The Luminous Blue Variable RMC 127 as Seen with ALMA and ATCA

RMC 127 (${05}^{{\rm{h}}}{36}^{{\rm{m}}}43\buildrel{\rm{s}}\over{.} 688$ $-69^\circ 29^{\prime} 47\buildrel{\prime\prime}\over{.} 52$ ICRS) was observed as part of an ALMA Cycle-2 project studying three Magellanic LBVs (Project ID: 2013.1.00450.S), including LBV RMC 143 (C. Agliozzo et al. 2017, in preparation) and candidate LBV LHA 120-S 61, hereafter S61 (Agliozzo et al. 2017a, hereafter Paper II). The observations consisted of a single execution of 80 minutes total duration on 2014 December 26 with 40 12 m antennas, with projected baselines from 10 to 245 m. The integration time per target was 16 minutes. A standard Band 7 continuum spectral setup was used, providing four 2 GHz width spectral windows of 128 channels of XX and YY polarization correlations centered at approximately 336.5(LSB), 338.5 (LSB), 348.5 (USB), and 350.5 (USB) GHz. Antenna focus was calibrated online in an immediately preceding execution, and antenna pointing was calibrated on each calibrator source during the execution (all using Band 7). Scans at the science target tuning on bright quasar calibrators QSO J0538-4405 and Pictor A (PKS J0519-4546; an ALMA secondary flux calibrator "grid" source) were used for interferometric bandpass and absolute flux-scale calibration. Astronomical calibration of complex gain variation was made using quasar QSO J0635-7516 interleaved with observations of the science targets approximately every six minutes.

As already mentioned in Paper II, atmospheric conditions were marginal for the combination of frequency and necessarily high airmass (transit elevation 43° for RMC 127), requiring extra calibration steps in order to minimize image degradation due to phase smearing, to provide correct flux calibration, and to maximize sensitivity by allowing inclusion of shadowed antennas. Details are presented in the Appendix, as they are expected to be of use for improving the calibration for similar ALMA observations in marginal weather conditions at high airmass and/or with significant airmass difference between targets and gain calibrator (QSO J0635-7516), especially at bands 7 and above. This was performed in collaboration with staff at the Joint ALMA Observatory (JAO) who are working on these aspects of calibration.

In this work, we used intensity images produced from naturally weighted visibilities in order to maximize sensitivity and image quality (minimize the impact of phase errors on the longer baselines). We imaged all spectral windows together ($343.5\,\mathrm{GHz}$ average; approximately $7.5\,\mathrm{GHz}$ usable bandwidth), obtaining an rms noise of $0.072\,\mathrm{mJy}\,{\mathrm{beam}}^{-1}$ in the image. The proposed sensitivity of $40\,\mu \mathrm{Jy}\,{\mathrm{beam}}^{-1}$ could not be achieved as no further executions were possible during the appropriate array configuration in Cycles 2 and 3. Therefore, the nebula was not detected. The central object was instead detected at $15\sigma$.

We separately imaged the pairs of spectral windows in the two receiver sidebands (337.5 and $349.5\,\mathrm{GHz}$ centers; approximately $3.75\,\mathrm{GHz}$ bandwidth each), yielding an rms noise of $\sim 0.10\,\mathrm{mJy}\,{\mathrm{beam}}^{-1}$ in the images. The two sideband images were used as an internal measure of the spectral index and as a cross-check on the data quality. Figure 1 illustrates the full bandwidth (7.5 GHz) map at 343.5 GHz. The synthesized beam is approximately $1\buildrel{\prime\prime}\over{.} 23\times 0\buildrel{\prime\prime}\over{.} 95$. Table 1 lists the details of the observations and of the resulting images, including date of observations, interferometer, central frequency, largest angular scale (LAS), synthesized beam size (FWHM), and its position angle (P.A.), peak flux density on nebula, and noise in the residual maps. Flux-calibration uncertainty is estimated to be 5% ($1\sigma$), although the peak flux may have a small additional systematic error to lower value due to residual phase smearing at a similar level. These uncertainties will be strongly correlated among the three images (average, LSB, and USB) due to the small fractional frequency differences (3.5% between sideband centers) and minimal differences in atmospheric transmission, so the measurement of spectral index from only the ALMA data should be entirely noise limited. Calibration and imaging of the ALMA data were performed using the Common Astronomy Software Applications (CASA) package, version 4.5 (McMullin et al. 2007).

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The 17 and 23 GHz ATCA data of RMC 127 were obtained as part of observations of three magellanic LBV nebulae (Project ID: C1973), including RMC 143 and S61. The observations were performed by using the array in the extended configuration (6 km) and the Compact Array Broadband Backend (CABB) receiver "15-mm Band" (16–25 GHz) during 2012 (see Table 1). We used observations of QSO J1924−2914, ICRF J193925.0−634245, and ICRF J052930.0−724528 to determine the bandpass, flux density, and complex gain solutions, respectively. We also determined the polarization leakages and applied the solutions to the data in order to calibrate the cross-hands visibilities. Once corrected, the visibilities were inverted by Fourier transform. We imaged the I, V, Q, and U Stokes parameters with a natural weighting for uv-data for the best sensitivity. In the intensity map, we detected the nebula and the central object (see Figure 1). We did not detect any polarization, as expected due to the low dynamic range. At 23 GHz, there are positional errors in declination, which are ∼0.4 arcsec, almost half a synthesized beam. A source of error can be the fact that the phase calibrator was systematically at lower elevations than the science target. Given the poor weather and the proximity to the 22 GHz water line, systematic errors in the estimation of the atmospheric path length may contribute to this astrometric error. More information on these observations and data reduction can be found in the paper dedicated to S61 (Paper II).

We also reanalyze the 5.5 and 9 GHz data from the ATCA observations performed in 2011 by using the CABB "4cm-Band" (4–10.8 GHz) receiver. These data were presented in Paper I. Here we reprocessed the data at 5.5 GHz by using a Briggs weighting scheme, with parameter robust = 0, in order to match the angular resolution at 9 GHz. The ATCA maps are shown in Figure 1 together with the ALMA one.

We also observed RMC 127 at the Very Large Telescope (VLT) with the instrument VISIR, as part of a project including RMC 143 and S61 (Project ID: 095.D-0433). An observing block in the narrow bandwidth filter PAH2$\_2$ (centered at 11.88 μm) was successfully executed on 2015 November 1. The source was observed at an airmass of 1.6 and the seeing in the V-band was not better than 1 arcsec. The observing mode was set for regular imaging, with a pixel scale of 0.045 arcsec. Four perpendicular nodding positions were used. RMC 127 was not detected, in part because the data were acquired for only 20% of the desired total exposure time. According to the VISIR Exposure Time Calculator, for a point source of $40\,\mathrm{mJy}$, the signal-to-noise ratio (S/N) would be $\lt 3\sigma$ in each sub-image. Therefore, the source could not be detected. We do not show the VISIR image because it is just noise, without detectable sources (the field of view is only 38 × 38 arcsec²).

We retrieved from the STScI data archive the ${\rm{H}}\alpha$ HST images of RMC 127 (Project ID: 6540), published by Weis (2003). The images were obtained with the Wide Field and Planetary Camera 2 (WFPC2) instrument using the ${\rm{H}}\alpha$-equivalent filter F656N and reduced by the standard HST pipeline. We reprocessed the data as described in Papers I and II. We obtained a final image that matches with Weis (2003). We show it in the top line of Figure 1.

In Figure 1, we show the interferometric radio and submillimeter maps of RMC 127, and we compare them with the archival HST ${\rm{H}}\alpha$ image, on the top right. The resolution of the radio maps corresponds to the synthesized beam and is shown with white ellipses.

The radio maps reveal for the first time the inner part of the nebula. From low to high frequencies, different components dominate in the distribution of the emission. At low frequencies, the nebula (very likely ionized by the central hot star) is the main source of radio emission, while at higher frequencies the central object dominates the emission. When the nebula is detected, the bipolar morphology is always evident. Previously, Weis (2003) recognized in the HST F656N ${\rm{H}}\alpha$ image an elongation culminating in the northern and southern caps. In the radio maps, in particular at 9 GHz, we notice an additional component at P.A. $\sim \,70^\circ$, a bar or a "diagonal arm." This forms with the two eastern and western rims ("vertical arms") a Z-pattern shape in the E–W direction. This is also visible in the HST F656N ${\rm{H}}\alpha$ image (see the black contour in the top-right panel), despite the spikes and artifacts (due to the bright central star) that affect the appearance of the nebular morphology. The radio maps present indeed a new insight into the core of the nebula.

At 5.5 and 9 GHz, the size of the nebula is approximately $7\times 6\,{\mathrm{arcsec}}^{2}$, or about $1.6\times 1.4\,{\mathrm{pc}}^{2}$, assuming a distance of $48.5\,\mathrm{kpc}$ for the LMC. The measured size is consistent with the estimate determined from the optical image (Weis 2003). Since at 5.5 and 9 GHz the LAS is at least twice the size of the source (Table 1), we do not expect any significant loss of flux at these frequencies due to the sampling of the uv plane.

At 17 GHz, the source has the same extension, and roughly, the same morphology as at lower frequencies. However, the LAS is comparable to the source size; for this reason, even if the integrated flux density is preserved, artifacts can appear in the image. We spatially integrated the flux density at 17 GHz. The new measurement together with the 5.5 and 9 GHz values (reported in Paper I) are listed in Table 2. They are all consistent with thermal free–free emission (see Section 3.3). In Table 2, we also list the peak flux density at the central object position.

Table 3.  Assumed and Derived Parameters for Model 1 (Isothermal, Constant Velocity, Fully Ionized Conical Outflow) and for Model 2 (Isothermal, Constant Velocity, Well-collimated Outflow with Recombinations)

	Model 1	Model 2
qv	0
qT	0
${\vartheta }_{0}$	0.5
qx	0	−0.2
ε	${1.34}_{-0.12}^{+0.15}$	${1.03}_{-0.10}^{+0.13}$
qn	$-{2.68}_{-0.29}^{+0.24}$	$-{2.05}_{-0.26}^{+0.21}$
${q}_{\tau }$	$-{4.02}_{-0.44}^{+0.36}$	$-{3.48}_{-0.38}^{+0.31}$
${q}_{{\rm{y}}}$	−0.52 ± 0.05	−0.60 ± 0.06
F	1.02 ± 0.10	1.18 ± 0.12

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At 23 GHz, the LAS is smaller than the source, and in fact, it is possible to detect only the compact central object and the edges of the nebula, while the extended flux is lost. At the ALMA frequency, the LAS is comparable to or larger than the size of the nebula as seen at lower frequency. However, we only detect the compact central source. The nebula around it is barely discernible. This is probably caused by the low brightness of the source at the ALMA frequency compared with the rms of the map. Assuming that the nebula emits through thermal optically thin free–free (Paper I), it is possible to estimate the total flux of the nebula at 343.5 GHz by extrapolating the measured flux density at low frequency with the typical power law (${S}_{\nu }\sim {\nu }^{-0.1}$). The resulting flux density at 343.5 GHz is $\sim 2\,\mathrm{mJy}$. If we consider the number of ALMA beams in the nebula, this flux density corresponds to an average brightness of $0.14\,\mathrm{mJy}\,{\mathrm{beam}}^{-1}$, which is only 2σ; therefore, it was not detected. Note that with the completion of observations of the ALMA project (ID: 2013.1.00450S) it would have been possible to also detect the free–free emission in the nebula.

At 9 GHz, the center of the nebula becomes as bright as the two rims. This is likely due to another emission component, which is partially resolved from the nebula at 17 GHz and also detected at 5σ in the map at 23 GHz, where it appears as a compact source (Figure 2). This object has an apparent elongation in nearly E–W direction at the 3σ level. The P.A. of this object is $\sim 110^\circ$, similar to the P.A. of the polarized emission detected by Schulte-Ladbeck et al. (1993). At the ALMA frequency, the central object is the dominant emission component.

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For the 23 GHz map, which is the highest-resolution map that we obtained, we used the task imfit of CASA to fit a 2D Gaussian to the central object in the image plane. The box region for the fit was selected around the $\sim 3\sigma$ contour level. The fit results in a Gaussian with FWHM = 0.71 ± 0.11 arcsec along the major axis. The source is marginally resolved. The deconvolution from the synthesized beam gives a size of 0.43 arcsec in R.A., equivalent to $\sim 3\times {10}^{17}\,\mathrm{cm}$, or about 0.1 pc, at the distance of 48.5 kpc. However, at the 3σ level, the contours of this object could still be confused with the noise in the map. Hence, the size provided above must be considered an upper limit.

In Table 1, we report the peak flux density over the nebula. While at lower frequencies (<23 GHz) the peak brightness is in the right arm (western rim) of the nebula, at 23 GHz and between 337.5 and 349.5 GHz, the peak of the emission is at the position of the star. At these ALMA frequencies, the peak flux density is almost three times higher than at 9 GHz (in the nebula), despite the ALMA synthesized beam being smaller.

The central object is not visible at 5.5 GHz. The reason can be confusion with the nebula emission, due to poor resolution at this frequency, combined with weaker emission. The latter possibility suggests a rising flux density distribution (e.g., ${S}_{\nu }\sim {\nu }^{\alpha }$), which is typical of stellar winds and self-absorbed emission. Note that the new map at 5.5 GHz has a synthesized beam almost identical to that at 9 GHz. We extract the peak flux density at 9 GHz ($0.36\pm 0.03\,\mathrm{mJy}$) at the position of the central object. Due to the low resolution, this is contaminated by the emission from the "diagonal arm." We then cut a slice along this arm, and fitted a Gaussian to the brightness profile in the slice along P.A. = 70°. The distribution peak corresponds to a brightness of 0.28 mJy and σ = 0.05 mJy. We subtract this value from the peak flux density at the position of the central object and derive a brightness of $0.08\pm 0.05\,\mathrm{mJy}$ at 9 GHz. At higher frequencies, we will refer to the peak flux densities in Table 2 extracted at the position of the central object. Their associated errors are the noise σ as estimated in the residual maps (flux-calibration errors are negligible).

We derive a weighted fit of the power law (${S}_{\nu }\sim {\nu }^{\alpha }$) between the centimeter and submillimeter flux densities of the central object (Figure 3). This gives us a spectral index α of 0.78 ± 0.05, which is higher than the canonical value for ionized winds with spherical symmetry and ${n}_{e}(r)\propto {r}^{-2}$ (Panagia & Felli 1975; Wright & Barlow 1975). Several mechanisms to explain the central object emission will be discussed in Section 4. A potential caveat with the flux density distribution may be the presence of systematic errors in each individual measurement (Table 2 and Figure 3) due to the differing beam sizes and the nebular contributions to the extracted central object brightness in the maps. However, given the large frequency coverage (9–349.5 GHz), we are confident of the derived spectral index.

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In Paper I, we derived an average spectral index $\alpha \sim 0.1$ from the spatially integrated flux densities at 5.5 and 9 GHz. With the new measurement at 17 GHz and the values from Paper I (see Table 2), the average spectral index is −0.03 ± 0.08 (Figure 3), typical of optically thin free–free emission, with the flux density slightly decreasing at high frequencies and a theoretical power law $\propto {\nu }^{-0.1}$.

The images at radio wavelengths have angular resolution and sensitivity that allow us to study any deviation from the typical thermal free–free emission inside the nebula by means of spectral index maps. The existence of nonthermal emission processes could indicate the presence of acceleration of particles up to the relativistic regime, due to shocks between the wind and the circumstellar environment, or due to the wind–wind interaction like in symbiotic systems, or other processes.

In colliding wind binary (CWB) models for WR+O systems, the turnover frequency is usually lower than 5.5 GHz (e.g., Dougherty 2010 and references therein). Therefore, in the observed range of frequencies, a hypothetical nonthermal component should be in the optically thin regime, with a negative spectral index. The maximum flux density is expected to be around 5.5 GHz or at lower frequencies. Negative spectral indices should be evident in the spectral index map obtained by comparing the 5.5 and 9 GHz images. We prefer not to use the map at 17 GHz to derive spectral index maps, since, as reported in Section 3.1, artifacts can be present.

A spectral index map has been derived from the data at 5.5 and 9 GHz. For both bands, the LAS is much greater that the source and no flux is lost. The 9 GHz map has been convolved with a two-dimensional Gaussian to match the beam at 5.5 GHz. After regridding the two maps in order to have the same pixel size, we computed the spectral index map and its associated error map (left and right panels of Figure 4, respectively) in each common pixel $\gt 3\sigma$. In the error map, the error in each pixel is dominated by thermal noise (flux-calibration errors are negligible). We also overlay the contours of the 9 GHz emission on top of the spectral index map. The mean spectral index over the nebula, ∼0.0, is still consistent with optically thin free–free emission from a nebular gas ionized by the central star. We exclude in our analysis the pixels at the borders, where the errors are high (up to 0.5). Around the central star, $\alpha \approx 0.6$–0.7, which is consistent with an ionized wind. Along the diagonal arm, that is, at P.A. = 70°, α varies between −0.2 and 0.2 which is consistent with typical bremsstrahlung emission. Near the northern and southern caps we find similar values of α, even if the associated error is much larger there. There is no evidence of a nonthermal component, at least at the resolution and sensitivity achieved by these observations.

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We queried the IR catalogs with the VizieR tool (Ochsenbein et al. 2000), and we extracted the flux densities of RMC 127 from 2MASS (Cutri et al. 2003), Spitzer/IRAC (Meixner et al. 2006), AKARI (Ishihara et al. 2010a, 2010b), WISE (Cutri et al. 2012), IRAS (Beichman et al. 1988), Spitzer/MIPS (Whitney et al. 2008; van Aarle et al. 2011), and Herschel (Meixner et al. 2013). In Figure 5, we plot the SED of RMC 127 from the near-IR to radio wavelengths. In addition to the two power laws associated with the ionized nebula and with the stellar wind in the radio and submillimeter, it is also possible to recognize a component of cool dust commensurate with a graybody. We also note that the photometry from about 1 to 8 $\mu {\rm{m}}$ traces neither a hot dust component close to the star nor cool dust in the outer nebula. The near-IR emission also shows an excess above the stellar photosphere (here we plot a range of reasonable effective temperatures for RMC 127 during its decline toward the quiescent state; e.g., Stahl et al. 1983; Walborn et al. 2008). Instead, the extrapolation of the stellar wind fit determined in the radio–millimeter range seems to account for the emission in the near-IR.

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We fit the SED from the mid- to the far-IR with a single-temperature graybody with power-law opacity index β. The slope in the Rayleigh–Jeans regime suggests high values for the parameter β, implying a grain size distribution dominated by small grains, similar to interstellar dust. The parameter β is mostly constrained by the Herschel PACS photometry. We found a range of characteristic temperatures between 71 and $90\,{\rm{K}}$ by varying β between 1.5, 2, and 2.5 (extreme case). The graybodies that fit the data, taking into account their uncertainty, are represented in gray. The graybody that best fits the data is plotted with a black solid line in Figure 5, with $\beta =2.0$. At longer wavelengths, the black solid line is summed with the nebula free–free model, while at shorter wavelengths the total emission is not computed because of uncertainty in the wind spectral index and in the stellar effective temperature (green + blue bands). Furthermore, the mid-IR range around 10 μm is known to be complicated by solid-state features that we cannot constrain.

The resulting characteristic temperature suggests that the mid- to far-IR emission arises from optically thin cool dust in the outer nebula (consistent with Bonanos et al. 2009). In the plot, the point indicated by the "ALMA total" label represents the 3σ upper limit to detect the total emission over the nebula (the upper limit is derived from the rms noise in the maps integrated over the area corresponding to the ionized nebula). The point-source detected with ALMA (black point) is clearly associated with the ionized gas in the stellar wind (Section 3.2).

The Reynolds model can account for different configurations of the jet, described as power-law dependencies of the physical parameters along the jet (coordinate r along the jet axis), such as jet width ($w\propto {r}^{\varepsilon }$), velocity ($v\propto {r}^{{q}_{v}}$), degree of ionization ($x\propto {r}^{{q}_{x}}$), temperature ($T\propto {r}^{{q}_{T}}$), and electron density ${n}_{{\rm{e}}}\propto {r}^{{q}_{n}}$ with ${q}_{n}=-{q}_{v}-2\varepsilon$. Assuming for the Gaunt factor ${g}_{\mathrm{ff}}\propto {\nu }^{-0.1}$, the absorption coefficient is ${k}_{\nu }\propto {r}^{{q}_{\tau }}$, where ${q}_{\tau }=\varepsilon +2{q}_{x}\,+2{q}_{n}-1.35{q}_{T}$.

Knowing the spectral index α of the wind, it is possible to determine how the jet width varies with distance (parameter ε) and therefore whether the jet is well-collimated or conical. The relationship between α and ε is

$$\begin{eqnarray}&&\alpha =2+\displaystyle \frac{2.1}{{q}_{\tau }}(1+\varepsilon +{q}_{T}).\end{eqnarray} \tag{ 1 }$$

In the case (Model 1) of an isothermal (${q}_{T}=0$), fully ionized (${q}_{x}=0$), and constant velocity outflow (${q}_{v}=0$), with α = 0.78 ± 0.05 derived from the observations, $\varepsilon \approx 1.34$, and then, being $\gt 1$, the jet opens toward the outside. Another interesting case (Model 2) to consider is that of an isothermal, constant velocity, exactly conical ($\varepsilon =1$) outflow with increasing recombinations (${q}_{x}=-0.2$) as the plasma propagates outwards.

The mass-loss rate can be written in a general form that takes into account all these parameters (for details, see Reynolds 1986):

$$\begin{eqnarray}\dot{M} & = & 5.27\times {10}^{-9}\,{v}_{\infty [\mathrm{km}{{\rm{s}}}^{-1}]}\,{S}_{[\mathrm{mJy}]}^{3/4}\,{D}_{[\mathrm{kpc}]}^{3/2}\,{\nu }_{[\mathrm{GHz}]}^{-3/4\alpha }\,{T}_{[{\rm{K}}]}^{-0.075}\\ & & \times {\nu }_{\max [\mathrm{GHz}]}^{3/4\alpha -0.45}\,\displaystyle \frac{\mu }{{x}_{0}}\,{\vartheta }_{0}^{3/4}\,{(\sin (\varphi ))}^{-1/4}\,{F}^{-3/4}\,[{M}_{\odot }\,{\mathrm{yr}}^{-1}],\end{eqnarray} \tag{ 2 }$$

where $F\equiv F({q}_{\tau },\alpha )\equiv \tfrac{{(2.1)}^{2}}{{q}_{\tau }(\alpha -2)(\alpha +0.1)}$. See Table 3 for a summary of the assumed and derived jet parameters.

In the equation, we use the flux density S at frequency $\nu =349.5\,\,\mathrm{GHz}$ and 48.5 kpc as the distance D of the object. We assumed $6420\pm 300\,{\rm{K}}$ for the gas temperature T (Smith et al. 1998), whose influence on the mass-loss rate is very weak. For the terminal velocity of the wind, we adopt ${v}_{\infty }=148\pm 14\,\mathrm{km}\,{{\rm{s}}}^{-1}$ (Agliozzo et al. 2017b). The angle $\varphi =90^\circ -i$ formed between the jet axis and the line of sight is a free parameter, which only weakly affects the result due to the $-1/4$ power dependence. Here we assume $\varphi =75^\circ$ (thus $i=15^\circ$). Finally, we set to unity the ionized fraction x₀ at the base of the outflow and the mean atomic weight of the gas $\mu =1$ (assuming a gas of mostly hydrogen). Note that we do not know the jet-opening angle ${\vartheta }_{0}$. An upper limit can be set equal to $0.5\,\mathrm{rad}$, a condition usually met in ionized jets (Mundt 1985; Reynolds 1986).

Another free parameter in Reynolds' treatment is the maximum frequency ${\nu }_{\max }$ in the SED, which we do not know. In fact, looking at Figure 5, the extrapolation of the wind SED from the radio and submillimeter wavelengths seems to approach the emission of the star in the near-IR. However, it is important to note that the dependence of the mass loss on ${\nu }_{\max }$ is weak, since it goes as $\dot{M}\propto {\nu }_{\max }^{0.135}$ in our case. A factor of 100 in ${\nu }_{\max }$ corresponds to a factor of less than 2 in $\dot{M}$. It is further important to note that the Reynolds equations are based on the approximation of the Gaunt factor that is valid in the radio regime, and that at $\nu \gt {10}^{12}$ Hz it deviates more than 30% from the correct value. In addition, the cutoff of the free–free emission at high frequency, given by the factor ${e}^{-h\nu /{KT}}$, should be taken into account when extrapolating the Reynolds equations to the near-IR. The cutoff frequency corresponds to 10¹⁴ Hz at $T\approx 6\,500$ K, i.e., a wavelength of a few microns. Furthermore, near the photosphere the wind is accelerated and it should be taken into account in the model. A reasonable value for ${\nu }_{\max }$ seems to be 10¹³ Hz. For the two model scenarios, we then have

$$\begin{eqnarray*}{\dot{M}}_{\mathrm{1,2}} & = & {C}_{\mathrm{1,2}}{\left(\displaystyle \frac{D}{48.5\mathrm{kpc}}\right)}^{1.5}\,\displaystyle \frac{{v}_{\infty }}{148\,\mathrm{km}\,{{\rm{s}}}^{-1}}{\left(\displaystyle \frac{{\vartheta }_{0}}{0.5}\right)}^{0.75}\,\mu \\ & & \times {\left(\displaystyle \frac{{\nu }_{\max }}{{10}^{4}\mathrm{GHz}}\right)}^{0.135}\,\sin {(\varphi )}^{-0.25}\,\times {10}^{-6}\,[{M}_{\odot }\,{\mathrm{yr}}^{-1}],\end{eqnarray*}$$

with the only difference being the normalizations ${C}_{1}={9.4}_{-2.0}^{+2.6}$ and ${C}_{2}={8.5}_{-1.8}^{+2.3}$.

The mass-loss rate can be a factor of two or more smaller than in the spherical case ($2.1\pm 0.4\times {10}^{-5}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$), as deduced from the equation of Panagia & Felli (1975). As described in Reynolds (1986), the effect of collimated winds is to reproduce the radio flux density very efficiently, despite lower mass-loss rates than in the standard spherical case. This means that for unresolved radio stellar objects, their mass-loss rates can be overestimated if the wind is not spherical.

Astrophysical objects that exhibit jets are usually associated with fast rotation and/or dense disks (e.g., Soker & Livio 1994; Livio 2000). We do not have evidence of a dense disk in our data (although Schulte-Ladbeck et al. 1993 and Davies et al. 2005 suggested the presence of a disk at a few stellar radii), but we also do know that RMC 127 is a fast rotator (with a projected rotational velocity of $\sim 105\,\mathrm{km}\,{{\rm{s}}}^{-1}$; Agliozzo et al. 2017b). A collimated outflow was discovered from the evolved B[e] star MWC 137 (Mehner et al. 2016).

Before running the wvrgcal program (Nikolic et al. 2012), which computes phase corrections from the WVR data, we preprocessed the raw WVR data to subtract a continuum contribution using a prototype algorithm implementation developed at JAO (W. Dent 2016, private communication). This was developed to subtract the thermal continuum contribution produced by water droplets from the WVR channel temperatures, as wvrgcal assumes only water vapor emission. In this case, it was primarily used to remove the thermal continuum due to shadowing (partially obstructed beam) from the WVR data, with the same reasoning. Reviewing the corrections applied to each antenna, compared with their predicted shadowing fraction for each scan, showed that this was successful, although in the future the correction may improve by using measured sky-coupling efficiencies of each antenna+WVR combination (a topic of active investigation within the ALMA project).

Due to the large airmass separation between the science targets and the gain calibrator, combined with limitations in the calibration of the WVR data (a fixed sky coupling efficiency and channel frequencies are currently assumed) and limitations in the atmosphere model used to derive the phase corrections from the WVR data, we found phase offsets between fields in the phase correction table produced by wvrgcal, which differed between antennas and did not correspond to real phase offsets (confirmed by looking at self-calibration phase solutions for phase over all time on RMC 127—discrepant antennas corresponded to those with noted field offsets in the wvrgcal results). This effect is under investigation as part of ALMA's continuing improvements to phase correction and antenna position determination. Without action, the image smearing due to these offsets made the WVR phase correction no significant improvement over not applying the correction. A simple solution of subtracting the field-averaged phase correction from the calibration table produced by wvrgcal was applied. This dramatically improved the image quality, resulting in over a 10% increase of the peak flux of RMC 127.

The ALMA observation frequently measured the system temperature, ${T}_{\mathrm{sys}}$, at the location of the gain calibrator QSO J0635-7516. The standard ALMA data reduction applies this ${T}_{\mathrm{sys}}$ directly to the science fields, on the assumption that the difference is negligible due to the proximity of the calibrator. This is a known limitation in ALMA's amplitude calibration strategy—casa provides simple interpolation of ${T}_{\mathrm{sys}}$ in time (between scans) and frequency (within each ${T}_{\mathrm{sys}}$ spectral window), but not yet in airmass. For the data set considered here, the ${T}_{\mathrm{sys}}$ error for the science targets by simply using that of the lower elevation gain calibrator was around 8%–10%, with the error being largest for antennas that were more shadowed (larger blocking fraction) toward the gain calibrator. A simple ${T}_{\mathrm{sys}}$ extrapolation scheme was developed to correct this, using a simple model and the autocorrelation amplitude during each of the scans. This works for this data set, as we used the TDM correlator mode, which produces linear autocorrelations (a quantization correction is applied in the correlator software, which cannot be applied in the higher resolution FDM mode). The channel-average autocorrelation data was used for this. The ${T}_{\mathrm{sys}}$ at the start and end of each scan was interpolated from the ${T}_{\mathrm{sys}}$ measurements on the gain calibrator using the following equation, taking an input ${T}_{\mathrm{sys},1}$ and the autocorrelation values ${V}_{1},{V}_{2}$ at the relevant times.

$$\begin{eqnarray}&&{T}_{\mathrm{sys},2}={T}_{\mathrm{atm}}\left(\displaystyle \frac{x}{1-x}\right);\quad x=\displaystyle \frac{{T}_{\mathrm{sys},1}}{{T}_{\mathrm{sys},1}+{T}_{\mathrm{atm}}}\displaystyle \frac{{V}_{2}}{{V}_{1}}.\end{eqnarray} \tag{ 4 }$$

A nominal atmosphere and blocking temperature ${T}_{\mathrm{atm}}=270\,{\rm{K}}$ was used, although the effect of varying this by plausible amounts was negligible for this case of ${T}_{\mathrm{sys}}\sim 200\,{\rm{K}}$.

We imaged the three calibrator sources in the execution as a cross-check of calibration and data quality. QSO J0538-4405 and Pictor A were point sources at the expected position. The gain calibrator, QSO J0635-7516, however showed significant source structure as shown in Figure 7. This is a known megaparsec-scale jet discovered by Chandra (Schwartz et al. 2000) and previously imaged at centimeter and optical/near-IR wavelengths (e.g., Mehta et al. 2009; Godfrey et al. 2012). Since analyzing our ALMA observation, maps from combination of calibrator scans in many ALMA observations have been presented by Meyer et al. (2017). To evaluate the effect of this structure on the phase calibration of the science targets, we used a clean component model of the source to both self-calibrate it and to correct the phases of the other fields. The maximum in the residual self-calibration phases of QSO J0635-7516 was around 3°, and there was no significant effect on the image of RMC 127, so we concluded that the source structure of QSO J0635-7516 was irrelevant and it was a suitable calibrator choice in this regard (and it would be even less significant with a smaller largest recoverable scale).

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