Asymmetric Drift: Why Older Stars Lag the Galaxy's Rotation

What Asymmetric Drift Actually Is

Imagine two stars at the Sun's galactocentric radius (R₀ ≈ 8.2 kpc). One is a freshly formed, blue star on a nearly circular orbit; the other is an ancient, metal-poor star whose orbit is elongated and tilted. Average many stars like the second one and their mean azimuthal velocity is measurably slower than the circular speed v_c. That deficit is the asymmetric drift, usually written v_a = v_c − ⟨v_φ⟩.

The name captures the observational fact that hot populations show a lopsided, or asymmetric, distribution of azimuthal velocities: there is a long tail toward low (even retrograde) rotation but no matching tail toward super-circular speeds, because stars cannot orbit faster than the circular speed at a given angular momentum without moving to a larger radius. So the mean is dragged backward.

• It is a property of a population, not of any single star.
• It grows with the population's velocity dispersion — i.e., with dynamical age.
• Its extrapolation to zero dispersion defines the Local Standard of Rest (LSR).

The Mechanism: Radial Pressure and the Jeans Equation

Stars are collisionless, but a large ensemble behaves like a gas with an anisotropic "pressure" set by its velocity dispersion. The radial Jeans equation for an axisymmetric disk balances gravity against gradients in this stellar pressure. Solving it for the mean rotation yields the classical asymmetric-drift relation:

v_a ≈ (σ_R² / 2·v_c) × [ σ_φ²/σ_R² − 1 − ∂ln(ν·σ_R²)/∂lnR ]

Here σ_R is the radial velocity dispersion, σ_φ the azimuthal dispersion, ν the stellar number density, and v_c the circular speed. The key takeaway is the leading factor: v_a scales as σ_R². Because pressure support (∝ σ²) subtracts from the centrifugal support a population needs, a hotter population can sit on the same guiding radius while rotating more slowly.

• The bracketed terms encode the disk's density and dispersion gradients (radial scale length h_R enters through ∂lnν/∂lnR = −R/h_R).
• Gustaf Strömberg (1946) established empirically that ⟨v_φ⟩ lag is linear in σ² — the fingerprint of this σ² scaling.

Characteristic Numbers and a Worked Example

Take an old thin-disk sample near the Sun with σ_R ≈ 38 km/s and v_c ≈ 235 km/s. The prefactor alone, σ_R²/(2·v_c) = 38²/(2·235) ≈ 3.1 km/s, is then multiplied by the bracket, which for realistic disk gradients (scale length h_R ≈ 2.5 kpc, ratio σ_φ²/σ_R² ≈ 0.45) is of order 5–7. That gives v_a ≈ 15–22 km/s, exactly what surveys find for the old thin disk.

• Young stars: σ_R ≈ 15 km/s → v_a only ~3–5 km/s.
• Thick disk: σ_R ≈ 60 km/s → v_a ≈ 35–50 km/s; measured median ≈ 38 ± 3 km/s.
• Halo: σ_R ≈ 150 km/s → the σ² scaling gives a lag of ~200 km/s, so the halo barely rotates in the Galaxy's frame.

Extrapolating ⟨v_φ⟩ to σ² = 0 across many subsamples pins down the Sun's own rotational motion relative to the LSR: RAVE data (Golubov et al. 2013) give V☉ ≈ 3.06 ± 0.68 km/s, smaller than the classical Hipparcos value of ~5 km/s.

How It Is Measured

Asymmetric drift is read directly off the kinematics of stellar samples once distances and velocities are known. The recipe: bin stars by a proxy for age or dispersion (metallicity, α/Fe ratio, spectral type, or mono-age tags), measure each bin's mean azimuthal velocity and its σ_R, and plot lag against σ². A straight line — the Strömberg relation — falls out, and its intercept at σ² = 0 gives the LSR.

• Hipparcos (1990s) provided the first precise parallaxes for this analysis.
• RAVE and LAMOST added millions of radial velocities and metallicities, revealing that metal-rich bins show larger drift (shorter scale length ~1.6 kpc) than metal-poor bins (~2.9 kpc).
• Gaia (DR2/DR3) now delivers 6D phase-space for over a billion stars, mapping v_a across galactocentric radii from ~6 to 16 kpc and confirming that older, hotter mono-age populations lag more.

The effect also appears in external galaxies (e.g., MaNGA integral-field surveys) as the difference between gas and stellar rotation curves.

How It Differs From Its Cousins

Asymmetric drift is easy to confuse with several related dynamical ideas; the distinctions matter.

• vs. the rotation curve / v_c: The rotation curve is the true circular speed set by the mass distribution. Asymmetric drift is the correction one must add back to a hot tracer's mean speed to recover v_c — crucial when using stars (rather than cold gas) to weigh the Galaxy.
• vs. velocity dispersion: Dispersion is the random scatter of velocities; asymmetric drift is a systematic offset of the mean. They are linked (v_a ∝ σ²) but conceptually distinct.
• vs. disk heating: Disk heating (by spiral arms, giant molecular clouds, mergers) is the physical process that raises σ over time; asymmetric drift is the kinematic consequence of that heating for the population's mean rotation.
• vs. the solar peculiar motion: The Sun's own offset from the LSR is derived from asymmetric-drift extrapolation, but is a single-star quantity.

Significance and Open Questions

Asymmetric drift is a workhorse of Galactic archaeology. Because v_a rises smoothly with age, it acts as a kinematic clock: the drift of a mono-age population records how much dynamical heating the disk has suffered since those stars formed, letting astronomers reconstruct the Milky Way's heating history and disentangle the thin and thick disks.

It is also essential for weighing the Galaxy. Any mass estimate that uses hot stellar tracers must correct for their lag; get v_a wrong and you misestimate v_c, and hence the local dark-matter density.

• Open issues: The classical relation assumes an axisymmetric, steady-state disk. Gaia has revealed the disk is not in equilibrium — it shows a phase-space spiral (the "Gaia snail"), warps, and streaming from the bar and spiral arms, all of which bias simple asymmetric-drift/LSR determinations.
• The precise value of V☉ and whether the LSR itself is well-defined amid these perturbations remain actively debated.
• Radial migration can move stars far from their birth radius, complicating the link between drift, age, and formation site.

Approximate kinematic properties of stellar populations in the solar neighbourhood (values are representative and vary between surveys). v_c ≈ 220–240 km/s.

Population	Radial dispersion σ_R (km/s)	Asymmetric drift v_a (km/s)	Approx. mean rotation (km/s)
Young thin disk (OB stars, open clusters)	~10–20	~2–8	~215–235
Old thin disk (K/M dwarfs, avg. age)	~35–40	~15–25	~200–210
Thick disk (α-rich, old, metal-poor)	~55–65	~35–50	~175–185
Stellar halo	~140–160	~180–220	~0–40 (near non-rotating)
Hypothetical zero-dispersion gas / newborn stars	0	0 (defines the LSR)	= v_c