THE SPATIOKINEMATICAL STRUCTURE OF H₂O AND OH MASERS IN THE "WATER FOUNTAIN" SOURCE IRAS 18460−0151

Table 1 summarizes the status of the VLBA observations and data reduction of the I18460 H₂O masers. VLBA observations were conducted three times during 2006 September–2007 February (BI033) and three times during 2008 September–2009 February (BI036). In the first set of observations, another H₂O maser source IRAS 18286−0959 was also observed at the same time (Paper II), therefore the on-source time for I18460 was limited to 3 hr. In the second set of observations, the antenna-nodding, phase-referencing technique was employed for astrometry of the I18460 H₂O masers, in which the maser and the phase-reference source J185146.7+003532 (hereafter abbreviated as J1851, 252 away from I18460) were observed in a source-switching cycle of one minute. In all of the six sessions, the continuum source OT 081 was also observed for 4 minutes in every 20 minutes for calibration of group-delay residuals and bandpass characteristics. The received signals were recorded at a rate of 128 Mbits s⁻¹ with 2 bit quantization into eight base-band channels (BBCs) in dual circular polarization. The centers of four pairs of BBCs, each of which has a bandwidth of 4 MHz, were set to LSR velocities of −55, 0, 120, and 240 km s⁻¹. The recorded data were correlated with the Socorro FX correlator using an integration period of 2 s. The data of each BBC was divided into 256 spectral channels, yielding a velocity spacing of 0.21 km s⁻¹ per spectral channel. The following coordinates were adopted as the delay-tracking centers in the data correlation:

α_J2000 = 18^h48^m4294, δ_J2000 = −01°48'3028 and

α_J2000 = 18^h48^m43027, δ_J2000 = −01°48'3046 for I18460 for the first and second sets of three sessions, respectively, and

α_J2000 = 18^h51^m46723080, δ_J2000 = +00°35'3236283 for J1851.

Table 1. Parameters of the VLBA Observations and Data Reduction for Individual Epochs

Observation	Epoch	V refa	Noiseb	Dynamic	Beamd	N fe
Code	(yy/mm/dd)	(km s−1)	(mJy beam−1)	Rangec	(mas)
BI033A	06/09/15	117.7	2.6	∼90	1.31 × 0.88, 27	34
BI033B	06/11/09	117.6	3.1	∼220	1.37 × 0.96, 174	27
BI033C	07/02/03	118.3	1.9	∼110	1.50 × 0.96, −127	16
BI036A	08/09/05	—f	12	∼30	1.77 × 1.18, 111	11
BI036B	08/11/18	—f	11	∼50	1.65 × 0.92, −21	10
BI036C	09/02/06	—f	9.7	∼40	1.58 × 0.95, −35	3

Notes. ^aLocal-standard-of-rest (LSR) velocity at the phase-reference spectral channel. ^brms noise in the emission-free spectral channel image. ^cAchievable best dynamic range on the spectral channel image. ^dSynthesized beam size resulting from natural weighted visibilities; major and minor FWHMs and position angle. ^eNumber of the detected maser features. ^fPosition- and phase-reference was J185146.7+003532.

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For the data reduction, we used the NRAO's AIPS package and employed a normal procedure. After calibration of group-delay residuals and bandpass characteristics using scans on OT 081, fringe fitting and self-calibration were made using a spectral channel that contained bright maser emission. Column 3 in Table 1 gives the LSR velocity of the spectral channel selected as phase- and position-reference. The obtained solutions of calibration were applied to the data in all spectral channels. Finally, image cubes of the maser source were synthesized in visibility deconvolution through the CLEAN algorithm. Because most of the H₂O maser spots (velocity components) were spatially partially resolved, calibration solutions and the associated visibilities were missing from relatively long baselines (B_λ ≳ 200 Mλ) in the image synthesis. As a result, naturally weighted visibilities associated with available self-calibration solutions yielded a typical synthesized beam of 1.5 mas × 1.0 mas. Columns 4 and 5 of Table 1 give values of the 1σ noise level and the synthesized beam pattern, respectively.

In each spectral channel of the synthesized image cube, using a POPS pipeline script including the AIPS task SAD, brightness peaks higher than 7σ noise level were identified as maser spots and their parameters as Gaussian brightness components were extracted. We determined the position of a maser feature, which is a physical maser clump consisting of a cluster of maser spots seen in consecutive velocity components and at almost the same position within the synthesized beam, as described in Imai et al. (2002). The peak-brightness velocity of a feature was determined by quadratic fitting of the peak intensities of the brightest three spots in the feature, then the position of the corresponding peak velocity was determined from linear interpolation of the positions of the two brightest spots.

For the astrometry of the I18460 H₂O masers, in the sessions of 2008–2009, all phase calibration steps were made using the data of J1851, the solutions were then applied to the data of I18460. Because the calibration of unknown zenith delay residuals was imperfect and I18460 is very close to the celestial equator, the synthesized maser source images were partially defocused, especially in the north–south direction. However, the obtained position accuracy of the H₂O masers (∼0.1 mas and ∼0.5 mas in the right ascension (R.A.) and declination (decl.) directions, respectively) is sufficient to measure the linear proper motions of the masers and to compare their coordinates with those of the OH masers. For measurement of relative maser proper motions, we used the image cube obtained from the astrometric analysis rather than that from the self-calibration scheme mentioned above.

The EVN observation of the I18460 OH masers (F_j = 1⁺ → 2^{−1 2}Π_3/2 at 1.612231f GHz) (project code EI009B) was conducted on 2007 June 11 using the following telescopes: Lovell 76 m in Jodrell Bank, Cambridge 32 m, Westerbork Synthesis Radio Telescope (14 25 m), Medicina 32 m, Noto 32 m, Effelsberg 100 m, Onsala 25 m, Torun 32 m, and Hartebeesthoek 26 m. We used the antenna-nodding phase-referencing technique (e.g., Beasley & Conway 1995) to obtain astrometric measurements for the maser source. This was possible for every telescope except the Lovell 76 m, which always observed I18460 without antenna nodding. I18460 and the phase-reference continuum emission source J183307.8+013511 (hereafter abbreviated as J1833) were scanned in a source-switching cycle of 5 minutes, resulting in the total duration of scans on I18460 being ∼3 hr. J183243.5+135744 was observed for 3 minutes in every 40 minutes for calibration of group-delay residuals and bandpass characteristics. The received signals were recorded at a rate of 128 Mbits s⁻¹ with 2 bit quantization into eight BBCs in dual circular polarization. One pair of BBCs had a bandwidth of 1 MHz and others have 4 MHz for observing the I18460 H₂O maser and the J1833 continuum emission, respectively.

The recorded data were correlated with the Mark IV processor in the Joint Institute for VLBI in Europe using an integration period of 4 s. The data of each BBC was divided into 512 and 32 spectral channels, respectively, for the maser and continuum observations. A velocity channel spacing of 0.36 km s⁻¹ was obtained for the maser data. The coordinates of I18460 adopted in the data correlation were the same as the first set of the coordinates for the VLBA data (Section 2.1). The following coordinates for J1833 were used in the data correlation:

α_J2000 = 18^h33^m07760875,

δ_J2000 = +01°15'3530098.

In the analysis of the EVN data, in addition to the standard calibration procedures as described in Section 2.1, calibration of residual delays due to the ionosphere was also applied using the AIPS task TECOR.⁷ Fringe fitting and self-calibration were carried out as done for our VLBA observations but using the data of J183243.5+135744. Phase referencing, fringe fitting and self-calibration were undertaken using the data of J1833. The calibration solutions were applied to the data of I18460. The image of J1833 and the image cube of the OH maser source were synthesized in visibility deconvolution through the CLEAN algorithm. Calibration solutions and their associated visibilities were lost from long baselines (B_λ ≳ 10 Mλ) on J1833, which has an extended structure; this resulted in a large beam size for the image synthesis of the OH maser source. Through the phase-referencing technique, we synthesized a maser image cube (referred to as the phase-referencing-based cube) and determined the absolute coordinates of the OH maser source.

In addition, in order to obtain a higher angular resolution image cube of the OH maser source, free from the effects of the extended structure of J1833, fringe fitting and self-calibration were also carried out using the OH maser data. The spectral channel at V_LSR = 111.7 km s⁻¹ was used as phase reference. The uniformly weighted visibilities yielded a synthesized beam of 97 mas × 23 mas at a P.A. = 11°. Thus we generated another maser image cube (referred to as the self-calibration-based cube). The OH masers were also spatially resolved on baselines to the Hartebeesthoek station, causing the elongated beam pattern in the north–south direction.

Figure 2 shows a comprehensive view of the spatiokinematics of H₂O masers in I18460 found in the first three epochs. As shown in Figures 2(a) and (b), the blueshifted (−68 km s⁻¹ ≲ V_LSR ≲ −17 km s⁻¹) and redshifted (V_LSR ≃ 242 km s⁻¹) components are separated by ≈120 mas, corresponding to a linear scale of ≈240 AU at 2 kpc. We detected highly collimated, fast proper motions of the blueshifted masers (μ ≈ 10 mas yr⁻¹) with respect to the central masers. However, we could not measure proper motions of the redshifted masers because they were detected at only the first epoch. Nevertheless we can approximate the relative proper motions of the blue-shifted masers with respect to the central masers as the velocity vectors of one side of the bipolar jet components. The maser locations and motions projected on the sky give a dynamical age of the jet of only ≈6 yr in the observation epochs of 2006 September–2007 February.

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The proper motions are well aligned along the jet axis, which is defined here to be a straight line connecting the blue-shifted masers with the red-shifted. The jet axis passes through the central masers. If we assume a circular distribution of the central masers (a thick grey circle in Figure 2(a)), the separation between the circle center (a plus symbol in Figure 2(a)) and the jet axis is only ≈10 mas (≈20 AU). Because of the limited number of jet masers, this paper does not discuss a precessing jet model as proposed by Imai et al. (2005) and Yung et al. (2011).

The center velocity of the two velocity components of the jet masers ranges between V_center ≈ 87–113 km s⁻¹, depending on which pair of the blue-shifted and red-shifted components are linked. Pairing of the V_LSR ≃ 242 and −17 km s⁻¹ components gives V_center ≈ 113 km s⁻¹, which is close to the systemic velocities derived from the central components and the OH masers (V_LSR ∼ 125 km s⁻¹) as mentioned in Sections 3.2 and 3.4, respectively. However, we cannot rule out pairing the V_LSR  ≃  242 and −67 km s⁻¹ components to derive the center velocity. We derive a three-dimensional flow speed of V_jet ≈ 180 km s⁻¹ at an inclination of i ≈ 32° with respect to the line of sight under the assumption of V_sys ≈ 87 km s⁻¹. If we assume V_sys ≈ 125 km s⁻¹, then we derive V_jet ≈ 150 km s⁻¹ at i ≈ 40°. The implication of the difference in the assumed systemic velocity is discussed in Section 4.2. In both cases, a position angle of the jet, P.A. ≈ 8° east from north, is derived.

As briefly mentioned in Section 3.1 and as shown in Figure 2(a), the distribution of a large fraction of H₂O maser features in the central component is well expressed by a (thick) ring with a radius of ≈18 mas (≈36 AU). The maser features located in the central region but outside the ring are distributed in the east–west direction, perpendicular to the jet axis. We are able to measure 11 relative proper motions of H₂O masers. As shown in Figures 2(b) and (c), the proper motions are also loosely collimated perpendicular to the jet axis and exhibit an expanding flow.

In order to derive the kinematical parameters of this central outflow, we undertook a least-squares-method-based model-fitting analysis as described by Imai et al. (2000) and Imai et al. (2012b). Using the model fitting, we derive a position vector of the originating point of outflow in the maser map, (ΔX₀, ΔY₀) and a velocity vector of the originating point, (V_0x, V_0y). They were estimated by minimizing a χ² value,

$$\begin{eqnarray} \nonumber \chi ^{2}& = & \frac{1}{3N_{\rm m}-N_{\rm p}} \sum ^{N_{\rm m}}_{i} \left\lbrace \frac{\left[\mu _{ix}-w_{ix}/(a_{{\rm 0}}D)\right]^{2}}{\sigma ^{2}_{\mu _{ix}}} \right. \\ & & \left. +\frac{[\mu _{iy}-w_{iy}/(a_{{\rm 0}}D)]^{2}}{\sigma ^{2}_{\mu _{iy}}} +\frac{[u_{iz}-w_{iz}]^{2}}{\sigma ^{2}_{u_{iz}}} \right\rbrace. \end{eqnarray} \tag{ 1 }$$

Here N_m = 11 is the number of maser features with measured proper motions, N_p = 4 the number of free parameters in the model fitting, a₀ = 4.74 km s⁻¹ mas⁻¹ yr kpc⁻¹ a conversion factor from a proper motion to a transverse velocity, and D ≡ 2.0 kpc the distance to the maser source from the Sun as determined below. μ_ix and μ_iy are the observed proper motion components in the R.A. and declination directions, respectively, $\sigma _{\mu _{ix}}$ and $\sigma _{\mu _{iy}}$ their uncertainties; u_iz the observed LSR velocity, and σ_iz its uncertainty. For simplicity we assume a radially expanding outflow. In this case, the modeled velocity vector, w_i (w_ix, w_iy, w_iz), is given as

$$\begin{equation} {\boldsymbol {w_{i}}} = {\boldsymbol {V_{\rm 0}}}(V_{{\rm 0}x},V_{{\rm 0}y}, V_{{\rm 0}z})+ V_{\rm exp}(i)\frac{\boldsymbol {r_{i}}}{r_{i}}, \end{equation} \tag{ 2 }$$

where

$$\begin{eqnarray} {\boldsymbol {r_{i}}} & = & {\boldsymbol {x_{i}}}(x_{i}, y_{i}, z_{i}) -{\boldsymbol {x_{\rm 0}}}(\Delta X_{\rm 0}, \Delta Y_{\rm 0}), \end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray} z_{i} & = & \frac{(u_{iz}-V_{{\rm 0}z}) \left(r^{2}_{ix}+r^{2}_{iy} \right)} {(u_{ix}-V_{{\rm 0}x})r_{ix}+(u_{iy}-V_{{\rm 0}y})r_{iy}}, \end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray} u_{ix} & = & \mu _{ix}a_{\rm 0}D,\quad u_{iy}=\mu _{iy}a_{\rm 0}D. \end{eqnarray} \tag{ 5 }$$

Table 6 gives the parameters derived through fitting. A magenta ellipse in Figures 2(a)–(c) indicates the estimated location of the originating point of the outflow; its size indicates the uncertainty of the location. The location appears biased to the eastern maser feature cluster due to the biased maser distribution and the complicated maser motions of the eastern cluster. The radial expansion velocities of the individual features are calculated after the model fitting using the following equation (Equation (7) of Imai et al. 2011):

$$\begin{eqnarray} &&V_{\rm exp}(i)=\frac{(u_{ix}-V_{{\rm 0}x})r_{ix}+(u_{iy}-V_{{\rm 0}y})r_{iy} +(u_{iz}-V_{{\rm 0}z})r_{iz}}{r_{i}}. \nonumber\\ \end{eqnarray} \tag{ 6 }$$

Figure 3 shows the distribution of the expansion velocities. The data points seem to concentrate around an expansion velocity of ≈9 km s⁻¹ near the outflow origin and ∼17 km s⁻¹ at the outer region. It is difficult, however, to recognize such outward acceleration from the limited number of data points. These values are typical of those seen in other AGB CSEs.

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Table 6. Parameters of the Best Fit Three-dimensional Spatiokinematical Models of the H₂O Masers in the Central Slow Flow

Parameter	Value
X0a (mas)	−4.7 ± 6.0
Y0a (mas)	−4.2 ± 4.5
V0xa (km s−1)	−1.4 ± 2.1
V0ya (km s−1)	2.4 ± 2.7
V0zb (km s−1)	124.7c
D (kpc)	2.1d
rms residual $\sqrt{\chi ^{2}}$	1.23

Notes. ^aRelative value with respect to the position-reference maser feature. ^bVelocity with respect to the local standard of rest. ^cAssumed systemic radial velocity, which does not affect the χ² value. ^dDistance is completely covariant with the z_i and V_exp(i) and cannot be determined: d ≡ 2.1 kpc.

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One can estimate the distance to I18460 using the statistical parallax method. This method assumes a uniform and random velocity field of gas clumps, and therefore a velocity variance on the plane of the sky is expected to be equal to that in the line of sight. The equality of transverse and line-of-sight (or radial) velocity variances is also applicable to a spherically expanding model, such as the case of I18460. From the variances of proper motions and radial velocities of maser features, $\sigma ^{2}_{\mu }$ and $\sigma ^{2}_{v}$, respectively, the source distance and its uncertainty, D and σ_D respectively, are estimated using the following equations (Schneps et al. 1981):

$$\begin{equation} D=\sigma _{v}/\sigma _{\mu }, \frac{\sigma _{D}}{D}\sim \left\lbrace \frac{1}{2N_{m}}+\frac{1}{4N_{m}}\left[1-\left(\frac{\epsilon _{\rm obs}}{\sigma ^{\rm obs}_{\mu }} \right)^{2}\right]^{-1}\right\rbrace ^{1/2}. \end{equation} \tag{ 7 }$$

We calculated a radial velocity variance, including a contribution from the expanding flow, $\sigma ^{2}_{v_{z}}=$ 40.38 (km s⁻¹)² from a mean square deviation from the systemic velocity. The obtained proper motion variance was corrected for its error, $\epsilon ^{2}_{\rm obs}$, by the following equation:

$$\begin{equation} \sigma ^{2}_{\mu } = \left(\sigma ^{\rm obs}_{\mu } \right)^{2}-\epsilon ^{2}_{\rm obs}. \end{equation} \tag{ 8 }$$

We obtained the corrected variances of proper motions, $(\sigma _{\mu _{x}},\sigma _{\mu _{y}}) =(0.61, 0.63)$ in units of mas yr⁻¹. Their errors, (0.38, 0.39) (mas yr⁻¹), were derived from the uncertainties of the measured proper motions. These values give statistical parallax distance values: 2.2 ± 0.6 kpc (between $\sigma _{\mu _{x}}$ and $\sigma _{v_{z}}$) and 2.1 ± 0.6 kpc (between $\sigma _{\mu _{y}}$ and $\sigma _{v_{z}}$), yielding a weighted mean value of D = 2.1 ± 0.6 kpc. The justification of the derived distance is discussed in Section 4.1.

We obtained five absolute proper motions of H₂O maser features observed in 2008–2009. Because of intrinsic fading of the H₂O masers, we detect the central component with a smaller number of features than that in 2006–2007. The northeast–southwest alignment and the proper motions of the H₂O maser features found in 2008–2009 were similar to those found in 2006–2007 (Figure 2(c)). Therefore, we can assume that the masers from the different epochs are likely associated with a common origin. Two out of the five maser features were detected in all three epochs in 2008–2009. We fitted their absolute motions with respect to the position-reference source J1851 to the modeled motions, each of which was assumed to be composed of a constant velocity motion and an annual parallactic motion (N_p = 5).

Table 7 shows the results of the maser motion fitting. We obtained annual parallax values of 0.45–0.58 mas, corresponding to a range of the distance to I18460 of 1.7–2.2 kpc. However, the time baseline was too short (only five months) and the degree of freedom in the model fitting was too low (2N_e − N_p = 1 where N_e = 3 is the number of observing epochs) for reliable analysis. Therefore, the derived parallax was used just to extract the non-negligible parallax modulations and to obtain more precise linear proper motions required for further analysis. Thus we derived the absolute proper motion of the position-reference maser feature (IRAS 18460−0151:I2013-19) of (μ_X, μ_Y) = (− 3.73 ± 1.17, −6.61 ± 0.41) mas in the celestial coordinates.

Figure 4 shows the relative proper motions of the H₂O maser features found in 2008–2009 with respect to the position-reference feature. They exhibit expanding flow motions, similar to the masers shown in Figures 2(b)–(c). This is clear even if we eliminate the motion of the feature, IRAS 18460−0151:I2013-17, which was detected at only two epochs and whose measured large relative proper motion was doubtful. Using the proper motion data of the features IRAS 18460−0151:I2013-16, 18, 19, and 20, we estimated the stellar motion to be $(\Delta _{\mu X}^{\ast }, \Delta _{\mu Y}^{\ast })\approx (0.49, 0.14)$ (mas yr⁻¹) with respect to the position-reference feature. This corresponds to an expanding velocity of the CSE of ≈5 km s⁻¹. The uncertainty of the relative stellar motion may be comparable to or smaller than this value. We added, therefore, this stellar motion to both the absolute proper motion of the reference feature and its error to obtain a stellar secular motion, (μ_X, μ_Y) = (− 3.24 ± 1.27, −6.47 ± 0.43) mas. The absolute coordinates of the reference feature were determined to be α_J2000 = 18^h48^m4302792 ± 000006, δ_J2000 = −01°48'3046141 ± 000019 in 2008 September.

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Figure 4 shows the velocity-integrated brightness contour map of the two velocity components of the OH masers obtained from the self-calibration-based image cube. The origin of the contour map is set to the position of the reference OH maser spot at V_LSR = 111.7 km s⁻¹, whose absolute coordinates were determined on the phase-referencing based image cube to be α_J2000 = 18^h48^m4302701 ± 000007, δ_J2000 = −01°48'304526 ± 00026. Interestingly, the position-reference H₂O feature and OH spot were located within 10 mas (see Section 3.3), corresponding to a linear scale of ≈20 AU, even taking into account the maser positions at the different epochs and the maser motions in the period of these epochs. The OH masers and the central H₂O ones have a common LSR velocity range (110–140 km s⁻¹) and indicate similar expansion velocities (10–20 km s⁻¹, Section 3.2). It is strongly suggested that these masers share a common origin.

Figure 5 shows the distribution of the OH masers in more detail. Each of the maser spots was resolved out on baselines to the Hartebeesthoek station: the spot size was estimated to be ≳25 mas. The blueshifted and redshifted clusters of OH maser spots were split into the east–west direction by a separation of ≈50 mas, comparable to the extent of the central component of H₂O masers. The origin of a systematic LSR velocity gradient visible in only the redshifted component is unknown and it should be investigated whether this velocity gradient is always visible. But we note that the directions of the elongation of the H₂O maser distribution (Section 3.2), the cluster splitting, and the velocity gradient are perpendicular to the axis of the H₂O maser jet (Section 3.1). Furthermore, the expansion speeds and the angular distribution sizes are equal for the central component of H₂O masers and the OH masers. These properties are similar to those of H₂O and OH masers in W 43A (Imai et al. 2002; Imai 2007; Imai et al. 2008), where the existence of H₂O masers that are not associated with the collimated jet was first claimed. However, the kinematics of the W43A H₂O masers looks different from that of the OH maser although the kinematic information was quite limited in that source. The central component of H₂O masers in I18460 is the first example whose spatiokinematical structure was determined through the construction of the radially expanding flow model as described in Section 3.2 and compared with the kinematics of the OH masers.

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The results of this paper favor a much shorter distance to I18460 (D ∼ 2.0 kpc) than the derived kinematic distance (D_kin ∼ 6.9 kpc). The latter value is obtained when one uses only the radial velocity and assumes a circular orbit of I18460 in the Milky Way. This suggests that this source is located close to a tangential point in the Milky Way. Using both the radial velocity and the proper motion (Section 3.3), D_kin ∼ 6.0 or 7.8 kpc is obtained. However, unless the maser source is of a young generation, the assumption of a circular orbit is unlikely (see also Section 4.4).

As described in Section 3.2, the statistical parallax distance to I18460 is estimated as D_stat = 2.1 ± 0.6 kpc. As shown in Figure 2, the distribution of the central components of H₂O masers is elongated in the east–west direction. In addition, as shown in Figure 3, the expanding flow appears to be accelerated outward. These results may affect this estimate of distance; the variance of proper motions may have a bias in the east–west direction. In practice, as already mentioned, the outward acceleration is negligible and the calculated results support that such a variance bias is also negligible. On the other hand, if these H₂O masers are associated with a face-on equatorial flow, then a transverse velocity variance larger than that in the radial direction is expected, causing a possible bias to a shorter distance. This possibility is also unlikely when taking into account the similarity of the kinematics of the H₂O masers to that of the 1612 MHz OH masers, which suggest spherical expansion. Thus, even the possible bias in D_stat cannot explain the much shorter distance to I18460. The annual parallax unambiguously rules out a large D_kin, although the uncertainty of the parallax is very large.

The driving mechanism of the WF jet is still in debate, but a comparison of the jet parameters with other parameters of the WF sources will shed light on the mechanism. For those WFs with an estimated three-dimensional jet velocity, however, we find so far no clear correlation among the three-dimensional velocity, dynamical age, and degree of collimation of the jet and the stellar luminosity (roughly evaluated with the IRAS flux at the 25 μm band multiplied by the square of the source distance).

An offset of the center velocity of a collimated jet from the systemic velocity of a CSE and an angular offset of the originating point of a collimated jet from that of a CSE are observable in the maser spatiokinematics. The existence of these offsets implies the existence of a binary system in which the jet and the CSE originate from different host stars. In the case of I18460, as shown in Figures 2 and 4 (see Sections 3.1, 3.2, and 3.4), an upper limit to the angular offset mentioned above was given to be ≲20 mas (≲40 AU at 2 kpc). The center velocity offset was derived to be 10–40 km s⁻¹ from the center velocity of the jet H₂O masers and the systemic velocity derived from the OH maser spectrum (see Section 3.1). The derived velocity offset is roughly consistent with those in IRAS 16342−3814 and IRAS 18286−0959, in which the center velocities of H₂O and OH masers differ by up to 30 km s⁻¹ (Claussen et al. 2009; Yung et al. 2011; Imai et al. 2013a, hereafter Paper I). However, uncertainties of these center velocities of the jet masers are large. Unless the point symmetry of the H₂O maser spectra is well examined, the large uncertainty of the center velocity of the jet cannot be reduced, so it prevents us from any realistic constraint on the orbital parameters of a supposed binary system or being convinced of the existence of the binary system.

Here, we consider the possibility of identification of a binary system, with one component driving the WF jet while the other hosts the CSE. The latter may be an O-rich intermediate-mass AGB or post-AGB star (Imai et al. 2012a), so here we assume a current stellar mass of ∼1 M_☉. In the case of W 43A, in which the center velocities of the H₂O, OH, and SiO masers are estimated to be consistent with one another within a few km s⁻¹, it is possible to consider a separation of 100 AU between two stars, which is comparable to the upper limit to the separation estimated from the maser observations (Imai et al. 2002, 2005, see also the case of OH 12.8−0.9, Boboltz & Marvel 2007). If a companion orbits the supposed star with a velocity of 10–40 km s⁻¹ as estimated in I18460, the separation of these stars may be in a range of 0.6–9 AU, which cannot be spatially resolved with the current analysis technique relying on the maser data. On the other hand, the case of the highest velocity offset corresponds to a velocity fluctuation of the host star of ≳0.3 km s⁻¹ at 9 AU and an orbital period of ≲30 yr. These derived parameters will be examined in future infrared and sub-millimeter observations which can resolve such a scale and which will enable us to conduct high-resolution spectroscopy of molecular lines associated with the central stars and the accompanying jets and CSEs. In any case, finding a symmetric distribution of the jet masers and a reasonable jet model may be necessary to more precisely estimate the center velocity of the jet, which is essential to identify a binary system.

It is noteworthy that the H₂O masers in I18460 had faded between the 2006–2007 and 2008–2009 seasons. It should be taken into account that stellar H₂O masers are highly variable in both their angular and velocity distribution and some of the variation will be correlated with stellar pulsation (e.g., Bowers & Johnston 1994). In the case of the WF jet masers, however, it is possible that we are observing the evolution of the jet on a timescale comparable to the estimated dynamical time scale (see Section 3.1). We have to confirm, using future long-term observations, whether we are observing the true "death" of a WF or recurrent jet ejections; this should reveal the role of the WF jet in shaping the future planetary nebula.

The AGB CSE/equatorial flow as well as the collimated fast jet is important components to probe the evolutionary status of the WF source. As mentioned in Section 3.4, the OH masers and the central component of H₂O masers in I18460 resemble those of AGB CSEs. Taking into account that these masers do not have a high expansion velocity (V_exp ≈ 8–15 km s⁻¹) and they trace only a limited volume of the CSE or equatorial flow, these masers likely have close association with each other as shown in some OH/IR stars.

It is noteworthy that the equatorial elongation in the H₂O/OH CSE is still marginal. It is suggested that the 1612 MHz OH masers are radially amplified and it is possible that their area projected on the plane of sky is sometimes smaller than that of H₂O masers. Even taking into account these factors, the noted properties of the OH and H₂O masers in I18460 imply that this CSE may be a relic AGB CSE rather than a product of recent rapid growth of an equatorial torus or flow as suggested by Huggins (2007). Because the collimated jet of I18460 still looks extremely young (it has a dynamical age of only ∼6 yr, see Section 3.1) it is too early to observe the intrinsic evolution of the equatorial flow even if it is recently launched. Huggins (2007) suggested a time lag of a few hundred years between the rapid growth of the equatorial torus and the ignition of the collimated jet. In practice, the dynamical age of the I18460 CSE is only ≈140 yr. Any dynamical age derived from the data of H₂O and OH masers may be much shorter than the true age of the dynamical component (i.e., jet or CSE). Nevertheless we believe that the former time scale is meaningful when comparing the dynamical time scales among the maser sources when discussing the evolution of the maser sources. In fact, Imai et al. (2005) and Boboltz & Marvel (2005) have found the temporal evolution of the H₂O maser jets in W 43A and OH 12.8−0.9 on the decade scale, respectively. In both cases, the expansion rate of the H₂O maser region in the jet is roughly consistent with that expected from the dynamical ages.⁸

It is unclear whether the existence of the relic AGB CSE indicates that its hosting source is in the early phase of the WF. As already mentioned, the dynamical ages of the CSEs are much longer than those of the jets. The jet will affect only the inner part of the CSE in the WF phase, and the volume of the interaction with the highly collimated jet will be still quite limited. Therefore, it is difficult to find any correlation between the kinematic parameters of the jet and the CSE with the overall properties of the CSE as traced by its infrared colors. However, if we suppose a beaming effect of H₂O and OH masers, the small interaction with the jet may enhance the difference in preferred locations of these masers in the CSE. Similar to 1612 MHz OH masers, H₂O masers in a CSE prefer radial beaming, in which the maser emission is amplified radially with respect to the central star (e.g., Takaba et al. 1994). In this case, one can see H₂O masers associated with the CSE if the collimated jet breaks up the CSE only along the plane of the sky while the CSE is still maintained in the line of sight. After checking the previous VLBI observations of WFs (Imai et al. 2002; Boboltz & Marvel 2007; Claussen et al. 2009; Day et al. 2010; Yung et al. 2011), we speculate that the central H₂O masers of the WFs, associated with relic AGB CSEs, may be visible in the case in which the jet inclination angle with respect to the line of sight is sufficiently large (i > 30°). This speculation should be further examined in future VLBI observations of other WFs.

As shown in Sections 3.2 and 3.3, we have derived the distance and the secular motion of I18460 to be D = 2.1 ± 0.6 kpc and (μ_X, μ_Y) = (− 3.24 ± 1.27, −6.47 ± 0.43) mas, respectively. Based on these values, we further estimate the location and the three-dimensional motion of I18460 in the Milky Way. Table 8 gives the list of relevant parameters. We note common properties of the WFs whose kinematics in the Milky Way have been estimated (IRAS 19134+2131, Imai et al. 2007; IRAS 18286−0959, Paper I). Although some of the WFs are located several hundred parsecs away from the Galactic mid-plane (IRAS 163424−3814, IRAS 19134+2131), a large fraction of the WFs is located in the Galactic thin disk as seen for massive-star forming regions. Nevertheless, their three-dimensional motions have large deviations by ≳50 km s⁻¹ from those expected from the circular Galactic rotation.⁹ It is expected that the motions of the WF sources have such large deviation as a result of dynamical relaxation during their relatively long lifetimes (>10⁷ yr). However, this is inconsistent with the observation that some of the WFs, including I18460, still persist in the Galactic mid-plane. Paper I points out the possibility of a binary motion for such a peculiar motion.