Local stellar kinematics from Hipparcos data

TL;DR

Using a kinematically unbiased Hipparcos-based sample of nearly 12{,}000 single main-sequence stars, the paper redefines local stellar kinematics as a function of colour and derives the Sun’s motion relative to the LSR, Parenago’s discontinuity, and the full velocity-dispersion tensor. It obtains $(U_0,V_0,W_0) = (10.0, 5.2, 7.17)$ km s$^{-1}$ (excluding very blue stars), detects a clear Parenago discontinuity at $B-V \approx 0.62$ mag, and finds a nonzero in-plane cross-term $\sigma^2_{xy}$ with a vertex deviation $\ell_v$ that indicates a significantly non-axisymmetric Galactic potential. The velocity-ellipsoid analysis reveals $oldsymbol\sigma^2$ diagonal components obey $\sigma_{xx} > \sigma_{yy} > \sigma_{zz}$, with eigenvalue ratios $\sigma_1/\sigma_2 \approx 1.6$ and $\sigma_1/\sigma_3 \approx 2.2$, and supports substantial heating from spiral structure and molecular clouds, with a disc scale-length constraint $R_0/R_d \approx 3.0$–$3.5$. Methodologically, the six independent tensor components are obtained by symmetry-enabled inversion of projected motions, using the projection framework $\mathbf p = {\bf A} \cdot \mathbf v$ and the tensor ${\boldsymbol\sigma^2}$, leveraging Hipparcos’ precise parallaxes to achieve robust, colour-resolved kinematic inferences. Overall, the study demonstrates that Hipparcos data enable precise, bias-free insights into solar-neighborhood dynamics and Galactic structure.

Abstract

(shortened) From a kinematically unbiased subsample of the Hipparcos catalogue we have redetermined as a function of colour the kinematics of main-sequence stars. The stars' mean heliocentric velocity nicely follows the asymmetric drift relation, except for stars blueward of B-V=0.1. Extrapolating to zero dispersion yields for the velocity of the Sun w.r.t. the LSR in km/s: U_0=10.00+/-0.36 (radially inwards), V_0=5.23+/-0.62 (in direction of galactic rotation), and W_0=7.17+/-0.38 (vertically upwards). A plot of velocity dispersion vs. colour beautifully shows Parenago's discontinuity: the dispersion is constant for B-V>0.62 and decreases towards bluer colour. We determine the velocity-dispersion tensor sigma^2_ij as function of B-V. The mixed moments involving vertical motion are zero within the errors, while sigma^2_xy is non-zero at about (10km/s)^2 independent of colour. The resulting vertex deviations are about 20 deg for early-type stars and 10+/-4 deg for old-disc stars. The persistence of the vertex deviation to late-type stars implies that the Galactic potential is significantly non-axisymmetric at the solar radius. If spiral arms are responsible for this, they cannot be tightly wound. Except for stars bluer than B-V=0.1 the ratios of the principal velocity dispersions are 2.2 : 1.4 :1, while the absolute values increase with colour from sigma_1=20km/s at B-V=0.2 to sigma_1=38km/s at Parenago's discontinuity and beyond. These ratios imply significant heating of the disc by spiral structure and that R_0/R_d=3 to 3.5, where R_d is the scale length of the disc.

Figures (6)

• Figure 1: Hertzsprung-Russell diagram ($M_{Hp}$ is the absolute magnitude in Hipparcos's own passband) of the 18 860 single Hipparcos stars with relative parallax errors less than 10 per cent. The lines are used to select the main sequence and have 16 054 stars between them.
• Figure 2: Hertzsprung-Russell diagram for the stars in our kinematical unbiased sample of 11 865 single main-sequence stars.
• Figure 3: The components $U$, $V$, and $W$ of the solar motion w.r.t. stars with different colour $B$-$V$. Also shown is the variation of the dispersion $S$ with colour.
• Figure 4: The dependence of $U$, $V$, and $W$ on $S^2$. The dotted lines correspond to the linear relation fitted ($V$) or the mean values ($U$ and $W$) for stars bluer than $B$-$V$=0.
• Figure 5: Velocity dispersions for stars in different colour bins. The top panel shows the mean rotation velocity (negative values imply lagging w.r.t. LSR) and the three main velocity dispersions. In the three bottom panels $\sigma^\prime_{ij}\equiv\mathrm{sign} (\sigma^2_{ij})\,|\sigma^2_{ij}|^{1/2}$ is plotted for the mixed components of the tensor $\sigma^2_{ij}$.