The methanol emission in the J₁– J₀ A⁻⁺ line series as a tracer of specific physical conditions in high-mass star-forming regions

ABSTRACT

We present results of the investigations of the properties of the methanol J₁ –J₀ A⁻⁺ line series motivated by the recent serendipitous detection of the maser emission in the 14₁ – 14₀ A⁻⁺ line at 349 GHz in S255IR-SMA1 soon after the accretion burst. The study includes further observations of several lines of this series in S255IR with the SMA, a mini-survey of methanol lines in the 0.8-mm range towards a sample of bright 6.7-GHz methanol maser sources with the IRAM 30-m telescope, and theoretical modelling. We found that the maser component of the 14₁ – 14₀ A⁻⁺ line in S255IR decayed by more than order of magnitude in comparison with that in 2016. No clear sign of maser emission is observed in other lines of this series in the SMA observations except the 7₁ – 7₀ A⁻⁺ line where an additional bright component is detected at the velocity of the maser emission observed earlier in the 14₁ – 14₀ A⁻⁺ line. Our LVG model constrains the ranges of the physical parameters that match the observed emission intensities. No obvious maser emission in the J₁ – J₀ A⁻⁺ lines was detected in the mini-survey of the 6.7-GHz methanol maser sources, though one component in NGC 7538 may represent a weak maser. In general, the maser effect in the J₁ – J₀ A⁻⁺ lines may serve as a tracer of rather hot environments and in particular luminosity flaring events during high-mass star formation.

1 INTRODUCTION

Methanol, CH₃OH, is an important component of the interstellar gas in regions of star formation. Methanol is known as a good tracer of the physical conditions of the molecular gas in high-mass star-forming regions (Sutton et al. 2004; Cragg, Sobolev & Godfrey 2005; Salii & Sobolev 2006). Due to its molecular structural properties, CH₃OH has a rich radio spectrum. The intensities and their ratios for the lines produced in different series of transitions depend on the physical conditions in molecular clouds and can be used for the estimations of the physical parameters (Sobolev 1992; Salii, Sobolev & Kalinina 2002; Salii & Sobolev 2006; Voronkov et al. 2006; Leurini et al. 2004, 2007). Under certain physical conditions in high-mass star-forming regions, a maser amplification can occur. Analysis of observational data has shown that there are two classes of methanol masers, Class I and Class II, which emit in different transition sets (Menten 1991a). Class II methanol masers reside closer to young stellar objects (YSOs) and trace circumstellar discs and inner parts of the outflows, while Class I masers are associated with more distant parts of the outflows and shocked regions (Sobolev et al. 2007).

Many methanol masering transitions have been observed. More than 20 Class I methanol maser lines (Ladeyschikov, Bayandina & Sobolev 2019, and the references therein) are observed nowadays. Nearly 30 among about 100 theoretically predicted Class II methanol maser transitions (Cragg et al. 2005) are listed as observed in the data base MaserDB.¹ New maser transitions are still getting discovered, e.g. 22 new Class II methanol masers were discovered in G358.931−0.030 in 2019 (Breen et al. 2019; Brogan et al. 2019; MacLeod et al. 2019). It is noteworthy that only five of those were listed as bright masers in the theoretical models (Cragg et al. 2005). Furthermore, a very bright line, ∼4000 K (∼6 Jy beam⁻¹ with the 0.10 × 0.15 arcsec² beam) at 349.1 GHz, detected in the high-mass star-forming region S255IR in 2016 with ALMA, was identified as the CH₃OH 14₁ – 14₀ A⁻⁺ transition and was qualitatively classified as an unpredicted Class II maser (Zinchenko et al. 2017). Remarkably, the transition mentioned above has never been observed or predicted to be masering (Sobolev, Cragg & Godfrey 1997; Cragg et al. 2005; Voronkov et al. 2012).

The maser emission in the 14₁ – 14₀ A⁻⁺ line was detected in S255IR SMA1 about 1 yr after the accretion burst event seen in the IR band by Caratti O Garatti et al. (2017). Subsequent observations in 2017 showed a significant (by about 40 per cent) decay of this maser line, in about the same amount as the decay of the submillimeter continuum emission (Liu et al. 2018). These data indicate that this maser emission can be related to the luminosity bursts during the process of high-mass star formation and raise the questions such as whether it can be observed in the other lines of this series, how frequent this phenomenon is in similar objects, and which physical conditions are required for the excitation of such masers.

In order to answer these questions, we performed further observations of S255IR in several methanol lines of the J₁– J₀ A⁻⁺ series at a high angular resolution and conducted a survey towards a sample of well-known strong Class II methanol maser sources in the 349-GHz line and simultaneously in several transitions of the same series. The state of activity of associated young stellar objects was checked by the 6.7-GHz methanol maser monitoring. Then, we performed theoretical modelling of the excitation of the corresponding transitions. The results are presented below.

2 OBSERVATIONS

2.1 S255IR SMA observations

The observations towards S255IR were carried out with the SMA on 2019 March 21 with the array in its extended configuration. The phase centre was set at J2000 |${\rm RA}= 06^{\rm h} 12^{\rm m} 54{{_{.}^{\rm s}}}015$| and Dec. = 17^○59′23|${_{.}^{\prime\prime}}$|05. The dual receiver observing mode was employed with the 345-GHz receiver centred at 302.97- and 400-GHz receiver centred at 353.86 GHz. The half-power width of the SMA primary beam is about 36 arcsec at 345 GHz.

The SWARM (SMA Wideband Astronomical ROACH2 Machine) correlator enabled a simultaneous spectral coverage of 32 GHz in total (290.97–298.97, 306.97–314.97, 341.86–349.86, and 357.86–365.86 GHz) and an uniform spectral resolution for all bands at a channel width of 140 kHz. The combination of the dual frequency setup and the back-end correlator allowed us to cover six methanol J₁ – J₀ A⁻⁺ transitions as listed in Table 1. 3C 279 served as the bandpass calibrator and asteroid Pallas was used for the absolute flux calibration (with its flux ranging from 1.88 Jy at 295 GHz to 2.7 Jy at 360 GHz). The nearby compact radio sources 0854+201 (∼2.0 Jy) and 0510+180 (∼1.8 Jy) were employed as the complex gain calibrators. Typical absolute flux density is estimated to have an uncertainty of ∼20 per cent.

We calibrated the data using the mir package (Scoville et al. 1993) and imaged the data using the miriad software (Sault, Teuben & Wright 1995). The projected baselines range from about 30 to 210 m, leading to an angular resolution of ∼1.0 × 0.8 arcsec² at 307 GHz and ∼0.9 × 0.6 arcsec² at 349 GHz under robust weighting. The resulting molecular line brightness sensitivity is 0.2 Jy beam⁻¹ or equivalently ∼3 K for a spectral resolution of 0.25 km s⁻¹.

2.2 IRAM 30-m observations

A total of 15 brightest 6.7-GHz Class II methanol maser sources were selected for our survey observations, which were performed with the 30-m IRAM radio telescope in 2019 January (see Table 2). We selected the objects with their flux densities at 6.7-GHz F > 1000 Jy according to the data base of astrophysical masers (MaserDb)² and at sufficiently high elevation at the 30-m IRAM site.

The observations were performed in the wobbler switching mode using the EMIR receiver in four frequency bands: 326.7–330.7, 329.5–334.5, 342.4–346.4, and 346.1–350.2 GHz. At these frequencies, the antenna HPBW and the spectral resolution are 7.5 arcsec and ∼1.4 km s⁻¹, respectively. The 1σ rms for different sources varied from 0.05 to 0.5 K in the 326.7–330.7 band and from 0.02 to 0.05 K in other bands.

The antenna temperature calibration was made by the standard chopper-wheel method. The data reduction was performed with the gildas package.³

2.3 Observations at the RT-32 of the Ventspils International Radio Astronomy Centre

At about the same time in 2019 January, a majority (six out of seven) of the sources with declination greater than 14° (see Table 2) were observed at the Ventspils International Radio Astronomy Centre at 6.7 GHz using the Irbene 32-m fully steerable radio telescope RT-32 with a cryogenic receiver at 6.7 GHz.  The Rohde & Swartz FSW43 spectrometer was used as the back-end to collect the spectral data. Standard frequency switch was used (Wilson, Rohlfs & Hüttemeister 2009) with 30-s-long switching steps and 30-min total on-source time. The back-end was configured to 2-MHz band with 4096 channels.

3 RESULTS

3.1 Methanol line emission in S255IR observed with SMA

The SMA data include the methanol lines of the J₁ – J₀ A⁻⁺ series with J = 4–7, 13, 14. In Fig. 1, we present in the upper image a superposition of spectra of these lines integrated over a circle of 3 arcsec in diameter. The signal-to-noise ratio in these data exceeds 100, which is good enough for a detailed study of the line profiles.

Five spectra out of six are reasonably well fitted by a single Gaussian with a peak at about 5 ± 0.05 km s⁻¹ (see the bottom panels of Fig. 1), which corresponds to the systemic velocity of the core (Zinchenko et al. 2015; Liu et al. 2020). The amplitude of this component is comparable for all transitions under consideration. The full width at half-maximum (FWHM) of this Gaussian is about 6 km s⁻¹ (with the uncertainties ∼0.1 km s⁻¹).

Clearly in the lines with J = 7 and possibly in those with J = 6, an additional peak at about 2.5 km s⁻¹ can be distinguished. We fitted this additional component by a Gaussian with a central velocity of 2.8 ± 0.1 km s⁻¹ and FWHM of 3.0 ± 0.1 km s⁻¹. It coincides with the maser feature reported by Zinchenko et al. (2017). The flux density of this component is 5.8 ± 0.2 Jy, whereas it is practically absent in the other lines of this series (see Fig. 1). We could not find any reasonable identification for this component with lines of other molecules.

Remarkably, the additional component is not detected confidently in the methanol 14₁ – 14₀ A⁻⁺ line at 349.1 GHz in the present observations. The amplitude of such component in this line is not more than ∼1 Jy, which is about 20 times weaker than that in 2016.

In Fig. 2, we present the first-moment map in the 2.8 km s⁻¹ component, obtained after the subtraction of the ‘main’ Gaussian component observed in all other lines. This map is overlaid with contours of the 0.9-mm continuum emission measured with ALMA (Zinchenko et al. 2017; Liu et al. 2018, 2020). It is important to note that the angular resolution of the ALMA observations was several times higher than in the SMA observations. The plot shows a clear velocity gradient the similar to that observed in the 14₁ – 14₀ A⁻⁺ maser line in 2016 (Zinchenko et al. 2017) and other lines in this object (Liu et al. 2020). Therefore, the probable maser emission arises in an extended region in the rotating disc-like structure around the protostar.

3.2 Methanol line emission observed with IRAM 30 m

According to Splatalogue⁴ there are about 80 methanol transitions with the excitation energy of the upper level <1000 K and the Einstein coefficient A_E > 10⁻⁹ s⁻¹ in the observed frequency bands. Three lines from the J₁ – J₀ A⁻⁺ series with J = 11, 13, and 14 are among them. One of the transitions is predicted as Class II methanol maser (at 330.793 GHz; Cragg et al. 2005), and a number of transitions are torsional exited (v_t = 1, 2).

No more than 20 methanol transitions were detected even towards the most line-rich sources such as G049.489−0.387, G111.542+0.776, and G192.600−0.048 with a confident signal-to-noise ratio, |${\rm S/N}\gtrsim5$| (Table 3). Methanol transitions that are blended with lines of others molecules were excluded from this list, since we could not conclude anything about the presence of their emission.

It is worth noting that only the lines of the J₁ – J₀ A⁻⁺ series and the line blend 5₄ – 6₃ A^{−−, + +} are detected in all sources. The brightest non-blending lines that are visible in 13 out of the 15 sources are presented in Fig. 3.

As can be seen in Fig. 3, towards most of the sources observed at 0.8 mm, the methanol line emission appears within the same velocity intervals as the Class II methanol maser at 6.7 GHz. However, no obvious bright maser effect is registered in any source in the sample. All observed methanol lines are rather broad (with their line widths ranging from 3 to 10 km s⁻¹). It is noteworthy that the lines of the J₁ – J₀ A⁻⁺ series are the brightest lines everywhere. This is most clearly seen in Fig. 4 (upper histogram), which shows the ratio of the intensities of all observed lines in the each of considered sources to the brightest line from the series J₁ – J₀ A⁻⁺ with J = 11 at 331.502 GHz. Only the line at 326.961 GHz (⁠|$10_{-1}-9_0\, E$|⁠) in the sources G049.489−0.387, G081.871+0.780, and G109.870+2.114 has higher intensities. This transition belongs to the |$J_{-1}-J-1_0\, E$| series and is considered as a Class I methanol maser candidate (Voronkov et al. 2012). In the sources G111.542+0.776 and G133.947+1.064, the intensities of this line are comparable with the intensities of the 11₁ – 11₀ A⁻⁺ line, and for other sources, we cannot say anything about the intensity of the |$10_{-1}-9_0\, E$| line due to large noise in the corresponding part of the band. We also note that we do not include in the histograms the lines at 346.202 and 346.204 GHz (5₄ – 6₃A⁻⁻ and 5₄ – 6₃A⁺⁺), since they are blended in all sources and we could not separate them correctly. As it can be seen in the lower histogram of Fig. 4, where the FWHM relations are presented, the lines of the series are broader then other methanol lines for all sources.

In some sources, one can see additional spectral components out of the range of the 6.7-GHz emission. For instance, in the source G133.947+1.064, an extra emission at ∼−50 km s⁻¹. The most notable spectral component in some methanol line emission out of 6.7-GHz emission ranges is seen in the G109.870+2.114 (Cep A). A significant differences between the line profiles of the J₁– J₀ A⁻⁺ series and other methanol lines are detected in the source G111.542+0.776 (NGC 7538C) spectra.

In G192.600−0.048, an enhanced emission at velocity about 3 km s⁻¹ in the 11₁ – 11₀ A⁻⁺ transition at 331.5 GHz can be seen. This emission is marginally noticeable in the spectrum of the 13₁ – 13₀ A⁻⁺ line (Fig 3).

This method can be applied only for the sets of transitions with thermal excitation. Thus, the transitions suspected in anomalous excitation were excluded from the consideration. They are the transitions from the J₁– J₀ A⁻⁺ series, the transition at 330.793 GHz, which are assumed to be Class II methanol maser, the transition at 326.961 GHz, which are assumed to be Class I methanol maser, and the transition at 334.426 GHz, which is a torsional excited transition. Blended lines at 346.202 and 346.204 GHz were also excluded. Moreover, only those lines with an S/N ratio greater than 3 were considered.

According to the rotational diagrams shown in Fig. 5, we found rotational temperatures, T_rot, ranging from ∼70 to ∼390 K, and methanol column densities, |$N_{\rm CH_3OH}$|⁠, ranging from 2 × 10¹⁵ to 10¹⁷ cm⁻² for the sources under consideration.

3.3 6.7-GHz masers observed with RT-32

The maser emission at 6.7 GHz observed with RT-32, Irbene, for all six sources has about the same velocity intervals that were presented in Hu et al. (2016). Some differences in the velocities of the main components may be related to the masers variability. Remarkably, for all 6 sources observed simultaneously both with RT-32 and with IRAM 30 m, the velocity of the brightest component at 6.7 GHz does not coincide exactly with the peak velocity of other methanol lines.

We note that the observations on 2019 January 9–10 are a part of the long-term monitoring program of these sources with RT-32. Based on those results, we can conclude that about 2 yr before and about 2 yr later the 2019 January observations, no strong variations of the 6.7-GHz maser emission were recorded (see an example in Fig. 6).

4 MODELLING METHANOL EMISSION

4.1 Methods of analysis

To interpret the observed brightness temperatures of the methanol lines, we resort to the data base compiled by Salii, Parfenov & Sobolev (2018), which tabulates the population numbers for quantum energy levels of methanol of ground and torsionally excited levels with v_t up to 2. To evaluate the population numbers for the quantum energy levels the large velocity gradient (LVG) approach was employed over a five-dimensional grid of physical parameters, which include the gas kinetic temperature (T_k, K), the hydrogen number density (⁠|$n_{\rm H_2}$|⁠, cm⁻³), the methanol specific column density (⁠|$N_{\rm CH_3OH}/\Delta V$|⁠, cm⁻³s), the methanol relative abundance (⁠|$N_{\rm CH_3OH}/N_{\rm H_2}$|⁠) and the line width (ΔV km s⁻¹). Dust emission and absorption within the emission region were taken into account in the way described in Sutton et al. (2004). It is assumed that the dust particles are intermixed with gas homogeneously and have the same physical temperature. Details of the LVG calculation can be found in Zinchenko et al. (2015) and Kirsanova et al. (2021).

Parameters in the data base are varied in the ranges from 10 to 600 K for T_k, from 3.0 to 9.0 for |$\lg (n_{\rm H_2})$|⁠, from 7.5 to 14.0 for |$\lg (N_{\rm CH_3OH}/\Delta V)$|⁠, from −9.0 to −5.5 for |$\lg (N_{\rm CH_3OH}/N_{\rm H_2})$|⁠, and finally at 1, 3, 5 km s⁻¹for ΔV. A beam filling factor for the methanol emission (⁠|$f = 10-100{{\ \rm per\ cent}}$|⁠) was included as an additional parameter in the methanol line intensity analysis. Since the line width is about 3 km s⁻¹in the sources under consideration, this value was fixed for all models here.

4.2 Emission in the J₁ – J₀ A⁻⁺ line series observed with the SMA in the S255IR

As mentioned above, six lines from the J₁ – J₀ A⁻⁺ series were observed with the SMA in S255IR. We attempted to find the physical conditions under which all these lines can be fitted sufficiently well not more than 3σ rms by a single component but could not find any set of parameters that provides such a fit. Intensities of the lines with J = 6 and 7 are underestimated in the models while those of the J = 4, 5, 13, 14 lines have been fitted reasonably well.

To find the conditions under which the lines with J = 7 is the brightest in the series, we study the dependence of the modelled peak brightness of the lines of the series on physical parameters. We used a fiducial model with parameters T_k = 160 K, |$\lg (N_{\rm CH_3OH}/\Delta V) = 11.5$|⁠, |$\lg (n_{{\rm H}_2} = 6.5$|⁠, |$N_{\rm CH_3OH}/N_{{\rm H}_2} = 10^{-6.5}, \Delta V = 3$| km s⁻¹, |$f=100{{\ \rm per\ cent}}$|⁠. These values are consistent with the best-fitting model for a set where transition with J = 7 was excluded from analyses. Varying parameters of the fiducial model one at a time we investigated dependence of the brightness temperature (T_br) of the lines on the parameters of the model. It can be seen from Fig. 7 that, with increasing temperature, the brightness maximum shifts towards transitions with higher J numbers.

Some dependence of the J number of the brightest line on the methanol specific column density and fractional abundance does exist. We have found that the J number of the brightest line does not change with variation of the number density in our models. This indicates that radiative processes play a major role in the excitation of the transitions of the J₁– J₀ A⁻⁺ series. This resembles Class II methanol maser excitation, which is predominantly radiative.

4.3 Conditions for maser emission in the J₁ – J₀ A⁻⁺ line series

Since we found in the spectral profile of the 7₁ – 7₀A⁻⁺ line at 314.860 GHz, a feature that is similar to the one detected by Zinchenko et al. (2017) and we could not explain it in the simple LVG model without beaming and other properties characteristic of the bright masers, we confined ourselves to qualitative exploration of possibilities for the maser amplification in the transitions of the J₁ – J₀ A⁻⁺ series. Consequently, we searched for conditions at which an inversion in the population numbers of transitions occurs.

There is a number of models where the level populations of the J₁ – J₀ A⁻⁺ series transitions are inverted in our calculations. Using the data base (Salii et al. 2018), we found out models with τ < −0.01 and <−0.1 (where maser amplification exceeds 1 and 10 per cent for transitions with the highest inversion in the series) for 19 transitions of the series (Table 4).

Transitions of the J₁ – J₀ A⁻⁺ series could be inverted with gas kinetic temperatures from 110 to 600 K (the upper edge of the gas kinetic temperatures in our data base). Methanol specific column density varies from 2.5 × 10⁸ to 5 × 10¹¹ cm⁻³s. The methanol abundances should exceed 10⁻⁷. Remarkably, there are no constraints on the hydrogen number density within the range of the data base. This is consistent with the classification of the masers in this series as Class II (as suggested in Zinchenko et al. 2017), which are characterized by radiative excitation.

According to Cragg et al. (2005), different maser lines series have different sensitivity to physical parameters. In our model for the Class II maser at 6.7 GHz, an inversion with τ < −1 occurs with gas kinetic temperatures from 40 to 90 K, methanol specific column density >10¹¹ cm⁻³s, methanol abundances ≥3 × 10⁻⁷, and hydrogen number density <4 × 10⁶ cm⁻³.

Within the scope of this paper, we provide only qualitative explanation of the maser occurrence in the transitions of the J₁ – J₀ A⁻⁺ series. However, we can mention directions in which the quantitative explanation of this maser phenomenon can be sought for. These are, first of all, computations within much more elaborated model that takes into account the differences in the temperatures of the pumping emission and the gas temperature within the maser sources, both of which are very important for the pumping of the Class II methanol masers (Sobolev & Deguchi 1994a; Cragg et al. 2005). Another point that has to be taken into account for explaining the maser intensities is the maser beaming effect that greatly affects methanol maser intensities and their ratios (Sobolev & Parfenov 2018).

However, we have to mention this can be not enough because available models did not show considerable maser emission in the J₁ – J₀ A⁻⁺ series. This is probably related to insufficient number of the methanol energy levels in the model computations, which is very important for the maser modelling or some simplifications in the available modelling (Sobolev & Gray 2012).

Taking into account this high complexity of the quantitative modelling of the masers in the J₁– J₀ A⁻⁺ series of transitions, in this paper, we are sticking to the qualitative analysis of this maser phenomenon.

4.4 Estimation of the physical condition in the sample sources

In the rotational diagrams (Fig. 5), one can see rather large deviations from LTE for most of the sources. Thus, we use the LVG approximation for estimating the physical parameters of the sources under consideration. For most of the sources, the values of T_obs obtained from the single Gaussian fitting were used. For G109.870+2.114, two Gaussian fitting was used since there are two clearly distinguished spectral components in the methanol spectra. Moreover, for G111.542+0.776, we computed the parameters both by one Gaussian fitting and two Gaussian fitting as will be discussed in Section 5.2.2. Using the methanol line intensities we estimated the physical parameters corresponding to the χ² minimum and their 68 per cent confidence intervals. We present the results in Tab. 5. The same set of the 11 brightest transitions was used in the analysis for all sources apart from the components G111.542+0.776 (−56.4 km s⁻¹) and G111.542+0.776 (−59.0 km s⁻¹). For them, we used all 16 detected lines. The line width value of 3 km s⁻¹for all sources under consideration was fixed in all models. For all sources, we made sure that the intensities of unregistered lines do not exceed 1σ.

5 DISCUSSION

5.1 Methanol emission in G192.600–0.048 by SMA observations

G192.600−0.048 (S255IR) is the first and so far the only source where the maser emission in the line belonging to the J₁ – J₀ A⁻⁺ line series has been detected (Zinchenko et al. 2017). This maser line was discovered in high angular resolution observations with ALMA in 2016 when it had the peak flux density of about 25 Jy. In the later ALMA observations in 2017, its peak flux density decayed by about 40 per cent (Liu et al. 2018). Substantial velocity gradient in the line emission was observed. As a result, the line spectrum of the brightest position in high resolution observations peaks at a velocity of about 2.3 km s⁻¹, while the spectrum of the line emission integrated over the whole emitting region with the size comparable to SMA beam peaks at a different velocity of ∼4 km s⁻¹.

The data presented here show that the flux density in this line had the value about 5 (SMA) and 6 Jy (IRAM 30 m) (Fig. 8). These values are consistent with each other within the calibration uncertainties and indicate a further decay of the maser emission to practically zero level since the line profile does not differ from the profiles of the other presumably thermal lines.

One can see (Fig. 8) that such a decay happens contemporaneously with the decay of the main component of the 6.7-GHz line. According to models presented by Cragg et al. (2005), the drop of the external dust temperature below about 150 K greatly reduces the 6.7-GHz maser line intensities. It could be the same reason for the decay of the emission in the 14₁ – 14₀ A⁻⁺ transition at 349.1 GHz.

At the same time, our SMA data show the brightest emission in the 7₁ – 7₀ A⁻⁺ line at 314.9 GHz (Fig. 1, upper panel). In the rotational diagram (Fig. 9), one can see that the total flux density (circle) for the J = 7 line has an excess in emission. When fitting the spectral profile of the 7₁ – 7₀ A⁻⁺ line with two Gaussian, we see an additional bright component at an velocity of about 2.8 km s⁻¹ (Fig. 1). This additional component is close in velocity to the maser component reported earlier by Zinchenko et al. (2017). This component is clearly seen in the 7₁ – 7₀ A⁻⁺ line and can be tentatively recognized in the profile of the 6₁ – 6₀ A⁻⁺ line at 311.9 GHz. In the other lines of the series, this component is not seen (Fig. 1).

As mentioned in Section 3.1, the 2.8 km s⁻¹ component of the 7₁ – 7₀ A⁻⁺ line is observed in an extended region and most probably arises in the rotating disc-like structure around the massive protostar.

Since the emission in the 2.8 km s⁻¹component of the 7₁ – 7₀ A⁻⁺ spectral profile coincides in velocity with the maser component of the 14₁ – 14₀ A⁻⁺ line observed in 2016 (Zinchenko et al. 2017), we propose that the spectral component at 2.8 km s⁻¹ of the 7₁ – 7₀ A⁻⁺ transition also has the maser nature. In Section 4.3 we have shown that under certain conditions, the maser occurrence for the transitions of the J₁– J₀ A⁻⁺ series is possible.

We see that in 2019, the maser component detected in 2016 in the 14₁ – 14₀ A⁻⁺ transition has practically disappeared, while the 7₁ – 7₀ A⁻⁺ transition probably shows the maser amplification. We tried to search for a set of physical parameters, which can explain such a situation. We found out that an inverted population in the transition 14₁ – 14₀ A⁻⁺ at 349 GHz requires temperatures above 170 K, specific column densities from 10⁹ to 2.5 × 10¹¹ cm⁻³s and a methanol fractional abundance above 3.16 × 10⁻⁷ (see Table 4). On the other hand, the transition 7₁ – 7₀ A⁻⁺ at 314 GHz can be inverted at temperatures from 140 K and with specific column densities from 3.2 × 10⁸ to 2.5 × 10¹¹ cm⁻³s. Thus, the situation when the transition 7₁ – 7₀ A⁻⁺ is inverted while the 14₁ – 14₀ A⁻⁺ transition is not masering can be realized at temperatures from 140 to 170 K. It is noteworthy that the values of the temperature and the methanol column density estimated from the rotational diagram (see Fig. 9) are consistent with this assessment.

Thus, we can conclude that it is very likely to be the case after accretion burst in S255IR that the dust cools down much more quickly than the gas. It is also necessary to mention that the accretion burst has a transient nature and non-stationarity effects can play important role in this case for the masers with the radiative source of pumping (Sobolev & Gray 2012; Maswanganye, van der Walt & Goedhart 2018). Both rise and drop in the maser emission in S255IR can be considerable on the time-scales of days (figs 1 and 2 in Szymczak et al. 2018), which is comparable to the time-scale of relaxation for Class II methanol masers with their lengthy and staggery pump cycles (Sobolev & Deguchi 1994b).

Finally, it is worth mentioning that the maser emission at 6.7 GHz spans from about 1 to 7 km s⁻¹. There are four weak peaks at the velocities from ∼2.3 to 4.8 km s⁻¹at 6.7 GHz, which corresponds to the suspected maser emission in the lines of the J₁ – J₀ A⁻⁺ series (see Fig. 10). At the same time, the main peak at 6.7 GHz is observed at a very different velocity (5.9 km s⁻¹). It shows that the conditions for the formation of the maser emission at 6.7 GHz and in the lines of the J₁ – J₀ A⁻⁺ series are quite different. This is reflected by our modelling estimations of parameters for inversion of populations of the J₁ – J₀ A⁻⁺ series levels and 6.7-GHz transition levels.

5.2 Survey with IRAM 30 m

Rotational diagrams display rather large scatter of points exceeding observational uncertainties for most of the sources (Fig. 5). It suggests that the excitation of the methanol transitions shows considerable deviations from LTE. So, for determining the physical parameters, we used non-LTE LVG approach and found the models that realize minimum χ² deviation from the observed values (Table 5). Unfortunately, the uncertainties of some estimates are very large. This may be caused by the small number of methanol lines that were confidently registered, for example, towards the sources G008.831−0.028, G035.200−1.736, and G188.946+0.886. On the other hand, large uncertainties can be caused by inhomogeneity of the source within the 7.5-arcsec beam, which is likely true for the most of the sample sources. For a more accurate estimation of the physical parameters, observations with a higher angular resolution are required.

Nevertheless, we may conclude that all of the sources, except G008.831−0.028 and G035.200−1.736, have T_k exceeding 100 K. These temperatures are within the range where inversion of population in the J₁ – J₀ A⁻⁺ series levels can occur (Fig. 11).

All of the sources in one Gaussian fit have number densities exceeding 3 × 10⁵ cm⁻³. For the sources G023.009−0.410 and G081.871+0.780 we find their number densities exceeding 3 × 10⁶ and 10⁸ cm⁻³, respectively, which, in combination with the temperatures of 190 and 180 K, correspond to hot cores.

The fractional abundances for most of the sources vary from 10⁻⁸ to 3 × 10⁻⁷. These methanol fractional abundances are higher than the values typically seen in the dark molecular clouds (∼10⁻⁹), and can be attributed to thermal evaporation of dust grain icy mantles. Temperatures above ∼80 K lead to evaporation of methanol from the dust grain mantles. Therefore, it is possible that most of the observed sources contain internal heating sources.

For the sources G192.600−0.048, G037.429+1.517, and G012.680−0.182, the beam filling factor is about 10–20 per cent with confidence 68 per cent. This means that these sources are very inhomogeneous within the 7.5-arcsec beam and probably consist of clumps with smaller sizes. Thus, the densities of the clumps could be higher than the densities estimated above. On the other hand, for the sources G049.489−0.387, G081.871+0.780, and G133.947+1.064, a beam filling factor of 80–100 per cent was estimated.

As can be seen in Fig. 11, only the velocity component at −56.4 km s⁻¹in G111.542+0.776 has all its physical parameters falling within the ranges within which the population inversion of the J₁ – J₀A⁻⁺ series is allowed. For this component, we see the inversion of the level populations of the J₁ – J₀ A⁻⁺ series of transitions in the modelled brightness temperatures. The physical parameters for this component differ from the others in its highest fractional abundance 3 × 10⁻⁶, its lowest methanol specific column density 3 × 10⁸ cm⁻³s, and a high temperature of 480 K. The hydrogen number density in this model was estimated with a large uncertainty as <3 × 10⁶ cm⁻³. This source G111.542+0.776 is discussed in more detail in Section 5.2.2

We therefore conclude that according to our model the population inversion in the J₁ – J₀A⁻⁺ series transitions is expected to be rare in the type of objects from our sample. This is consistent with our observations, in which the sources do not show obvious maser features.

5.2.1 Emission in the source G109.870+2.114

There are spectral components at two distinct velocities: about −5 and −10 km s⁻¹ in the methanol line profiles towards Cep A (Fig. 3). One can see that the spectra of the lines from the J₁– J₀A⁻⁺ series have almost equal peaks at both velocities, though in the J = 11 line at 331.502 GHz, the component at −10 km s⁻¹ is brighter. At the same time, the emission at −10 km s⁻¹ in the other considered methanol lines is obviously weaker compared to the emission at −5 km s⁻¹.

The emission at ∼−5 km s⁻¹ is associated with the brightest radio continuum source in this region, HW2, where Patel et al. (2005) detected the presence of a flattened disc-like structure. The emission from the Class II methanol maser at 6.7 GHz is associated with the HW2 disc and there is no emission at the other velocity for this transition.

The spectra with profiles similar to those of the lines from the J₁– J₀ A⁻⁺ series, with two components at about −5 and −10 km s⁻¹, were observed by Brogan et al. (2007) with a resolution of 1–2 arcsec in a number of molecular lines. The authors concluded that some species exhibit a main peak of emission at only one of the two distinct velocities. For example, CH₃OH, NH₂CHO, and H₂CS emit predominantly at −5 km s⁻¹ but HC₃N, SO₂ emit at −10 km s⁻¹. Meanwhile, they note that ‘a few abundant high-density tracers like CH₃CN and C³⁴S show emission of nearly equal strength towards both positions’ (Brogan et al. 2007). Apart from the kinematic dichotomy, the authors reported a thermal differentiation with temperature about 120 K for the object emitting at velocity −5 km s⁻¹and 230–310 K for the other object emitting at −10 km s⁻¹.

According to Jiménez-Serra et al. (2009) and the references therein, the object associated with the emission at −10 km s⁻¹is likely the powering source of the small-scale SiO outflow and hosts a massive protostar. These authors proposed that since this object has not yet ionized its surroundings, it is at an earlier stage of evolution than the HW2 source. Consequently, we could conclude that the lines of the series are tracing a hot region around the protostar. Another possibility is that the emission at −10 km s⁻¹ is formed in the HW3d source, which is also associated with a high-mass young stellar object (Chibueze et al. 2012). This has to be examined with high-angular-resolution observations.

5.2.2 Spectral peculiarity in the source G111.542+0.776

In the spectra of the lines of the J₁ – J₀ A⁻⁺ series from G111.542+0.776 (NGC 7538C), one can see clearly non-Gaussian profiles while for other bright lines the spectral profiles are Gaussian (see Fig. 3). Apart from the main spectral component at |$V_{\rm lsr}\, -59$| km s⁻¹, a relatively weak spectral component at the V_lsr about −56 km s⁻¹can be distinguished. It is unlikely an interloper from some other molecule since the same velocity component are present in three lines with different frequencies and there are no corresponding components in the other sources.

The component at V_lsr about −56 km s⁻¹ was the brightest component in the 6.7-GHz maser spectra observed in 1991 and 1999 (Menten 1991b; Szymczak, Hrynek & Kus 2000). According to the observations in 2012 by Hu et al. (2016), this spectral component has an intermediate brightness among the other components at 6.7 GHz. If we overlay the spectra of the brightest line from the J₁– J₀ A⁻⁺ series at 331.505 GHz with the maser emission at 6.7 GHz observed in 2019 January (see Fig. 12), we can see that the additional spectral component at −56.4 km s⁻¹ at 331.5 GHz coincides with the two relatively weak maser components at −56.8 and −56.0 km s⁻¹ at 6.7 GHz. Pestalozzi, Elitzur & Conway (2009) detected maser emission in the 6.7- and 12-GHz methanol lines at these velocities and interpreted it as the emission from an edge-on disc. Beuther, Linz & Henning (2013) indicated the presence of active star formation processes in the form of fragmentation, infall, and outflows in the object. Moreover they report two distinct bright components in the spectrum of the 15₁ – 15₀ A⁻⁺ methanol line at 356 GHz (see fig. 3 from Beuther et al. (2013)). This line belongs to the series under consideration. The authors noted that the 15₁ – 15₀ A⁻⁺ line ‘is among the few lines that do not show any absorption at high spatial resolution’ and said that it looks like maser emission or could be emission tracing a circumstellar disc with a high excitation temperature. It is noteworthy that the velocities of the components in the 356-GHz line spectrum from Beuther et al. (2013) are in general agreement with the line velocities reported here. In addition, Goddi, Zhang & Moscadelli (2015) noted that there are some indications of a rotating core with two small discs in the source at the velocities under consideration.

In order to distinguish the emission of different components, we fitted all observed methanol lines with two Gaussian having fixed velocity values of −59 and −56.4 km s⁻¹, and a fixed line width of 3.5 km s⁻¹ for the latter component. We do not consider the emission from blends at 346.202 72 and 346.204 27 GHz since the velocity difference between them is comparable to that between components, so distinguishing components in these blended lines is impossible.

Using the methanol line intensities that were determined from the two-Gaussian fit, we estimated the physical parameters of these components (corresponding to the χ² minimum) and their confidence intervals (Table 5).

By the LTE analysis of the NH₃ emission, Goddi et al. (2015) suggested that the molecular gas in the core has a temperature of 280 K, with a potential hotter component up to 500 K that coincides with our estimates in Table 5.

Remarkably, that populations of the J₁ – J₀ A⁻⁺ series levels are inverted in the model for the component at V_lsr = −56.4 km s⁻¹. In contrast, in the model for the component at V_lsr = −59 km s⁻¹ all transitions have quasi-thermal excitation. Despite the similar temperatures (about 500 K), the best-fitting models have a large difference in the specific column density and number density (2.5 × 10⁹ cm⁻³s and 10³ cm⁻³ for the component at V_lsr = −56.4 km s⁻¹, while 10¹⁴ cm⁻³s and 10⁶ cm⁻³ for the component at V_lsr = −56.4 km s⁻¹). At low densities, the populations of the energy levels usually do not follow the Boltzmann distribution, so it is easier to achieve great deviation from LTE in the form of population inversion. Furthermore, to produce the inversion of level populations we need sufficiently high column density, however, according to our model the specific column density should not exceed ∼4 × 10⁹ cm⁻³s (Table 4).

The modelling results and observational data presented above indicate that the component observed in the J₁ – J₀ A⁻⁺ series at V_lsr = −56.4  km s⁻¹ may well be a weak maser.

5.3 The J₁ – J₀ A⁻⁺ methanol line series as a tracer of the physical conditions in star-forming regions

Our observational data and theoretical modelling show that masering is possible in the J₁ – J₀ A⁻⁺ methanol line series under certain conditions. These conditions imply rather high gas temperature (>110 K). The required temperatures are different for different transitions within the series (from >110 K for transition with J = 1 to >210 K for transition with J = 19), which makes it possible to constrain the temperature from observations of a set of lines.

The case of S255IR shows that the maser effect in these lines can be an important tracer of luminosity bursts in high-mass star-forming regions. In such cases, the temporal variations of the physical parameters can be investigated. The model used here is rather simple. A more advanced approach has to be used to achieve better estimates of the physical parameters.

The maser effect in the lines of the J₁– J₀ A⁻⁺ methanol line series is rather rare in our sample, which is composed of a set of the brightest 6.7-GHz methanol maser sources. However, it is worth noting that the physical conditions required for the maser effect in these lines are apparently significantly different from those for the 6.7-GHz methanol masers. It is possible that the J₁ – J₀ A⁻⁺ methanol masers are more frequent in other types of astronomical objects such as hot cores.

In general, the maser effect in these lines is rather weak in this sample and hardly can be discovered in single-dish observations. However the existing submillimeter interferometers are well suited for this purpose.

6 CONCLUSIONS

Motivated by the recent detection of the unpredicted maser emission in the 14₁ – 14₀ A⁻⁺ line towards the high-mass star-forming core S255IR-SMA1 (Zinchenko et al. 2017), where the disc-mediated accretion burst happened in 2015, we performed an observational and theoretical study of the maser effect in the J₁ – J₀ A⁻⁺ methanol lines:

• The maser emission in the 14₁ – 14₀ A⁻⁺ line at 349.1 GHz towards S255IR-SMA1 detected in 2016, decayed to a zero level in early 2019. At the same time we almost certainly detected a maser component in the 7₁ – 7₀ A⁻⁺ line at 314.9 GHz and probably in some other lines of this series towards this object. A simple theoretical model shows that the corresponding change of the brightest maser line of the series can be explained by the temperature decrease in S255IR-SMA1 since 2016. At the same time, our current modelling does not explain the observed line ratios and maser line intensities. This is possibly a result of the model simplicity and non-stationarity effects in the maser pumping.

• Up to 20 methanol lines were detected in a sample of the brightest 6.7-GHz methanol maser sources at the frequencies from 326.7 to 350.2 GHz in the observations with the IRAM 30-m telescope. There is no obvious (bright) maser emission in the lines of the J₁ – J₀ A⁻⁺ series. However, the emission in the lines of this series is relatively bright in all sources. In some of these sources, there are spectral components that probably represent weak masers. In particular, an additional spectral component at V_lsr ∼ −56 km⁻¹ in the J₁ – J₀ A⁻⁺ line series in the source G111.54+0.77 (NGC 7538C) was detected. The best-fitting model has inverted level populations for transitions of the J₁ – J₀ A⁻⁺ series.

• The maser effect in the lines of the J₁ –J₀ A⁻⁺ series is rare and is probably observed in quite hot and probably dense environments. Theoretical modelling supports this view. It does show inverted populations for these lines under such conditions. Therefore, maser emission in these lines may accompany luminosity flare events, like that in S255IR in 2015, and can probably serve as an indicator of the flare events.

ACKNOWLEDGEMENTS

We are thankful to Sergey Parfenov for discussions of the methanol maser activity and the referee for comments and suggestions that helped us to clarify our statements and improve the presentation. This work is based on observations carried out under project number 155-18 with the IRAM 30-m telescope. Institut de Radioastronomie Millimétrique (IRAM) is supported by Institut national des sciences de l'Univers/Centre national de la recherche scientifique (INSU/CNRS, France), Max-Planck-Gesellschaft (MPG, Germany), and Instituto Geográfico Nacional (IGN, Spain). SVS and AMS were supported by the Russian Ministry of Science and Higher Education, No. FEUZ-2020-0030 for the work on the modelling of the CH₃OH emission using rotational diagram method. This work was supported by the Russian Science Foundation grant Nos 17-12-01256 (the preparation of the observations, the SMA data analysis and the general discussion) and 18-12-00193-P (modelling of the CH₃OH excitation using LVG approach and the observations at the 30-m IRAM telescope). The initial IRAM data reduction and IRAM data analysis were supported by the Russian Foundation for Basic Research grant 20-52-53054 and IRAM. The maser excitation analysis by AMS was supported by the BASIS Foundation. SYL acknowledges the support from Ministry of Science and Technology through the grant MOST-109-2112-M001-026. AA acknowledges the support from the Latvian Council of Science Project ‘Research of Galactic Masers’ Nr.: lzp-2018/1-0291.

DATA AVAILABILITY

The data used in this paper are available by request from the corresponding author.

Footnotes

REFERENCES