errors in kinematic distances and our image of the milky way galaxy

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No. 6, 2006KINEMATIC DISTANCE ERRORS 2379Fig. 4.—(a) Rotation curve given by the background potential (solid line) compared with the measured rotation curve. For the inner galaxy, the rotations measuredfor both positive (dotted line) and negative longitudes (dashed line) are presented. The rotation curve corresponding to the outer galaxy is also shown (dash-dotted line).(b) Rotation curve given by the background potential (solid line) compared with the average of the north and south rotation curves (dotted line) and the mean azimuthalvelocity of the gas in the simulation (dashed line). Note that both the mean velocity and the mean rotation curve are above the background rotation curve for most of theradial domain.side of the tangent point by looking at the galactic latitude extensionof the source (Fish et al. 2003), or by using observed intermediateabsorption features (Watson et al. 2003; Sewilo et al.2004). For this investigation I decided to cheat: I looked upwhich side of the tangent point the gas parcel fell on, and chosethe measured distance accordingly.Figure 5a shows the error in measured distance with respect tothe real distance in the model. Recalling Figure 4, the observerwould determine different rotation curves for the northern andsouthern sides of the galactic center. Accordingly, in determiningthe kinematic distance for Figure 5a, the rotation curve usedis that of the corresponding side of the galactic center. It isFig. 5.—Error in the measured kinematic distance (d ) obtained under the assumption of circular orbits following (a) the measured rotation curve and (b) therotation given by the background potential. Sections of 7 around the galactic longitudes l ¼ 0 and 180 were excluded. Although the error in most of the galactic diskis of the order of 0:5 kpc, it is significantly larger at the positions of the spiral arms. The sharp edges at the positions of the tangent points are a consequence of the factthat the terminal velocities do not occur at those points. The errors in measured kinematic distances are larger when the real ( background) rotation curve is used. [See theelectronic edition of the Journal for a color version of this figure.]
2380 GÓMEZVol. 1321 In order to diminish spurious interpolation effects, each gas parcel was spreadusing a two-dimensional Gaussian weight function into a 3 ; 3 grid-cell regionaround the position corresponding to that parcel’s galactic longitude and measureddistance.Fig. 6.—Remapping of the gas distribution resulting from the kinematic distancesusing the measured rotation curves in Fig. 4a and assuming circular gasorbits. Note the regions near the tangent points and the corotation circle, wherelittle or no gas is mapped to.noticeable that although the errors are on the order of 0:5 kpcinmost of the galactic disk, they are significantly larger at thepositions of the spiral arms (as hinted by Gómez & Cox 2004b).This fact has a special impact in studies of the spiral structure ofthe Galaxy that rely on kinematic distances, since it distorts theimage the observer would generate (see x 4.1).There is another significant feature in Figure 5. Although theterminal velocity does not really arise from the tangent point, thecircular orbits assumption assigns gas observed near terminal velocityto that point. This generates a feature in the errors thatcorresponds to the locus of the tangent points. Again, the error issignificant at the position of the spiral arms and would generatelarge errors in the determination of distances to objects that tracethe spiral structure.The assumptions of circular orbits and different rotation curvesfor positive and negative longitudes are, of course, inconsistent.One solution is to fit a single rotation curve to both sides of theGalaxy. In order to test this method the average of both rotationcurves was taken, and the equivalent of Figure 5a was calculated.The result was that the magnitude of the error in the kinematicdistances was approximately the same, but the area with error>0.5 kpc spanned a larger fraction of the disk.Suppose now that the imaginary observer somehow managesto obtain the large-scale distribution of stellar mass in the modelgalaxy. This would allow the derivation of the real rotation curvefrom the background axisymmetric potential. If the observer nowuses that real rotation to determine kinematic distances, evenlarger distance errors would be obtained, especially for the innergalaxy, as shown in Figure 5b. This counterintuitive result arisesbecause, at this point of the simulation, the gas has already adoptedorbits that are not only influenced by the background potentialbut also by the large-scale magnetic field (likely different fromthe field in the initial conditions) and the torques and resonancesgenerated by the spiral perturbation. Although the real rotationcurve is consistent with the most important determinant of thegas rotation velocity (the background mass distribution), it doesnot include other influences in that velocity, while the ‘‘wrong’’rotation curve determined from gaseous terminal velocities moreclosely reflects the real motion of the gas (recall Fig. 4, in whichthe measured rotation curve is systematically above the truerotation).Although intrinsically inconsistent, the two different measuredrotation curves are used in the remainder of this investigation sincethat procedure leads to smaller distance errors. The results presentedin x 4.1 are even more noteworthy if the average or the realrotation curves are used.4.1. The Galaxy DistortedConsider now that the imaginary observer is trying to studythe spiral structure of the galaxy he/she lives in. The procedurewould consist of translating the longitude-velocity data obtainedfrom a diffuse gas survey, for example, into a spatial distributionusing the kinematic distances that result from the assumption ofcircular orbits that follow the measured rotation curve. 1 The resultingmap is shown in Figure 6. Note that the features describedfor Figure 1 (namely, the four spiral arms, the 4 kpc high-densityring, and the corotation low-density ring) all but disappear, whilenew fictitious features, such as the structure in the outer Galaxy,are formed as a consequence of the oscillations in the outer rotationcurve. Also significant in this figure are the regions wherelittle or no gas is assigned by the mapping, namely, the bandsnear the corotation circle and the quasi-triangular regions nearthe tangent point locus. (These nearly empty regions are significantlylarger when the background or the mean rotation curvesare used to determine the distance to the observed gas parcel.)The imaginary observer would likely conclude that his/herhome galaxy has two ill-defined spiral arms. If a logarithmic spiralmodel were forced, an 11 pitch angle and a density contrastmuch stronger than that in the numerical model would be found.Another possibility for determining the distance to a gas parcelconsists of comparing the line-of-sight velocity of the parcelwith the predicted velocity obtained from some model for theGalactic structure. For the numerical model described in x 2, givena Galactic longitude, Figure 3 is searched for the required velocity,and the corresponding distance is read out. 2 Althoughthe same procedure to solve the ambiguity with respect to thetangent point is used, the noncircular motions introduce new distanceambiguities for certain longitude-velocity values (up to 11,although 3 is a more typical number). When these ambiguitiesappear, they occur close to each other, making their resolutiondifficult. So, when reconstructing the map of the galaxy, the gasdensity is equally split among these positions.The result is shown in Figure 7. The new distance ambiguitiesstill introduce spurious structure, such as the splitting of the spiralarms. Nevertheless, the number and position of the arms, thestructure around the corotation radius, and the lack of features inthe outer galaxy are recovered. The imaginary observer wouldlikely conclude that his/her home galaxy has four arms with 9 and 12N5 pitch angles, although he/she would also find nonexistentbridges and spurs. On the other hand, it should be consideredthat the imaginary observer would not see thermal or turbulent2 A simple C language program that provides a distance given a Galactic longitudeand line-of-sight velocity value and uncertainty is available at http://www.astrosmo.unam.mx/~g.gomez/publica/. In that program the resulting distanceis given as a range instead of a central value and uncertainty, since the velocitydistancemapping makes the distance probability distribution neither uniform inthe range nor peaked around a central value.
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