Revista Mexicana de Astronomía y Astrofísica ISSN: 0185-1101 [email protected] Instituto de Astronomía México Teixeira, R.; De Souza, R. E.; Dos Anjos, S. STELLAR KINEMATICS IN THE LOCAL DISK Revista Mexicana de Astronomía y Astrofísica, vol. 34, 2008, pp. 64-67 Instituto de Astronomía Distrito Federal, México Available in: http://www.redalyc.org/articulo.oa?id=57116170016 How to cite Complete issue Scientific Information System More information about this article Network of Scientific Journals from Latin America, the Caribbean, Spain and Portugal Journal's homepage in redalyc.org Non-profit academic project, developed under the open access initiative RevMexAA (Serie de Conferencias), 34, 64{67 (2008) STELLAR KINEMATICS IN THE LOCAL DISK R. Teixeira,1 R. E. De Souza,1 and S. Dos Anjos1 RESUMEN A partir de las distancias y movimientos propios para unas 22000 estrellas del Hipparcos, describimos la distribuci´on de velocidades residuales mediante la superposici´on de dos Gaussianas, en vez de una sola, como es costumbre. La muestra se seleccion´o de acuerdo con la magnitud, color, posici´on gal´actica y distancia, y se separ´o en seis grupos segun´ el tipo espectral, tres de ellos de tipo temprano y tres tard´ıos. Verificamos que para las estrellas tempranas nuestra representaci´on no ofrece ventajas. Sin embargo, para las tard´ıas, la representaci´on mediante dos Gaussianas describe mejor la distribuci´on de velocidades. Nuestros resultados senalan~ claramente la existencia de dos poblaciones cinem´aticas distintas entre los tres grupos tard´ıos: una de ellas con dispersi´on de velocidades grande, la otra con dispersi´on pequena.~ Las dos poblaciones se encuentran presentes en ambos grupos; s´olo difieren sus proporciones. ABSTRACT From Hipparcos distances and proper motions for approximately 22000 stars we described the residual velocity distribution by the superposition of two Gaussians instead one as traditionally used. The sample of stars was selected by magnitude, color, Galactic position and distance and ranged in 6 spectral-type groups, 3 of early-type and 3 of late-type stars. We verified that for the early-type stars no gain is attained with our representation but for the late-type stars it is clear that the superposition of two Gaussians better describe the velocity distribution. Our results clearly point to the existence of two different kinematic populations very well characterized in the three late-type star groups: one population with high velocity dispersion and another with low velocity dispersion. It is still more interesting since the high and the low velocity dispersion population is the same in all the three groups. The core of this work was published in De Souza & Teixeira 2007. Key Words: stars: kinematics | Galaxy: kinematics and dynamics 1. INTRODUCTION two basic questions that arise naturally: How can we best describe the velocity distribution? How can we The kinematic description of the local disk stars do that with the available data? is fundamental to the understanding of the struc- Using the trigonometric parallaxes and proper ture, formation and evolution of the Milky Way. motions from the Hipparcos catalog (ESA 1997) for The statistics of velocities in the solar neighborhood approximately 22000 stars we attempted to answer Ed. Christine Allen, Alex Ruelas, & Ramachrisna Teixeira provides a database to describe the dependence of these two questions. To better represent the veloc- the disk kinematics on age, metallicity and spectral ity distribution and consequently to better take into group (Stromgren 1987; Soubiran & Girard 2005). account the change of the velocity dispersion with The velocity field in the neighbourhood of the age, we fitted to the data two Gaussians instead of Sun is traditionally described by a single Gaussian one. To overcome the difficulty due to the lack of in each component of the spatial motion as proposed radial velocity for most of the considered stars we by Schwarzschild (1907). It is not difficult to see developed a strategy that allows us to obtain the ve- © 2008: Instituto de Astronomía, UNAM - IV Reunión sobre Astronomía Dinámica en Latinoamérica that this one-Gaussian model is not the best fit for locity ellipsoid only from the tangential components, the data. Many groups of stars can present a large vl and vb, of the spatial velocity (De Souza & Teix- spread of age and this model does not take this fact eira 2007). into account. On the other hand, most work on this theme was faced with the difficulty of obtaining the components of the spatial motion from the available 2. DATA SELECTION data; more specifically, radial velocities and/or dis- Our work is based on a sample of 22392 Hip- tances are often missing. In our work we deal with parcos stars (ESA 1997) selected basically with the 1 same criteria adopted by Mignard (2000) in his work Instituto de Astronomia, Geof´ısica e Ci^encias At- mosf´ericas, USP, Rua do Mat~ao, 1226, Cidade Universit´aria, about stellar kinematic: only single stars, stars lying 05508-090, S~ao Paulo, Brazil ([email protected]). in the distance interval of 0.1{2.0 kpc, with com- 64 KINEMATICS IN THE LOCAL DISK 65 TABLE 1 3.1. Ellipsoid velocity determination SELECTED DATA GROUPED BY As a consequence of the lack of distance and/or SPECTRAL-TYPE radial velocity measurements many works on this theme, as we can see in the literature, are limited B{V Spec. type Nstar to a small number of stars. However, even if we can- 0.00{0.15 A0{A5 4202 not obtain the individual velocity for each object, we can obtain the statistic quantities σu, σv and σw that 0.15{0.30 A5{F0 3185 describe the velocity ellipsoid, from only the tangen- 0.30{0.45 F0{F5 2837 tial components of the spatial motion vl and vb. In 0.85{1.15 K0{K5 6533 other words, we are working with the projected dis- 1.15{1.40 K5{M0 3350 tribution in the radial direction. 1.40{1.60 M0{M5 2285 In the present case, we have no radial velocities for the most of the stars. So, we construct the ve- locity distribution for the tangential components vl pleteness greater than 70% based on the Tycho cat- and vb: alogue (ESA 1997) as function of Galactic latitude, 2 magnitude and color. Mignard (2000) also imposed 1 vl −1 s(vl) = exp 2 ; a limit of 60-90 km s depending on the spectral p2πσvl −2σvl type for the residual velocity. Here we work with a 2 −1 1 vb limit of 100 km s that corresponds approximately t(vb) = exp 2 : (2) p v 2σvb to 3 times the velocity dispersion in the disk. These 2πσ b − stars were grouped into spectral types: 3 groups of These distributions provide the velocity disper- early-type and 3 of late-type, as show in Table 1. sions σv and σv from which we obtain the velociy The criterion of distance and the observational mag- l b dispersions σu, σv and σw (equation 3). For a de- nitude limit of the Hipparcos satellite compells us, tailed development of this formalism see De Souza for the late type stars, to work only with the giant & Teixeira (2007). and sub-giant stars. Thus, the main-sequence late type stars were not considered here. In turn, the cos2 l stars with B{V between 0.45{0.85 were not selected 2 2 2 σvl = 2 + sin l σu ; due to the mixed characteristics of this sample. Γv 2 2 2 2 2 2 sin l sin b cos b 2 σvb = cos l sin b + 2 + 2 σu ; (3) 3. DATA TREATMENT STRATEGY Γv Γw The components, u (Galactic center direction), where Γv = σu/σv and Γw = σu/σw are the v (direction of increasing Galactic longitude) and w anisotropy parameters that describe the dispersion Ed. Christine Allen, Alex Ruelas, & Ramachrisna Teixeira (direction to North Galactic Pole) of the spatial ve- of the velocity ellipsoid in terms of the dispersion in locity are obtained from the observational quantities the Galactic center direction. distance and proper motion, from which we deter- To develop this strategy we need to make some mine the tangential components, vl and vb, and the hypotesis to compensate for the fact that vl and vb radial velocity, as indicated in the following equa- are not in a fixed direction. To overcome this ob- tions: stacle we work in equal area sectors of the celestial sphere imposing on each sector the hipothesis that © 2008: Instituto de Astronomía, UNAM - IV Reunión sobre Astronomía Dinámica en Latinoamérica u = vr cos l cos b vb cos l sin b vl sin l ; − − the directions of sectors vl and vb are fixed, corre- v = vr sin l cos b vb sin l sin b + vl cos l ; − sponding to the direction of the center of the sector. w = vr sin b + vb cos b : (1) This is the same as saying that the velocity disper- sions σvl and σvb are constant in each sector. Here, From these components we can describe the ve- we divided the celestial sphere in 72 equal area sec- locity distribution in each direction. In general, as tors having in each sector about 300 stars. The ideal said, this is done by the fit of a single Gaussian to was to work with smaller sectors, but in this case, the data. Of course, in this way, we are able to per- we would have had only a few stars per sector. form a kinematic study only for the stars for which Thus, using equation (3) we obtain by the least we know all the observational data, that is, the dis- squares method, the values of σu, σv and σw in each tances, proper motions and radial velocities.