T he 3-D kinem atics of w ater m asers around the sem iregular
variable R T V irginis
arXiv:astro-ph/0302389v1 19 Feb 2003
H iroshiIm ai1;2;3,K atsunoriM .Shibata2;4,K evin B.M arvel5,Philip J.D iam ond6,Tetsuo
Sasao2,M akoto M iyoshi2,M akoto Inoue4,V ictor M igenes7,and Yasuhiro M urata8
A B ST R A C T
W e report observations of water m asers around the sem iregular variable RT V irginis (RT
V ir),w hich have been m ade w ith the Very Long B aseline A rray (V LB A ) ofthe N ationalR adio
A stronom y O bservatory (N R A O ) at ve epochs, each separated by three weeks of tim e. W e
detected about 60 m aser features at each epoch. O verall,61 features,detected at least tw ice,
were tracked by their radialvelocities and proper m otions. T he 3-D m aser kinem atics exhibited
a circum stellar envelope that is expanding roughly spherically w ith a velocity of ’ 8 km s 1 .
A sym m etries in both the spatialand velocity distributions ofthe m aser features were found in
the envelope, but less signi cant than that found in other sem iregular variables. System atic
radial-velocity drifts ofindividualm aserfeatureswere found w ith am plitudesof 2 km s 1 yr 1 .
For one m aser feature, we found a quadratic position shift w ith tim e along a straight line on
the sky. T his apparent m otion indicates an acceleration w ith an am plitude of33 km s 1 yr 1 ,
im plying the passage ofa shock wave driven by the stellarpulsation ofRT V ir. T he acceleration
m otion is likely seen only on the sky plane because of a large velocity gradient form ed in the
accelerating m aserregion.W e estim ated the distance to RT V ir to be about220 pc on the basis
ofboth the statisticalparallax and m odel- tting m ethods for the m aser kinem atics.
Subject headings: m asers| stars: individual(RT V ir)| stars:evolved,m ass-loss,pulsation
1. Introduction
1M
izusaw a A strogeodynam ics O bservatory, N ational
A stronom ical O bservatory, M izusaw a, Iw ate 023-0861
Japan
2 V LB IE xploration ofR adio A strom etry P roject O ce,
N ational A stronom ical O bservatory, M itaka, Tokyo 1818588,Japan
3 Joint Institute for V LB I in E urope, Postbus 2, 7990
A A D w ingeloo,the N etherlands
4 V LB I Space O bservatory P rogram m e P roject O ce,
N atinal A stronom ical O bservatory, M itaka, Tokyo 1818588,Japan
5 A m erican A stronom ical Society, 2000 Florida A venue
N W Suite 400,W ashington D C 20009
6 M E R LIN /V LB I Facilities, Jodrell B ank O bservatory,
U niversity of M anchester, M accles eld, C heshire SK 11
9D L,U nited K ingdom
7 D epartm ent ofA stronom y,U niversity ofG uanajurato,
A pdo Postal144,G uanajuato C P 36000 G T O ,M exico
8 Institute of Space and A stronautical Science, 3-1-1,
Y oshinodai,Sagam ihara,K anagaw a 229-0022,Japan
U nderstanding the dynam ics ofm ass loss ow s
in circum stellarenvelopesofevolved starsisoneof
the m ost im portant areas ofresearch in the overallm assdevolution ofstarsand the cycling ofthe
interstellar m edium . Fundam entally,m aterialon
thesurfaceofan evolved stargetscolderand form s
dustw hile itism oving into interstellarspace.T he
new ly form ed dust is accelerated by the stellar
radiative pressure and form s an expanding envelope.H owever,such processesarecom plicated because the related phenom ena occur in a dynam ically and physically unstable region. M aser em ission produced from silicon m onoxide (SiO ),water
vapor (H 2 O ), and hydroxyl (O H ) m olecules are
com m only found in m any circum stellar envelopes
(e.g.,R eid & M oran 1981;Elitzur 1992).B ecause
ofthe com pactness(dow n to 0.1 A U )ofindividual
m aser features, or probably physical gas clum ps
1
(e.g.,C olom eretal. 1992;Im aietal. 1997),they
are good tracers for investigating the kinem atics
ofthe envelopes using very long baseline interferom etry (V LB I).M ulti-epoch observations ofSiO
m asers around M ira variables,w hich are located
closer to a stellar surface than other m asers,using the Very Long B aselineA rray (V LB A )suggest
that circum stellar envelopes ofM ira variables are
not necessarily spherically sym m etric,very likely
due to anisotropicm assejection on the stellarsurface (e.g., D iam ond & K em ball 1999). O n the
other hand,shock waves are also expected sim ultaneously,w hich are driven by the periodic variation in stellarradiative pressure to the dustin the
envelopes. T hese shock waves caused by stellar
pulsation are form ed near the stellar surface and
transported to larger distances from the star.
T he gas dynam ics of circum stellar envelopes
can also be studied w ith m ulti-epoch observations of water m asers w ith V LB I. T he dynam icalchange ofthe envelope due to stellarpulsation
is not so signi cant ( 10% ) in the near-vicinity
ofstellar surface,a so-called "radio atm osphere"
and a "m olecular atm osphere" (R eid & M enten
1997). In fact, the am plitude of the expansion
and contraction m otions seen in SiO m asers in
this region is sm all (10-20% , D iam ond & K em ball 1999). O n the other hand, in the outer region (T 1000 K ) w here water m asers are excited,dust form ation starts and shock waves are
enhanced due to dust-induced radiative pressure
(e.g.,H ofner,Feuchtinger,& D or et al. 1995).
A shock wave is expected to produce rapid velocity changes (acceleration/deceleration) by up to
10 km s 1 in front and in back of it, these w ill
be directly detected as radial-velocity drifts and
properm otionsdeviating from a constantvelocity
m otion. T he present V LB I technology enables us
to detect such acceleration/deceleration m otions
w ith an accuracy of 10 m icroarcseconds ( as) in
position and of0.1 km s 1 in radialvelocity.Such
trials have recently started (e.g.,Ishitsuka et al.
2001,hereafter I01). W ater m asers are also good
tools to directly estim ate the distances to evolved
starsusing know ledge oftheir3-D velocity vectors
(radialvelocities and proper m otions),a m ethod
w hich does not rely on the standard distance ladder m ethods (M arvel1997). D istance estim ation
w ith water m aser data w illbe applicable to distance m easurem ents for m any evolved stars invis-
ible atopticalwavelengthsafterexam ining the reliability and com paring w ith other m ethods.
H erewepresentthe3-D m otionsand theradialvelocity driftsofwaterm asersassociated w ith the
sem iregular variable star RT V irginis (RT V ir),
w hich have been m easured from V LB A data. RT
V ir is one of the brightest water m aser sources
(e.g.,B owers& Johnston 1994,hereafterB J;Yates
& C ohen 1994, hereafter Y C ; R ichards et al.
1999a,hereafter R C B Y ;Yates et al. 2000,hereafterY R G B ).T heperiod ofstellarpulsation ofRT
V ir has been estim ated to be ’ 155 d w ith som e
irregularity (e.g.,K holopov etal. 1985;Etoka et
al. 2001). Im aiet al. (1997) (hereafter Paper I)
found anotherpulsation period of375 d using data
obtained by the A m erican A ssociation ofVariable
StarO bservation (A AV SO ).R adial-velocity drifts
ofthe water m asers,w ith tim e,have been found
from V LB I observations (Paper I), however, the
origin of the drifts and the true m aser kinem aticsare notyetclearbecause ofinsu cientangular
resolution and a sm allam ount of proper m otion
data (c.f.,R C B Y ;Y R G B ).
Section 2 describes the V LB Iobservations and
data reduction.Section 3 sum m arizestherevealed
3-D kinem atics of the water m asers and the detection ofacceleration ofone m aser feature in its
proper m otion. Section 4 discusses the dynam ics
ofthe circum stellarenvelope ofRT V ir,w hich exhibits acceleration. M easurem ents ofthe distance
to RT V ir are also m entioned there.
2. O bservations and D ata R eduction
T he m onitoring observations of water m asers
around RT V ir w ith the V LB A have been m ade
at ve epochs during 1998 M ay{A ugust, w ith
a separation of 3 weeks between the successive
two epochs. Table 1 sum m arizes the status of
the observations. Each of the observations had
a duration of 4 hrs including scans towards RT
V ir and the calibrator 3C 273B for clock o set and com plex-bandpass calibration. T he received signals were recorded w ith one base-band
channel (B B C ) w ith a center velocity at VL SR =
17.0 km s 1 and a bandw idth of 4 M H z in dual
circular polarization m ode. T he correlated data
were processed w ith 1024 velocity channels and a
velocity spacing of0.056 km s 1 in each channel
at 22.24 G H z.
2
T heproceduresin data reduction using N R A O ’s
A IPS and m aser position m easurem ent we have
applied were alm ost the sam e as those presented
in section 2.2 ofIm ai etal. (2000)and section 3.1
ofIm ai,D eguchi,& Sasao (2002)(hereafterPaper
III), respectively. In the present work,the com plex bandpass characteristics were obtained from
data on 3C 273B w ith an uncertainty ofless than
1 in phase.Foram plitude calibration,we applied
a tem plate spectrum ofthe water m aser em ission
obtained from the auto-correlation data. T he velocity channelat VL SR ’ 17.1 km s 1 was selected
as reference for fringe tting and self-calibration
(see table 1). T he naturally weighted visibility
data created a synthesized beam of 0.41 m as
0.94 m asw ith a position angle of7 .6.T he detection lim it was typically 200 m Jy beam 1 at a 5noise levelin m apsw ithoutbrightm aserem ission.
T he positionalaccuracy for a m aser feature was
lim ited typically to 50 as m ainly because ofthe
extended structure ofthe feature.
3. R esults
sizes ofthe m aser features. O nly 36 ofthe m aser
features were detected at least three tim es, indicating that individualm aserfeatures turn on and
o on a tim e scale oftypically 1{2 m onths.R C B Y
and Y R G B reported m aser proper m otions ofup
to 3 m as in 70 days in the year 1996,the values
were slightly larger than those m easured in the
presentpaper(typically 1{2 m asin 80 daysin the
year 1998).
Figure 1 show s changes in positions and radial
velocities of m aser features detected ve tim es.
O ne can nd jum ps in positions and radial velocities w ithin the above stability criteria in som e
m aser features (e.g. RT V ir:I2002 20). T hese
m aser features were blended w ith nearby (closer
than 0.5 m as)m aserfeatures,forw hich itwasdi cultto exactly trace theirvelocitiesand positions.
O n the otherhand,we found notonly properm otions thatwere well t by a constant-velocity m otion butalso exhibited linearradial-velocity drifts
in som e features. W e also found an acceleration
m otion fora feature in itsproperm otion,w hich is
described in detailin section 3.3.
3.1. P roper M otions of W ater M aser Features
3.2. T he 3-D K inem atics of the R T V ir
ow
T he waterm asersin RT V irwere spatially well
resolved into individual m aser features w ith the
V LB A synthesized beam . Each m aser feature is
com posed ofa com pact (< 1 A U ) bright part and
an extended structure.A sa result,about60 m aser
features have been detected at every observation.
Table 1 show s the num bers ofm aser features detected atindividualepochs.Previousobservations
w ith larger synthesized beam s (Paper I; R C B Y ;
Y R G B ) m ay not be able to distinguish som e of
individualm aser features because ofthe crow ded
distribution ofm aser features in the beam .
W e traced the position and radial velocity of
each m aser feature, w hich had been stable from
one epoch to anotherw ithin 1 km s 1 in radialvelocity and 0.5 m asin position.W ealso checked the
stability of spatialpatterns of the m aser feature
(alignm entofvelocity com ponentsorspots,Paper
III).A totalof60 m aserfeatureswere detected at
least tw ice and their relative proper m otions and
radial-velocity drifts were m easured. Table 2 lists
m easured properm otionsand radial-velocity drifts
ofm aser features. T he estim ation ofuncertainty
in proper m otion takes into account the apparent
Figure2 show sthe angulardistribution and the
3-D m otions ofm aser features. T he features exhibit an elongation in their spatial distribution
and a radial-velocity gradientin the east{westdirection, w hich have been visible in previous observations (B owers, C laussen, & Johnston 1993;
B J;Y C ;PaperI;R C B Y ;Y R G B ).T he 3-D m aser
kinem aticsclearly exhibitsan expanding ow ,not
rotation. T he kinem atic ow looks clearer w hen
including in the diagram the 60 m aserfeaturesdetected at least tw ice than w hen only including 36
features detected at least three tim es. B ecause
ofthe crow ded distribution ofm aser features and
very short lifetim es of m aser features, m isidentication of feature m otions should be taken into
account especially for the features detected only
tw ice. W e m ade further analyses,however,using
allofthe properm otion data in the presentpaper.
3.2.1. A nalysis based on the velocity variancecovariance m atrix
W e perform ed analysis based on diagonalization of the variance{covariance m atrix (V V C M )
3
ofour obtained m aser velocity vectors (B loem hof
2000; I01). T he velocity dispersions used in the
V V C M analysis are the quantities directly determ ined by a properm otion m easurem entthatlacks
the absolute position reference. T he V V C M diagonalization is done by obtaining eigenvectors
and eigenvalues for the V V C M ,w hich correspond
to the kinem atic axes of the ow and velocity
dispersions along the axes, respectively. T hus,
the V V C M analysis is an objective and m odelindependent m ethod. T he diagonalized V V C M
was as follow s,
1
0
@
xx
yx
zx
xy
yy
zy
xz
yz
zz
0
1
A = @
23:84 3:09 4:19
3:09 24:11 7:17 A
4:19 7:17 21:09
only a system ic bulk m otion,or the m otion ofthe
star,and a location ofthe starasfree param eters.
T hen,we also estim ated a distance to RT V irand
the velocity eld ofthe radialexpansion. In the
presentpaper,we assum ed the speed ofthe radial
expansion ofa m aser feature i,Vexp (i),as a function of the distance to a m aser feature from the
origin ofthe out ow ,ri,w hich is expressed as
Vexp (i) = V0 + V1
;
(2)
w here V0 isthe intrinsic velocity atthe stellarsurface,V1 the velocity at a unit distance r0 , the
power-law index indicating the apparentacceleration ofthe ow . W e applied the tting technique
step-by-step,excluding m aserfeaturesw ith unreliably largedistancesfrom theout ow origin (> 000.3
or66 A U at220 pc). Table 3 show sthe bestsolutionsobtained in the analyses.Figure 3 show sthe
distribution offeatures w ith expanding velocities
obtained using equation (10)ofIm ai etal. (2000)
versusdistancesfrom theestim ated position ofthe
centralstar.
T hrough this procedure,we found that several
m aser features had negative expansion velocities
or infallm otions towards the star (see also gure
2). A lthough som e ofthe features were detected
atleastatthree epochs,itis stillunclearw hether
they were tracing actualphysicalm otions. W hen
including these infalling m aser features,the bestt function indicates a slow (Vexp < 5 km s 1 ) expansion ofthe ow w ith m arginaldeceleration ( gure 3b). T hese are inconsistent w ith the suggestion thattheRT V ir ow hasan expansion velocity
Vexp ’ 10 km s 1 in the water m aser region and
radialacceleration toward the outerO H m aserregion (R C B Y ).T he estim ated position ofthe star
is roughly at the center ofthe w hole m aser distribution but slightly biased toward clusters of the
blue-shifted m aser features located at the southwest ofthe w hole region. T he estim ated position
ofthe expansion centerorthe starislocated close
to the centerofthe "ring" found in the m aserdistribution. N o m aser feature is located w ithin 30
m as(7 A U )from thestar,indicating a "quenching
zone" ofwater m aser em ission (Y C ).
O n the other hand,w hen excluding the m aser
featuresexhibiting infall,a higherexpansion velocity Vexp ’ 8 km s 1 was obtained. T he estim ated
0
1
15:03
0
0
) @
0
32:79
0 A ;
0
0
21:22
ri
r0
(1)
w here ij = ji is a variance (i = j) or a covariance (i 6
= j) of m easured m aser m otions in
the i- and j-axes (x, y,or z) in unit of km 2s 2 .
To estim ate uncertainties ofthe obtained values,
we also perform ed a M onte C arlo sim ulation generating V V C M s w ith arti cialerrors around the
values obtained in the m easurem ent. T he eigenvectorcorresponding to the largesteigenvalue (velocity dispersion)had an inclination of24 .7 4 .6
w ith respect to the sky plane and a position angle of 35 .8 14 .9, w hich is roughly parallel to
both of the directions of the elongation and the
velocity gradient m entioned above. T his im plies
the bipolarity of the RT V ir ow , but is not so
signi cant,since the velocity dispersion isroughly
equal in all directions; a ratio of the eigenvalue
was 2.47:1.67:1 (c.f.,the ratio of6.1:2.0:1 in R
C rt,I01).
3.2.2. M odel tting for the m aser kinem atics
W e also m ade a least-squares m odel- tting
analysis assum ing a spherically expanding ow
m odel, details of w hich have already been described in Im ai etal. (2000)(c.f. G w inn,M oran,
& R eid 1992). W e used weights proportionalto
the square ofthe accuracy ofa m easured proper
m otion.
First,we adopted radialexpansion m otions of
m asers w ith independent speeds and estim ated
4
location of the star is very close to blue-shifted
clusters ofm aserfeatures. W e could not nd converging solutions in w hich the stellar position is
close to the center of the ring m entioned above.
T hus,the spatialdistribution ofthe m asers is expected to be signi cantly asym m etric (see also gure 2). T his is consistent w ith the estim ation by
B J.M aser features apparently spread out to 200
m as ( 45 A U ) from the star (see also gure 3),
w hich is larger by a factor of 2{3 than that previously estim ated (B owers,C laussen,& Johnston
1993; B J;Y C ). T he size of the m aser-quenching
zoneisreduced to 10 m as( 2 A U ).T heestim ated
system ic radialvelocity ofthe staralso hasan o setof 3 km s 1 from the value adopted by above
previous papers.
Figure 4 show s the estim ated 3-D spatiokinem atics ofthe water m asers projected in three
directions. M ost ofthe m aser features exhibit radialexpansion w ithoutrotation around the starat
the diagram origin. C ontrary to the asym m etric
spatialdistribution ofm aser features,asym m etry
in the velocity eld is not seen; m aser features
seem to have only a bias in the spatialdistribution. T hus,the kinem atics ofthe RT V ir ow is
wellexpressed by a radially expanding ow (c.f.,
Paper I; R C B Y ; Y R G B ) and the radial-velocity
gradient in the east-west direction should be due
to the bipolarity ofthe ow but w ith weak collim ation.
tem poralchangesin spatialand velocity structures
ofm aserfeaturesw ith tim e.G w inn (1994)pointed
out that the observed line w idth is likely a ected
by the subsonic bulk m otions w ithin the feature
( 0.5 km s 1 ) and the di erent hyper ne transitionsofthe H 2 O line (butnegligible).B ecausethe
two e ects w illalso a ect the radial-velocity drift
m easurem ents,the velocity variations larger than
0.5 km s 1 can be taken into account as possible
accelerations.
N evertheless,som eofthem aserfeatureschanged
theirvelocitiesw ith tim eatconstantrates,orconstantaccelerations.Figure 5 show s the histogram
of the m easured radial-velocity rates. T he drift
ratesofthese featuresare equalto orsm allerthan
1 km s 1 yr 1 and quite sim ilarto those thathave
been com m only detected for 15 yrs w ith singledish observations (Lekht et al. 1999). M aser
features w ith larger drift rates (> 2 km s 1 yr 1 )
exhibit jum ps in velocities, w hich are likely due
to blending ofa few very close by m aser features
as m entioned in section 3.1. Such large velocity drifts were also found in som e m aser features
detected in less than four epochs. T hus, radialvelocity drifts around 1 km s 1 yr 1 com e from
single m aser features and m ay indicate acceleration/deceleration ofthe features. Previous V LB I
observations(PaperI;I01)havealso detected such
system atic radial-velocity driftsin a sm allnum ber
ofm aserfeatures.W e did not nd,however,a correlation between radial-velocity and acceleration
(see gure 6).
W e have also looked for m aser features exhibiting acceleration/deceleration m otionsin their
proper m otions. Sim ilar to m easurem ents of
the radial-velocity drifts, we traced positions of
brightest peaks ofindividualm aser features. T he
m ethod to de ne the feature position was described in Paper III.N ote that ux-weighted positions (e.g., M arvel 1997) are often a ected by
extended and weak velocity com ponents. Figure
7a show sthetim e variation in spatialstructuresof
the position-reference feature (RT V ir 2002I:33)
and the adjacent features. W e nd that the reference feature haschanged in spatialstructure from
one epoch to another. M ost ofthe m aser features
had sim ilar variation in their internalstructures,
w hich m akes it m ore di cult to judge w hether
an apparent acceleration m otion really re ects a
true one or a physicalm otion ofthe m aser cloud.
3.3. A cceleration m otions found in w ater
m aser features
W e have m easured radial-velocity driftsofindividualm aserfeaturesby m easuring a radialvelocity atthe brightnesspeak ofeach m aserfeature in
the sam e m annerasthatin PaperIII.B ecause we
m easured the velocitiesw ith accuracy betterthan
a velocity channel spacing of 0.056 km s 1 , the
uncertaintiesofthe velocity driftrateswere calculated by assum ing a m easurem enterrorto beequal
to this value. T he uncertainties were as sm allas
0.3 km s 1 yr 1 in the best case. Table 2 gives
the m easured radialvelocity drifts of m aser features. Figure 1 presents tim e variations in radial
velocities ofindividualm aser features w ith longer
lifetim es.
T he changes in radialvelocity are usually less
than the velocity w idths of m aser features (0.5{
2.0 km s 1 ,seetable2)and likely to bea ected by
5
B ecause V LB I observations lose the absolute position coordinate,we can notcalibrate the change
in spatialstructure ofthe reference feature forthe
properm otion m easurem ents.A ssum ing thatthis
change is com ing from the subsonic bulk m otions
w ithin the feature m entioned above, an uncertainty of 0.5 km s 1 (0.5 m as yr 1 ) likely contam inates the m easured relative proper m otions
ofother m aser features.
N evertheless,we found a m aser feature candidate that m ay exhibit a true acceleration m otion,
in w hich the feature m oved by a distance m uch
larger than the size of the feature itself. Figure
7b show s the tim e variation ofthe candidate,RT
V ir 2002I:47,and the adjacentfeatures. Figure 8
show sthetrajectory ofthecandidateand a m odel,
w hich adopts a constantacceleration and is tted
wellto the observed trajectory. T he acceleration
vector ([ 18.5,27.1]in units of km s 1 yr 1 ) has
a position angle of( 34 ,w hich is roughly parallelto the m ean properm otion vector([ 2.2,10.4]
in unit of km s 1 ,subtracting the m ean proper
m otion show n in table 3) w ith a position angle of
12 and the position vector ([ 2,46]in unit of
m as) w ith a position angle of 2 . T he m easured
acceleration m otion vector is a relative one w ith
respect to that ofthe reference feature,or we are
m easuring it in the fram e in w hich the reference
feature has a constant velocity m otion. Expecting spherically sym m etric acceleration m otions in
the featuresRT V ir2002I:47 and 33 w ith respect
to the centralstar,the relative acceleration vector
would be closerto the properm otion vectorofthe
feature RT V ir 2002I:47. A dopting this acceleration,the feature increased in speed from 1 km s 1
to 16 km s 1 .
N ote that the apparent acceleration ofthe featurewasseen only on thesky plane(’ 33 km s 1 yr 1 ),
butnotalong the line-of-sight( 0.1 km s 1 yr 1 ).
O ther m aser features also exhibited apparently
rapid acceleration m otions on the sky plane but
m uch sm aller ones along the line-of-sight as m entioned above ( 3 km s 1 yr 1 ).
4. D iscussion
4.1. Stellar position in the H 2O m aser distribution
T he stellar position ofRT V ir in the circm stellarenvelopehasbeen estim ated in severalm anners
6
based on the m aser m aps or position-velocity diagram s. A ll of the results suggest that the star
is close to the center ofthe H 2O m aser distribution or the m iddle between the blue-shifted and
red-shifted clusters of m aser features (e.g., B ow ers,C laussen,& Johnston 1993;Y R G B ).Y C and
B ains et al. (2002) found a "quenching zone",
w ithin w hich no m aser em ission is found. R eid
& M enten (1990) found that a radio continuum
source from the sem iregularvariable W H ya is located at the center ofa "ring" found in the H 2O
m aser distribution.
O n the otherhand,the dynam icalcenterofthe
expanding ow estim ated in the presentpaperhas
a large o set ( 40 m as) over the uncertainty in
the m odel tting (see table 3). T he stellar position can be exam ined by sim ultaneously m aking
proper m otion m easurem ents such as those in the
presentpaperand observationsoftheradio continuum source ofRT V ir such as that m ade by R eid
& M enten (1990).Itisexpected thatthe asym m etry ofthe 3-D distribution ofm aser features (see
gure 4)derived a biasin the m odel tting.Longterm observations,over severalyears,w illreduce
such distribution asym m etry.
4.2. D istance to R T V ir
T he estim ation of the distance to RT V ir has
been m ade w ith severalm ethods: a trigonom etric parallax w ith the H IPPA R C O S satellite (140
pc) and bolom etric distance assum ing a P-L relation (120{360 pc,e.q.,B J;Y C ;Yuasa & U nno
1999).In the presentpaper,we m ade the distance
estim ation on the basis of the 3-D kinem atics of
the RT V ir water m asers using both, the statisticalparallax and the m odel- tting m ethods. A s
described in section 3.2.1,the feasibility ofthese
m ethods was exam ined by the objective analysis
using V V C M , w hich show s no rotation or other
peculiar m otion in the velocity eld (see also gure 5). In the m odel- tting m ethod,the detailof
w hich has already been described in section 3.2.2
and table3,weobtained distancevaluesof226 16
pc in the analysis using only m aser features exhibiting expansion.
W hen including infalling features in the analysis,the distance value was85 12 pc. T hen we obtained an expansion velocity Vexp 5 km s 1 (see
gure 3),w hich issm allerthan the value obtained
by R C B Y (V exp ’ 10 km s 1 ). T he results of
R C B Y suggested that the circum stellar envelope
is accelerated gradually toward the outside,from
2-3 km s 1 in the SiO m aser region closest to the
star to 20{30 km s 1 in the O H m aser region
m ost distant from the star. It is expected that
R C B Y ’s results re ected a "steady" ow of RT
V ir. B ecause, as expected in theoretical m odels
(e.g.H ofner,Feuchtinger,& D or et al. 1995),
infallm otions occur as a result ofa tim e-variable
phenom enon,orshock wave,the infalling features
are needed to be excluded in the m odelassum ing
the steady ow . T hus,the above distance value is
concluded to be underestim ated.
O n the other hand, the statistical-parallax
m ethod (G enzel et al. 1981) gave distance values of237 29 pc (232 27 pc and 243 29 pc for
the x {Vz and the y {Vz data,respectively) and
214 28 pc (211 27 pc and 216 28 pc forthe x {
Vz and y {Vz data, respectively) w hen using all
3-D m otion data and only the data used in the
form er m odel tting, respectively. T he distance
values obtained in the form er m odel- tting and
the statistical parallax m ethods are quite consistent w ith each other, and the weighted-m ean
distance value of220 30 pc isadopted forRT V ir
in this paper.
N ote thatthe statisticalparallax m ethodsused
only m aser features w ith m easured proper m otions. A dopting a radialvelocity dispersion of66
m aser features detected in the rst epoch w hen
the largest num ber of features were detected, a
distance value of279 32 pc was obtained. T hus,
the radial velocity dispersion tends to have the
larger value, w ith respect to the proper m otion
dispersion, w hen including m aser features w ithout m easured proper m otions. T his im plies that
m aser features w ithout m easured proper m otions
have the di erent kinem atics from that ofm aser
features w ith the proper m otions. T he distance
estim ation in this paper was the rst successful
one for a water m aser source around a low -m ass
M ira-type star next to those around supergiants
exhibiting m any long-lived water m aser features
(M arvel1997).
m atics,som etim es exhibit clear bipolarity or signi cant asym m etry. Even if taking into account
the lim ited physicalconditions for m aser excitation, such asym m etry is evident throughout the
revealed 3-D m aser kinem atics. A t the end ofthe
A G B phase in stellar evolution,such asym m etry
w ill be tightly related to form ation of elongated
planetary nebulae,som e ofw hich are created by
stellar jets (e.g., Im ai et al. 2002). T he asym m etry,however,has been also found in sem iregular variables (e.g.,B owers,C laussen,& Johnston
1993;B J;Y C ;I01),w hich has been considered to
be at the early-A G B phase. T he present and previous works (e.g.,M arvel1997: I01;Yates et al.
2000) have proven that radial-velocity gradients
seen in water m aser distributions are due to the
bipolarity, not the rotation of m ass-losing ow s.
O n the other hand, m any M ira and sem iregular
variables, including RT V ir, do not clearly show
the ow bipolarity yet,having m ajor/m inor axis
ratios of 2. It is stilldi cult to discuss the relation am ong the asym m etry, m ass-loss rate, radius,and expansion velocity ofa m ass-losing ow
due m ainly to the lim ited num ber ofsam ple stars
availablefordata ofthe 3-D m aserkinem aticsand
foraccurate distances.In thispaper,we speculate
about the weak asym m etry ofthe RT V ir ow .
W e re-estim ated a m ass-loss rate for RT V ir
adopting the described spherically-expanding
ow m odel. T he density of m aterial (hydrogen m olecules) in the ow is determ ined from
predictions by a m aser excitation theory as 106
109 cm 3 (e.g.,C ooke & Elitzur
cm 3
nH 2
1985;Elitzur 1992). A dopting the radius of the
ow in the water m aser region, r ’ 44 A U , at
d ’ 220 pc (distribution size of’ 200 m as),an expansion velocity,Vexp ’ 8 km s 1 ,we obtained a
m ass-loss rate of M_ 1.5 10 7 (nH 2 /106 cm 3 )
M yr 1 ,w hose lower lim it is roughly consistent
w ith that estim ated by B J.A dopting the relation
between a radius ofthe water m aser distribution
and a m ass-loss rate found by C ooke & Elitzur
(1985)and Lane etal. (1987),the m ass-lossrate
ofRT V ir should be m uch larger than this value
(c.f.,3 10 6 M yr 1 ,B J).
O n the other hand,M ira-type stars w ith relatively large m ass-loss rates and larger ow radii
have sym m etric kinem atics (e.g.,B J).In O H /IR
stars w ith larger m ass-loss rates, 1612-M H z O H
m asersexhibitlargerand sym m etric distributions
4.3. A sym m etry of the m ass-loss process
in sem iregular variables
T he m orphology and the kinem atics ofcircum stellar envelopes (or m ass-losing ow s) ofevolved
stars,w hich are traced by the water m aser kine7
(e.g.,C hapm an & C ohen 1986). It is considered
that the intrinsic bipolarity or asym m etry of a
m ass-losing ow is obscured by the grow ing envelope as the m ass-loss rate increases. In this case,
RT V irw illbe in the transition during an increase
in its m ass-loss rate. W e have to take into account,however,cases of supergiants,w hich have
m uch higherm ass-lossratesbutm ostofw hich exhibit signi cant asym m etry.
N otethatthe expansion velocity and the radius
ofa m ass-losing ow determ ined seem to be tim e
dependent. W ater m asers around R A qlare one
ofthe exam ples(B J).T he bipolarity ofthe m aser
distribution was signi cant after the m axim um of
the light curve and vice versa. A sim ilar variation in the m aser distribution has been con rm ed
for RT V ir, but w hen a stellar pulsation period
of375 d is adopted (Paper I).A dopting this tendency,waterm asersaround RT V irwere observed
around the light m axim um , in w hich the m aser
distribution was larger than those observed w ith
theV LA (B owers,C laussen,& Johnston 1993;B J)
butsm allerthan thoseobserved w ith the Japanese
V LB IN etwork (J-N et,Paper I).Ifwe could m easure m aser proper m otions w ith the J-N et data,
the bipolarity would be exhibited m ore clearly.
T he tim e dependence ofthe bipolarity should be
exam ined w ith m onitoring observationsforlonger
than a few cycles ofthe pulsation period.
tureshaving intensity variation w ith tim e.In fact,
in short duration (< a few m onths) the velocity
drifts have not exhibited the sam e drift direction
am ong m aser features in both the previous and
the present V LB I observations (see gure 6,also
Paper I;I01).
O n the other hand, theoreticalm odels adopting shock wavesdriven by stellarpulsation predict
thata shock wavecreatesacceleration/deceleration
ofa m ass-losing ow and generates rapid velocity
changes during the passage of the shock (a few
m onths)(e.g.,H ofner,Feuchtinger,& D or etal.
1995). T he velocity changes are expected to be
10 km s 1 and 2 km s 1 at the inner (r 5
A U ) and the outer (r 50 A U ) region of water
m aser excitation, respectively. T he acceleration
m otion observed in a feature’s proper m otion,as
m entioned in section 3.3,is quite consistent w ith
the theoreticalprediction.
It has been a long-term issue w hether change
in the location ofa m aserfeature istracing actual
physicalm ovem ent of the gas in a clum p rather
than som e kind of non-kinem atic e ect, such as
traveling excitation phenom ena orchance realignm ent ofcoherency paths through the m asing gas.
R ecent observations,however,have strongly suggested the form er in hydroxyland water m asers;
all of the observations have show n that individual m aser features persist in both their spatial
and radial-velocity patterns throughout their m otion fordistancesm uch largerthan theirow n sizes
(e.g.,B loem hof,M oran,& R eid 1996;Torrelles et
al. 2001a,b;Paper III).T he m aser feature (RT
V ir I2002:47,see gure 7 and 8) exhibited a large
acceleration on the sky,butsim ultaneously a large
position drift of 2 m as, a stable radial velocity
(variation lessthan 0.2 km s 1 ). T hisfeature also
exhibited a persistentV -shaped pattern form ed by
a cluster ofm aser spots,w hich have radialvelocities successively changing by 0.056 km s 1 from
one spot to another. T hese strongly support that
this m aser feature traces the m ovem ent of a gas
clum p throughout ve observation epochs.
T he larger acceleration on the sky plane
(over 10 km s 1 ) than that in the line-of-sight
(’ 1 km s 1 yr 1 ) is likely due to the beam ing effect ofm aser radiation. Taking into account the
hydrodynam icaltreatm ent of a m aser clum p, an
apparentacceleration m otion ofa brightnesspeak
r
in the m aserclum p isexpressed as, dV r
Vr @V
@r ,
dt
4.4. O rigin of apparent acceleration m otions
Long-term m onitoring observationshaveshowed
that there are apparent radial-velocity drifts of
water m aser features that have occurred sim ultaneously and exhibited the sam e drift direction
(acceleration/deceleration) am ong several m aser
features (Lekht et al. 1999). T his im plies a
change ofthe velocity eld in the m ass-losing ow
due to the stellarpulsation assuggested above.In
the case ofRT V ir,such acceleration/deceleration
observed islikely excited by stellarpulsation w ith
a period of’ 375 d (Im aietal. 1997)ratherthan
’ 155 d (e.g., K holopov et al. 1985; Etoka et
al. 2001). Such system atic velocity drifts m ay
be detectable only w ith m onitoring observations
spanning atleastone year.Itis because there are
sm allchanges in the drift rates on this tim e scale
and because it is som etim es di cult to rem ove
data exhibiting velocity jum psdue to blended fea8
w here Vr and r are the velocity eld asa function
of distance from the star, r, and the location in
the clum p,respectively.A ssum ing a velocity drift
of30 km s 1 yr 1 ,a m ean velocity of8 km s 1 ,a
1
m as 1 is exvelocity gradient of @V
@r ’ 4 km s
pected at 220 pc. T his velocity gradient is larger
than that observed in the above m aser feature on
the sky plane ( 1 km s 1 m as 1 ) and that expected from a steady accelerating envelope in the
region of the H 2 O m asers estim ated by B ains et
al. (2002),
@V
@r
V
6 km s 1
’
r
20A U
those estim ated in the J-N et observations. T he
estim ated velocity eld of the ow is roughly
spherically sym m etric, w hile the m aser spatial
and velocity distribution looks weakly asym m etric. A dopting the above ow m odel and taking
into account a statistical parallax, we estim ated
the distance to RT V ir as to be 220 30 pc. W e
found radial-velocity drifts of m aser features of
2 km s 1 and speculated that the drifts larger
than > 2 km s 1 aredueto blending ofa few m aser
features w ithin a sm allregion in space and velocity. W e also found an acceleration m otion in the
proper m otion of a m aser feature w ith a rate of
33 km s 1 yr 1 and indicating radialacceleration.
Such acceleration m otionsseen both in the line-ofsightand on the sky plane are explained by a single com m on phenom enon: passages ofpulsationdriven shock waves in the circum stellar envelope.
T he possible variation in the m aserexpansion size
and distribution asym m etry w ith tim e as wellas
observed acceleration m otionsshould beexam ined
in future observations w ith tim e intervals longer
than a few cycles ofthe stellar pulsation.
0:1 km s 1 m as 1 :
(3)
Ifsuch a large velocity gradientisgenerated along
the line-of-sight,the velocity-coherentpath is too
shortto producestrong m aseram pli cation occurring in a velocity w idth ofless than 1-2 km s 1 .
A dopting a velocity-coherentpath 10 tim esaslong
as the observed feature size ( 1 m as),an acceleration m otion of less than 1{2 km s 1 yr 1 is expected along the line-of-sight. T hus, only large
acceleration along the sky plane is detectable.
T he present paper is the rst approach to directly detect the pulsation-driven shock waves,
w hich should be identi ed in future worksby nding sim ultaneously severalm aserfeaturesperform ing such acceleration m otions and by elucidating
the relation between the occurrence ofthe acceleration and the stellar light curve.
N R A O is a facility of the N ational Science
Foundation, operated under cooperative agreem ent by A ssociated U niversities, Inc. H . I. was
nancially supported by the R esearch Fellow ship
ofthe Japan Society ofthe Prom otion ofScience
for Young Scientist.
R EFER EN C ES
B ains, I., C ohen, R . J., Louridas, A .,
R ichards, A . M . S., R osa-G onzalez, D .,
& Yates, J.A . 2002, M N R A S, subm itted
(astro-ph/0211473)
5. Sum m ary
O ur m onitoring V LB A observations of water
m asersaround RT V irhave revealed the 3-D kinem atics of water m asers in m ore detail and detected the acceleration m otions of water m aser
features. B ecause of the good angular resolution (’ 1 m as) and tim e separations (’ 3 weeks in
ve epochs), we were able to m easure 60 proper
m otions and radial-velocity drifts of m aser features. C arefully dealing w ith m aser features exhibiting infall towards the star, we obtained a
spherically-expanding ow m odel from the 3-D
m aser kinem atics. T he estim ated expansion velocity of ’ 8 km s 1 is consistent w ith that previously suggested. T he estim ated outer radius of
the m aser distribution, ’ 45 A U , was 2{3 tim es
as large as those previously estim ated,except for
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T his 2-colum n preprint w as prepared w ith the A A S LA TEX
m acros v5.0.
10
Table 1:Status ofthe V LB A observationsand position-reference feature in the proper-m otion m easurem ent
O bservation status
E poch
1 ....
2 ....
3 ....
4 ....
5 ....
D ate
(1998)
M ay 11
M ay 31
June 19
July 12
A ugust 1
U T span
03:00{07:00
01:30{05:30
00:00{04:00
22:30{02:30
21:00{01:00
M aser
features
detected
66
62
53
50
53
P osition-reference m aser feature (R T V ir: I2002 33)
L SR
D oppler
velocity
( km s 1 )
17.14
17.16
17.10
17.10
17.10
P eak
intensity
at E poch 1
(Jy beam 1 )
29.6
73.1
82.3
84.2
63.5
11
P osition relative to the m ap origin
x=
cos
(m as)
83.885
0.000
0.002
0.015
0.034
y=
(m as)
6.922
0.069
0.025
0.059
0.077
Table 2:Param etersofthe water m aser features identi ed by proper m otion toward RT V ir
M aser1
featu re
(R T V ir:
I2002)
1 ......
2 ......
3 ......
4 ......
5 ......
6 ......
7 ......
8 ......
9 ......
10 .....
11 .....
12 .....
13 .....
14 .....
15 .....
16 .....
17 .....
18 .....
19 .....
20 .....
21 .....
22 .....
23 .....
24 .....
25 .....
26 .....
27 .....
28 .....
29 .....
30 .....
31 .....
32 .....
33 .....
34 .....
35 .....
36 .....
37 .....
38 .....
39 .....
40 .....
41 .....
42 .....
43 .....
44 .....
45 .....
46 .....
47 .....
48 .....
49 .....
50 .....
51 .....
52 .....
53 .....
54 .....
55 .....
56 .....
57 .....
58 .....
59 .....
60 .....
O ffset2 ;3
(m as)
R .A .
89.79
90.09
63.40
83.71
112.87
110.78
109.81
110.78
112.01
115.57
110.97
79.21
82.47
80.38
85.89
86.21
87.32
87.59
108.43
1.35
105.53
87.55
27.73
66.42
27.22
62.84
63.71
53.53
24.46
48.42
1.90
0.37
0.00
1.26
0.10
0.81
1.04
2.91
0.09
1.05
19.18
10.56
11.84
12.01
10.56
10.22
10.33
9.97
10.56
73.88
77.68
64.93
63.63
62.61
62.22
32.04
15.22
15.02
14.20
14.30
d ecl.
7.95
7.53
8.82
6.99
14.68
26.95
26.29
27.00
29.95
16.36
27.49
46.69
48.46
47.83
49.26
48.79
50.13
54.85
52.72
9.16
49.51
53.13
89.82
59.16
88.85
58.57
58.24
57.89
88.86
58.95
3.14
2.81
0.00
22.67
23.27
14.73
0.18
3.67
0.19
0.25
34.53
31.90
34.22
34.57
31.79
30.73
30.78
30.55
30.91
48.96
44.51
45.77
42.68
34.55
49.67
30.98
28.06
18.85
28.45
28.29
P rop er m otion 3
(m as y r 1 )
x
1.55
2.02
3.53
10.17
10.95
8.54
7.83
7.11
5.62
14.64
10.35
8.03
1.54
0.73
5.63
7.20
6.47
6.53
12.10
0.28
8.25
6.23
1.73
2.38
1.85
5.38
3.48
7.33
3.01
6.23
0.70
6.03
0.00
9.60
7.50
2.22
0.30
2.82
0.29
1.22
4.49
2.04
0.07
1.59
0.55
4.22
5.49
2.66
2.51
7.97
10.79
9.97
6.23
4.60
4.31
5.02
2.65
3.39
0.62
4.81
x
0.32
1.02
0.60
0.25
0.86
0.29
0.85
10.84
1.24
1.95
0.97
0.33
3.24
2.20
0.25
0.60
0.87
0.55
1.42
0.38
1.82
0.60
0.71
1.52
2.48
0.76
2.71
2.21
0.69
2.09
0.61
1.07
0.27
2.81
3.39
1.36
0.55
1.92
0.25
0.21
0.29
0.36
0.27
1.03
0.39
0.73
0.53
0.20
0.96
0.66
0.07
1.46
1.88
0.36
2.84
0.42
1.09
0.81
1.39
1.18
y
2.98
0.26
10.58
1.14
7.58
2.08
5.06
5.04
0.31
4.85
0.54
10.06
9.20
11.49
6.55
6.70
4.92
8.85
5.74
0.13
8.48
6.42
7.42
10.97
16.60
6.22
7.90
2.98
12.58
4.43
1.52
2.30
0.00
1.37
0.15
2.18
0.65
1.18
1.33
2.07
4.48
4.01
2.21
3.40
1.17
5.12
6.37
2.49
7.79
7.66
7.30
6.10
4.24
4.01
5.94
6.84
0.89
5.02
1.31
2.13
R ad . m otion 4
(k m s 1 )
y
0.36
2.18
0.54
0.28
0.59
0.56
1.35
9.27
0.99
4.77
1.59
0.42
1.63
1.22
1.05
0.24
0.79
1.26
1.44
0.62
1.83
1.45
1.22
5.06
3.62
0.58
5.51
2.52
0.70
1.56
1.88
1.09
0.43
4.22
5.93
1.56
0.70
3.07
0.25
0.23
0.37
1.16
0.49
0.91
3.31
2.01
0.76
0.82
2.66
0.48
0.08
1.74
1.86
0.33
2.01
0.44
0.50
2.28
1.45
1.53
Vz
7.57
7.53
7.17
6.89
6.39
6.26
6.18
6.17
6.06
5.99
5.84
5.47
5.30
5.22
5.20
5.14
4.57
4.03
4.03
4.03
3.97
3.97
3.68
3.66
3.58
3.50
3.32
3.19
3.14
2.66
2.00
1.52
1.06
0.99
0.99
0.96
0.76
0.62
0.62
0.62
2.68
3.07
3.26
3.32
3.38
3.43
3.70
3.76
3.77
3.84
4.43
5.33
5.47
5.75
5.76
6.28
7.09
7.13
7.26
7.42
V z7
0.72
0.71
0.77
0.72
0.63
0.39
0.30
0.44
0.51
0.50
0.18
0.86
0.53
0.63
0.65
1.01
0.44
0.44
0.71
0.62
0.53
0.66
0.31
0.74
0.37
0.26
0.47
0.47
0.45
0.23
0.95
0.76
1.14
0.47
0.50
0.42
0.79
0.29
0.29
0.67
0.45
0.50
0.34
0.51
0.50
0.16
0.93
0.41
0.60
0.60
0.76
0.44
0.76
1.00
0.45
0.46
0.58
0.95
0.60
0.74
1
R V d rift5
(k m s 1 y r 1 )
V_z
0.02
0.82
1.74
1.64
0.24
0.41
0.91
0.73
2.39
0.87
0.84
0.75
0.82
1.59
0.82
0.53
0.02
0.39
0.86
1.78
0.20
0.22
0.93
0.33
1.15
0.06
3.37
2.06
0.59
1.12
0.62
4.02
0.23
0.25
1.79
1.73
0.42
2.03
0.00
1.00
0.15
0.09
1.58
0.91
0.49
2.19
0.00
1.34
2.17
1.65
0.43
0.97
2.28
0.33
1.17
1.09
0.33
2.20
2.77
0.72
V_z 8
0.35
1.38
0.46
0.31
0.33
0.45
0.74
1.45
0.45
1.38
0.74
0.45
1.45
1.45
0.45
0.31
1.38
0.46
0.66
0.31
0.74
0.45
0.45
1.45
1.45
0.31
1.45
1.38
0.31
1.38
0.69
0.74
0.31
1.53
1.53
0.74
0.45
1.53
0.69
0.45
0.31
0.74
0.45
0.66
1.45
0.45
0.31
0.45
0.74
0.31
0.31
1.26
1.26
0.45
1.45
0.31
0.45
1.45
0.74
0.66
P eak in ten sity at five ep och s
1)
(Jy b eam
E p. 1
57.40
...
24.65
132.00
4.09
14.20
8.38
15.67
7.72
...
5.48
7.29
2.91
4.31
...
10.71
...
0.58
...
0.40
0.59
1.42
...
1.15
0.42
1.23
0.51
...
0.42
...
...
14.30
29.58
...
...
4.08
30.95
...
...
...
0.51
19.30
5.05
...
34.77
...
50.30
47.30
46.85
2.04
5.05
...
...
131.05
9.66
0.61
1.06
2.31
0.64
...
E p. 2
E p. 3
... 110.33
...
...
...
19.70
47.40 127.00
6.99
4.56
12.10
8.32
5.35
3.44
12.46
...
5.66
4.18
...
...
6.22
2.78
9.04
9.50
1.98
...
4.14
...
7.86
8.41
14.30
14.20
...
...
0.51
...
...
0.74
0.76
1.05
0.73
0.68
1.16
0.76
0.38
...
0.72
...
0.48
...
1.14
0.94
0.51
...
...
...
0.50
0.52
...
...
8.59
6.38
...
6.82
73.11
82.28
5.37
5.57
4.59
5.63
...
3.11
24.80
14.66
2.19
2.86
14.80
...
20.60
...
0.43
0.67
...
1.70
4.35
3.33
...
2.22
12.06
...
12.40
2.14
36.97
22.61
6.58
5.26
23.60
5.39
3.74
2.73
6.45
8.27
...
2.32
...
2.79
40.61
11.10
3.13
...
0.56
...
0.97
0.71
0.88
...
0.67
0.64
...
0.58
E p. 4
...
90.08
48.50
81.51
...
3.30
...
...
2.18
2.24
...
12.11
...
...
...
8.26
3.66
0.38
...
1.90
...
0.42
0.38
...
...
0.64
...
0.35
0.54
0.27
3.74
...
84.17
...
...
...
16.32
...
9.72
11.00
1.69
...
2.73
3.47
...
3.86
11.83
...
...
4.38
20.40
4.24
7.21
6.68
...
0.86
0.43
...
...
0.60
E p. 5
12.00
12.41
...
25.90
2.54
...
...
...
...
2.39
...
...
...
...
4.98
10.70
2.42
...
2.45
0.21
...
...
0.22
...
...
0.41
...
0.27
0.35
0.15
...
...
63.47
...
...
...
...
...
...
7.36
1.34
...
...
2.28
...
4.51
7.44
...
...
2.16
27.00
...
...
...
...
0.77
...
...
...
0.33
In fall6
In fall
In fall
In fall
In fall
In fall
In fall
In fall
In fall
In fall
In fall
In fall
In fall
In fall
In fall
In fall
In fall
In fall
In fall
In fall
In fall
W ater m aser features detected toward RT V ir. T he feature is designated as RT V ir:I2002 N ,w here N is
the ordinalsource num ber given in this colum n (I2002 stands for sources found by Im aiet al. and listed in
2002).
2
Param etersat the rst epoch w hile the feature was being detected.
3
R elative value w ith respect to the location ofthe position-reference m aser feature: RT V ir:I2002 34.
4
R elative radialvelocity w ith respect to the assum ed system ic velocity ofVL SR = 18.2 km s 1 .
5
Secular drift rate ofa radialvelocity.
6
Infall: exhibiting a negative expansion velocity in the m odel tting adopting only expanding features.
7
M ean fullvelocity w idth ofm aser feature at halfintensity.
8
U ncertainty obtained w hen assum ing a m easurem enterrorofa radialvelocity,w hich equalsto the channel
spacing (0.056 km s 1 ).
12
Table 3:B est- t m odels for the m aser velocity eld ofthe RT V ir out ow
Including infalling features O nly expanding features
Param eter
Features nally used
Velocity:
V0x3 ( km s 1 ) ......
V0y3 ( km s 1 ) ......
V0z4 ( km s 1 ) ......
Position:
x0 (m as) ............
y0 (m as) ............
R adialout ow :
V0 ( km s 1 ) ........
V1 ( km s 1 arcsec )
....................
D istance d (pc)
p .........
R M S residual S 2 ......
Step 11
Step 22
Step 11
46
O sets
1.9 0.7
0.7 0.5
05
2.6 0.3
0.4 0.4
0.7 0.3
Step 22
48
3.2 1.4
4.3 1.0
05
3.5 0.6
3.8 0.7
2.5 0.5
39 6
57 3
13 5
31 2
Velocity eld
11 9
14 6
8 5
15 6
...6
...6
...6
2707
3.02
...6
...6
...6
2707
2.33
6.6 0.6
2.0 1.5
0.51 0.39
226 16
4.33
0.1 0.4
1.5 0.1
0.40 0.03
87 12
6.84
1
A ssum ing independent expansion velocities ofm aser features.
A sum m ing a com m on expansion velocity eld expressed by equation (12) ofIm ai et al. (2000).
3
R elative value w ith respect to the position-reference m aser feature.
4
R elative value w ith respect to VL SR 18.2 km s 1 .
5
Step 1 assum es the system ic radialvelocity: V0z 0.0 km s 1 .
6
T he solution determ ines a radialout ow velocity Vexp(i) independently for each feature w ith a proper
m otion.
7
D istance is com pletely covariantw ith the zi and Vexp(i) and cannot be determ ined: d 270 pc.
2
13
Fig. 1.| A sam ple ofm easured proper m otions and the D oppler velocity drifts ofm aser features that had
been detected in ve epochs. T he num ber added after "RT V ir:I2002" for each proper m otion show s the
assigned nam e. Solid linesin plotsofproperm otionsshow tlinesassum ing constantvelocity m otions.T he
solid lines in the plots ofthe D oppler velocity drift show t lines assum ing constant acceleration m otions.
14
Fig. 2.| T he 3-D velocity eld ofwater m aser features around RT V ir. A 3-D velocity vector ofa feature
is indicated by a cone. T he m ean velocity vector of the m aser features was subtracted from each of the
observed velocity vectors. (a): the 3-D m otions of61 m aser features,each ofw hich had been detected at
least tw ice,are show n. T he plus sym bols indicate the locations ofthe star,estim ated by the m odel tting
using proper m otions exhibiting both expansion and infall(pink) and only expansion (green). (b): Sam e as
(a) but for 36 m aser features,each ofw hich had been detected at three epochs.
Fig.3.| T he expansion velocity ofa m aserfeature againstthe distance from the position ofthe centralstar.
T hese param eters were estim ated after the m odel tting. T he expansion velocity was calculated by using
the equation show n by Im ai etal. (2000).A solid line show sthe velocity eld asa power-law function w ith
respect to the distance from the star. (a): For the case w hen excluding infalling features,having negative
expansion velocities. (b): For the case w hen including allm aser features w ithin a reasonable distance from
the star (< 300 m as,corresponding to 66 A U at 220 pc).
15
Fig. 4.| Estim ated 3-D positions and m otions of water m aser features in RT V ir. T he positions and
m otions are w ith respect to those of the out ow ’s origin determ ined by a m odel t. T he position of the
arrow indicates that ofa m aser feature. T he direction and length ofthe arrow indicates the direction and
the m agnitude ofthe m aserm otion,respectively.Top: Frontview (X Y -plane)forthe positionsand m otions
plot. Bottom left: Top view (X Z -plane). Bottom right: East-side view (Z Y -plane).
16
14
3-4 epochs
5 epochs
Number of features
12
10
8
6
4
2
0
-4
-3
-2
-1
0
1
2
3
-1
4
-1
Radial velocity drift rate (km s yr )
Fig. 5.| H istogram ofdrift rates ofm aser features’radialvelocities. M aser features are divided into two
groups,features detected atallepochs and those detected at3 or4 epochs. M aserfeatures detected only at
two epochs have been excluded.
3
(a)
Radial velocity drift rate (km s-1yr-1)
Radial velocity drift rate (km s-1yr-1)
3
2
1
0
-1
-2
-3
3-4 epochs
5 epochs
0
10
20
30
40
50
(b)
2
1
0
-1
-2
3-4 epochs
5 epochs
-3
-8
-6
-4
-2
0
2
4
6
8
Vz-V* (km s-1)
Distance from the star (AU)
Fig. 6.| D ependence ofthe radial-velocity driftofa waterm aserfeature on itslocation and radialvelocity.
(a): A gainst distance from the star (b) A gainst radialvelocity w ith respect to the assum ed stellar velocity
(VL SR = 18.0 km s 1 ). N o correlation is found between radial-velocity drifts and locations/radialvelocities.
17
Relative position offset (mas)
-1
Fig. 7.| Spatialstructures ofm aser features and
theirtim e variation in the two selected elds. T he
num beradded after"RT V ir:I2002"foreach m aser
featureshow stheassigned nam e.Each ofthe lled
circles show s a velocity com ponent (m aser spot).
R adialvelocities ofspots change by 0.056 km s 1
from one spot to the adjacent spot. (a): M aser
features around the m ap origin. T he positionreference feature, RT V ir: I2002 33, is spatially
xed at the m ap origin to m ake m easurem ents of
m aser proper m otions,but w illm ove from south
to north so that it expands w ith respect to the
star. (b): M aser features exhibiting acceleration
m otions. T he m aser feature on a black line, RT
V ir:I2002 47,show s a clear constant acceleration
m otion and thedevelopm entofitsV -shaped structure. T he m aser feature had kept its brightness
peak closeto the creaseofthe V -shaped structure.
3
-1
Relative R.A. offset (-18.5+1.5 km s yr )
-1
-1
Relative Decl. offset (27.1+3.3 km s yr )
2
1
0
120
Feature position:
(-10.654, 31.150) @ 170 DOY
140
160
180
200
220
Day of year in 1998
Fig. 8.| T he tem poralposition variation ofthe
m aser feature RT V ir:I2002 47,w hich apparently
show san acceleration m otion. Solid lines indicate
ts to the position variation in R .A .and decl.directionsassum ing a constantacceleration m otion.
T he positions of the m aser feature at individual
epochs were de ned to be at the brightness peak
am ong the m aser spots in the m aser feature and
m easured w ith uncertainties less than 100 as. A
verticalbar w ith the feature is an extension size
ofthe feature,or a distribution size ofthe spots
in the feature.
18