Distance and Proper Motion Measurement of the Red Supergiant, S Persei, with VLBI H2O Maser ...

28 Pages·2010·2.08 MB·English

Distance and Proper Motion Measurement
of the Red Supergiant, S Persei,
with VLBI H O Maser Astrometry
2
0 Y. Asaki1,2
1
Institute of Space and Astronautical Science, 3-1-1 Yoshinodai, Chuou, Sagamihara, Kanagawa 252-5210,
0
2 Japan

l [email protected]
u
J

0 S. Deguchi3
3
Nobeyama Radio Observatory, Nobeyama, Minamimaki, Minamisaku 384-1305, Japan

]
A [email protected]
G
. H. Imai4
h
p Department of Physics and Astronomy, Graduate School of Science and Engineering, Kagoshima
-
o University, 1-21-35 Korimoto, Kagoshima 890-0065, Japan
r [email protected]
t
s
a
[
K. Hachisuka5

3
Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China
v
4 [email protected]
7
8
4 M. Miyoshi6
.
7
Division of Radio Astronomy, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo
0
181-8588, Japan
0
1 [email protected]
:
v and
i
X
r M. Honma7
a
Mizusawa VLBI Observatory, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo
181-8588, Japan
[email protected]
1Institute ofSpaceandAstronauticalScience, 3-1-1Yoshinodai,Chuou,Sagamihara,Kanagawa252-5210, Japan
2DepartmentofSpaceandAstronauticalScience,SchoolofPhysicalSciences,TheGraduateUniversityforAdvancedStudies
(SOKENDAI),3-1-1Yoshinodai,Chuou,Sagamihara,Kanagawa252-5210, Japan
3NobeyamaRadioObservatory,Nobeyama,Minamimaki,Minamisaku384-1305,Japan
4DepartmentofPhysicsandAstronomy,GraduateSchoolofScienceandEngineering,KagoshimaUniversity,1-21-35Kori-
moto,Kagoshima890-0065, Japan
5Shanghai AstronomicalObservatory, ChineseAcademyofSciences,Shanghai 200030, China
6DivisionofRadioAstronomy,NationalAstronomicalObservatoryofJapan,2-21-1Osawa,Mitaka,Tokyo181-8588,Japan
7MizusawaVLBIObservatory,NationalAstronomicalObservatoryofJapan,2-21-1Osawa,Mitaka,Tokyo181-8588,Japan
1
ABSTRACT
We have conducted VLBA phase-referencing monitoring of H2O masers around the red su-
pergiant,SPersei,forsixyears. Wehavefittedmasermotionstoasimpleexpanding-shellmodel
with a common annual parallax and stellar proper motion, and obtained the annual parallax as
0.413 0.017mas,andthestellarpropermotionas( 0.49 0.23masyr−1, 1.19 0.20masyr−1)
± − ± − ±
inrightascensionanddeclination,respectively. Theobtainedannualparallaxcorrespondstothe
trigonometric distance of 2.42+0.11 kpc. Assuming the Galactocentric distance of the Sun of
−0.09
8.5 kpc, the circular rotational velocity of the LSR at the distance of the Sun of 220 km s−1,
and a flat Galactic rotation curve, S Persei is suggested to have a non-circular motion deviat-
ing from the Galactic circular rotation for 15 km s−1, which is mainly dominated by the anti
rotation direction component of 12.9 2.9 km s−1. This red supergiant is thought to belong to
±
the OB association, Per OB1, so that this non-circular motion is representative of a motion of
the OB association in the Milky Way. This non-circular motion is somewhat larger than that
explained by the standard density-wave theory for a spiral galaxy, and is attributed to either
a cluster shuffling of the OB association, or to non-linear interactions between non-stationary
spiralarmsandmulti-phaseinterstellarmedia. Thelattercomesfromanewviewofaspiralarm
formationintheMilkyWaysuggestedbyrecentlargeN-body/smoothedparticlehydrodynamics
numerical simulations.
Subject headings: stars: supergiants, masers, Galaxy: structure
1. Introduction
consistent with that of h+χ Per, so that S Per
Phase-referencingVLBItechniqueiscapableof is thought to belong to the OB association. We
determining positions of celestial objects relative can therefore determine the distance and three-
tobackgroundcalibratorswithsub-milliarcsecond dimensional motion of the OB association in the
accuracy (Bartel et al. 1986). Absolute position spiral arm by measuring the annual parallax and
changes of Galactic maser sources can be directly proper motion of the member star.
detected on the sky using this technique, and We report results of phase-referencing VLBI
the observables are very useful for measuring an- monitoring of the H2O masers associated with
nual parallaxes or trigonometric distances to the S Per over six years with the Very Long Base-
sources and their proper motions (e.g., Xu et al. line Array(VLBA) ofthe NationalRadio Astron-
2006;Hachisukaetal.2006). Inaddition,themea- omy Observatory (NRAO). The observations are
sured trigonometric distance and proper motion described in Section 2. Data reduction including
together with the radial velocity of a source can astrometricanalysesispresentedinSection3. The
provideusacompletethree-dimensionalkinematic results are presented in Section 4. We discuss the
information without model assumptions. results in Section 5 and summarize this study in
There are a number of Galactic evolved stars Section6. Theresultspresentedherereplacethose
with circumstellarH2O masers,which are observ- reported previously by Asaki et al. (2007a). In
able with VLBI at 22 GHz. The red supergiant, this paper, we define that the Local Standard of
S Persei(hereafter,S Per),is one such targethar- Rest (LSR) is a reference frame at the position of
boringH2O masersaswellas SiO andOHmasers the Sun and moving in a circle around the cen-
(e.g.,Alcoleaetal.1990;Richards1996). Thisstar ter of the Milky Way. We adopt the IAU stan-
is separated by 1.5◦ from a double cluster, h and dard values for the Galactocentric distance of the
χ Persei (hereafter, h+χ Per, see Figure 1), lo- Sun, R0 = 8.5 kpc, and the circular rotational
cated at the outer edge of the Perseusarm, which velocity of the LSR at the distance of the Sun,
involves a large group of more than 20 red super- Θ0 =220 km s−1. We also assume a flat Galactic
giant stars. The cluster is the most massive open rotationcurve aroundthe Sun. For almost all the
cluster within 3 kpc from the Sun and belongs to parts, we adopt a Solar motion of 20 km s−1 rela-
the OB association, Per OB1. Humphreys (1975) tive to the LSRto the directionof(α1900, δ1900)=
reported that the radial velocity of S Per is fairly (18h, 30◦) for the radial velocity (radio definition
2
oftheLSR).HereafterthisSolarmotionisreferred spect to the positionally reliable ICRF source. A
toasthestandardSolarmotion,andtheLSRwith largerseparationanglewilltakealongertelescope
thestandardSolarmotionisreferredtoasthetra- slew time, and therefore a longer switching duty
ditional LSR. In the following analyses, we adopt cycle. In general, the larger the separation angle
the systemic velocity of S Per of 38.5 km s−1 and/or the longer the switching duty cycle is, the
−
(Diamond et al. 1987) in the traditional LSR. On more difficult is phase-referencing at 22 GHz due
the other hand, because the Galactic parameters to stochastic tropospheric phase fluctuations. We
are known to involve some uncertainties (McMil- selected a lower observing frequency of 15.3 GHz
lan & Binney 2010), we discuss the observational for the pair of KR143 and ICRF 0244+624 to re-
results adopting more realistic values for the So- duceacoherencelosseffectduetothetropospheric
lar motion in Section 5.2, which was determined phase fluctuations. The switching cycle time, ts,
from the average motion of a number of stars in for the phase-referencing is listed in Table 1.
the solarneighborhoodobservedwith the Hippar- Inthefirstthreeepochs,20-minphase-referencing
cos satellite. For the proper motion, we adoptthe sequenceat22GHzwasinterleavedby2-to3-min
heliocentric coordinates. calibratorobservations. Inthelastfiveepochs,20-
min phase-referencing sequences at 22 GHz and
2. Observations 15 GHz were conducted in turn, and each se-
quence was interleaved by short calibrator scans
Figure 1 shows sky positions of the observed
at the same frequency. VLBI cross-correlation
sources. VLBI phase-referencing observations of
wascarriedoutatthe VLBAcorrelationcenterin
S Per at 22.2 GHz have been conducted together
Socorro to generate VLBI fringe data with 1024-
witha closelylocatedcontinuumsourceasa posi-
frequency channels, corresponding to a velocity
tionalreferenceataseparationangleof0.2◦. This
resolution of 0.2107 km s−1. In the first-epoch
positional reference source was initially selected
cross correlation, a wrong position with an offset
from the 6-cm northern sky catalogue (Becker et
by 4 arcsecwas used as a phase trackingcenter of
al. 1991) and the Texas survey (Douglas et al.
S Per. This mistake was recovered in the course
1996). Later we found that this source is cata-
of data reduction process. The observed pairs of
logued under the number 143 in the 21-cm radio
sources in our monitoring program are listed in
continuum survey of the Galactic plane by Kallas
Table 2 together with their separation angles.
& Reich (1980) (the so-called “KR survey”) and
anouterGalaxyVLAsurveybyFich(1986)based
3. Data reduction
onthe KRsurvey,sothatthe sourceisreferredto
hereafter as KR143. Imai(2001)for the first time We analyzed the VLBI data using the stan-
confirmed that KR143 is detectable with VLBI dard NRAO data reduction software, Astronom-
observations at 22 GHz, while we could not find ical Image Processing Software (AIPS), version
an optical counterpart for KR143. We have con- 31DEC06. There were two data reduction series:
ducted a total of eight-epoch VLBI observations one for the pair S Per and KR143, and another
over six years with the ten VLBA antennas. The one for the pair KR143 and ICRF 0244+624.
observing epochs are listed in Table 1.
Two intermediate-frequency (IF) bands with 3.1. Initial calibrations
16-MHz bandwidth in left-hand circular polariza-
Initial calibration tasks were common for both
tionwererecorded. TheseIFbandsarecontinuous
the pairs of sources. First, the amplitude calibra-
in frequency. The H2O maser emissions of S Per tionwasconductedby usingthe measuredsystem
has been received with the lower IF band (IF1)
noisetemperaturesandgainvariationdata. Inthe
whiletheupperIFband(IF2)wasusedtoimprove
next step, Earth Orientation Parameters (EOP)
the Signal-to-Noise Ratio (SNR) for KR143. We
errors, two-bit sampling bias in the analogue-to-
have also conducted phase-referencing observa-
digital (A/D) conversion in VLBI signal process-
tionsofapairofKR143andICRF0244+624with
ing, antenna parallactic angles, and ionospheric
a separation angle of 4.8◦ in the last five epochs
dispersive delays were corrected.
to check the position stability of KR143 with re-
Inthefirstthreeepochs,NRAO150,J0102+5824
3
and 3C 84 have been observed as calibrators at gaincalibrationdata,whichwereappliedtothere-
22.2 GHz, while the former two have been ob- maining frequency channels to make image cubes
served as calibrators in the last five epochs. At for the same maser region. The images were pro-
15.3 GHz, NRAO 150 and J0102+5824have been duced for all channels separately in the velocity
observed as calibrators in the last five epochs. range of 23 and 61 km s−1 with the step of
Among them, NRAO 150 was used both in the 0.2107 km−s−1 in th−e traditional LSR. To pick up
data reduction series for calibrating relative clock maseremissioninitially,weusedthe2-DGaussian
offsets and phase offsets between the independent componentsurveytaskSADineachvelocitychan-
antennas. Phase differences between the two IF nelmap. BasedontheresultsofSAD,wevisually
bands were also removedby using the NRAO 150 inspected the surveyed Gaussian components one
fringe data. In the next steps of data analysis, a byone. Westoredtheimagepixelslargerthan3-σ
customizeddata reductionpathwasusedfor each noiselevelforavisuallyconfirmedmaseremission.
pair of the sources. Hereafterwedefine amaser“spot”asanemission
inasinglevelocitychannel,andamaser“feature”
3.2. Data reduction for S Per and KR143 as a group of spots observed in at least two con-
at 22 GHz tinuous velocity channels at a coincident or very
closely located positions.
For the maser data analysis, the Doppler shift
ForKR143imaging,theDopplercorrectionand
in S Per spectra due to the Earth rotation and
Earth’s Kepler motion were corrected with the bandpass calibration were skipped because the
spectrum was averagedfor the continuum source.
AIPS spectrum channel correction task, CVEL.
The observed frequencies of the maser lines were Since there was no S Per’s maser emission in IF2,
converted to radial velocities with respect to the complex gain calibrationdata for IF1 was ap-
plied to IF2, whose phase and delay biases from
the traditional LSR using the rest frequency of
22.235080 GHz for the H2O 616 523 transition. IF1wasalreadyremovedintheinitialcalibration.
− The synthesized image of KR143 with the pixel
The spectrum deformation due to the receiver
sizeof50µaswasobtainedbyusingtwoIFbands,
complex gain characteristics was calibrated with
the NRAO 150 spectrum in the CVEL process. so that the image SNR is higher than that with
the single IF band by a factor of √2. The SNR
The 4 arcsec error in the position of S Per’s
ofKR143phase-referencedimagesrangesbetween
phase tracking center in the first epoch was cor-
18 and 37 at 22 GHz.
rected with the AIPS visibility phase correction
task UVFIX. Note that, although the S Per vis-
3.3. DatareductionforKR143andICRF0244+624
ibilities might be subject to the coherence loss
at 15 GHz
as a result of the cross correlation task with the
phase tracking center error, the following astro- The Doppler and bandpass correction were
metric analysis is not affected. skipped for both sources in processing of the
We inspected the cross-power spectra for all 15 GHz data as unnecessary. ICRF 0244+624
the baselines in order to select frequency chan- was imaged with the 50-µas pixel size to obtain
nels of emission which would be unresolved and the complex gain calibration data. This calibra-
nothaverapidamplitude–timevariation. Wethen tion data were applied to the KR143 fringe at
carried out fringe-fitting by using the AIPS task 15 GHz before imaging. Synthesized images of
FRING, with an option of no delay search for KR143weremade with the 50-µaspixelsize. The
the selected channel. The fringe-fitted data were SNR of KR143 phase-referenced images ranges
image-synthesizedwith a50-µaspixelfor aregion between 7 and 17 at 15 GHz.
of 4096 4096 pixels, roughly a 200 200-square
× × 4. Results
masregionbyusingtheAIPStaskIMAGR.Using
this image as an initial model, phase and ampli-
4.1. KR143’s position
tude self-calibration was conducted.
Withtheaboveprocessesfromthefringe-fitting Phase-referenced radio maps of KR143 are
to the self-calibration, we obtained the complex dominatedbyaweaksinglecomponentbothat15
and 22 GHz. For the present astrometric study,
4
we firstly determined the position of KR143 with distance of 4 kpc, for comparison.
respect to ICRF 0244+628at 15 GHz, which had The spatial distribution of the image peaks of
not been determined to high precision previously. KR143 at 15 GHz are shown in the top plot of
In this paper, the position of ICRF 0244+624 Figure 3. This plot also shows the 1-σ ellipse (a
in J2000 is adopted as 2h44m57s.696746 and solid line). One possible reason for the observed
+62◦28′6′′.515030 in right ascension and decli- changeposition ofthe peaks is inaccuraciesin the
nation, respectively. Since ICRF 0244+624 has VLBI correlator model for the phase-referencing
shown a very simple structure in the radio maps, astrometry for the pair of the observed sources.
wetreatedthe peakpositionofthe imageasapo- We conducted Monte Carlo phase-referencing ob-
sitionally stable point in the sky. We assume that servation simulations for the pair of KR143 and
KR143’s position at 22 GHz is consistent with ICRF0244+624toexaminewhether the observed
that at 15 GHz, and astrometric analysis of S Per position change could be explained by the un-
was determined with respect to this position. certainties of the VLBI correlator model. For
Since imagesof KR143have rather low SNR, a generatingsimulatedphase-referencingfringes,we
Gaussian fitting for the detected component may used a VLBI observationsimulator,ARIS (Astro-
beaffectedbyarathersevereimagedistortiondue nomical Radio Interferometer Simulator, Asaki et
toahighimagenoiseeveniftheobjectconsistsof al. 2007b). In the simulations, we assume flux
only a single component. In addition, the phase- densities of KR143 and ICRF 0244+624 of 20
referencing image may be distorted by the resid- and500mJy,respectively,whichweredetermined
ual phase errors, introduced, e.g., by the static from our observations. The sources were assumed
tropospheric delays. We used the peak position to be point-like sources. The simulated observa-
of KR143’s image as the positional reference in tion schedule and observing system settings such
orderto minimize those effects in determining the as the recording bandwidth and A/D quantiza-
position. Thepositionmeasurementerrorwascal- tion level were adopted from actual VLBA obser-
culated from the beamwidth over the SNR at the vations. There weretwo simulationseries: one in-
peak. cluded 1-σ static tropospheric excess path length
For the astrometric measurements of Galac- error to the zenith (zenith EPL error) of 3 cm
tic sources, a positional reference should be a (e.g., Reid et al. 1999), and the other one used
background extragalactic source such as an Ac- the zenith EPL error of 6 cm. We made 100 tri-
tive Galactic Nuclei (AGN). However, because als for each of the zenith EPL error cases. The
we hardly know whether KR143 is a suitable simulation results are shown in the middle and
background source, we then investigated how bottom plots of Figure 3 for the 1-σ zenith EPL
positionally stable KR143 is with respect to error of 3 and 6 cm, respectively. In the case of a
ICRF 0244+624. Figure 2 shows a time variation zenith EPL error of 6 cm, the simulation results
of the KR143’s position in the last five epochs are consistent with the observation results. Since
of our experiment. Assuming that KR143 is a some of our observations were conducted during
Galactic source for which the annual parallax is the summer period, it is quite natural that the
significant,wecarriedoutaLevenberg-Marquardt zenith EPL errorwouldbe around6 cm. We con-
non-linear least-square analysis to obtain the an- clude that the KR143’s position change is mainly
nual parallax and proper motion, but could not duetothe zenithEPLerrorofseveralcentimeters
find a reliable solution because the χ2 value per in the VLBI correlator model. Hereafter we refer
degreeoffreedomwasquitelarge,nolessthan57. a relativepositionerrorfora pairofpoint sources
Thissuggeststhattheannualparallaxandproper with the phase-referencing due to uncertainties in
motion are below our threshold because KR143is aVLBIcorrelatormodelfortheatmosphericEPL,
sufficientlyfarfromtheSun. Thisthresholdisde- antennapositions,EOP,andotherphaseerrorfac-
termined by the accuracy of the relative position tors as an astrometric error.
measurements in phase-referencing for the pair of The measured flux densities of KR143 are
the sources. Figure 2 also displays a sinusoidal shown in Figure 4 together with the data from
pattern of our least-square analysis result as well thepreviousworkbyDouglasetal.(1996),Kallas
as another sinusoidal pattern for a source at the & Reich (1980), Condon et al. (1998), Becker et
5
al. (1991), Fich (1986), and Imai (2001). Note at epochs D, E, F, and G were all detected at the
that, for the measurements of the flux density of same velocity channel with the SNR of at least
KR143 from our radio images, we conducted a 6; (2) in addition to the above epochs, they were
phase-self-calibration process. Figure 4 resembles detected with the SNR of at least 6 at least at
asynchrotronpower-lawspectrum,makingitvery oneoftheotherepochsatthesamevelocitychan-
likely that KR143 is an AGN. Although there is nel; (3) no significant velocity drift larger than
currently no concrete evidence that KR143 is not 0.25 km s−1 yr−1 was observed for the features
located in or near our Galaxy because of the un- involving the selected spots; and (4) morphology
known redshift, we assume throughout this paper does not significantly change between the epochs.
that KR143 is an AGN. The relative position of We selected 44 maser spots from eight maser fea-
KR143ontheskywithrespecttoICRF0244+624 tures.
is determined with the standard errors of 61 and SecondlywecarriedouttheLevenberg-Marquardt
116 µas in right ascension and declination, re- least-squareanalysisforthei-thmaserspottoob-
spectively, from all the five epochs. The absolute taintheinitialposition,(∆αi , ∆δi ),atepochA,
A A
position of KR143 is listed in Table 3. the constant proper motion, (µi cosδ, µi), along
α δ
with the annual parallax, πi, both in right ascen-
4.2. Astrometry of S Per
sion and declination. In the initial trial, reduced
χ2 values of the analysis were in the range from
In the phase-referencing astrometric analysis
a few tens to a few hundreds. These large values
for S Per, we investigated the time variation of
indicate that there must be unaccountederrorsin
the peak positions of the maser spots with re-
the analysis. As explained above, we expect that
spect to the peak position of the 22-GHz phase-
the astrometric error in our observation is 6 and
referencedradioimageofKR143. Toestimatethe
14µas forrightascensionanddeclination,respec-
astrometricerrorwiththeVLBIphase-referencing
tively. On the other hand, internal morphological
for the pair of S Per and KR143, we conducted
time variations of the maser features during the
Monte Carlo simulations of phase-referencing ob-
monitoringperiodofoversixyearscannotbeneg-
servationsforthepairofthesesourcesat22.2GHz
ligible, as already pointed out in previous studies
with ARIS. In the simulations, we assumed that
(e.g., Imai et al. 2007). For diagnostic purposes,
flux densities of S Per and KR143 of 1 Jy and
we added position uncertainties of 0.2 mas for
20mJy,respectively,andthatSPerwasa contin-
epochs A and H, 0.1 mas for epochs B and C,
uumsource. ThetroposphericzenithEPLerrorof
and 0.05 mas for epochs D, E, F, and G to the
6 cm was set as found in the simulation described
astrometricerrorbothforrightascensionanddec-
aboveforthe pair ofKR143andICRF0244+624.
lination. This resulted in making the reduced χ2
Duetothesmallseparationangleandfastantenna
switching,thesimulationsshowthatthe1-σerrors values equal to unity in our least-square analy-
in the relative position are 6 µas and 14 µas in sis. This additional position uncertainty which
we attribute to the unpredicted time variations
right ascension and declination, respectively. We
in maser morphology is referred to hereafter as
used these standard deviations to provide the as-
a maser morphology uncertainty. Table 4 lists
trometric error for the pair of the sources in the
the least-square analysis results for each of the
following analysis.
selected maser spots. Figure 6 shows the analy-
Figure 5 shows the spatial distribution of the
sis result of one of the maser spots (spot-ID 39
H2O maser emission of S Per for all the epochs.
in Table 4). Figure 7 shows the histogram of
The maser emission is spread within a roughly
the evaluated annual parallaxes for the 44 maser
circular structure with a radius of about 60 mas.
spots. The weighted average of the evaluated an-
We identified 77 maser features consisting of 478
nual parallaxes is 0.414 0.006 mas.
maser spots in all the available epochs. For ob- ±
We thirdly conducted a combined fitting with
tainingthetrigonometricparallaxandpropermo-
ourleast-squareanalysisforthe44maserspotsto
tion of the star, we conducted the following four
obtainthetrigonometricdistancetoSPer. Inthis
steps. Firstly, we selected a limited number of
step, we assumed that all the maser spots have
maser spots to evaluate the annual parallax. Our
a common annual parallax, π∗, which is one of
selection criteria are as follows: (1) maser spots
6
the fitting parameters. This combined fitting re- sition measurement error to each maser spot at
sult for π∗ is 0.413 mas, almost identical to the eachepoch. Apositionoffsetduetotheastromet-
weightedaverageofthe44annualparallaxes. The ric error is applied to all the maser spots at each
parameter fitting error in π∗ was 0.006 mas from epoch. A position offset due to the maser mor-
a covariance matrix of our least-square analysis. phology uncertainty is applied to all the maser
In obtaining the annual parallax, two system- spots included in each of the eight maser fea-
atic errors have to be considered. One is the as- tures at each epoch. We investigated the follow-
trometric error, and the other one is the maser ing error cases: (1) only position measurement
morphology uncertainty which provides a com- error; (2) only astrometric error; (3) only maser
mon position offset to the member spots in a cer- morphology uncertainty; and (4) a combination
tain maser feature. The most conservative esti- of all the three errors above. We generated 100
mate of the obtained annual parallax error be- data sets for each of the four cases and carried
comes 0.040 mas, which is calculated from the out the Levenberg-Marquardt least-square analy-
above statistical error of 0.006 mas multiplying sis. Root-mean-square errors from the average of
by a factor of √44 under an assumption that the the 100 obtained annual parallaxes were 3, 9, 15,
position error of the selected maser spots are not and 17 µas for the cases of 1, 2, 3, and 4, respec-
independent. Hachisuka et al. (2009) applied a tively. The maser morphology uncertainty dom-
methodto averagepositionsofanumber ofmaser inates the annual parallax error in our combined
spotsfromthreefeaturesofW3(OH)watermasers fittingwhiletheastrometricerrorcorrespondstoa
before their parallax fitting in order to avoid the relativelysmallpart. Itisreasonabletoadoptthe
maser morphology uncertainty, and achieved a 6- value of 17 µas as an upper limit of the trigono-
µasaccuracyintheannualparallaxmeasurement. metric distance uncertainty, corresponding to the
We note that the impact of the astrometric er- trigonometric distance of 2.42+−00..1019 kpc. We then
roronthe annualparallaxmeasurementis not re- conducted our least-square analysis to obtain in-
ducedevenifanumberofmaserfeaturesaresimul- dividualpropermotionsofallthe478maserspots
taneously processed. On the other hand, the im- with π∗.
pact of the maser morphology uncertainty can be Theobtainedpropermotionsofthemaserspots
reduced in processing multiple maser features be- are considered to be a combination of an expand-
causethe positionoffsetdue tothiserrorbecomes ingflowofthecircumstellarenvelop(CSE)andthe
randomized. Since there are eight maser features proper motion of the red supergiant in the Milky
in our analysis, the error quantity of 0.040 mas is Way. We finally conducted a model fitting anal-
overestimated. Figure 8showsthe positionresid- ysis assuming a spherically expanding flow model
uals of the selected44 maserspots after removing described by Imai et al. (2000) and Imai et al.
the obtainedannualparallaxof0.413mas,proper (2003). Inthemodelfitting,weestimatedthedis-
motionsandinitialpositions. Itisnoticedthat,al- tributioncentroidindicatingthestellarpositionas
though a small positive trend can be seen in right well as the stellar proper motion separated from
ascension at epoch D, there are not apparently the expanding shell motion of the CSE. We ob-
obvious systematic errors at central four epochs tainedthestellarpropermotioninrightascension
from D to G. It is also recognizable that system- as µ∗ cosδ = 0.49 0.23 mas yr−1, and in dec-
α
atic errorsare patially seen for specific maser fea- lination as µ∗−= ±1.19 0.20 mas yr−1. This
δ
− ±
tures possibly due to the time variations in the propermotionis consistentwiththat listedin the
maser morphology (see, for example, spot-ID 41– Tycho-2Hipparcoscatalogue,( 0.1 1.8, 2.8
44 (feature-ID 8) at epochs D, E, and F). 1.8) mas yr−1, within its uncer−taint±y (Hog−et a±l.
To evaluate contributions of those systematic 2000). The centroidof the maserdistribution was
errors to the obtained annual parallax, we con- determinedwithanaccuracyof8masinbothright
ducted simulations of the combined fitting analy- ascension and declination. Results of our astro-
sis by using fake data sets imitating the selected metric analysis for S Per are listed in Table 5. A
maser spots with the position measurementerror, residualtimevariationofthe maseremissionafter
astrometric error, and maser morphology uncer- removing the annual parallax and stellar proper
tainty. A random position offset due to the po- motion is shown in Figure 9. Internal proper mo-
7
tions of the identified 478 maser spots are shown the difference in locations between the outer edge
in Figure 10 along with their radial velocities. maser sources and those located in the inner part
of the arm. Hence, the estimated width of the
5. Discussions Perseus arm is at least 0.7 kpc.
∼
5.1. Distance to S Per 5.2. Three-dimensional motion of S Per
in the Milky Way
Ourmonitoringprogramdeterminedthetrigono-
metric distance to S Perto be 2.42+−00..1019 kpc with- The stellar proper motion of S Per enables us
out model assumptions. Marvel (1996) estimated to discuss the three-dimensionalkinematics ofthe
a distance to this star as 2.3 0.5 kpc by means evolved star in the Milky Way. In this subsec-
±
of a statistical parallax method, in which relative tion, we use realistic values of the Solar motion 1,
proper motions of the H2O maser spots are fitted (U⊙,V⊙,W⊙)=(7.5,13.5,6.8)kms−1 (Francis&
toanexpandingshellwherepropermotionsofthe Anderson 2009; see also discussions in McMillan
outermost spots are equal to the radial velocities & Binney 2010). Let us estimate a non-circular
of the maser spots with no significant proper mo- motion of S Per in LSR at the red supergiant.
tions. The statistical parallax distance coincides This star has a rather large non-circular motion
with the trigonometric one within the measure- of 15 km s−1 at the Galactocentric distance of
ment uncertainties. The trigonometric parallax 10.4 kpc: the non-circular velocity components
greatly improved the accuracy of the distance: are 3.3 2.3 km s−1 toward the Galactic center,
the uncertainty is five times better than that of 12.9 2±.9 km s−1 towardthe anti-directionof the
the statistical parallax. Gala±cticrotation,and6.3 3.1kms−1 towardthe
±
S Per is considered to belong to Per OB1 be- south pole.
causetheradialvelocityofSPerisconsistentwith RecentVLBIastrometricobservationsofGalac-
thatofthis OBassociation(Bidelman 1947). The tic maser sources have revealed large non-circular
double cluster, h+χ Per, whose distance was de- motions of several objects in the Perseus arm.
termined to be 2.34 kpc with the 2-percent accu- Figure 11 presents the non-circular velocity com-
racy from the H-R diagram (Slesnick et al. 2002) ponents of S Per along with those from other
isalsoincludedinPerOB1,sothatSPerisinthe maser objects in the Perseus arm. Although this
vicinity of the double cluster in the OB associa- non-circular motion is not sensitive to R0 and Θ0
tion. TheapparentradiusofPerOB1isabout4◦, with the 10-percent variation, we have to admit
correspondingtoa 170-pcradiusatthedistance that, if there is a 10-percent dip in the Galac-
∼
of h+χ Per. S Per is located on the far side of tic rotation curve at the Galactocentric distance
Per OB1. of 9–10 kpc (Sofue et al. 2009), the lag of S Per
RecentVLBIastrometricobservationsofGalac- from the Galactic rotation (V component) be-
tic H2OandCH3OHmasersourcesinthe Perseus comes smaller. However, such a rotation curve
arm have been used to measure their trigonomet- cannot remove all the observed non-circular mo-
ric distances. Figure 11 shows the locations of tions of the maser sources in the Perseus arm, or
suchGalactic masersclosetoSPerinthe Perseus evenmakesseveralofthemlarger. Moreover,such
arm in a face-on view of the Milky Way (Xu et peculiarmotionscanbefoundforGalacticmasers
al. 2006; Sato et al. 2008; Moellenbrock et al. in star forming regions (SFRs) not only along the
2009; Moscadelli et al. 2009; Reid et al. 2009a). Perseus arm, but also along the local spur, Outer
In the figure, we depict only the H2O masers for and Inner arms (Reid et al. 2009b; Rygl et al.
NGC281West;measurementsusingthemethanol 2010). These two papers also discuss a large lag
masers result in a smaller trigonometric distance of the V component of the SFRs from a flat rota-
than using the H2O masers (Rygl et al. 2010). tioncurvetogetherwithaHipparcosSolarmotion
From this figure, it is clear that S Per, as well
as NGC 281 West, are located at the outer edge 1U⊙ isthevelocitycomponentdirectedtotheGalacticcen-
of the Perseus arm. Assuming a pitch angle of ter, V⊙ is the component toward the circular rotational
the spiral arm of 16.5◦ (Reid et al. 2009b), we directionintheGalactic plane,andW⊙ isthecomponent
perpendicular to the Galactic plane and directed to the
can estimate the width of the Perseus arm from Galacticnorthpole.
8
of Dehnen & Binney (1998). On the other hand, narioisasfollows: Consideringtheageofh+χPer
McMillan & Binney (2010) reanalyzed the sam- is 12.8 1.0 Myrs (Slesnick et al. 2002), a cloud
±
ples published by Reid et al. (2009b) in order to shuffling took place near the precursor molecular
estimate the Galacticrotationaswellasthe Solar cloud of Per OB1 around a few tens of Myrs ago
motion. Their fitting result of the V⊙ component because of radiation pressure from precedent OB
of 11 km s−1, instead of 5.2 km s−1 of Dehnen stars and/or supernova explosions in the Galactic
& Binney (1998), can reduce such the large lags. plane. ThemolecularcloudlaterformingPerOB1
However the Galactic SFRs still seems to have has been accelerated in the out-of-disk direction.
10 20 km s−1 peculiar motions even with the S Per was formed in the molecular cloud ahead of
−
revised Solar motion, and those non-circular ve- alargeSFRaroundthedoublecluster. Thiscloud
locity components in the Galactic plane somehow shuffling also might affect the in-disk non-circular
show randomness. These non-circular motions do motions of the cloud. Another item of observa-
not quantitatively match a standard understand- tional evidence for a cloud shuffling causing the
ing of the stationary density-wave theory (Lin & non-circular motion was provided by Sato et al.
Shu 1964) and a standing galactic shock solution (2008) and Rygl et al. (2010) for NGC 281 West.
in a tight-winding spiral potential (Roberts 1969; Itwassuggestedthatlargenon-circularmotionsof
Roberts & Yuan 1970). NGC 281 West masers were due to the supershell
One of the reasons for such peculiar motions generated by supernova explosions.
may be attributed to an intrinsic space motion of Another new idea to explain the non-circular
each SFR. Lee & Lim (2008)found that there are motions of the Galactic SFRs arises from large
new SFRs in the southern HI shell in Per OB1, N-body/hydrodynamics numerical simulations.
andthatthenewstarshavelargersouthernveloc- Baba et al. (2009) showed that, with their high-
ities due to the up-to-date cloud shuffling caused resolution numerical model of a spiral galaxy
by h + χ Per. According to the cloud-shuffling and their original N-body/gas simulation code
model, a molecular cloud is swept up by UV ra- (Saitoh et al. 2009), the non-circular motions
diation pressure from nearby OB stars, perhaps of the SFRs were explained by natural conse-
together with supernova explosions. Star forma- quence of non-linear interactions between non-
tions are triggered in the cloud to form OB asso- stationary spiral arms and multi-phase interstel-
ciations. At the same time, the compressed cloud lar media. With their numerical simulations of
willbeacceleratedintheanti-directiontotheorig- a disk galaxy, they found that young stars with
inal sources causing the cloud shuffling. Cappa & ages 50 Myr in a spiral galaxy have large and
≤
Herbstmeier (2000) reported on an HI superbub- random non-circular motions. This idea can be
ble with 2◦-radius centered at h+χ Per. How- applied to S Per and Per OB1 because the ages
ever, S Per, located inside the superbubble, does of those objects are younger than 50 Myr. The
not move away from the double cluster, so that N-body+hydrodynamicssimulationsalsorevealed
this star does not seem to be formed in a process that molecular clouds in a spiral galaxy can have
of the cloud shuffling caused by h+χ Per. a velocity dispersion of several km s−1 in the ver-
Althoughwecannotfindatraceofclustershuf- tical direction to the disk (J. Baba, 2009, private
flingsourcesotherthanh+χ Peratthismoment, communications), so that a rather large peculiar
the cloud shuffling model still provides us an at- motion of Per OB1 vertical to the Galactic plane
tractive idea in order to explain the large non- couldbeexplainedwithoutacloudshuffling. Since
circular motion of the OB association and S Per. we have quite limited samples with the measur-
It is interesting that Lee & Lim (2008) also re- able non-circular motions of the young objects in
ported that proper motions of stars in Per OB1 the Milky Way, it is very important to measure
based on the Hipparcos measurements show a ve- the distances and proper motions of the spiral
locity componentdownwardto the Galactic plane arm objects to compare with those simulation re-
(towardtheSouthGalacticpole),sothatthenon- sults. A deep understanding of the dynamics of
circular motion of S Per may be representative of theGalacticspiralarmsandtheoriginofthenon-
a motion of the molecular cloud in which the OB circular motions of SFRs will be possible in near
stars and S Per were formed. The plausible sce- future when massive numerical simulations can
9
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