Kinematics of the local disc from the RAVE survey and -TGAS

1 Annie C. Robin , Abstract: We study the Bienaymé et al (2015). We show studies. However we find a V⊙ Olivier Bienaymé2, kinematics of the thin and thick that this model is able to of 1 km/s, essentially due to the José G. Fernández-Trincado1, discs using the Besançon reproduce the kinematics of the inclusion of the variation of the Céline Reylé1 population synthesis model local discs in great detail. It asymmetric drift with distance together with RAVE DR4 and reproduces well the velocity to the plane. The TGAS-RAVE 1. Institut Utinam, Besançon Gaia first data release (TGAS). distribution in a wide solar sample allows to constrain the 2. Observatoire Astronomique de We account for the asymmetric neighbourhood. The U⊙ and W⊙ thin and thick disc dynamical

Strasbourg drift computed from fitting a components of the Solar motion evolution, as well as Stäckel potential to orbits agree well with previous determining the Solar motion.

100 160 The asymmetric drift (Fig. 1) is computed for each disc sub- 90 140 80 component of the Besançon Model (BGM) by fitting a 120 70 Stäckel potential to orbits in the gravitational potential defined 100 60 by BGM distribution (Bienaymé et al. 2015). 50 80

40 Vlag km/s Vlag km/s 60 30 After simulating RAVE-TGAS fields with BGM, we compute radial 40 20 velocity distributions in bins of temperature and , and 20 10 we adjust model parameters using an ABC-MCMC algorithm. The 0 0 2 4 6 8 10 12 0 1 2 3 4 5 6 parameters are indicated in table 1, mainly : Solar motion, vertex Rgal (kpc) Zgal (kpc) deviation, age-velocity dispersion of the thin disc, velocity Fig. 1: Asymmetric drift computed from the Stäckel approximation of the BGM ellipsoids of the thick disc, and gradients of velocity potential for subcomponents 2 to 7 (thin disc, with ages increasing in solid red, long- dispersion. dashed green, short-dashed blue, dotted magenta, dashed yellow-cyan), and for the Table 1 shows results, assuming an age-velocity dispersion as a young (dotted-dashed black) and old (dotted-dotted- dashed red) thick discs. Left 3rd order polynomial (A, B, C). Similar results are obtained with panel: as a function of R for z =0; Right panel: as a function of z for R = R⊙. gal gal gal various mathematical function for this relation (shown in fig. 2).

Table 1: Results of the MCMC fit of RAVE+TGAS distribution and proper motions, assuming two Fig. 2: Evolution of the vertical velocity rotation curves (Caldwell & Striker 1981 or Sofue 2015) dispersion of the thin disc with age. The solid lines show the best fit solutions for the 3 different formulae (fit 1: blue, 2: magenta, 3: cyan, see text), while the symbols indicate the Gómez et al. (1997) values from Hipparcos (red plus) and Holmberg et al. (2009) (green triangles). Black dotted line is the relation from Sharma et al. (2014) while black dashed line is the one from Bovy et al. (2012).

x10-2 0.22 9 0.20 0.20 8 0.18 0.18 7 RAVE Vlos 0.16 TGAS µ� TGAS µ� 0.16 0.14 6 0.14

0.12 0.12 5 0.10 0.10

4 Normalised count Normalised count Normalised count 0.08 0.08 3 0.06 0.06 2 0.04 0.04

1 0.02 0.02 0.00 0 0.00 -50 -40 -30 -20 -10 0 10 20 30 40 50 -150 -100 -50 0 50 100 150 -50 -40 -30 -20 -10 0 10 20 30 40 50 pmdec HRV pmra Fig. 3: Histograms of RAVE (Kordopatis et al, 2014) radial velocity distributions and TGAS (Gaia collaboration, Brown et al, 2016) proper motions for hot stars defined as Teff>5200K (solid lines) and cool stars (dashed lines) defined as Teff<5200K. Data: black lines; Best fit model: red lines.

Conclusions: References : 1) When taking into account the asymmetric drift variations with R for gal Bienaymé, O., Robin, A. C., & Famaey, B. 2015, A&A, 581, A123 zgal , the Solar motion is found to be (U⊙=13 km/s, V⊙=1 km/s, W⊙=7 Bovy, J., Allende Prieto, C., Beers, T. C., et al. 2012, ApJ, 759, 131

km/s), while using the simple formula V⊙ was found significantly larger. Our Caldwell, J. A. R. & Ostriker, J. P. 1981, ApJ, 251, 61 new value is in good agreement with Golubov et al (2013) who found Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2016, A&A, 595, A2 Gómez, A. E., et al. 1997, in ESA Special Publication, Vol. 402, Hipparcos - V⊙=3km/s from RAVE iDR4. Venice ’97, ed. R. M. Bonnet et al, 621–624 2) The overall fit of this new dynamical and kinematical model Golubov, O., Just, A., Bienaymé, O., et al. 2013, A&A, 557, A9 reproduces very well the radial velocity distributions from RAVE, as well as Holmberg, J., Nordström, B., & Andersen, J. 2009, A&A, 501, 941 the proper motions from Gaia-TGAS in a wide solar neighbourhoud and Kordopatis, G., Gilmore, G., Steinmetz, M., et al. 2013, AJ, 146, 134 specifically for different metallicity bins and temperature bins (fig. 3). Sharma, S., Bland-Hawthorn, J., Binney, J., et al. 2014, ApJ, 793, 51 For more details: Robin, Bienaymé, Fernández-Trincado, Reylé, accepted Sofue, Y. 2015, PASJ, 67, 75 in A&A, astroph:1704.06274