Analysis of H2O Masers in Sharpless 269 using VERA Archival data --- Effect of maser structures on astrometric accuracy

Abstract

Astrometry using H2O maser sources in star forming regions is expected to be
a powerful tool to study the structures and dynamics of our Galaxy. Honma et
al. (2007) (hereafter H2007) claimed that the annual parallax of S269 is
determined within an error of 0.008 milliarcsec (mas), concluding that S269 is
located at 5.3 kpc +- 0.2 kpc from the sun, and R= 13.1 kpc. They claimed that
the rotational velocity of S269 is equal to that of the sun within a 3% error.
This small error, however, is hardly understood when taking into account the
results of other observations and theoretical studies of galactic dynamics. We
here reanalyzed the VERA archival data using the self-calibration method
(hybrid mapping), and found that clusters of maser features of S269 are
distributed in much wider area than that investigated in H2007. We confirmed
that, if we make a narrow region image without considering the presence of
multiple maser spots, and only the phase calibration is applied, we can
reproduce the same maser structures in H2007. The distribution extent of maser
spots in the feature differs 0.2 mas from east to west between our results and
H2007. Moreover, we found that change of relative positions of maser spots in
the cluster reaches 0.1 mas or larger between observational epochs. This
suggests that if one simply assumes the time-dependent, widely distributed
maser sources as a stable single point source, it could cause errors of up to
0.1 mas in the annual parallax of S269. Taking into account the internal
motions of maser spot clusters, the proper motion of S269 cannot be determined
precisely. We estimated that the peculiar motion of S269 with respect to a
Galactic circular rotation is ~20 km/s. These results imply that the observed
kinematics of maser emissions in S269 cannot give a strong constraint on
dynamics of the outer part of the Galaxy, in contrast to the claim by H2007.

Full text

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arXiv:1201.4238v1 [astro-ph.GA] 20 Jan 2012
Analysis of H2O Masers in Sharpless 269
using VERA Archival data
— Effect of maser structures on astrometric accuracy
Makoto Miyoshi
Division of Radio Astronomy, National Astronomical Observatory of Japan,2-21-1 Osawa,
Mitaka, Tokyo 181-8588, Japan
Yoshiharu Asaki
Institute of Space and Astronautical Science, 3-1-1 Yoshinodai, Chuou, Sagamihara,
Kanagawa 229-8510, Japan
Keiichi Wada, Hiroshi Imai
Graduate School of Science and Engineering, Kagoshima University,1-21-35, Korimoto,
Kagoshima, Kagoshima 890-0065, Japan
Abstract
Astrometry using H2O maser sources in star forming regions is expected to be
a powerful tool to study the structures and dynamics of our Galaxy. Honma et
al. (2007) (hereafter H2007) claimed that the annual parallax of Sharpless 269
is determined within an error of 0.008 milliarcsec (mas), concluding that S269
is located at 5.3 kpc ± 0.2 kpc from the sun, and its galactrocetnric distance is
R = 13.1 kpc. From the proper motion, they claimed that the galacto-centric
rotational velocity of S269 is equal to that of the sun within a 3% error. This
small error, however, is hardly understood when taking into account the results
of other observations and theoretical studies of galactic dynamics. We here
reanalyzed the VERA archival data using the self calibration method (hybrid
mapping), and found that clusters of maser features of S269 are distributed in
much wider area than that investigated in H2007. We confirmed that, if we make
a narrow region image without considering the presence of multiple maser spots,
and only the phase calibration is applied, we can reproduce the same maser
structures in a maser feature investigated in H2007. The distribution extent of
maser spots in the feature differs 0.2 mas from east to west between our results
and H2007. Moreover, we found that change of relative positions of maser
spots in the cluster reaches 0.1 mas or larger between observational epochs.
Email addresses: makoto.miyoshi@nao.ac.jp (Makoto Miyoshi),
asaki@vsop.isas.jaxa.jp (Yoshiharu Asaki), wada@astrophysics.jp (Keiichi Wada),
hiroimai@sci.kagoshima-u.ac.jp (Hiroshi Imai)
Preprint submitted to New Astronomy January 23, 2012

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This suggests that if one simply assumes the time-dependent, widely distributed
maser sources as a stable single point source, it could cause errors of up to
0.1 mas in the annual parallax of S269. Taking into account the internal motions
of maser spot clusters, the proper motion of S269 cannot be determined precisely.
We estimated that the peculiar motion of S269 with respect to a Galactic circular
rotation is ∼ 20 km s−1. These results imply that the observed kinematics of
maser emissions in S269 cannot give a strong constraint on dynamics of the
outer part of the Galaxy, in contrast to the claim by H2007.
Keywords:
(H2O), INSTRUMENTS:VERA
ISM:star forming regions, ISM:individual (Sharpless 269), masers
1. Introduction
Very long baseline interferometric (VLBI) astrometry of the Galactic maser
sources is expected to be a powerful probe for investigation of the structure
and kinematics of the Milky Way. The Very Long Baseline Array (VLBA), the
European VLBI Network (EVN), and the Japanese VERA (VLBI Exploration
of Radio Astrometry) have been used to measure annual parallaxes and proper
motions of star-forming regions and red super-giants in spiral arms of the Milky
Way (Reid et al., 2009; Sato et al., 2010, and references therein). Reid et al.
(2009) reported that these young sources have large peculiar motions (i.e., de-
viations from circular rotation) as large as 30 km s−1. Such large peculiar
motions are incompatible with the prediction from the conventional theory of
quasi-stationaryspiral arms (Lin & Shu , 1964; Bertin & Lin, 1996), but in good
agreement with recent theoretical high-resolution N-body/hydrodynamical sim-
ulations (Baba et al., 2009; Wada, Baba, & Saitoh, 2011). Baba et al. (2009)
suggested that spiral arms in the Milky Way are not stationary; in their simula-
tions the arms recurrently form and vanish. Owing to gravitational interactions
between the time-dependent spiral potential and the ISM, they showed that the
dense gas and star forming regions have large peculiar velocities.
Among the star forming regions whose distances have been measured using
VLBI, Sharpless 269 (S269) is of special interest. Honma et al. (2007) (hereafter
H2007) measured the annual parallax and the secular proper motion of S269 us-
ing the VERA, and reported that S269 is located at the galactocentric distance,
R, of 13.1 kpc, and its galactocentric rotational velocity is equal to (within 3%)
that of the Sun with assumptions of R0= 8 kpc, and Θ0= 200 km s−1. From
these results, they concluded that the flat rotation of the disk of the Milky
Way extends to 13 kpc from the Galactic center. On the contrary, Oh et al.
(2010) observed star forming regions AFGL 2789 and IRAS 06058+2138 using
the VERA, and concluded that their rotation velocities are significantly smaller
than the value derived from the assumption of the flat rotation. Since the galac-
tocentric distances of these two objects are 8.8 and 9.7 kpc, respectively, they
suggested that there is a dip in the rotational velocity at around R ∼ 9 kpc.
If those objects have large peculiar velocities as suggested by the theoretical
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studies, their motions may not place strong constraints on the rotation curve.
If S269 has almost the same rotational speed of the sun at R = 13 kpc with a
small peculiar motion as suggested by H2007, then we should consider how we
can reconcile this to other observations and theories.
H2007 reported that the annual parallax, π, of S269 is 0.189 ± 0.008 mas,
which corresponds to 5.28+0.24
−0.22kpc. Given the source distance of 5.28 kpc, the
proper motion vector was estimated to be (vl, vb) = (−4.60 ± 0.81, −3.72 ±
0.72) km s−1. The errors in the annual parallax and proper motions of S269 are
a factor of 3 to 5 smaller than those in recent other VLBI astrometric observa-
tions for star forming regions (e.g., Sato et al., 2010). H2007 showed that maser
sources of S269 have a simple disk-like structure aligned in the east–west direc-
tion on a scale of 0.4 mas and a radial velocity to the LSR in the range of 19.0 and
20.1 km s−1. Previous observations, however have suggested more complex and
time-varying structure in a wider field (Lo & Burke , 1973; Genzel et al., 1977;
White et al., 1979; Cesaroni , 1990; Migenes et al., 1999; Lekht et al., 2001a,b).
From the H2O maser spectrum shape of the double or triple peaks around
VLSR= 14 to 22 km s−1, two possible structures were proposed by Lekht et al.
(2001a): one is an expanding envelope, and the other is an edge-on (Keplerian)
disk around a protostar. Lekht et al. (2001b) reported on a sinusoidal velocity
drift at VLSR ∼ 20 km s−1, and concluded that it is due to turbulent motions
of masing clouds because the estimated central mass is too small to be a pro-
tostar. A wide field spatial distribution for the H2O in S269 was shown with
the VLBI fringe rate mapping technique by Migenes et al. (1999). They found
four velocity components at VLSR
= 16.5,17.3,19.4,and 20.7 km s−1spread
over 1.3 arcseconds on the sky. They also reported that the spatial component
VLSR = 19.4 km s−1was the strongest in their VLBI observation. However,
the velocity structure of these sources was not studied. Single-dish observation
in July 1996 (Lekht et al., 2001b) obtained a single peak around 20.3 km s−1,
which probably coincides with the 19.4 km s−1peak in Migenes et al. (1999).
Three-dimensional velocity estimate of star forming regions may cause big
uncertainty in the derived three-dimensional motion in the Milky Way because
we can often find outflow-like structure in masers which may not reflect the mo-
tions of the mass center. We have to search the velocity components carefully
to estimate the motion of the mass centers. In addition, as demonstrated later
spatial distributions of maser sources also affect the accuracy of VLBI astrom-
etry even for the individual maser spots. Therefore we have to investigate the
distribution in a wide field for star forming regions.
In this paper, we focus on the structures of water maser source in S269
whether it is simple and stable enough to achieve the high accuracy in astrom-
etry using the VERA archival data1. In section 2 we describe the observational
specifications. Maser emissions in a wide sky area (1.6 arcseconds square) as
1Rygl et al. (2008) and Rygl et al. (2010) reported that they failed to measure the annual
parallax for S269’s methanol masers with the EVN while they obtained the annual parallaxes
of five other star forming regions with accuracy as good as ∼ 0.02 mas.
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well as their time variations, or relative proper motions, of the maser spots
are shown in section 4. We discuss comparison our results with H2007 and ef-
fects of the internal motion of S269 on the Galactic dynamics in section 5 and
summarize this study in section 6.
2. Observations
As described in H2007, observations have been conducted over one year at
6 epochs on Nov 18 in 2004 (Day of Year, or DOY, 2004/323), and Jan 26,
Mar 14, May 14, Sep 23, and Nov 21 in 2005 (DOY2005/026, DOY2005/073,
DOY2005/134, DOY2005/266 and DOY2005/326). The H2O masers at 22 GHz
from the S269 region have been observed using a 2300 km scale array consisting
of four antennas of the VERA (Mizusawa, Iriki, Ogasawara, and Ishigaki-jima;
see Kobayashi et al. 2008 in more detail) with the left hand circular polariza-
tion for almost 8 hours. The recording bandwidth for the maser emission was
8 MHz at epochs 1, 4, 5, and 6, covering the velocity range of 112 km s−1.
At epochs 2 and 3, the recording bandwidth was 4 MHz to cover the veloc-
ity range of 57 km s−1. The recorded data was processed with the Mitaka
FX correlator to produce cross correlated data with the 256 and 512 frequency
channels for epochs 2 and 3, and the others, respectively, so that the frequency
spacing is 15.625 kHz for all the epochs, corresponding to the velocity spacing
of 0.21 km s−1. All the VERA antennas have a dual beam receiving system
for phase-referencing (Kobayashi et al., 2008), and a closely located reference
source, J0613+1306, was observed simultaneously in the observations. However,
we did not carry out data analysis of the reference source because our purpose
here is concentrated on investigation of the spatial and velocity distributions of
S269’s H2O masers.
3. Reduction Methods
In our data reduction, we could not obtain uniform signal-to-noise ratio
through all of the epochs because the atmospheric attenuation were unexpect-
edly highly variable dependent on observing season in Japan. In Table 1 and
Figure 1, we show the variations of system noise temperatures for all the anten-
nas.
Basically we followed a standard manner of spectral line VLBI data reduc-
tions with AIPS (NRAO) package. However, because of insufficient (u, v) cov-
erage of the VERA observations, we found many confusing emission peaks due
to the side-lobes coupled with still-not-perfect amplitude calibration. In such a
situation, mapping accuracy can depend on the details of data reduction. Here
we note the details of our data reduction in order to assure the reproducibility
of our mapping results.
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Table 1 Time average of the system noise temperature of each stations for all
the epochs.
Epoch
epoch 1
epoch 2
epoch 3
epoch 4
epoch 5
epoch 6
Mizusawa [K]
692
242
240
205
276
137
Iriki [K]
596
230
161
479
234
117
Ogasawara [K]
280
181
428
311
283
1050
Ishigaki [K]
289
799
328
834
443
417
3.1. Visibility Calibrations
In order to get reliable images, we must perform calibrations of phase, am-
plitude, and bandpass characteristics of visibility data. For visibility-amplitude
calibrations, we first performed the task ACCOR with SOLINT=0.1. Using
auto-correlation spectra, the task ACCOR corrects amplitude errors in cross-
correlation spectra suffered from sampling thresholds. Then we used the task
APCAL to generate an amplitude calibration SN table, which includes the in-
formation of antenna gain curve (from GC table) and system noise temperatures
(from TY table) of each station. Furthermore, we applied the amplitude solu-
tions obtained from the self calibration method using the task CALIB.2
For visibility-delay, rate, and phase calibrations, we used the task FRING
with SOLINT=1.0 (SOLSUB=0.1) in order to obtain the clock offset and rate
from the strong continuum source, J0530+13 inserted between S269 observing
scans. As for fine phase calibrations, we relied on the self calibration solutions
from the CALIB in AIPS at the last stage of calibrations (SOLINT=0.1, SOL-
SUB=0.05). The self calibrations were at first performed at the peak frequency
channels corresponding to the VLSR= 19.5 km s−1(248 ch, 88 ch, 90 ch, 266 ch,
239 ch, and 240 ch in frequency at respective epochs). The frequency and ve-
locity resolutions were common through all the observational epochs. Although
these channels contained strong maser emissions, the maser structures were not
a single spot but at least two spots with comparable intensities. The solutions of
calibrations from these methods were applied to not only the reference channel
but all of the velocity channels.
As for bandpass calibrations we used the task BPASS in AIPS with total
2In general, measurements of the system noise temperatures and antenna gain parameters
are insufficient to calibrate the VLBI data, because the errors in VLBI data are so large that
we cannot rely on conventional calibration and mapping methods often done in connected
interferometers. Self calibration in hybrid mapping method provides us powerful solutions for
calibrating VLBI data. Today most VLBI maps are obtained after the calibration through
hybrid mapping method. For the VERA, due to the insufficient (u, v) coverage, it is sometimes
difficult to get the optimized solution with hybrid mapping.
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power spectra of calibrator continuum sources and got the amplitude bandpass
characteristics. After these calibrations, we performed corrections of velocity-
shift due to diurnal rotation of the earth using the task CVEL in AIPS.
3.2. How to Make Maps
3.2.1. Search for Masing Regions
To find the whole region of H2O maser emissions, instead of fringe rate
mapping, we used wide area synthesis imaging with low spatial resolutions.
We performed synthesis imaging of the 2 × 2 arcseconds area in all velocity
channels of four epoch’s data (the 1st, the 3rd, the 5th, and the 6th epochs).
The 2 × 2 arcseconds area was covered with 4096 × 4096 grids. Namely, each
cell size is about 0.5 mas. From these coarse maps, we selected positions for
synthesis imaging with fine spatial resolution. We selected positions where the
first CLEAN components of the different epochs’ data coincided with each other
within 0.1 arcsecond. In addition to the positions, we added 0.3 arcseconds
square areas around the three positions where strong maser emissions were found
(around positions C, D, and E shown in Figure 9). We thus selected 42 of
100 × 100 mas areas to be mapped with higher spatial resolution.
3.2.2. Fine Synthesis Imaging of the Selected 42 Areas
We mapped the 42 squares with 4096×4096grids. Each cell size is 24.4µ arc-
seconds. For the synthesis imaging, we used the task IMAGR in AIPS with
parameters NITER=3000, GAIN=0.01, and FLUX=15 mJy. The selected min-
imum flux density level of a CLEAN component, FLUX=15 mJy is presumably
lower than the array sensitivity. Because the absolute flux density of the data
has an uncertainty due to insufficient amplitude calibrations, we used the lower
level in order to achieve an adequate subtraction.
3.3. Measurements of Maser Positions
In order to avoid subjective selections of maser spots, we ran the task SAD
in AIPS automatically with its default parameters. We divided the respective
4096×4096grid areas into 25 sub-areas (4×4 mas square), and ran the task SAD
in each sub-area and measured maser spot positions. This selection method
partially failed to select some maser positions around strong masers because
such regions include not a few numbers of high level peaks due to the side-lobes.
However, we adopted the automatic SAD selection to prioritize objectivity in
selecting maser spots. By the SAD selection we found a lot of peak positions.
The numbers of peaks with flux density ≥ 6σ are given in Table 2. Presumably,
side-lobes or not real maser spots mingle among the selected peaks by the SAD
method. It was quite difficult to select only real maser spots from these maps.
To completely avoid selecting peaks that are not real, criteria other than their
signal-to-noise ratios (SNR) are required.
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Obs EpochPeak Number
(> 6σ)
238
354
379
660
177
789
1σ Noise Level
(Jy/Beam)
1.37
4.82 × 10−1
4.88 × 10−1
1.22
1.09
5.78 × 10−1
1
2
3
4
5
6
Table 2 Numbers of the maser emission peaks selected by the SAD method.
1σ noise levels were measured from the VLSR = 18.5 km s−1channel at the
100 × 100 mas field centered at (980 mas, 370 mas) in the map of Figure 9.
4. Results
Section 4.1 shows the cross power spectra of the H2O maser in the present
data analysis. Sections 4.2 and 4.3 show the spatial distributions of the H2O maser
emissions and its time variation in the individual maser spot clusters and the
whole area of S269. Relative proper motions of the maser clusters are presented
in section 4.4. Here we define a “maser spot” as the origin of a maser emission
in a single velocity channel map, and a “maser feature” as a group of maser
spots with different velocities gathered at a common place. We also use the
term “maser cluster” as a group of maser features with a common motion.
4.1. Cross power spectra of H2O masers in S269
Figure 2 shows the cross power spectra of the H2O maser emissions in
S269 obtained with the Mizusawa–Iriki baseline (1300 km length) for all the
six epochs.It is important to note that there are complex maser emission
peaks in the radial velocity range from 8 to 20 km s−1, and that the line profile
is changed on a time scale shorter than one year, as reported by Lekht et al.
(2001a). The most prominent emission can be seen at VLSRof 19.5 km s−1, and
the line profile of H2O maser spectrum changes significantly in one year. Note
also that there are several emission peaks in the spectra at VLSRof 17 km s−1at
epoch 2, VLSRof 18 km s−1at epoch 3, and VLSRfrom 8 to 11 km s−1at epochs 5
and 6. The signal-to-noise ratio (SNR) of the cross power spectrum at epoch 1
seems worse than those at the other epochs. This is mainly because the system
noise temperatures of these two stations at epoch 1 were unusually a factor of
2 to 5 higher than those at other epochs and also because the observing time of
S269 was about half of those in other epochs.
In the cross power spectrum at epoch 1, there are several peaks between
VLSR= 0 to 5 km s−1, but they are not maser emissions. This is due to strong
artificial signals at Iriki station. We found the artificial signals at 21.233 GHz
(corresponding to VLSR = 35 km s−1), 22.235 GHz (corresponding to VLSR=
0 km s−1), and 22.237 GHz (corresponding to VLSR = −22 km s−1) in sky
frequency, one of which caused the peaks at VLSRfrom 0 to 5km s−1.
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4.2. Arcsecond scale distribution of H2O masers in S269
Figures 3, 4, and 5 show the spatial distribution of the maser spots and
position-velocity diagrams for all the six epochs. We identified seven maser
groups (A through G). All of them show strong time variation. At epoch 1,
only group C was strong (SNR > 40). C and E were strong at epoch 2, D and
E at epoch 3, C and D at epochs 4 to 6. Groups C, E, F and G all lay in
VLSRranging from 18 to 20 km s−1. The maser emissions from VLSR = 8 to
14 km s−1came from a single group denoted as D. The distribution of masers
was qualitatively consistent with the map obtained by Migenes et al. (1999).
They identified four sources at 16.5, 17.3, 19.4 and 20.7 km s−1, which roughly
coincide with groups A, C, E and G. They used a fringe-rate mapping method
to obtain the positions of the four peaks in their spectrum. Therefore, they did
not obtain the velocity structures of the individual sources. The fact that they
did not report the velocity distribution within each maser group does not mean
the observed groups were single points.
4.3. Structure of individual maser groups
Figure 6 shows the internal maser structures of groups A to G. The structure
of A is taken from epoch 6, that of B is from epoch 4, those of C, D, and E
are from epoch 3, and those of F and G are from epoch 6. Each maser group
consists of one or two features. One feature typically has a spatial size over 1
mas and a velocity range of 2 km s−1. Groups D and E consist of two features,
while other groups consist of one feature. As shown in the panel for group
A, the typical beam size is 1.4 × 0.9 mas. For maser spots in group C, SNR
is higher than 100. From the high SNR, we can expect that the error of the
relative position is small down to 0.01 mas. For other maser spots, SNR is in a
range of 10–20. This implies that a possible position error is 0.1 mas or larger.
Group C is the brightest among the clusters A-F, and it should correspond
to the maser cluster studied in H2007. H2007 detected the maser spots with
VLSRfrom 19.0 to 20.1 km s−1, which were distributed over an angular range
of 0.4 mas in the east–west direction. While we detected from group C in wider
velocity range of 18.8 to 21.4 km s−1as shown in Figure 6.
7 (a), the maser spots in the same velocity range as reported by H2007 show a
more compact distribution within an angular range of 0.2 mas. We discuss the
difference between the two maps in section 5.1.
The left two panels of Figure 8 show the relative positions of the maser
spots in group C with respect to the position of the maser spot at VLSR =
19.5 km s−1. Positional deviations at epochs 1 and 4 are larger than those at
other epochs: positions at epochs 2, 3, 5, and 6 are consistent with one another
within the positional accuracy of 0.05 mas. Judging from the system noise
temperatures, the large positional deviations at epochs 1 and 4 were caused
by the bad atmospheric conditions as noted in section 2. The plot shows that
change of relative positions of maser spots in the cluster reaches 0.5 mas between
observational epochs (see section 4.1 on possible errors in the annual parallax).
As shown in Fig.
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4.4. Relative Proper Motions of Maser Clusters
Figure 10 shows the proper motions of maser clusters relative to the VLSR=
19.5 km s−1spot in group C. First, we searched proper motions of maser spots
from groups A to G (Figure 9). Among the selected peaks, we searched for
relative proper motions of maser spots with the following three criteria.
1. Peaks which are higher than 20σ noise level at each epoch.
2. Peaks whose displacements are less than a corresponding proper motion
of 3.5 mas yr−1.
3. Peaks whose velocity shifts are less than 0.5 km s−1.
For peaks in the two fields of groups F and G, where the maser spots were
well isolated, we selected peaks which are higher than 7σ noise level at each
epoch. Because these two maser groups show relatively weak emissions but the
existence of the groups is certain, these masers cannot be neglected in order to
investigate the internal motions of the masers in S269 regions. We found 22 sets
of proper motions using the first criterion. Using the looser criterion on SNR,
we found more 4 sets of proper motions and 1 set of proper motion from the two
groups F and G respectively. In Table 3 we show the detected proper motions
of maser spots with these criteria.
After detecting proper motions of maser spots, we combined all maser spots
data showing common proper motions in order to obtain independent motions.
First of all, from the proper motions data set, we omitted data using positions of
epoch 1 and 4 as these two epochs were under fairly bad atmospheric conditions.
We combined and averaged proper motions and velocities of maser spot data
whose velocity difference was within 1 km s−1in order to derive independent
motions of maser clusters.
Table 4 gives the parameters of derived proper motions of maser clusters.
Apparently, the maser clusters in groups C, D, E and G form an arc-like struc-
ture with the proper motions implying an expanding shell. Since the number of
clusters is limited, it is possible to judge that this structure and motion could
be just a coincidence.
5. Discussion
We have re-analyzed the VERA archival data of S269. We found that (a)
maser emissions in S269 are distributed over around 1.6 arcseconds, (b) the
maser emissions are found from a wide radial velocity range between 8 and 20
km s−1, (c) there are multiple maser groups in the 1.6 × 1.6 arcsecond area at
around the radial velocity of 19.5 km s−1, and (d) the structure of the brightest
source (group C) is different from the single source reported in H2007. In section
5.1, we discuss the origin of the discrepancy in the obtained maser structure
between our result and that of H2007. In section 5.2, we discuss the implication
of the internal maser motions on the constraint on the galactic rotation curve
of the Milky Way.
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5.1. Comparison with the map of H2007
In Figure 7, we show the distribution of maser spots of group C and that of
H2007, for the same epoch. Both show velocity gradients in the east-west direc-
tion, but H2007’s spots in the velocity range of VLSR= 19.0 to 20.1 km s−1are
distributed over 0.4 mas, while those in our result have a more compact distri-
bution within 0.2 mas. We consider the possibility that the difference between
our methods of analysis and those of H2007 caused the difference in the im-
ages. The primary difference between the two methods is that we have made
the image from hybrid mapping, while H2007 used the phase-referenced data to
determine the absolute positions of the maser spots. This difference of the map-
ping techniques themselves does not seem to cause significant differences in the
determination of the internal structure. Rather, the reasons for the difference
lie in differences in the treatment of the data.
We noted the following two major differences. First, H2007 did not find
groups E and G, which are in the same velocity range as group C. Second, when
they performed the analysis of the data, they applied corrections for the atmo-
spheric delays of stations to the visibility data in order to obtain a reasonable
result. They noted: “To calibrate them, residual zenith delays were estimated
as a constant offset that maximizes the coherence of the phase-referenced map.
Typical residuals of zenith delay are 1 to 5 cm, but in the worst case (during
the summer at Ishigaki-jima station) it was as large as 20 cm”.
They maximized the coherence by adjusting the residual atmospheric excess
path-length3, Lsof individual stations, under the following assumptions:
1. The excess path-length δLSto be adjusted at station S is δLS= LS× (sec ZS269−
sec Zref), where ZX is the zenith angle of source X at station S and LS
is the residual atmospheric zenith delay at station S.
2. The residual atmospheric zenith delay LSis constant during one observa-
tional session.
3. The correct estimate of the residual excess path-length LSgives the correct
map of S269.
We investigated how these assumptions can change the map. For this pur-
pose we created a map using the method which is effectively equivalent to that
used in H2007. The difference between the standard imaging method and this is
summarized as follows. In the standard imaging method one uses fine solutions
of both amplitude and phase from self-calibration with an optimized model im-
age, however here we used self-calibration only for phase solutions using a point
as the image model. Calibration of phase φ is equivalent to that of excess path-
length L due to the equation φ = 2πL/λ (where λ is observing wavelength).
We assumed that the source in one velocity channel has a single point when we
performed the phase self-calibration. We limited the imaging area to a narrow
region (100×100 mas span). If they performed wide-area imaging, they should
have found multiple sources as we found. (Hereafter we call the map obtained
3In other words, ”residual atmospheric delay”.
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by the above mentioned method as the PPN map: Phase-only self-calibration
with an one-Point model and Narrow field mapping). In Figure 7 we show the
PPN map overlaid with the result of H2007. We can see that the PPN map
reproduces the main feature of the H2007 map. In particular, the width of the
distribution of maser spots is 0.4 mas for both results. We ignored the presence
of multiple sources and performed only the phase calibration in the PPN map.
This suggests that the result of H2007 is affected by the imaging area and choice
of the calibration method.
Figure 8 shows the time variation of the relative positions of the maser spots
in group C with respect to that at the velocity of 19.5 km s−1revealed by the
standard mapping and the PPN method. It is clearly seen that the distribution
of the spots along the right ascension in the PPN is ∼ 0.1 mas wider than
that in the standard mapping method, so that the difference between the two
as shown in Figure 7 can be reproduced for all the epochs. It is worth noting
that, assuming that the standard mapping method produce true maser emission
images better than the PPN method because the PPN method uses a single point
source model even if the structure is complicated, the positional shift seen in the
PPN map causes an astrometric error, which depends on the source structure.
Provided that this positional shift have the same direction and the same
quantity for all the epochs, following astrometric analysis to obtain annual par-
allaxes and proper motions can make a correct estimation of the annual parallax.
On one hand, if the positional shift have a one-year periodical variation, the de-
rived annual parallax may have a bias of 0.1 mas in the worst case. If the
positional shift appears randomly, the annual parallax error could be between
0 − 0.1 mas by chance. From our comparison between the standard mapping
method and the PPN method, and between the PPN method and the map
shown in H2007, we suspect that H2007 applied a simple source model in their
analysis which does not include a widely distributed maser emission as shown
in this report, so that their annual parallax have a hidden error of 0.1 mas in
the worst case.
5.2. Effects of the internal motions in S269 on the Galactic dynamics
One of the most important claims in H2007 is that motion and distance
to S269 give a strong constraint on the shape of the outer rotation curve of
the Milky Way: the difference of rotational velocities at the Sun and at S269
(which is claimed to be located at 13.1 kpc away from the Galactic center) is
less than 3%. However, our reanalysis suggests that we cannot give that strong
constraint on the outer rotation curve only by the VERA observation of S269,
if we consider the complicated internal structures of maser clusters and their
motions as well as their time variability.
We calculated the UV W velocities of the independent maser clusters us-
ing relative proper motions and radial velocities, assuming that H2007 velocity
corresponds to that of the VLSR = 19.5 km s−1in the maser spot in group
C. The results are summarized in Table 5. The average UVW of these maser
clusters in S269 is (4.4 ± 6.1,−16.7± 18.4,12.2± 18.7 km s−1). Assuming that
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H2007 obtained the correct distance to S269, the rotational velocity at 13 kpc
is 183 ± 19.4 km s−1.
The rotational velocity at 13 kpc, 183 ± 19.4 km s−1, is consistent with
other measurements. Owing to the large internal motion of masers in S269,
the observed proper motion of S269 with respect to the Local Standard of Rest
cannot give a strong constraint on kinematics of the outer part of the Galaxy,
in contrast to the claim by H2007. Taking into account the internal motion of
∼ 20km s−1, the rotational velocity of S269 is consistent with other previous
observations outside of the solar circle (Sofue et al., 2009).4
5.3. Difficulties in VLBI astrometry using H2O masers in star forming regions
VLBI astrometry using H2O maser sources has made great progress in
decades as a powerful tool to investigate structures and dynamics of the Milky
Way Galaxy (e.g. Reid et al., 2009; Sato et al., 2010). However, our result pre-
sented here illuminates essential difficulties in this methodology. Major intrinsic
problems are: 1) H2O masers in star forming regions are not necessarily located
in the ‘center of mass’ of the objects, 2) the masers are not in general “point ”
sources, and their distributions are time-variable, and 3) they often show com-
plicated internal motions. Additionally, the different results between H2007 and
the present work suggested that the data calibration in VLBI observations of
star forming regions is not straightforward, and still need improvement.
One should also note that the shapes of H2O masers are not point-like and
their spatial extent are often comparable to observational beam size. For ex-
ample, we found that average size of H2O masers in S269 is 0.72 ± 0.50 mas
(HPBW) based on a Gaussian shape fitting, which is comparable to the VERA
synthesized beam size at 22 GHz (Figure 6). The distributions of masers often
change between observational epochs, which brings additional errors on position
of the objects.
Moreover, H2O maser sources in a star forming region often show internal
motions, i.e. spots apparently moves in terms of the center of mass of the region.
Such internal motions are typically a few tens of km s−1, and therefore it is hard
to estimate the kinematic motions of the objects in the Galaxy. This could be
solved by introducing a model of internal motions (e.g. expanding outflows) of
maser spots (e.g. Imai et al., 2000; Asaki et al., 2010). However, this suggests
that a large enough number of spot motions should be measured over many
years, and that the motions are often too complicated to be fitted by a simple
kinematic model.
Finally, one should note that the astrometric results of star forming regions
using the VLBI technique is still carefully considered. For example, in S269,
as shown in section 5.1, the difference of data calibration and the assumption
for measurement may cause up to 0.1mas ambiguity in the astrometric results.
Although it would be hard to overcome the intrinsic difficulties in H2O masers of
4The annual parallax measurements using the clusters newly found in this paper will dis-
cussed elsewhere (Asaki et al. in prep.).
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star forming regions, one could reduce errors in astrometry by searching maser
spots as many as possible in a large enough area, and those spots should be
observed over many years.
6. Summary
We have reanalyzed VERA archival data of S269, and found several maser
clusters distributed over 1.6 arcseconds on the sky.
spots in the strongest maser feature differs from that obtained by H2007 with
∼ 0.2 mas. We confirmed that this discrepancy is caused by unrealistic as-
sumptions and insufficient procedures of analysis. If we assume only a single
spot in one velocity channel and perform self phase-only calibration, the results
of H2007 are reproduced. We also found that the relative proper motions
and radial motions of multiple maser clusters are quite large, and therefore the
absolute proper motion of S269 does not pose a tight constraint on the rotation
curve of the Milky Way as was claimed by H2007.
that change of relative positions of maser spots in the cluster reaches 0.1 mas
or larger between observational epochs. All these results imply that the annual
parallax of S269 could not be determined within an error of ∼ 0.1 mas using
assumptions of a single point source model for such widely distributed maser
sources.
Thus the maser astrometry should be performed carefully with consideration
about structure and the time-variation of maser source. The internal motions
of maser clusters among the system also be considered for Galactic astrometry.
The VLBI astrometric accuracy depends on the way of data analysis. Thus, the
details, as well as the results, should be noted clearly for refinement by future
ages.
The distribution of maser
Our analysis also shows
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