First Detection of Circular Polarization in 4.7 GHz Excited OH Masers

Only one observation was made of this source, the date and duration of which are presented in Table 2 labeled G. Our 4.765 GHz I spectrum is shown in black in Figure 1(a). Parameters of a Gaussian profile fitted to the Stokes I component, shown in red on the plot, are listed in Table 2. This maser, with a flux density of only S_ν = 0.6 Jy, is weak and, hence, has a poor signal-to-noise ratio (SNR). Our measured flux densities and velocities of our fitted Gaussians are different from those of 0.53 and 3.41 Jy at v = −16.83 and –16.31 km s⁻¹ reported by H.-H. Qiao et al. (2022), so there is clearly some variability in the source between the two sets of observations.

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No linear polarization was found above the noise level, but we did find circular polarization at a level of 5% as can be seen from the green line in Figure 1(b), which is noisy due to the low SNR for this data. This V spectrum shows the characteristic sine-wave shape expected when the velocity shift between RCP and LCP Gaussian profiles is small, as first pointed out by J. A. Galt et al. (1960; see their Figure 1). The red line is a plot of scaled dI/dv determined from the Stokes I profile in Figure 1(a) and is a good fit to the green line. The green line in Figure 1(c) is a plot of Stokes V/I as a percentage, and the red line is a straight-line fit to this data over the width of the emission.

The sine-shaped curve of the V spectrum and the straight-line fit to the V/I plot are consistent with (but not exclusive to) a single spot of circularly polarized emission (see Appendix A). However, the sine-shaped curve lacks the symmetry of a pure theoretical treatment. This asymmetry will be addressed later when we discuss the skewness parameter presented in Table 2.

The circular components of the maser signal were determined using RCP = (I + V)/2 and LCP = (I − V)/2. The parameters of single Gaussians fitted to these profiles are listed in Table 3 in the top row labeled G. Following standard practice, the full width at half maximum (FWHM) of the maser profiles are listed rather than the standard deviation σ of the Gaussians. They are related by FWHM .

A new feature in the I spectra of the 4.765 GHz exOH emission in Mon R2 is the presence of a broad thermal component. This profile has been observed in all our spectra taken with the GBT (including one where there was no significant maser emission). In Figure 2 this thermal component is shown on 2021 November 27 before the recent flaring episode began, and on 2024 January 27 when the maser had a flux density S_ν 19.11 Jy. This signal is too weak to be identified in the HartRAO spectra, and because thermal emission usually occurs over a large area, it would have been resolved out by MERLIN observations. Hence, if this thermal component has been present since the 1990s, it would not have been noticed in previous observations. Because the Q, U, and V spectra are the difference between two orthogonal components, the thermal component, which is assumed to be unpolarized, is automatically absent.

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When the maser started flaring again in mid 2023, the thermal profile was still present and had to be subtracted from the spectra to determine the pure maser emission. To achieve this, the I spectrum was fitted with two or three Gaussians: one for the thermal profile and the other one or two to model the maser emission. For all observations except that on 2023 July 6, a single Gaussian fitted to the maser emission left large residuals, but when two Gaussians were fitted the residuals consisted only of noise. This fitting procedure gave the parameters for the thermal Gaussian profile, which could then be subtracted from the I spectra to leave the maser components.

In Table 2 the observation dates of Mon R2 are listed together with the time spent on-source, and the ensuing rms noise in our spectra. Gaussian parameters fitted to the thermal and Stokes I components for each session are also listed, together with the skewness of the I profile, which will be discussed in more detail in Section 4.4.

The thermal emission variability between the observations is larger than the uncertainties in the fitted Gaussian parameters. This could be due to extracting a weak signal from the maser signal, which is 2 orders of magnitude larger than the thermal flux density. An observation made on 2021 November 27 had almost no maser emission so the spectrum was dominated by the thermal component. A Gaussian profile fitted to this spectrum had a flux density S_ν =  76(6)mJy, a central velocity v = 11.32(4) km s⁻¹, and an FWHM Δv = 1.60(8) km s⁻¹, where the figures in parentheses are the uncertainties of the least significant figures. Adding the thermal components of all our 18 observations of Mon R2 together and then fitting a Gaussian gives parameters of peak flux density S_ν = 87(1) mJy, velocity of peak v = 11.143(12) km s⁻¹, and FWHM Δv = 1.71(3) km s⁻¹. This is noticeably different from the values from 2021 November 27, which could indicate that the maser has an influence on the thermal component. This will require further investigation.

Plots of the Stokes I, Stokes V, RCP and LCP, and V/I for two epochs are shown in Figure 3. The black I component is the data, fitted with a single Gaussian in red. The green V profile displays the sine-wave shape expected for the difference between two closely spaced Gaussians and is fitted well by the derived scaled red dI/dv curve. In the 2023 July 6 spectrum, the V shape is reasonably symmetrical while in all other Mon R2 (and G173) observations reported here, there is an asymmetry between the positive and negative sections of the V profile. In the bottom plot the green V/I data is fitted with a red straight line.

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The circular components of the maser signal were determined using RCP = (I + V)/2 and LCP = (I − V)/2. The parameters of single Gaussian profile fitted to these data are presented in Table 3. The velocity separation 2δ between the RCP and LCP components is small; δ measured from the Gaussian fits is listed in Table 4 together with values determined by two other methods, which are described in Section 4.5.

The evolution of the Mon R2 flaring can be traced using the data from Tables 2 and 3. The peak flux density I, the peak velocity μ, and the FWHM are plotted in Figures 4(a), (b), and (c), respectively, together with the values for the RCP and LCP components. The amplitudes of the circular components are similar and follow the behavior of the Stokes I flux density. The peak velocities μ of the three components all vary synchronously with a fairly constant separation between each of them. The FWHM of the single Gaussian profiles show that all three components vary synchronously. This gives us confidence that the fitted functions are reliable measures of the line profiles.

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The variations in the flux density are an intrinsic property of the maser, whereas the variations in the peak velocity μ and the FWHM appear to be related to the skewness. Long-term monitoring of masers shows that the central velocity may drift slowly with time (G. C. MacLeod et al. 2023), but not usually over the short time periods of our data. The width of maser profiles can vary if they are made up of multiple spots of emission that cannot be resolved in space or velocity, but the sine-wave shape of the V curves is consistent with a single spot of maser emission, which should remain constant. A more likely explanation for the temporal changes in μ and FWHM is that they are due to the influence of the skewness, which affects the values of these two fitted Gaussian parameters. Skewness is discussed in the next section.

The f parameter listed in Table 3 is a measure of the difference in amplitude between the RCP and LCP profiles. Because the f values all have values close to unity, the asymmetry between the positive and negative portions of the Stokes V sine curve cannot be due to amplitude differences between the circular components. An unexpected observation from this study is that the Stokes I, RCP, and LCP maser line profiles are distorted Gaussians. The models of interstellar H₂O masers developed by W. D. Watson et al. (2002) examined the second-order deviation of Gaussian symmetry known as kurtosis, but did not look at the third-order asymmetry known as skewness. Unsaturated methanol lines have been found to display kurtosis (L. Moscadelli et al. 2003). Both the G173 and Mon R2 sources have a single maser line profile and show a measure of skewness that is evident when trying to fit the spectra with a single Gaussian.

Skewness in Gaussian profiles of maser lines has been considered previously (W. H. T. Vlemmings & H. J. van Langevelde 2005); however, for comparison of masers with different intensity and FWHM, it is important to use a normalized skewness formula. The asymmetry of the maser lines was measured using Fisher’s moment coefficient of skewness (D. N. Joanes & C. A. Gill 1998), given by

where is the velocity distribution mean and σ_s is its standard deviation. The spectrum data are represented by velocity v_i and intensity S_i in each channel. Because noise on either side of the maser line contributes to the value of skewness, the calculation is sensitive to and the velocity range used. After testing, a range of was used. This is sufficient to include all the skewness of the distribution, while minimizing the noise on either side of the maser line. The center velocity μ and standard deviation σ of a Gaussian fit to the maser line are not the same as and σ_s of the skewed distribution. Hence, an iterative process was used to determine values for and σ_s, using the Gaussian fit parameters as starting values.

The skewness of the Mon R2 Stokes I, RCP, and LCP Gaussian profiles determined using Equation (1) are plotted in Figure 5(a). Noise in the data, in particular at the tails of the distribution, affects the skewness calculation. This introduces deviations in the calculated skewness, which produces erratic behavior, as can be seen in the plot. Overall, the skewness in all three components follows a similar pattern, showing a slow rise followed by a fall.

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To try and improve the calculations, an alternative method of measuring skewness was tested. In all cases, we found we could fit the skewed profiles with two Gaussians, leaving residuals no larger than the noise. It is beyond the scope of this paper to determine if the two Gaussian fit is a general feature of a skewed Gaussian profile, or if we were just fortunate to be able to restrict the fits to only two components. These two Gaussians were added together to produce a profile that is not affected by the noise associated with the observed data. This summed profile was then analyzed using Equation (1). The skewness calculated using the two Gaussian model is shown in Figure 5(b). Comparison with Figure 5(a) shows a much smoother change in skewness.

The skewness plotted in Figure 5(b) has an inverse behavior to that of the center velocity μ and FWHM shown in Figures 4(b) and (c), suggesting that the changes in these parameters are related to variations in the skewness of the profile. Using our two Gaussian model, the peak velocity of the combined spectra was calculated, and it also underwent shifts matching the behavior of the single Gaussian fits. Therefore, it appears that the skewness is affecting the physical conditions in the column of masing gas. It is noteworthy that the skewness is not related to the intensity of the maser, but it does affect the peak velocity and FWHM. This is clearly an area that needs to be investigated further.

Our analysis suggests several reasons why our data represent skewed profiles as opposed to two overlapping maser lines.

Modeling Stokes V using each profile from the two Gaussian model and then adding them together produces V spectra that do not match our observed data.

The smooth change in skewness seen in Mon R2 (see Figure 5(b)), and the corresponding changes in the maser velocity and FWHM, appear to be related. In contrast, heights for the two fitted Gaussians display a less coherent variation over time.

Finally, e-MERLIN imaging of the Mon R2 maser on 2024 October 14 produced only one spot of emission at its resolution of 40 mas. Assuming a distance of 830 pc to Mon R2, this corresponds to ∼33 au. This does not rule out the possibility of two unresolved maser spots, but a single spot is consistent with our results.

The separation in velocity between the circular components is equal to 2δ where ±δ is the shift in velocity due to the Zeeman effect on the RCP and LCP components from the zero B field position. The value of δ has been determined using three different methods, not all of which are independent. However, the different methods do provide a consistency check on the various values.

Method 1. The RCP and LCP profiles have been fitted with single Gaussians to determine the amplitude A, central velocity μ, and FWHM of the lines. Our velocity spectral resolution of 0.0225 km s⁻¹ facilitated using about 30 channels to fit the line profiles, thereby producing velocity uncertainties lower than the resolution of the spectra.

Method 2. In Appendix A it is shown that if the RCP and LCP profiles are formed from single spots of emission with Gaussian shapes, then, provided δ ≪ σ, V/I is a straight line with a slope m = δ/σ² (Equation (A8)). By fitting a straight line to the observed V/I plot, and using σ from the Gaussian fitting procedure, a value for δ can be determined. Because this method relies on results from the Gaussian fitting procedure it is not an independent method. Unfortunately, skewness has an influence on the straight line and hence the method’s accuracy, which we have not found a way to cater for.

Method 3. When the separation between RCP and LCP is small, the derivative of the Stokes I spectrum with respect to v is proportional to the Stokes V spectrum. Specifically for Gaussians of equal amplitude dI/v = −V/δ, as shown in Appendix B. As seen in Figures 1 and 3, the scaled dI/dv fits the V spectrum remarkably well. This approach has been used previously to determine magnetic field strengths of Zeeman split lines (T. H. Troland & C. Heiles 1982; I. Kazes & R. M. Crutcher 1986; R. M. Crutcher et al. 1993; F. Yusef-Zadeh et al. 1996).

The values of δ determined using the above three methods produce similar results as seen in Table 4 for G173 (G) and Mon R2 (1–16) and plotted in Figure 6. Method 1 can be applied under all circumstances, whereas Methods 2 and 3 are only applicable if δ ≪ σ, which is the situation for these measurements. Method 1 and Method 3 have similar values but the uncertainties for Method 1 are larger than for Method 3. Because the profiles are skewed Gaussians, the straight-line relationship for V/I is affected and produces values that differ from the other two methods, but not by much. Method 3 relies on fitting only one parameter, thereby producing the smallest uncertainties. The strength of the LOS magnetic field B_LOS has been calculated from the values of Method 3.

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In Table 1 of R. D. Davies (1974), an approximate value for the conversion factor ν/B ∼ 10⁻³ MHz G⁻¹ for the separation between the RCP and LCP components is given. For our determinations of the magnetic field strength B, which are based on δ rather than 2δ, we set ν/B = 5 × 10⁻⁴, which gives a value v/B = 3.15 × 10⁻² km s⁻¹ G⁻¹ with which to calculate B from our velocity measurements. This factor is still uncertain and could be higher or lower than this, but it is easy to modify our values if, or when, a more reliable value becomes available. Based on this conversion factor the Landé factor for the J = 1/2 level is g_J = 3.5 × 10⁻⁴, which is smaller than the uncertainties in the current values for g_J in the gs and first excited state of OH.

The observed maser circular polarization results from the portion of the magnetic field B along the observer’s LOS, which for B at an angle θ to the LOS becomes . The value of θ cannot be determined from the circular polarization measurements alone, the linear component is needed for this. The negative B_LOS value for G173 and the positive value for Mon R2 indicate one field pointing away from the observer and the other towards the observer, depending on the convention adopted (see T. Robishaw & C. Heiles 2021; their Section 6.3).

As shown in Figure 6 and Table 4, the velocity shift values change over time, with uncertainties smaller than the variations. We believe these changes are real and are related to variations seen in the maser’s linear polarization (P. Fallon & D. Smits 2024). These polarization changes and the mechanism causing them will be presented separately (P. Fallon & D. P. Smits 2025, in preparation).

There are no 6.0 GHz exOH maser observations toward either of these sources with which to compare magnetic field measurements, but there are some gsOH surveys that have been done, as well as some methanol observations.

The VLA survey of A. L. Argon et al. (2000) found four spots of 1665 gsOH masers toward G173, all with LCP only. The velocities of these spots differ by 4–7 km s⁻¹ from the 4.765 GHz maser so they are probably in a separate position. K. A. Edris et al. (2007) found one spot each of 1.665 and 1.667 GHz lines at LCP only at velocities of v = −10.88 and −10.53 km s⁻¹, which are different from those of the earlier VLA discoveries. Full Stokes observations were made by M. Szymczak & E. Gérard (2009) who found 1.665 and 1.667 GHz masers with both RCP and LCP, but the LCP components were much stronger than the RCP spots, so that Stokes V was nearly 100% LCP. No Zeeman pairs were identified. These spots did not have a high degree of linear polarization. VLA observations made by O. S. Bayandina et al. (2021) found five spots of 1.665 GHz RCP and two of LCP but no obvious Zeeman pairs and the velocities were different from our 4.765 GHz maser. At 1.667 GHz there was one spot each of RCP and LCP but they were at different positions so not a Zeeman pair. The velocities of the gsOH lines have varied in each of the above observations, indicating that this is a source that is undergoing changes. The isolated RCP and LCP spots are consistent with a magnetic field that is stronger than 10 mG, allowing only one mode to grow.

Observations of Zeeman splitting in the methanol 6.7 GHz line were made using the Effelsberg 100 m telescope by W. H. T. Vlemmings (2008). The nonparamagnetic methanol molecule has a small Landé g-factor, producing a separation of 0.049 km s⁻¹ G⁻¹. A magnetic field of B = 19(2) mG was measured at a velocity around v = −13 km s⁻¹. This is about 7 times smaller than our estimate but it is also at a different velocity and in the opposite direction from the magnetic field we measured.

Mon R2 was found to have 1.665 and 1.667 GHz maser spots in both RCP and LCP in the VLA survey of A. L. Argon et al. (2000), but none of these spots manifested as Zeeman pairs. The M. Szymczak & E. Gérard (2009) full Stokes survey found RCP and LCP spots in 1.665 and 1.667 GHz, dominated by the RCP components. The 1.667 GHz Stokes V component has a sine-wave shape, which could indicate Zeeman splitting but the positions of the spots were not determined with enough resolution to locate them at the same position. The peaks of the sine wave are separated by ∼1 km s⁻¹ so if they were a Zeeman pair the magnetic field would be <10 mG and the maser spot velocities are slightly different from that of the 4.765 GHz maser, so probably not in the same region.

There are methanol 6.7 GHz masers in the Mon R2 region, but they are variable and at slightly different velocities from the 4.7 GHz exOH maser. G. Surcis et al. (2015) detected some weak linear polarization (P_l < 5%), and one spot with circular polarization of 0.6%. The magnetic field associated with this spot was very weak.

Conventional wisdom posits that magnetic fields in star-forming regions lie in the range of 1–10 mG. These measurements have been made predominantly using the Zeeman splitting of 1.7 and 6.0 GHz masers, which are sensitive to fields in this range. The problem with this method is that it is not sensitive to fields much stronger than 10 mG. As the field strength grows, so too does the separation between the RCP and LCP components. If this separation becomes large enough, velocity coherence along the length of the maser will only occur in one component, the other one will not be amplified. In array maps of star-forming regions, isolated RCP and LCP spots are seen, but these cannot be used to determine magnetic field strengths. This is a limitation of the currently used OH masers to measure magnetic fields: they can only measure fields within a limited range of strength, above that only one component appears as a maser, and so the field strength cannot be determined. Stronger fields could exist, but a different tool is needed to measure them. Zeeman splitting of 4.7 GHz exOH masers is a tool that can measure stronger fields than those of the gs and 6.0 GHz exOH maser lines.

The 13.441 GHz F = 4 → 4 transition of the , J = 7/2 state of OH has also been used by J. L. Caswell (2004) to measure magnetic fields in star-forming regions. These masers are rare, which suggests they require very specific conditions for their existence. The Landé g-factor for this transition is smaller than for the 1.7 and 6.0 GHz OH masers, producing a velocity separation of 0.018 km s⁻¹ mG⁻¹. The maximum magnetic field measured by J. L. Caswell (2004) was 10.7 mG, with no single polarity spots being found, but given their delicate nature these masers might also not support large Zeeman shifts. It might be worth searching again for these and other excited OH masers to see what size fields they occur in.