GHz due to the squared dependace of the flux density with frequency and will be difficult to detect. Longmore et al. (2007) had used the Australia Telescope Compact Array to search for 22 GHz emission towards 24 of the objects presented here. Nine of these sources fall into the radio-quiet category and of these seven exhibit compact (30 → 3 ′′ ) continuum emission. This result strongly suggests that some of our radio quiet sources are associated with HCHII regions, or indeed UCHII regions undetected at 8.6 GHz. However, because HCHII regions are thought to be the precursors of UCHII regions, we are still be selecting for two different evolutionary states.
The most obvious explanation for the offset is due to the timescales on which we expect massive young stellar objects to progress to develop a detectable UCHII region. In essence, clumps containing very high mass objects will evolve very rapidly and will spend only a short time in hot core and earlier phases. Because of the short timescales involved, very massive hot cores will also likely be deeply embedded. The first indication of star-formation activity may be when the expanding HII region begins to disperse the surrounding molecular gas. Anecdotal evidence supporting this explanation is already emerging from uniform searches for MYSOs, such as the Red MSX Source (RMS) survey (Hoare et al. 2004, Mottram 2008). The less evolved MYSOs identified in the survey have a significantly smaller upper-mass-cutoff compared to the UCHII regions detected. No MYSO counterparts are found to the most massive UCHII regions, implying that the UCHII phase is the first indication of star-formation in the most massive clumps.
We believe differences between the radio-bright and radioquiet samples may be attributed to evolution, with the caveat that the highest luminosity objects do not spend significant time in an 'isolated maser' phase.

DETAILED COMPARISON BETWEEN SUB-SAMPLES
The aim of this molecular survey is to investigate the utility of molecular lines in the 3-mm band to act as 'molecular clocks'. In this section we consider the differences between sub-samples divided from the source list based on associations with tracers of potentially different evolutionary states.
In Paper 1 we examined the link between hot cores, 6.67 GHz CH3OH masers and UCHII regions. We found that CH3CN was brighter and more commonly detected towards masers associated with UCHII regions, than towards 'isolated' masers. Assymetries in the HCO + versus H 13 CO + line profiles were interpreted as inward (blue skewed) or outward (red skewed) gas motions. We also examined the associations with mid-infrared emission in the Midcourse Space Experiment (MSX) images and found 11 dark clouds (seen in absorption against the 8 µm Galactic background) and 67 in emission. Many of the sources also exhibited high velocity line wings, indicative of outflows. Based on these results we separate the source list into sub-samples based on the following criteria: • Presence or absence of radio emission from a UCHII region.
• Presence or absence of high velocity line-wings in HCO + , HNC or 13 CO.
• Presence or absence of blue-skewed HCO + line profiles, indicating infall.
In the following analysis we contrast the sub-samples by looking for differences in the median properties. A KS-test is used to assess the similarity of the two distributions and trends are found based Figure 10. The bars in this horizontal histogram represent the difference between the median values of two distributions, normalised to the standard deviation of the combined sample. Here, we compare spectral line luminosity in sources with and without UCHII regions. A positive value means the line is more luminous towards UCHII regions. To assess the significance of the differences, we compute the KS-statistic (left column) and associated percentage probability (right column). As a visual aid, the greyscale of the bars is scaled to the probability. Probabilities smaller than approximately two per cent (dark bars) indicate significant differences. Figure 11. Differences in the median linewidth, for sources with and without an associated UCHII region. The linewidths were measured in two ways: by fitting a Gaussian to the line profile and measuring the full-width at halfmaximum, or by integrating under the line and computing the equivalent width (HCN only). Other details are as in Figure 10.  on large differences in the median values, coupled with a low probability that the sub-populations are drawn from the same parent distribution.
Initially, we compare the spectral line luminosities calculated from the integrated line intensity multiplied by the square of the distance to the source. If the distance is well known then comparisons of line luminosities will potentially reveal intrinsic differences between the sub-samples. However, the error in the distance for this sample is relatively large (±0.65 kpc ≈ 20 per cent), and increases drastically towards Galactic longitudes < 5 • , where the model Galactic rotation curve begins to break down. Only the strongest trends will be seen using such a comparison.
We also compare the distance-independent linewidths. Linewidths in massive star forming regions are generally much greater than the thermal width and are indicators of the level of turbulence present in the gas. Turbulence arises from bulk motions of gas, is often associated with energetic phenomena, such as outflows, and is correlated with star formation activity (e.g. Dobbs et al. 2005).
The ratio of two spectral line intensities is unaffected by the distance and constitutes a much better probe of the physical and chemical conditions. The dominant errors are due to the relative accuracy with which the data has been calibrated and the unknown beam-filling factors. The results presented here are based on data taken over four years and the calibration error in the data has been determined to be better than 30 per cent in most cases. The uncertainty due to the beam filling factors is given by the ratio of the solid angles over which the two molecules emit, (Ω1/Ω2), and may be large for dense-gas tracers which subtend angles smaller than the beam. The trends underlying the data should still be visible given the sample size.
Ideally, in a search for molecular clocks the abundances should be compared directly. Unfortunately, the small number of transitions observed in this work make it difficult to constrain the column densities accurately. Two or more transitions of a single molecule are needed to solve for the optical depth, excitation temperature and column density. We have been able to determine the column densities of thermal CH3CN and CH3OH through the rotational diagram method, and by assuming an excitation temperature or [ 12 C] / [ 13 C] abundance ratio, we have calculated the column densities of N2H + and HCO + . Here we compare the beamaveraged column densities of these molecules directly to find the abundance ratios.
Lastly, we contrast the differences in a suite of measured physical parameters such as bolometric luminosity, gas-mass, rotational-temperature and mid-infrared flux density, drawn from this and other work.
The important differences are summarised in section 6.4. Figure 10 illustrates the difference in line luminosity between sources with and without 8 GHz radio continuum emission (from UCHII regions) in the Mopra beam: the radio-loud and radio-quiet sub-samples, respectively. As with CH3CN and HCO + in Paper 1, we find that the luminosity of the remaining transitions is enhanced towards the radio-loud sub-sample. The median line luminosity is greater by 0.65-σ, on average, where σ is the standard deviation of the combined sample. Thermal CH3OH stands out as having the most significantly different distribution and the largest difference in line-luminosity, followed by H 13 CO + , CH3CN, HNC and N2H + . We find the median linewidths of all species are broader to- Figure 14. Differences in other computed and measured parameters, for sources with and without an associated UCHII region.

Radio-loud versus radio-quiet sources
wards the radio-loud sub-sample (see Figure 11). CH3OH exhibits the greatest differences, closely followed by N2H + and H 13 CO + , all of which have statistically different distributions according to the KS-test. HCO + , HCN, HNC and CH3CN have broader lines on average, however the distributions are not significantly different. The differences in the median linewidth between the radio-loud and -quiet subsample range from 0.37 km s −1 to 1.62 km s −1 , greater than can be attributed to thermal broadening and most likely due to the greater turbulent energy in the gas associated with UCHII regions. The differences found between the linewidths and lineluminosities are echoed in a comparison of the raw integrated line intensities. Figure 12 shows the difference in the median values of the 28 intensity ratios between eight molecules. The median intensity of CH3OH and, to a lesser extent, CH3CN, are clearly enhanced with respect to all other molecules. Statistically, the most significant difference in intensity ratio occurs between CH3OH and other molecules, specifically N2H + and 13 CO. The [CH3CN/ 13 CO] and [H 13 CO + / 13 CO] ratios also stand out as being significantly greater towards the radio-loud sub-sample. Figure 13 illustrates a comparison of the median beamaveraged column densities of four molecules: CH3CN, CH3OH, HCO + and N2H + . Again, thermal CH3OH stands out as having greater a column density, and hence a higher abundance, towards the radio-loud sub-sample.    The median differences between other measured and calculated properties are shown in Figure 14. The median bolometric luminosity and median mass of the radio-loud sub-sample is significantly greater than for the isolated masers (see section 5). The rotational temperature derived from CH3CN is similar in both groups, however, the CH3OH rotational temperature is significantly greater in the radio-bright group (also see Figure 8).

Sources with and without CH3CN
CH3CN was detected towards 58 sources (70 per cent), however the detection rate towards the radio-loud sub-sample (19 sources) was 90 per cent. The enhanced luminosities and masses of our UCHII regions may bias the results of a comparison between CH3CN-bright and CH3CN-dark groups. We therefore exclude any regions with radio emission from the comparison. In practise, we find that the major results are robust to the presence of UCHII regions.
The differences in median line luminosity between the two groups presented in Figure 15 are not as pronounced as in the previous section, however, all lines are marginally (0.07-σ) more luminous towards the CH3CN-bright sub-sample. HCO + and HCN have the most significantly different distributions. We note that the HCO + and HCN profiles are affected by self absorption, with the CH3CN-bright group containing the most extreme examples. The significant difference in the HCO + luminosity is also not reflected in the optically thin H 13 CO + isotopomer, suggesting that an abundance difference is unlikely. The greatest difference in the median values occurs in 13 CO, followed by CH3OH and H 13 CO + .
Linewidths are also biased towards being greater in the sample with detected CH3CN (see Figure 16). HCO + exhibits the most significant difference, followed by CH3OH, although a KS-test cannot distinguish between the populations with confidence.
When we examine the line intensity ratios in Figure 17 a similar picture emerges to the case of the UCHII regions. Thermal CH3OH stands out, as its intensity relative to all other lines is enhanced in the CH3CN-bright sub-sample. We also see evidence for enhanced N2H + emission. In contrast, 13 CO emission is relatively weak towards the CH3CN-bright sub-sample. These ratios are highly suggestive of different environmental conditions in the dense gas, (traced by N2H + and CH3OH) compared to the more extended gas (traced by 13 CO), and correlate well with the line luminosities. Figure 18 shows the differences in the median column densities of CH3OH, HCO + and N2H + . Again, the thermal CH3OH column is seen to be significantly enhanced towards the CH3CN bright group, echoing the result from comparing the raw line ratios.
The difference in the median values of other derived parameters are displayed in Figure 20. Sources with detected CH3CN have significantly brighter thermal continuum emission at 1.2-mm wavelengths. This translates into a mean mass higher by ∼300 M ⊙ , omitting UCHII regions or ∼600 M ⊙ , including UCHII regions. Histograms of the mass distributions for the two groups are plotted in Figure 19 (left), and show significant differences. All other parameters presented in Figure 20 are similar for both sub-samples.
The division of the sample into populations with and without detected CH3CN may be a somewhat artificial distinction. While CH3CN emission may be present in more distant sources, it may fall below our 2-σ detection threshold of 80 mK. Emission over a small solid angle will suffer from high beam-dilution factors, further compounding the problem. The distributions of distance in the two samples, plotted in Figure 19 (right), are similar, except for a tail of more distant objects without CH3CN. This difference suggests that a small fraction of non-detections may be attributable to sensitivity limits.
We also split the sample via other criteria (see the introduction to this Section), however, the chemical and physical differences are not as significant. The results of these investigations are presented as an online supplement.

The effect of beam dilution
As mentioned in Section 4.6, the beam filling factors constitute an unknown source of error when comparing the intensities or column densities of two molecules. If both emitting regions subtend angles (θ) smaller than the beam, then we must correct for the relative volume filling factor, given by (θ1/θ2) 2 . Assuming the emitting regions have similar characteristic sizes in all sources, the relative beam filling factors will average to ∼ 1 over the entire sample. However, if one species generally fills the beam while the other species is generally beam-diluted (i.e., one has constant angular size while the other doesn't, then we would expect a 1/distance 2 dependence in the line intensity ratios). Figure 21 presents two plots of line intensity ratio versus distance. The left panel plots the CH3CN/CH3OH ratio versus distance. The emission from both molecules is expected to derive from regions smaller than the 36 ′′ Mopra beam, even for nearby sources. We see the line-ratios are not correlated with distance, consistent with a constant ratio between the angular sizes of the species. The right panel plots the CH3CN/N2H + ratio versus distance. Assuming N2H + emission closely follows the dust morphology (e.g., Pirogov et al. 2003), we have shown in Table 9 that the beamdilution factor is generally close to 1. In Figure 21  source is moved further away. We see the scatter in measured lineratio increases with distance making it difficult to interpret the data and, in addition to beam dilution, chemical and physical differences in the sources affect the line intensity ratios. Omitting the UCHII regions (squares) and considering only isolated masers (crosses), we see a possible trend towards decreasing CH3CN/N2H + ratio with increasing distance. This trend does not approach the 1/distance 2 dependence expected, but it may indicate that some of our comparisons will include beam dilution effects for CH3CN.

Interpretation and discussion
It is clear we are seeing significant differences between sources associated with different tracers. In this section we summarise the differences between the sub-samples and suggest some possible interpretations of the results.

UCHII regions vs isolated masers
The clearest distinctions exist between isolated CH3OH masers and those with UCHII regions. The result found in Paper 1, where the CH3CN and HCO + lines were shown to be more luminous and have greater linewidths in the presence of a UCHII region, has been extended to the other observed species. When we examine the raw line intensity ratios, thermal CH3OH distinguishes itself as being relatively intense towards the radio loud sources. This is reflected in both the higher median column density and CH3OH rotational temperature. We interpret this result as evidence for an enhanced abundance of CH3OH in relatively warm gas nearby the UCHII regions. Significant differences are also found between other tracers of high and low density gas. The [CH3CN/ 13 CO], [N2H + / 13 CO] and [H 13 CO + / 13 CO] ratios are enhanced in the radio-loud subsample, possibly indicating different excitation conditions or abundances in the 'core' compared to the 'envelope' gas. Interestingly, when compared to all other lines, the relative brightness of the hotcore tracer CH3CN is not significantly greater, yet we detect it towards 95 per cent of UCHII regions and only 63 per cent of the isolated masers.
A potential explanation for the median offset in lineluminosity and linewidths between the radio -quiet and -loud samples may be found in the significantly greater bolometric luminosity and gas-mass of the radio-loud sample. Simply put, more luminous clumps will likely have a greater flux of IR-photons and higher gas temperatures. Under these conditions one would expect to see more luminous spectral lines. Linewidth is commonly used as a proxy for star formation activity, and hence evolutionary state, as it is largely dependent on turbulence in massive star forming regions. However, on the scale of molecular clouds (3-20 pc) the linewidth has also been empirically correlated with the cloud mass (Solomon et al. 1987), possibly due to multiple (sub)-clumps with different velocities within the beam. It is unclear which effect dominates in our sample. Figure 22 plots the linewidth N2H + versus the gas-mass. N2H + is chosen as it is optically thin and has been shown to trace the dense regions of the molecular clouds (e.g., . A weak correlation is observed which may account for some of the linewidth differences between the groups, however we cannot rule out an evolutionary effect. That the relative intensity and abundance of CH3OH is greater towards the radio-loud sources likely reflects real chemical differences between the sub-samples. This may be interpreted as evidence for the more advanced evolutionary state of the radio-loud sample. The CH3OH abundance is predicted to be enhanced by a number of mechanisms as a massive young stellar object evolves. In the hot-core phase it is known to be evaporated from the dust grains as the heating source evolves (Charnley et al. 1995). The abundance of CH3OH is also predicted to be enhanced in the walls of outflow cavities, where it is sputtered from the grains by lowvelocity shocks (Hogerheijde 2005).

CH3CN-bright vs CH3CN-dark
In this and the remaining comparisons we removed the radio-loud sources from the list, as their higher intrinsic luminosities may bias the results. We find sources with detected CH3CN are also biased towards having greater line-luminosities and linewidths, although these differences are not as pronounced as with the radio-loud versus radio-quiet division. The most striking result is the significant tendency for thermal CH3OH to be brighter and have a greater column-density in the CH3CN bright group. This is not unexpected as the CH3CN and CH3OH abundances are predicted to increase with time in hot cores (Charnley et al. 1995). We also see evidence for more turbulent and energetic conditions in the dense gas (traced by N2H + and CH3OH) compared to more extended and diffuse gas (traced by 13 CO), implying a more advanced evolutionary state in the CH3CN-bright sub-sample. Interestingly, the CH3CN-bright sub-sample also has a significantly greater median mass, which may bias this result. CH3CN is also not detected in sources with distances greater than 10 kpc, suggesting that a small number of sources may contain CH3CN below the sensitivity limit of our survey.

MSX-bright vs MSX-dark
All species in the MSX-dark sample have marginally greater lineluminosities and linewidths compared to their MSX-bright counterparts, with the 13 CO linewidth being especially notable. This is unexpected, as infrared dark clouds have been postulated to be the young and quiescent precursors to hot cores and UCHII regions (Rathborne et al. 2006). HCO + and CH3OH tend to be brighter and CH3OH marginally more abundant in the MSX-dark sub-sample, although this is not judged to be significant. Other parameters are similar in both sub-samples. Given the small number of sources in the MSX-bright subsample (9 -11 sources), none of the observed differences are large enough to draw any definite conclusions from the data.

Line-wings vs no line-wings
There are no significant differences between the median lineluminosities when the sources are divided into sub-samples with and without high-velocity line-wings. Differences between the HCO + linewidth distributions can be attributed to unidentified lowvelocity linewings. 13 CO is significantly brighter (relative to other lines) in the sources without linewings and CH3CN is biased towards being brighter and more abundant in the sub-sample with linewings. No distinguishing differences are seen in the physical parameters or IR-colour ratios.

Infall profiles vs no infall profiles
The properties of sources with and without HCO + 'infall-profiles' are close to identical. Little difference is seen between the median line-luminosities, linewidths or line intensity ratios. Biases in the H 13 CO + and HCO + line ratios can be attributed to selection effects.
The online material contains additional discusion and figures pertaining to the previous three paragraphs.

Further discussion
Is the mass of the hot core related to the dust mass? Figure 23 shows a plot of CH3CN beam averaged column density versus mass of gas derived from 1.2-mm continuum emission. A clear positive correlation is seen between the two. If we assume the column of CH3CN is a proxy for the mass of the hot core, then it follows that the mass of the hot core increases with the mass of the extended clump. The relationship is well fit by MCH 3 CN ∝ M 0.5 dust and assuming the density is constant within the gas, this implies that M hot core ∝ M 0.5 dust . This is consistent with the results of Cesaroni (2005) who found that the hot core is an continuation of the clump, and there is no break in the approximately 1/r 2 density power law. Rather, the hot core is differentiated by temperature and excitation conditions influenced by the central heating source.
(ii) H2 volume densities have also been estimated from the surface brightness and extent of 1.2-mm emission. The mean value is 5 × 10 4 cm −3 , however, we note that the assumptions inherent in the calculation introduce large unknown uncertainties in values for individual sources.
(iii) Rotational temperatures derived from CH3OH range from 3.0 K to 14.0 K, with a mean value of 6.67 K. These anomalously low temperatures strongly suggest that the CH3OH is subthermally excited. Assuming a common excitation temperature, we find the abundance ratio of A to E-type CH3OH ranges from 0.5 to 2.8, with a mean of 1.5, consistent with previously published values.
(iv) N2H + is found to be optically thin towards most of the sample. Likewise the CH3OH rotational diagrams are consistent with low optical depths in the J = 2 -1 transitions. 13 CO, HCN and HNC all exhibit line profile asymmetries and may be significantly optically thick.
(v) The luminosity/gas-mass relationship for the sample is found to follow a rough power law of the form L∝ M 0.68 , meaning that the lower mass clumps are over-luminous and the higher mass clumps are under-luminous. We find that the gas-mass of the clumps is comparable to or greater than the mass of the stellar content (implied by the luminosity). We interpret this as an indicator of young ages, as the newborn massive stars still retain their natal molecular clouds.
(vi) The radio loud sub-sample (UCHII regions) is on average more massive and more luminous than the radio-quiet sub-sample (isolated masers). We argue that the the most likely explanation for this disparity is due to the comparatively rapid timescale over which the most massive objects evolve into HII regions. The first significant tracer of star-formation in these objects may be radiocontinuum emission from a HCHII or UCHII region. It is also possible that some of the isolated maser sample contains hyper-compact HII regions which are too optically thick to detect at 8 GHz. In either case there is a clear age difference between the subsamples.
(vii) We separated the source list into sub-samples associated with different tracers of evolution and compared their median physical and chemical properties. Our findings are as follows: • All spectral lines are brighter and more luminous towards the radio loud sample, extending the result found in Paper 1.
• The thermal CH3OH brightness and abundance is found to be enhanced (compared to other species) in radio-loud and CH3CN-bright sources. We suggest that in single-dish observations thermal CH3OH may be used as a crude molecular clock to indicate the evolutionary state of a clump.
• Given the small sample size, conclusions drawn from a comparison of MSX-bright and MSX-dark sources are not significant. It is worth noting, however, that linewidths and lineluminosities are generally greater in the infrared dark clouds, indicating perhaps that when selected using CH3OH masers, darkclouds conceal objects at later stages of evolution.
• We divided the source list into sub-samples with and without high velocity linewings and HCO + -infall-profiles, but found no significant differences in chemical or physical properties.
(viii) We find that the beam-averaged CH3CN column density is correlated with the gas-mass derived from 1.2-mm emission. This suggests that the mass of the hot-core is dependent on the mass of the clump in which it is embedded. quantum numbers. β J→J ′ quantum numbers. γ J F → J ′ F ′ quantum numbers. κ Energies of the upper levels relative to the J K = 1 −1 level for E-type CH 3 OH, and relative to the J K = 0 0 level for A-type CH 3 OH.  Walsh et al. (1997) originally detected a 6.67 GHz methanol towards G10.10-0.72. Subsequent observations (S. Ellingsen, private communication) have failed to detect the maser emission, hence we discard the source from ours sample in the remainder of this work.