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Appendix A: Water maser lines

Table A.1 gives some properties of the sub-mm maser lines resolved by ALMA and the well-known 22 GHz maser.

Appendix B: Observations and data processing

VY CMa was observed by ALMA on 2013 16–19 August using 16–20 12 m antennas. The primary objective of these Science Verification (SV) observations was to demonstrate the ability to observe on baselines up to 2.7 km and develop calibration techniques involving strong, narrow spectral lines. Three separate configurations or scheduling blocks (SBs), covering each of the maser lines, are referred to as the 321 GHz, 325 GHz, and 658 GHz SBs; details are given in Table B.1. These were divided into one or more spectral windows (spw) covering ~850−1700 km s^-1 (depending on SB). Each spw was divided into 3840 channels, but as a result of Hanning smoothing in the correlator, the finest effective velocity resolution is approximately double the channel spacing, that is, 0.45 km s^-1 for 321 and 658 GHz, and 0.9 km s^-1 at 325 GHz. The data and scripts (including a description of the procedures) used for calibration and initial imaging are available from http://almascience.eso.org/alma-data/science-verification. As a Science Verification project, some observational methods were experimental, for example the duration of phase-referencing cycles turned out to allow a few phase ambiguities at the highest frequencies. Methods such as band-to-band phase transfer and fast switching will be available in future. These observations required very dry atmospheric conditions, so the weather determined their duration within the time available for Science Verification. Normal ALMA calibration and imaging procedures were followed, using CASA². Each SB was executed three times at different hour angles, giving a total time on VY CMa at each frequency of ~1.5 h in addition to calibration observations. The phase-reference source J0648-3044 was observed in 1.5 min scans, bracketing 6.75 min on VY CMa for the 321 GHz SB and 5.25 min for the 325 and 658 GHz SBs.

Antenna positions were updated where required, and applied corrections derived from system temperature and water vapour radiometry measurements. The precipitable water vapour (PWV) was 0.3 mm except for the last of the three 658 GHz observations, when it was 0.7 mm. The water vapour radiometry corrections produced very significant improvements, especially for the 658 SB taken at 0.7 mm PWV. A small amount of bad data were excised.

The bright QSO J0522-3627 was used for bandpass calibration. This was observed for the default duration of 5.25 min in each of the three executions of the 321 GHz SB. However, it was only observed for 2.5 min in each of the 325 GHz and 658 GHz SBs. After all calibration was complete, we checked the variation of the imaged continuum emission with frequency within each SB. The channel-to-channel position scatter was as expected from the signal-to-noise ratio (S/N), without any systematic position shift, and the flux density was consistent with the expected spectral index ~2, so we are satisfied that the bandpass does not lead to misleading results. The main symptom was that the noise rms decreased more shallowly than the expected inverse square-root dependence on the number of channels averaged. The position uncertainties were also affected by dynamic range limitations in imaging and by possibly incomplete modelling of the atmosphere in the deep water-absorption lines.

Pallas was used as the primary flux scale calibrator (Butler-JPL-Horizons 2012, ALMA Memo 594), selecting baselines shorter than the first null in the visibilities. Using the 321 GHz SB, the flux density derived from Pallas for the phase-reference source, J0648-3044, was 0.433 ± 0.008 Jy at reference frequency 316.093 GHz, spectral index α−0.80 ± 0.03. Since the 325 GHz data covered similar frequencies but had a poorer S/N than the 321 GHz data, we extrapolated the 321 GHz values to the relevant frequencies for the 325 GHz data. At 658 GHz, the flux density of J0648-3044 derived from Pallas is 0.28 Jy, compared with 0.24 ± 0.02 Jy extrapolated from 321 GHz. This may not be a fair comparison, since there is no guarantee that the spectral index is linear from 321 to 658 GHz, but it suggests that the error could be up to 15%.

The phase-reference source, J0648-3044, 9° from VY CMa, was used to derive time-dependent phase and amplitude corrections. The phase could be connected smoothly between successive scans for most antennas and times, but in a few cases where there was an ambiguity, the target scan affected was excluded from the initial imaging.

After applying instrumental and calibration source corrections, the VY CMa data in each SB was adjusted to constant velocity with respect to the local standard of rest (LSR). All velocities are given as V_LSR. Low-resolution cubes were made for each data set to identify line-free continuum, and we made preliminary images to check the astrometry. In each SB, the brightest maser channel was identified and imaged, providing a starting model for self-calibration. After several iterations, the solutions were applied to all channels. The solutions were applied to all channels and to the data initially excluded because of the phase-referencing ambiguities noted above.

The bandwidth corresponding to the sum of line-free channels (spread over the whole observing bandwidth) Δ_{ν cont} and the image noise rms σ_{rms cont.} are given in Table B.1. The mean frequencies were 316 and 319 GHz for the data sets referred to as 321 and 325 GHz. The continuum channels were imaged using natural weighting, which gave a synthesised beam of () at 321 and 325 GHz, and () at 658 GHz. In all cases the beam position angle (PA) was ~28°.

The shortest baseline was 14 m, and inspection of the visibility amplitudes against baseline length shows that the flux density remains quite steady out to 70 m at 658 GHz and 170 m at 321−325 GHz, suggesting that we recover all the flux on scales <6′′ or <13′′ at the higher or lower frequencies. We compared the total continuum flux densities with literature values (Fu et al. 2012; Kamiński et al. 2013; Muller et al. 2007; Shinnaga et al. 2004). All the measurements using ~1′′ aperture lie close to a spectral index of 2.2 ± 0.2. Those taken using a larger aperture, such as at 658 GHz from Shinnaga et al. (2004) and by Knapp & Woodhams (1993) using the James Clerk Maxwell Telescope (effective aparture ~18′′), are higher, for instance 0.62 ± 0.04 Jy at 240 GHz, 2.18 ± 0.24 Jy at 353 GHz and 9.7 ± 1.5 Jy at 677 GHz. This suggests that there is an extended component of dust on scales larger than we sampled.

The continuum was subtracted from each data set and partial uniform weighting (Briggs weighting with robust = 0.5 as defined by CASA) was used to image the masers, giving beam sizes of () and () at 321/325 and 658 GHz, respectively. No spectral averaging was applied, so the measurements for each maser channel are not completely independent as a result of the Hanning smoothing in the correlator. All image extents were ≤80% of the primary beam, so no primary beam correction was applied.

The maser peak brightnesses and S/N in each of the cubes were 321 GHz: 426.6 Jy beam^-1, S/N 2010; 325 GHz: 271 Jy beam^-1, S/N 1330; 658 GHz: 361 Jy beam^-1, and S/N 764. In the maser line wings (not dynamic-range limited but affected by the atmosphere) the σ_rms noise values were 4, 15, and 40 mJy for 321, 325, and 658 GHz, respectively. The values for all spw at lower resolution are given in Table B.1.

We measured the positions of the masers and continuum peaks by fitting two-dimensional Gaussian components using the aips task sad. We did not attempt to resolve the individual components since the smallest beam size ~50 mas is much larger than the probable maser beamed size, although this might be possible for the brightest masers. Thus all flux densities are measured over the restoring beam. The relative position uncertainties are given by (beam size)/S/N (for fairly sparse uv coverage in narrow channels; Condon et al. 1998; Richards et al. 2012). We selected components >3σ_rms at 321 and 325 GHz or >4σ_rms at 658 GHz (where σ_rms was measured separately off-source for each channel) and rejected those that obviously coincided with sidelobes. We rejected components that did not form series of at least three in successive channels, within the maximum position uncertainty.

The total flux in fitted maser components at 321, 325, and 658 GHz is 95%, 65%, and 76% of the integrated map flux density for each SB. However, the fraction of flux recovered in components is no higher for channels containing peaks >100 Jy, implying that the main loss is due to deconvolution errors putting power into sidelobes, since the 325 and 658 GHz masers are more affected by atmospheric conditions. The component selection method avoids locating spurious positions, at the expense of loss of peak flux. We grouped the maser components into features comprising series of components in successive channels within the position errors, as in Richards et al. (2012), and attempted to cross-match the clumps of different transitions but found no significant associations. In each case, 5−10% of features have pairs within 50 mas, 2 km s^-1 , but applying a 50 mas shift to one data set produces a similar number of pairs, so this seems like random coincidence.

Appendix C: Maser modelling

Figure 8 compares the physical conditions needed to excite the observed maser transitions (at 22 GHz and 321 and 325 GHz) within the ground-vibrational state. Here, we present results obtained with an excitation model that included the combined effects of collisional excitation by H₂, spontaneous radiative decay, and radiative trapping of infrared transitions. We adopted the latest quantal rate coefficients (Daniel et al. 2011) for collisionally induced transitions amongst the lowest 45 rotational states of ortho- and para-H₂O, together with an extrapolation (Neufeld 2010) to the next 75 rotational states. We treated the effects of radiative trapping with the use of an escape probability method and the assumption of a steep velocity gradient in a single direction (e.g. Neufeld & Melnick 1991). The results plotted here are for an effective water column density, N(H₂O) = n(H₂O) / (dv/ dz) of 10¹⁷ cm^-2 per km s^-1; based upon the density and velocity profiles obtained for VY CMa by Decin et al. (2006), this value is appropriate for the general outflow at distances in the range 150 to 750 au, corresponding to angular offsets of 125 to 625 mas (the region within which most of the maser spots are located). The plotted contours show, as a function of temperature and H₂ density, the negative optical depths predicted in the direction of the velocity gradient. These optical depths were computed in the unsaturated limit, where the population inversion is assumed to be undiminished by the effects of stimulated emission.

The contours labelled zero mark the boundary of the region within which the level populations are inverted. That region covers a broad range of densities and temperatures for all three transitions considered, although the 321 GHz maser gain drops rapidly below ~1000 K, as expected given its relatively high upper state energy. Similar calculations, not presented here, for the 658 GHz transition show a similar behaviour; this transition, too, shows a significant maser gain only at high temperature. Clearly, in the limit of high density, the population inversion for any transition inevitably disappears as the level populations approach LTE. However, the quenching density above which the population inversion vanishes varies from transition to transition and is clearly lowest for the 325 GHz transition. This behaviour may explain why the 325 GHz spots, as plotted in Figure 5 (purple squares), have a larger inner boundary than the other masing transitions.

Despite the large overlap of the regions in parameter space within which strong maser amplification can occur (Fig. 8), there are few or no exact coincidences between the 321 and 325 GHz maser spots observed simultaneously. As noted previously, this may simply reflect the tendency of the exponential amplification process to accentuate small differences in opacity.

© ESO, 2014