Trigonometric Parallaxes of Star Forming Regions in the Perseus Spiral Arm
Y. K. Choi, K. Hachisuka, M. J. Reid, Y. Xu, A. Brunthaler, K. M. Menten, T. M. Dame
TTrigonometric Parallaxes of Star Forming Regionsin the Perseus Spiral Arm
Y. K. Choi , , K. Hachisuka , M. J. Reid , Y. Xu , A. Brunthaler , K. M. Menten , and T.M. Dame [email protected] ABSTRACT
We report trigonometric parallaxes and proper motions of water masers for 12 massive starforming regions in the Perseus spiral arm of the Milky Way as part of the Bar and Spiral StructureLegacy (BeSSeL) Survey. Combining our results with 14 parallax measurements in the literature,we estimate a pitch angle of 9 ◦ .9 ± ◦ .5 for a section of the Perseus arm. The 3-dimensionalGalactic peculiar motions of these sources indicate that on average they are moving toward theGalactic center and slower than the Galactic rotation. Subject headings: astrometry — Galaxy: kinematics and dynamics — Galaxy: structure — masers —stars: formation
1. INTRODUCTION
Although our Galaxy is known to be a barredspiral galaxy, it is very difficult to determine itsstructure owing to our location within its disk.Considerable uncertainties still exist regarding thenumber and locations of spiral arms, the lengthand orientation of the central bar and the rota-tion curve. Kinematic distances have often beenused to infer spiral structure, however, they havelarge uncertainties stemming from inaccuracies inthe adopted Galactic rotation model and the exis-tence of significant peculiar (non-circular) motions(Xu et al. 2006; Reid et al. 2009b).Using very long baseline interferometry (VLBI),one can measure trigonometric parallaxes to mas-sive star forming regions with accuracies of order ± µ as (Honma et al. 2012; Reid et al. 2014). Max-Planck-Institut f¨ur Radioastronomie, Auf demH¨ugel 69, D-53121 Bonn, Germany Korea Astronomy and Space Science Institute, 776,Daedeokdae-ro, Yuseong-gu, Daejeon, 305-348, Korea Shanghai Astronomical Observatory, ChineseAcademy of Science, Shanghai, 200030, China Harvard-Smithsonian Center for Astrophysics, 60 Gar-den Street, Cambridge, MA 02138, USA Purple Mountain Observatory, Chinese Academy ofSciences, Nanjing 210008, China
The Bar and Spiral Structure Legacy (BeSSeL)Survey is a National Radio Astronomy Observa-tory (NRAO) key science project that aims tostudy the spiral structure and kinematics of ourGalaxy by measuring trigonometric parallaxes andproper motions of hundreds of massive star form-ing regions with the Very Long Baseline Array(VLBA).The Perseus arm has been proposed as oneof the two dominate spiral arms of the Galaxy,emanating from the far side of the Galactic bar(Churchwell et al. 2009). Toward the Galacticanticenter, the Perseus arm is relatively close tothe Sun and parallaxes and proper motions of 14sources in the Perseus arm have already been ob-tained with the VLBA, the VLBI Exploration ofRadio Astrometry (VERA) array, and the Euro-pean VLBI Network (EVN) (Asaki et al. 2010;Hachisuka et al. 2009; Moellenbrock et al. 2009;Moscadelli et al. 2009; Niinuma et al. 2011; Oh etal. 2010; Reid et al. 2009a; Rygl et al. 2010; Sakaiet al. 2012; Sato et al. 2008; Shiozaki et al. 2011;Xu et al. 2006; Zhang et al. 2013). http://bessel.vlbi-astrometry.org/ The National Radio Astronomy Observatory is a facility ofthe National Science Foundation operated under coopera-tive agreement by Associated Universities, Inc. a r X i v : . [ a s t r o - ph . GA ] J u l ere we present trigonometric parallaxes andproper motions of 12 massive star forming regionsin the Perseus spiral arm in the outer Galaxy.Combined with results from the literature (withone duplicate source, G094.60–1.79), we have alarge sample of 25 sources located in the Perseusarm. These parallax measurements extend oursampling of the arm to smaller and larger Galac-tic longitudes (in the second and third quadrants)and essentially double the number of Perseus armsources with trigonometric parallaxes.In Section 2, we describe our observations anddata reduction. We present the parallax andproper motion results in Section 3. In Section4, we discuss the Galactic locations and peculiarmotions of the sources in the Perseus spiral arm.Finally, we summarize our results in Section 5.
2. OBSERVATIONS
We performed multi-epoch observations withthe VLBA under program BR145. We observedthe 6 –5 masing transition of H O at a rest fre-quency of 22.23508 GHz toward 12 star formingregions in outer Galaxy. Three maser sources pro-jected close to each other on the sky were observedin one group, each with 2 to 4 background quasars.We observed each group at 6 epochs spread overone year. The dates of the observations are listedin Table 1; they were optimized to allow an accu-rate parallax measurement for water masers last-ing seven months or longer.In order to measure trigonometric parallaxes,we used phase-referenced observations, switching(every 20–30 s) between the maser target andan extragalactic continuum source, selected frompreviously known calibrators from ICRF1 (Ma etal. 1998) and ICRF2 lists or from our VLBAcalibrator survey (Immer et al. 2011). The ob-served sources are listed in Table 2. Strong con-tinuum sources were also observed to monitor de-lay and electronic phase differences among therecorded frequency bands. In order to calibrateatmospheric delays, we placed four 0.5-hr “geode-tic blocks” (Reid et al. 2009a) spaced every twohours.The data were correlated in two passes with http://gemini.gsfc.nasa.gov/solutions/2010a/2010a.html the DiFX software correlator (Deller et al. 2007)in Socorro, NM. Four dual-circularly polarized fre-quency bands of 8 MHz bandwidth were processedwith 16 spectral channels for each frequency band.The one dual-polarized band that included themaser emission was re-processed with 256 chan-nels, giving a velocity channel spacing of 0.42 kms − . The data reduction was performed with theNRAO Astronomical Image Processing System(AIPS) package and ParselTongue scripts (Kette-nis et al. 2006) following the procedure describedin Reid et al. (2009a). This work made use of the Swinburne University of Tech-nology software correlator, developed as part of the Aus-tralian Major National Research Facilities Programme andoperated under license. able 1Observation Information Project Source Epoch 1 Epoch 2 Epoch 3 Epoch 4 Epoch 5 Epoch 6BR145E G100.37–3.57 2010 May 16 2010 Aug 09 2010 Oct 12 2010 Nov 27 2010 Dec 31 2011 May 13BR145F G108.20+0.58 2010 Jun 05 2010 Sep 02 2010 Nov 26 2010 Dec 12 2011 Jan 30 2011 May 31G108.47–2.81 2010 Jun 05 2010 Sep 02 2010 Nov 26 2010 Dec 12 2011 Jan 30 2011 May 31G111.25–0.77 2010 Jun 05 2010 Sep 02 2010 Nov 26 2010 Dec 12 2011 Jan 30 2011 May 31BR145G G183.72–3.66 2010 Apr 23 2010 Jun 20 2010 Aug 23 2010 Sep 25 2010 Nov 16 2011 Mar 21BR145K G229.57+0.15 2010 Oct 07 2011 Jan 04 2011 Mar 09 2011 Apr 16 2011 Jun 02 2011 Oct 04G236.81+1.98 2010 Oct 07 2011 Jan 04 2011 Mar 09 2011 Apr 16 2011 Jun 02 2011 Oct 04G240.31+0.07 2010 Oct 07 2011 Jan 04 2011 Mar 09 2011 Apr 16 2011 Jun 02 2011 Oct 04BR145P G094.60–1.79 2011 May 15 2011 Aug 07 2011 Oct 21 2011 Nov 22 2012 Jan 08 (2012 May 09)G095.29–0.93 2011 May 15 2011 Aug 07 2011 Oct 21 2011 Nov 22 2012 Jan 08 2012 May 09BR145V G108.59+0.49 2010 Dec 10 2011 Feb 21 2011 Apr 30 2011 May 29 2011 Jul 17 2011 Nov 25G111.23–1.23 (2010 Dec 10) 2011 Feb 21 2011 Apr 30 2011 May 29 2011 Jul 17 2011 Nov 25
Note.—
Column 1 lists the project code. Each project has three target sources, but Column 2 only lists the massive starforming regions reported in this paper. Each project was observed at 6 epochs, and the dates are shown in Columns 3 – 8.The dates in parentheses are observed, but not used for the parallax/proper motion fitting. able 2Source Information Source R.A. (J2000) Decl. (J2000) θ sep P.A.(h m s) ( ◦ ’ ”) ( ◦ ) ( ◦ )G094.60–1.79 21:39:58.2701 +50:14:20.994 – –J2137+5101 21:37:00.9862 +51:01:36.129 0.9 –31J2150+5103 21:50:14.2662 +51:03:32.264 1.8 +63J2145+5147 21:45:07.6666 +51:47:02.243 1.7 +28G095.29–0.93 21:39:40.5089 +51:20:32.808 – –J2137+5101 21:37:00.9862 +51:01:36.129 0.5 –127J2150+5103 21:50:14.2662 +51:03:32.264 1.7 +100J2145+5147 21:45:07.6666 +51:47:02.243 1.0 +62J2139+5300 21:39:53.6244 +53:00:16.599 1.7 +1G100.37-3.57 22:16:10.3651 +52:21:34.113 – –J2217+5202 22:17:54.4607 +52:02:51.370 0.4 +140J2209+5158 22:09:21.4869 +51:58:01.833 1.1 –111G108.20+0.58 22:49:31.4775 +59:55:42.006 – –J2243+6055 22:43:00.8093 +60:55:44.199 1.3 –39J2254+6209 22:54:25.2930 +62:09:38.725 2.3 +15J2257+5720 22:57:22.0461 +57:20:30.197 2.8 +158G108.47–2.81 23:02:32.0813 +56:57:51.356 – –J2301+5706 23:01:26.6266 +57:06:25.508 0.2 –46J2258+5719 22:58:57.9412 +57:19:06.463 0.6 –54J2257+5720 22:57:22.0461 +57:20:30.197 0.8 –62G108.59+0.49 22:52:38.3150 +60:00:51.888 – –J2243+6055 22:43:00.8130 +60:55:44.212 1.5 –52J2254+6209 22:54:25.2930 +62:09:38.725 2.2 +6J2301+5706 23:01:26.6266 +57:06:25.508 3.1 +158J2258+5719 22:58:57.9412 +57:19:06.463 2.8 +163G111.23-1.23 23:17:20.7888 +59:28:46.970 – –J2339+6010 23:39:21.1252 +60:10:11.850 2.9 +76J2258+5719 22:58:57.9412 +57:19:06.463 3.2 –132J2257+5720 22:57:22.0460 +57:20:30.196 3.4 –129J2254+6209 22:54:25.2926 +62:09:38.724 3.9 –46G111.25–0.77 23:16:10.3555 +59:55:28.527 – –J2339+6010 23:39:21.1251 +60:10:11.850 2.9 +85J2254+6209 22:54:25.2930 +62:09:38.725 3.5 –50J2258+5719 22:58:57.9412 +57:19:06.463 3.4 –139G183.72-3.66 05:40:24.2276 +23:50:54.728 – –J0540+2507 05:40:14.3428 +25:07:55.349 1.3 –2J0550+2326 05:50:47.3909 +23:26:48.177 2.4 +100G229.57+0.15 07:23:01.7718 –14:41:34.339 – –J0721–1530 07:21:13.4914 –15:30:41.009 0.9 –152J0724–1545 07:24:59.0063 –15:45:29.370 1.2 +156J0729–1320 07:29:17.8177 –13:20:02.272 2.0 +48J0721–1630 07:21:49.1377 –16:30:19.746 1.8 –171G236.81+1.98 07:44:28.2367 –20:08:30.606 – –J0741–1937 07:41:52.7874 –19:37:34.828 0.8 –50 . RESULTS In this section we present parallaxes and propermotions of 22 GHz H O masers for 12 massivestar forming regions. The change in position of amaser spot relative to a background source is mod-eled with a sinusoidal parallax signature and a lin-ear proper motion in right ascension and declina-tion. Since systematic errors, associated with un-compensated atmospheric delays, generally exceedthose of random noise, we added “error-floors” inquadrature to the formal position uncertainties inboth coordinates. The error-floor values were de-termined by requiring the reduced χ ν of the post-fit residuals to be near unity in each coordinate(Reid et al. 2009a).A bright H O maser spot was used as thephase reference in order to calibrate the contin-uum source data and then measure position offsetsused for parallax and proper motion fitting. Whenwe estimated a parallax using several maser spotsin one source, the quoted parallax uncertainty isthe formal fitting uncertainty multiplied by √ N (where N is the number of maser spots) in orderto account for possible correlations among the po-sition measurements for the maser spots. Figures1–12 show positions for the maser spots relative to the background sources as a function of timeand the parallax and proper motions fits. The fit-ting results are summarized in Table 3. Detailedinformation for each source is presented in the Ap-pendix.When there were numerous maser spots, we at-tempted to fit an expanding model to the internal(relative) motions (as in G108.47–2.81, G111.25–0.77, and G236.81+1.98) in order to estimate themotion of the central, exciting star directly. De-tails of this model fitting procedure are in Sato etal. (2010).For sources with few maser spots, the propermotion for the central star was estimated froman unweighted average of all the measured abso-lute proper motions. For these cases, since watermaser motions relative to the central star typi-cally are tens of km s − , we adopted a 5 to 15km s − uncertainty for each velocity component,converted to an angular motion with the mea-sured distance. Several criteria were used to esti-mate the uncertainties in the motion componentsof the central star, depending on the complexityand width of the maser spectrum (as an indicationof the likely outflow speed) and the difference be-tween the water maser V LSR values and the ther-mal CO value (also an indication of the magni-tude and likelihood of un-modeled outflow issues).While ± − was used as the additional uncer-tainty for the components of motion for G095.29–0.93, G108.59+0.49, and G240.31+0.07, ±
10 kms − was used for G094.60–1.79, G100.37–3.57,G108.20+0.58, G111.23–1.23, and G183.72–3.66,and ±
15 km s − was used for G229.57+0.15.
4. The Perseus Arm4.1. Location and Pitch Angle
The maser sources were assigned to the Perseusarm based on matching their longitudes and ve-locities to a prominent “track” in the longitude–velocity ( l − v ) space of CO emission that is gen-erally associated with this arm. Note, that wedid not use our parallax measurements to assignsources to the arm. This removes a potential se-lection bias for defining the arm and its properties.We plot these sources on a CO l − v diagram fromDame et al. (2001) in Figure 13.With trigonometric parallax measurements, wecan accurately locate the massive star forming re-5 able 2— Continued
Source R.A. (J2000) Decl. (J2000) θ sep P.A.(h m s) ( ◦ ’ ”) ( ◦ ) ( ◦ )J0745–1828 07:45:19.3291 –18:28:24.799 1.7 +7J0735–1735 07:35:45.8125 –17:35:48.501 3.3 –39J0739–2301 07:39:24.9981 –23:01:31.885 3.1 –158G240.31+0.07 07:44:51.9676 –24:07:42.372 – –J0745–2451 07:45:10.2645 –24:51:43.770 0.7 +175J0749–2344 07:49:51.7793 –23:44:48.788 1.2 +72J0740–2444 07:40:14.7167 –24:44:36.684 1.2 –120 Note.—
Column 1 gives the names of the maser and backgroundsources. Columns 2 and 3 list the absolute positions of the referencemaser spot and background sources. Columns 4 and 5 give theangular separations ( θ sep ) and position angles (P.A.) east of northof the background sources relative to maser sources. Fig. 1.— Parallax and proper motion fit for G094.60–1.79. Plotted are positions of the maser spot at V LSR =–45.89 km s − relative to three background sources J2137+5101 (red triangles), J2150+5103 (green squares)and J2145+5147 (blue hexagons), respectively. Left panel: sky-projected motion of the maser with respectto background source labeled with the first and last epochs. Middle panel: the position offsets of the maseralong the east ( α cos δ ) and north direction ( δ ) as a function of time. The best-fit model in the east andnorth directions are shown as continuous and dashed lines, respectively. Right panel: same as the middlepanel but with fitted proper motions subtracted (parallax curve). Sixth epoch is not used for the fitting. (Acolor version of this figure is available in the online journal.)6ig. 2.— Parallax and proper motion fit for G095.29–0.93. Plotted are positions of the maser spot at V LSR =–35.67 km s − relative to four background sources J2137+5101 (red triangles), J2150+5103 (green squares),J2145+5147 (blue hexagons) and J2139+5300 (yellow circle), respectively. The three panels are describedin Figure 1. (A color version of this figure is available in the online journal.)Fig. 3.— Parallax and proper motion fitting for G100.37–3.57. Plotted are positions of the maser spot at V LSR = –38.37 km s − relative to two background sources J2209+5158 (red triangles), J2209+5158 (greensquares) and J2217+5202 (blue hexagons), respectively. Since J2209+5158 has structures, the maser spotwas detected in two separate regions. The three panels are described in Figure 1. (A color version of thisfigure is available in the online journal.) 7ig. 4.— Parallax and proper motion fit for G108.20+0.58. Plotted are positions of the maser spot at V LSR = –54.16 km s − relative to three background sources J2243+6055 (red triangles), J2254+6209 (greensquares) and J2257+5720 (blue hexagons), respectively. The three panels are described in Figure 1. (A colorversion of this figure is available in the online journal.)Fig. 5.— Parallax and proper motion fit for G108.47–2.81. Plotted are positions of the maser spot at V LSR =–55.79 km s − relative to three background sources J2301+5706 (red triangles), J2258+5719 (green squares)and J2257+5720 (blue hexagons), respectively. The three panels are described in Figure 1. (A color versionof this figure is available in the online journal.) 8ig. 6.— Parallax and proper motion fit for G108.59+0.49. Plotted are positions of the maser spot at V LSR = –53.47 km s − relative to three background sources J2243+6055 (red triangles), J2254+6209 (greensquares) and J2301+5706 (blue hexagons) and J2258+5719 (yellow circles), respectively. The three panelsare described in Figure 1. (A color version of this figure is available in the online journal.)Fig. 7.— Parallax and proper motion fit for G111.23–1.23. Plotted are positions of the maser spot at V LSR =–49.94 km s − relative to three background sources J2339+6010 (red triangles), J2258+5719 (green squares)and J2254+6209(blue hexagons), respectively. The three panels are described in Figure 1. 1st epoch is notused for the fitting. (A color version of this figure is available in the online journal.)9ig. 8.— Parallax and proper motion fit for G111.25–0.77. Plotted are positions of the maser spot at V LSR = 67.53 km s − relative to two background sources J2339+6010 (red triangles) and J2258+5719 (greensquares), respectively. The three panels are described in Figure 1. (A color version of this figure is availablein the online journal.)Fig. 9.— Parallax and proper motion fit for G183.72–3.66. Plotted are positions of the maser spot at V LSR =4.58 km s − relative to two background sources J0540+2507 (red triangles) and J0550+2326 (green squares),respectively. The three panels are described Figure 1. (A color version of this figure is available in the onlinejournal.) 10ig. 10.— Parallax and proper motion fit for G229.57+0.15. Plotted are positions of the maser spot at V LSR = 57.11 km s − relative to four background sources J0721–1530 (red triangles), J0724–1545 (green squares),J0729–1320 (blue hexagons) and J0721–1630 (yellow circles), respectively. The three panels are described inFigure 1. (A color version of this figure is available in the online journal.)Fig. 11.— Parallax and proper motion fit for G236.81+1.98. Plotted are positions of the maser spot at V LSR = 42.31 km s − relative to two background sources J0741–1937 (red triangles) and J0745–1828 (greensquares), respectively. The three panels are described in Figure 1. (A color version of this figure is availablein the online journal.) 11ig. 12.— Parallax and proper motion fit for G240.31+0.07. Plotted are positions of the maser spot at V LSR = 67.53 km s − relative to three background sources J0745–2451 (red triangles), J0749–2344 (greensquares), J0740-2444 (blue hexagons), respectively. The three panels are described in Figure 1. (A colorversion of this figure is available in the online journal.) Table 3Parallaxes and Proper Motions
Source Parallax Distance µ x µ y V LSR (mas) (kpc) (mas yr − ) (mas yr − ) (km s − )G094.60–1.79 0.253 ± +0 . − . –2.59 ± ± ± ± +0 . − . –2.75 ± ± ± ± +0 . − . –3.66 ± ± ± ± +0 . − . –2.25 ± ± ± ± +0 . − . –3.13 ± ± ± ± +0 . − . –5.56 ± ± ± ± +1 . − . –4.37 ± ± ± ± +0 . − . –2.02 ± ± ± ± +0 . − . +0.38 ± ± ± ± +0 . − . –1.33 ± ± ± ± +0 . − . –2.49 ± ± ± ± +0 . − . –2.43 ± ± ± Note.—
Column 1 lists source names. Columns 2 and 3 give the measured parallaxand the distance converted from the parallax. Columns 4 and 5 are proper motions in theeastward ( µ x = µ α cosδ ) and northward ( µ y = µ δ ) directions. Column 6 lists V LSR of the starforming region. 12ig. 13.— Locations of high mass star forming regions with parallaxes superposed on a CO l − v diagramfrom the CfA 1.2-m survey (Dame et al. 2001). Sources presented in this paper are indicated with circlesand those from literature with squares. The grey shadowed line traces the Perseus spiral arm (Vall´ee 2008);the width of the line denotes a ±
10 km s − velocity dispersion. (A color version of this figure is available inthe online journal.)gions of the Perseus arm of the Milky Way. As-suming the distance to the Galactic center R tobe 8.34 kpc (Reid et al. 2014), Figure 14 showsthe locations of our sources in the Milky Way asred circles, together with previous results from theliterature as blue squares.For simplicity, we assume that a section of aspiral arm follows a log-periodic function:ln R = ln R ref − ( β − β ref ) tan ψ (1) , where R and β are Galactocentric radius and az-imuth, respectively, R ref is the radius at a refer-ence azimuth β ref , and ψ is the spiral pitch an-gle (i.e., the angle between a spiral arm and atangent to a Galactocentric circle). Galactocen-tric azimuth is defined as the angle between theSun and the source as viewed from the center,with azimuth increasing with Galactic longitudein the first quadrant. We estimated two parame-ters, R ref and ψ using a Bayesian approach, whichminimized the “distance” from the straight linedescribed by Equation (1), variance weighted bythe uncertainty in this direction, and described indetail in Reid et al. (2014).Using the 25 sources with parallax measure- ment that are assigned to the Perseus arm (basedon matching to CO l − v tracks), we estimate thearm pitch angle to be 9 ◦ .9 ± ◦ .5, with an armwidth of 0.38 kpc, where ln R ref = 2.29 ± β ref = 13 ◦ .6 (uncertainties give 68% confidenceranges). The arm width was estimated by addingan “astrophysical noise” term, reflecting a non-zero arm width, in quadrature with measurementuncertainty when fitting for the pitch angle. Themagnitude of this noise term was adjusted to givea χ ν per degree of freedom of unity for the residu-als. In Figure 15, we plot the data and fitted linewhose slope is tan ψ .Pitch angles for the Perseus spiral arm have pre-viously been estimated by Reid et al. (2009b) andSakai et al. (2012). Reid et al. (2009b) reported avalue of 16 ◦ . ± ◦ . ◦ . ± ◦ . R ) only. Since distance uncertainties af-fect both axes in Equation (1), i.e., ln R and β , abetter approach is to minimize the residuals per-pendicular to the best fit line. As a test, we re-fit the data used by Reid et al. (2009b) with our13 y (kpc) x (kpc) Outer Arm
P e r s e u s A r m
S a g i t t a r i u s A r m
Scutum-Centaurus
Norma Arm
G.C.Sun o Q1Q4 Q2Q3
Fig. 14.— Schematic view of the spiral arms of the Milky Way after Tayler & Cordes (1993) with updates. R = 8.34 kpc (Reid et al. 2014) is assumed. The location of the central bar (Benjamin et al. 2005) is alsoreported. The positions of the Perseus arm sources previously measured with trigonometric parallaxes areshown in blue squares together with the present measurements in red circles. (A color version of this figureis available in the online journal.) 14mproved Bayesian approach and obtained an es-timated pitch angle of 15 ◦ . ± ◦ .
4. This gives asimilar pitch angle as the previous estimate, butwith a larger and more realistic uncertainty. Withthis uncertainty, the old result is statistically con-sistent with the new result. Of course the newresult benefits from using a much larger sampleand should be preferred.Based on the spiral pattern fit results, we obtaina distance between the Sun and the Perseus spiralarm of 2.0 ± l = 180 ◦ , β = 0 ◦ ). Since the Sagittarius arm islocated at 1.4 ± Using the parallax distances to convert propermotions to linear speeds and combining withDoppler radial velocities, we can calculate thethree-dimensional space motions for the massivestar forming regions in the Perseus spiral arm.Assuming R = 8.33 ± = 243 ± − , dT/dR = –0.2 ± − kpc − andSolar Motion components of U (cid:12) = 10.7 ± − , V (cid:12) = 12.2 ± − and W (cid:12) = 8.7 ± − from B1 model in Reid et al. (2014)which used as a strong prior the Sch¨onrich et al.(2010) Solar Motion, we calculate the peculiar mo-tion components (U s , V s , W s ) of the sources. U s is toward the Galactic center, V s is in directionof Galactic rotation, and W s is toward the northGalactic pole. The estimated peculiar motions forthe sources are listed in Table 4.The variance-weighted average of the peculiarmotion components for 25 sources in the Perseusarm are U s = 9 . ± . − toward the Galacticcenter, V s = − . ± . − in the direction ofGalactic rotation, and W s = − . ± . − to-ward the north Galactic pole. For the comparison,when we assume R = 8.34 ± = 240 ± − , dT/dR = –0.2 ± − kpc − and Solar Motion components of U (cid:12) = 10.7 ± − , V (cid:12) = 15.6 ± − and W (cid:12) = 8.9 ± − from A5 model in Reid et al. (2014), weobtained U s = 9 . ± . − , V s = − . ± . − , and W s = − . ± . − . The av-erage peculiar motion in the direction of Galacticrotation is affected by the V (cid:12) component of solarmotion. These peculiar motion values indicate that onaverage sources in the Perseus arm are moving to-ward the Galactic center and move slower thanfor circular Galactic orbits. Compared with theaverage peculiar motions of the 100 sources withparallaxes in many arms, ( U s = 2 . ± . − and V s = − . ± . − from B1 model, Reidet al. (2014)), the Perseus arm sources have higheraverage peculiar motions and it seems to be a char-acteristic of the arm at least in the second andthird quadrants.The general claim of the spiral density wavetheory in literature from 1960s is that peculiarmotions should be toward the Galactic center andcounter to the Galactic rotation. Our result isconsistent with that claim.As for kinematic distances, indeed, the pecu-liar motions affect them. As shown in Table 5, thestandard kinematic distance, which do not con-sider the average peculiar motions of sources (i.e., U s = V s = W s = 0 km s − ), are biased higherthan the true (parallax) values in the second quad-rant. The “revised kinematic distances” (Reid etal. 2009b) using the average peculiar motion ofthe Perseus arm ( U s = 9.2 km s − , V s = –8.0 kms − , and W s = –2.3 km s − ) have better agree-ment with the distance from the parallax than thestandard kinematic distance in the second quad-rant. In the third quadrants, revised kinematicdistances may be somewhat biased toward largerdistances compared to parallax values. This por-tion of the Perseus arm may have a smaller U s peculiar motion than the average for all sources.Therefore, when calculating (revised) kinematicdistances, for Perseus arm sources in the thirdquadrant, one should probably use U s ∼ − . Clearly, more parallax/proper motion mea-surements are needed to better understand aver-age peculiar motions along the Perseus arm.15 l og ( R / k p c ) β (deg) Fig. 15.— Plot of the logarithm of Galactocentric radius (R) vs. Galactocentric azimuth ( β ) for the Perseusspiral arm sources with our measurements in red circles and the literature in blue squares. The slope of theline is proportional to tangent of a pitch angle, ψ . (A color version of this figure is available in the onlinejournal.) 16 able 4Peculiar Motions of Sources in the Perseus Arm Source Alias U s V s W s Ref.(km s − ) (km s − ) (km s − )G043.16+0.01 W49(N) –7.6 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Note.—
We assumed R = 8.33 ± = 243 ± − , dT/dR = –0.2 ± − kpc − and Solar Motion components of U (cid:12) = 10.7 ± − , V (cid:12) = 12.2 ± − and W (cid:12) = 8.7 ± − from B1 model in Reid et al. (2014) to determine thepeculiar motions (U s , V s , W s ) in Columns 3–5. U s is the motion toward the Galactic center,V s is in direction of Galactic motion, and W s is toward the North Galactic Pole (NGP).Column 5 indicates references. (1) This paper; (2) Asaki et al. (2010); (3) Hachisuka et al.(2009); (4) Moellenbrock et al. (2009); (5) Moscadelli et al. (2009); (6) Niinuma et al. (2011);(7) Oh et al. (2010); (8) Reid et al. (2009a); (9) Rygl et al. (2010); (10) Sakai et al. (2012);(11) Sato et al. (2008); (12) Shiozaki et al. (2011); (13) Xu et al. (2006); (14) Zhang et al.(2013) 17 able 5Parallaxes and Kinematic Distances Source D π D Stdk D Revk (kpc) (kpc) (kpc)W49(N) 11.11 +0 . − . +0 . − . +0 . − . G048.60+0.02 10.75 +0 . − . +0 . − . +0 . − . G094.60–1.79 3.95 +0 . − . +0 . − . +0 . − . G095.29–0.93 4.85 +0 . − . +0 . − . +0 . − . G100.37–3.57 3.46 +0 . − . +0 . − . +0 . − . G108.20+0.58 4.41 +0 . − . +0 . − . +0 . − . G108.47–2.81 3.24 +0 . − . +0 . − . +0 . − . G108.59+0.49 2.47 +0 . − . +0 . − . +0 . − . G111.23–1.23 3.33 +1 . − . +0 . − . +0 . − . G111.25–0.77 3.34 +0 . − . +0 . − . +0 . − . NGC 7538 2.65 +0 . − . +0 . − . +0 . − . IRAS 00420+5530 2.17 +0 . − . +0 . − . +0 . − . NGC 281 2.82 +0 . − . +0 . − . +0 . − . NGC 281(W) 2.38 +0 . − . +0 . − . +0 . − . W3(OH) 1.95 +0 . − . +0 . − . +0 . − . S Per 2.42 +0 . − . +0 . − . +0 . − . IRAS 05168+3634 1.88 +0 . − . +9 . − . +3 . − . G183.72–3.66 1.59 +0 . − . +11 . − . +13 . − . IRAS 06061+2151 2.02 +0 . − . +0 . − . +2 . − . S 252 2.10 +0 . − . +3 . − . +7 . − . G192.60–0.04 1.52 +0 . − . +1 . − . +2 . − . S 255 1.59 +0 . − . +1 . − . +2 . − . G229.57+0.15 4.59 +0 . − . +0 . − . +0 . − . G236.81+1.98 3.07 +0 . − . +0 . − . +0 . − . G240.31+0.07 5.32 +0 . − . +0 . − . +0 . − . Note.—
Column 1 lists source names. D π is the distanceconverted from the measured parallax. D Stdk is the kinematicdistance without considering the average peculiar motions.D
Revk is the revised kinematic distance using U s = 9.2 km s − , V s = –8.0 km s − , and W s = –2.3 km s − . The kinematicdistances are calculated for R = 8.33 kpc, Θ = 243 km s − ,dT/dR = –0.2 km s − kpc − and Solar Motion componentsof U (cid:12) = 10.7 km s − , V (cid:12) = 12.2 km s − and W (cid:12) = 8.7 kms − from B1 model in Reid et al. (2014). When we determinethe uncertainties in the kinematic distances, we considered a 7km s − uncertainty in V LSR . Kinematic distances for sourcesnear the Galactic anticenter intrinsically have large uncertain-18ies and, thus, kinematic distances should be avoided for thesesources. 19 . CONCLUSION
We measured parallaxes and proper motions of12 massive star forming regions in the outer por-tion of the Perseus arm in the second and thirdGalactic quadrants. Combined with 14 resultsfrom the literature, we estimated the pitch angleof this section of the Perseus arm to be 9 ◦ .9 ± ◦ .5.We also calculated the three-dimensional Galacticmotions and find that on average the sources inthe Perseus arm are moving toward the Galacticcenter and slower than the circular Galactic rota-tion.Financial support by the European ResearchCouncil for the ERC Advanced Grant GLOSTAR(ERC-2009-AdG, grant agreement No. 247078)is gratefully acknowledged. This work was sup-ported in part by the Chinese National ScienceFoundation through grants NSF 11133008 and theKey Laboratory for Radio Astronomy, ChineseAcademy of Sciences. Facilities:
VLBA 20 . APPENDIX
We present details of parallax and proper motion fits for each source. Tables 6–17 summarize the results.The uncertainties of parallaxes and proper motions in the tables are the formal fitting uncertainties.
G094.60–1.79 is also known as AFGL 2789, and its parallax was measured to be 0.326 ± ± ± − and –3.6 ± − in right ascension and declination, respectively(Oh et al. 2010). Since the H O masers were not detected at our last (sixth) epoch in our observations, weused only 5 epochs with 7 maser spots and 3 background sources for the fitting. When we calculated thepeculiar motion in Table 4, we used an unweighted average of our measurements and Oh et al. (2010) for theparallax and proper motion, yielding a parallax of 0.29 ± ± − in right ascension and –3.8 ± − in declination. The LSR velocity measured from CO emission is–43 km s − and –49 km s − from water maser emission. We adopted –46.0 ± − for the V LSR . G095.29–0.93 is associated with an infrared source, 2MASX J21394111+5120356, and its radial velocityis –42.4 km s − from CS(2–1) emission (Bronfman et al. 1996), –36.5 km s − from CO emission and –41 kms − from the water maser spectrum. We adopted –38.0 ± − for the V LSR . The parallax and propermotions are obtained from 3 maser spots and 4 background sources.
G100.37–3.57 is associated with the HII region CPM 37 (IRAS22142+5206). H O maser emission wasobserved between –50 and –15 km s − , and it is highly variable over the observation period. The radialvelocity is –36.5 km s − from CO emission. We adopted –37.0 ± − for V LSR . G108.20+0.58 has a radial velocity of –49.2 km s − from CS(2–1) emission (Bronfman et al. 1996). Theparallax is measured using 2 maser spots and 3 background sources. We used –49.0 ± − for V LSR . G108.47–2.81 is associated with IRAS 23004+5642. We used 6 maser spots and 3 background sourcesto fit parallax and proper motions. The radial velocity is –54 km s − from CO emission, and we used thisvalue to obtain the peculiar motions. We fitted the data of the relative motions with respect to the referencemaser spot ( V LSR = –65.48 km s − ) to expansion model (Sato et al. 2010). The expansion velocity is 3.4 ± − and the center of expansion is (0.00 ± ± V x , V y , V r ) = (–14.1 ± ± ± − . These values correspond to µ x = –0.92 ± − and µ y = 0.14 ± − at the distance of 3.24 kpc. Adding these motions to theabsolute motion of the reference maser spot, we obtained an absolute proper motion of the central star tobe µ x = –3.13 ± − and µ y = –2.79 ± − . Figure 16 shows spatial distribution andrelative motions with respect to the center of the expansion of water masers toward G108.47–2.81. G108.59+0.49 is associated with IRAS 22506+5944 and its radial velocity is measured to be –52 km s − from CO emission. We fitted parallax and proper motions using 2 maser spots and 4 background sources. G111.23–1.23 is associated with IRAS 23151+5912 and its radial velocity is –54.4 km s − from CS(2–1)emission (Bronfman et al. 1996). We observed 4 background sources, but J2257+5720 was discarded fromthe parallax fitting since the structure of the quasar changed over time. We used 2 maser spots and 3 quasarsto fit parallax and proper motions. G111.25–0.77 is associated with IRAS 23139+5939 and its V LSR = –43 km s − from CO emission. Weobserved 3 background sources. However, we did not use J2254+6209 for the parallax fitting, since it wasnot detected at the first and sixth epoch. We obtained parallax and proper motions from 4 maser spots and2 background sources. We fitted the data of the relative motions with respect to the reference maser spot( V LSR = –51.26 km s − ) to expansion model (Sato et al. 2010). The expansion velocity is 2.6 ± − and the center of expansion is (0.09 ± ± V x , V y , V r ) = (8.3 ± ± ± − . These values correspond to µ x = 0.52 ± − and µ y = –0.21 ± − at the distance of 3.34 kpc. Adding these motions to the absolute motionof the reference maser spot, we obtained an absolute proper motion of the central star to be µ x = –2.02 ± − and µ y = –2.31 ± − . Figure 17 shows spatial distribution and relative motionswith respect to the center of the expansion of water masers toward G111.25–0.77.21able 6: Parallax and Proper Motion for G094.60–1.79Maser Background v LSR
Parallax µ α µ δ Source (km s − ) (mas) (mas yr − ) (mas yr − )G094.60–1.79 J2137+5101 –43.78 0.293 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± < µ > –48.66 –2.59 ± ± v LSR
Parallax µ α µ δ Source (km s − ) (mas) (mas yr − ) (mas yr − )G095.29–0.93 J2137+5101 –35.25 0.231 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± < µ > –35.67 –2.75 ± ± v LSR
Parallax µ α µ δ Source (km s − ) (mas) (mas yr − ) (mas yr − )G100.37–3.57 J2217+5202 –38.37 0.304 ± ± ± ± ± ± ± ± ± ± < µ > –38.37 –3.66 ± ± v LSR
Parallax µ α µ δ Source (km s − ) (mas) (mas yr − ) (mas yr − )G108.20+0.58 J2243+6055 –53.74 0.222 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± < µ > –53.95 –2.25 ± ± v LSR
Parallax µ α µ δ Source (km s − ) (mas) (mas yr − ) (mas yr − )G108.47–2.81 J2301+5706 –54.52 0.310 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± < µ > –55.01 –2.21 ± ± D e c o ff s e t ( m a s ) −80.0−77.5−75.0−72.5−70.0−67.5−65.0−62.5−60.0 V L S R ( k m / s ) Fig. 16.— Locations and motions of water masers toward G108.47–2.81. Motions are with respect to thecenter of the expansion (0, 0). Color denotes the LSR velocities of maser spots. (A color version of thisfigure is available in the online journal.)Table 11: Parallax and Proper Motion for G108.59+0.49Maser Background v LSR
Parallax µ α µ δ Source (km s − ) (mas) (mas yr − ) (mas yr − )G108.59+0.49 J2243+6055 –53.47 0.273 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± < µ > –53.68 –5.56 ± ± v LSR
Parallax µ α µ δ Source (km s − ) (mas) (mas yr − ) (mas yr − )G111.23–1.23 J2339+6010 –49.94 0.348 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± < µ > –50.16 –4.37 ± ± v LSR
Parallax µ α µ δ Source (km s − ) (mas) (mas yr − ) (mas yr − )G111.25–0.77 J2339+6010 –39.05 0.303 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± < µ > –45.47 –2.54 ± ± D e c o ff s e t ( m a s ) −51.0−49.5−48.0−46.5−45.0−43.5−42.0−40.5−39.0 V L S R ( k m / s ) Fig. 17.— Locations and motions of water masers toward G111.25–0.77. Motions are with respect to thecenter of the expansion (0, 0). Color denotes the LSR velocities of maser spots. (A color version of thisfigure is available in the online journal.) 26 has a parallax of 0.629 ± V LSR from CO emission is 2.5 km s − . The H O masers are variable over our observations. Since mostof maser spots disappeared at the 3rd epoch and only 2 spots survived for more than 2 epochs, we could notget internal motions.
G229.57+0.15 is associated with IRAS 07207–1435. The H O maser emission ranges from 45 km s − to60 km s − with a predominantly double-peak spectrum. The radial velocity is 43 km s − from CO emission.We adopted 47 ±
10 km s − for V LSR . We measured parallax and proper motions from one maser spotdetected at all epochs and 4 background sources. Because of the source’s low declination, the error in rightascension is much smaller than that in declination.
G236.81+1.98 is associated with IRAS 07422–2001 and its radial velocity is 43 km s − from CO emission.Four background sources were observed, but two of them (J0735–1735 and J0739–2301) were not used forthe parallax fitting. J0735–1735 and J0739–2301 are separated by about 3 degrees from the maser sourceand mostly in the north-south direction. J0735–1735 has structure, which is likely caused by atmosphericdistortion and J0739–2301 was not detected after the third epoch. Because of the source’s low declination,the error in right ascension is much smaller than that in declination.We fitted the data of the relative motions with respect to the reference maser spot ( V LSR = 42.31 kms − ) to expansion model (Sato et al. 2010). The expansion velocity is 0.5 ± − and the center ofexpansion is ( 0.05 ± ± V x , V y , V r ) = (10.5 ± ± ± − . These values correspond to µ x = 0.72 ± − and µ y = 0.56 ± − at the distance of 3.07 kpc. Adding these motions to the absolute motion of the reference maserspot, we obtained an absolute proper motion of the central star to be µ x = –2.49 ± − and µ y = 2.67 ± − . Fig. 18 shows spatial distribution and relative motions with respect to the centerof the expansion of water masers toward G236.81+1.98. G240.31+0.07 is associated with 2MASS J07445196–2407399 and its V LSR is 67.0 km s − obtained fromCO emission. The parallax was measured using 3 maser spots and 3 background sources. Because of thesource’s low declination, the error in right ascension is much smaller than that in declination.Table 14: Parallax and Proper Motion for G183.72–3.66Maser Background v LSR
Parallax µ α µ δ Source (km s − ) (mas) (mas yr − ) (mas yr − )G183.72–3.66 J0540+2507 4.58 0.632 ± ± ± ± ± ± ± < µ > ± ± v LSR
Parallax µ α µ δ Source (km s − ) (mas) (mas yr − ) (mas yr − )G229.57+0.15 J0721–1530 57.11 0.214 ± ± ± ± ± ± ± ± ± ± ± ± ± < µ > ± ± v LSR
Parallax µ α µ δ Source (km s − ) (mas) (mas yr − ) (mas yr − )G236.81+1.98 J0741–1937 42.31 0.310 ± ± ± ± ± ± ± < µ > ± ± (cid:0) (cid:0) (cid:0) (cid:0) D e c o ff s e t ( m a s ) V L S R ( k m / s ) Fig. 18.— Locations and motions of water masers toward G236.81+1.98. Motions are with respect to thecenter of the expansion (0, 0). Color denotes the LSR velocities of maser spots. (A color version of thisfigure is available in the online journal.) 28able 17: Parallax and Proper Motion for G240.31+0.07Maser Background v LSR
Parallax µ α µ δ Source (km s − ) (mas) (mas yr − ) (mas yr − )G240.31+0.07 J0745–2451 67.95 0.194 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± < µ > ± ± EFERENCES
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