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  • Barbara Jesline

Do you know: How do we determine motion of Sun?

Updated: Mar 9, 2020

~Professional Article~


Stellar kinematics is the observational study or measurement of the kinematics or motions of stars through space. The subject of stellar kinematics encompasses the measurement of stellar velocities in the Milky Way and its satellites as well as the measurement of the internal kinematics of more distant galaxies. Measurement of the kinematics of stars in different subcomponents of the Milky Way including the thin disk, the thick disk, the bulge, and the stellar halo provides important information about the formation and evolutionary history of our Galaxy. Kinematic measurements can also identify exotic phenomena such as hypervelocity stars escaping from the Milky Way, which are interpreted as the result of gravitational encounters of binary stars with the supermassive black hole at the Galactic Center.


The velocity distribution of the stars in the solar neighborhood plays a key role in understanding the global structure, dynamical features, and evolution of the Milky Way. Although it is often approximated with a multidimensional Gaussian profile, the velocity distribution of the stars in the solar neighborhood is actually very complicated. The mean value of the velocity distribution should be around zero, given that the Galactic disk is in a static state. However, observations have found many substructures (Dehnen 1998; Zhao et al. 2009; Siebert et al. 2011; Antoja et al. 2012; Xia et al. 2014), which may be associated with the perturbation of the Galactic bar and spiral arms or belong to old tidal debris of disrupted clusters or dwarf galaxies (Dehnen 2000; Fux 2001; Famaey et al. 2005; Antoja et al. 2011), in the velocity distribution. These substructures may shift the mean velocity slightly away from zero by a few km/s.


The component of stellar motion toward or away from the Sun, known as radial velocity, can be measured from the spectrum shift caused by the Doppler effect. The transverse, or proper motion must be found by taking a series of positional determinations against more distant objects. Once the distance to a star is determined through astrometric means such as parallax, the space velocity can be computed. This is the star's actual motion relative to the Sun or the local standard of rest (LSR). The latter is typically taken as a position at the Sun's present location that is following a circular orbit around the Galactic Center at the mean velocity of those nearby stars with low-velocity dispersion. The Sun's motion with respect to the LSR is called the "peculiar solar motion".


The velocity distribution can be characterized by the velocity ellipsoid, which reflects the mass distribution and evolution of the Milky Way, assuming that most of the detected stars are in equilibrium. The earliest study of the stellar velocity ellipsoid was done by Schwarzschild (1908). From then on, many works have found that the age of stars is correlated with the velocity distribution. Specifically, older stars show larger velocity dispersion, and vice versa (Parenago 1950; Roman 1950, 1952; Dehnen & Binney 1998; Quillen & Garnett 2001; Nordström et al. 2004; Holmberg et al. 2007, etc.). This is usually thought to be because the scattering of the disk stars increases over time. For the stars younger than ~8 Gyr, the scattering is most likely due to encounters with substructures, e.g., giant molecular clouds, in the disk (Holmberg et al. 2007). The age–velocity dispersion relation (AVR) reflects the evolutionary history of the Galactic disk.


In an ideal axisymmetric disk, the velocity ellipsoid near the disk midplane should be aligned with the cylindrical coordinates. However, since the Galactic disk contains a rotational central bar and a number of spiral arms, the velocity ellipsoid will not match this ideal case. On the contrary, it deviates from the cylindrical coordinates near the Galactic midplane. Dehnen & Binney (1998, hereafter DB98) reported that the vertex deviation of the velocity ellipsoid measured from Hipparcos proper-motion data is ~10°. Smith et al. (2012, hereafter S12) confirmed that the vertex deviation of the metal-rich stars in the SDSS sample is consistent with DB98. Moreover, the authors also showed that the tilt angle relative to the Galactic midplane is about

10° to
15° for the velocity ellipsoid at
> 0.5 kpc. Recently, lots of new works have been done with the data from large stellar spectroscopic surveys, e.g., Binney et al. (2014) and Sharma et al. (2014) based on RAVE (Kordopatis et al. 2013), Bovy et al. (2014) based on APOGEE (Ahn et al. 2014), and Recio-Blanco et al. (2014) based on the Gaia-ESO survey (Gilmore et al. 2012).


The components of space velocity in the Milky Way's Galactic coordinate system are usually designated U, V, and W, given in km/s, with U positive in the direction of the Galactic Center, V positive in the direction of galactic rotation, and W positive in the direction of the North Galactic Pole. The peculiar motion of the Sun with respect to the LSR is (U, V, W) = (11.1, 12.24, 7.25) km/s,

with statistical uncertainty (+0.69−0.75, +0.47−0.47, +0.37−0.36) km/s and systematic uncertainty (1, 2, 0.5) km/s. (Note that V is 7 km/s larger than estimated in 1999 by Dehnen et al.


The relation between proper motion and velocity components of an object. At emission, the object was at distance d from the Sun and moved at angular rate μ radian/s, that is, μ = vt / d with vt = the component of velocity transverse to line of sight from the Sun. (The diagram illustrates an angle μ swept out in unit time at tangential velocity vt.).


Upcoming article: How do these measurements utilize in galaxy level study?