On the Solar Velocity

Abstract

The recent Gaia data release (Gaia Collaboration et al. 2018a) provides astrometry for over a billion sources, of which more than seven million also have line-of-sight velocities, permitting their full 3D heliocentric velocities to be determined. To put these velocities in a galactocentric reference frame requires knowledge of the velocity of the Sun with respect to the Galactic center, v , while decomposing them into galactocentric cylindrical coordinates, (V R , V , V z), also requires knowledge of R 0 , the distance to the Galactic center (GC). In this note we highlight the implications of the recent contribution by the GRAVITY collaboration (Gravity collaboration et al. 2018) in the determination of v. Traditionally v has been derived by decomposing it into the solar motion, u , the velocity of the Sun with respect to the solar neighborhood defined by local stellar samples, and the velocity of the local standard of rest (LSR), v LSR : v = u + v LSR. (1) Consistent with the assumption of axisymmetry, v LSR is typically assumed to correspond to the circular velocity at the Sun's location. Such an approach was taken, for example, by Gaia Collaboration et al. (2018b) when mapping the (V R , V , V Z) velocity fields from Gaia astrometry and line-of-sight velocities. However, in clear contradiction with the assumptions made, the resulting velocity maps clearly show large scale non-circular streaming motions in the plane. More recent definitions of the LSR allow for a non-axisymmetric Galaxy, so that v LSR includes the non-circular streaming motions at the Sun, but the diculty of estimating v LSR essentially means that its uncertainty is of the order of the magnitude of the streaming motions (⇡ 10 km s 1), significantly larger than the uncertainties in u and dominating the uncertainty of any estimate of v based on Eq. 1. Recently the GRAVITY collaboration used observations of the star S2 orbiting SagA*, assumed to be at the center of the Galaxy, to determine the distance to the GC to be R 0 = 8.122 ± 0.033 kpc. It should be noted that this estimate of R 0 is absolute, being based on positional and spectroscopic observations of a resolved binary, and that its precision is nearly an order of magnitude better than earlier determinations (Bland-Hawthorn & Gerhard 2016). The first consequence of knowing R 0 is the immediate improvement in the decomposition of velocities in a galacto-centric coordinate system. (See Figure 1.) In addition, as pointed out by Reid & Brunthaler (2004), a direct measure of R 0 allows the determination of the component of v orthogonal to the line-of-sight to the GC via the measured proper motion of SagA* which, assuming that SagA* is stationary at the GC, is just the apparent reflex motion of v. Thanks to the exceptional precision of R 0 the uncertainty of this velocity component is now of the order of 1 km s 1. Others have already applied this in new derivations of the circular velocity curve of the Milky Way (McGaugh 2018; Eilers et al. 2018). However, a closer inspection of the GRAVITY results reveals an additional hidden treasure for Galactic studies. Among the fitted parameters is the parameter ˙ z 0 = 1.9 ± 3 km s 1 , a correction to the assumed v velocity component toward SagA* modelled as (˙ z 0 +11 km s 1), using U = 11 km s 1 based on Schönrich et al. (2010). (Private communication , F.Eisenhauer.) This velocity component results in a systematic Doppler shift in the spectroscopic observations of S2, and introduces a delay in the arrival times of the observations due to the changing distance between the observer and the SagA*-S2 system (i.e. the Rømer e↵ect). In any case, as U is fixed, their determination of the component of v toward the GC is e↵ectively independent of the solar motion.