[Paper Review] The Galactic potential and dark matter density from angular stellar accelerations

Malte Buschmann, Benjamin R. Safdi+1 more|arXiv (Cornell University)|Mar 8, 2021

Stellar, planetary, and galactic studiesPhysics and Astronomy59 references16 citations

TL;DR

This paper proposes using angular stellar accelerations from astrometric surveys like Gaia to directly measure the Milky Way's gravitational potential and local dark matter density. By analyzing the joint likelihood of stellar angular accelerations, the method detects the disk potential at ~3σ significance and the local dark matter density at ~2σ when combined with solar acceleration measurements, offering a model-independent probe of Galactic dynamics.

ABSTRACT

We present an approach to measure the Milky Way (MW) potential using the angular accelerations of stars in aggregate as measured by astrometric surveys like Gaia. Accelerations directly probe the gradient of the MW potential, as opposed to indirect methods using e.g. stellar velocities. We show that end-of-mission Gaia stellar acceleration data may be used to measure the potential of the MW disk at approximately 3$\sigma$ significance and, if recent measurements of the solar acceleration are included, the local dark matter density at ~2$\sigma$ significance. Since the significance of detection scales steeply as $t^{5/2}$ for observing time $t$, future surveys that include angular accelerations in the astrometric solutions may be combined with Gaia to precisely measure the local dark matter density and shape of the density profile.

Motivation & Objective

• To develop a direct, model-independent method for measuring the Milky Way's gravitational potential using angular stellar accelerations.
• To constrain the local dark matter density with minimal assumptions about stellar kinematics or equilibrium.
• To reduce reliance on indirect methods such as rotation curves or Jeans equations, which depend on strong assumptions about symmetry and equilibrium.
• To enable future surveys to precisely measure the dark matter halo, disk, and bulge components using acceleration data.
• To provide a data-driven approach to systematic uncertainty testing via signal scrambling, enhancing robustness of results.

Proposed method

• Uses angular accelerations (γα, γδ) as additional parameters in astrometric solutions beyond standard five parameters (RA, DEC, PM, parallax).
• Applies a joint likelihood analysis over N ≈ 10^9 stars to detect collective acceleration signals despite individual star signals being too weak.
• Projects detection significance scaling as t^5/2 with observation time t, enabling future high-precision measurements.
• Corrects for the Sun's acceleration in the Galactic frame by modeling a⊙ = −∇Φ(r⊙), using the solar position r⊙ = 8.224 ± 0.071 kpc.
• Performs statistical validation via scrambling model predictions across stars to test for systematic biases and validate the null hypothesis.
• Combines Gaia DR2 and Hipparcos data to demonstrate feasibility, with results consistent with statistical uncertainties.

Experimental results

Research questions

• RQ1 Can angular stellar accelerations from astrometric surveys like Gaia be used to directly measure the Milky Way's gravitational potential?
• RQ2 To what extent can this method constrain the local dark matter density independently of velocity-based or equilibrium assumptions?
• RQ3 How does the detection significance of the disk potential and dark matter density scale with observation time?
• RQ4 What systematic effects might bias the acceleration-based inference, and how can they be tested using data-driven methods?
• RQ5 Can future surveys combine Gaia data with their own acceleration measurements to achieve high-precision constraints on the MW's mass components?

Key findings

• End-of-mission Gaia data is projected to detect the disk potential at ~3σ significance using angular stellar accelerations.
• When combined with the solar acceleration measured from quasar proper motions in Gaia EDR3, the local dark matter density can be constrained at ~2σ significance.
• The detection significance for both the disk and dark matter components scales as t^5/2 with observation time, enabling high-precision measurements in future surveys.
• A scrambling test of model predictions across stars shows that systematic effects are subdominant compared to statistical uncertainties, validating the robustness of the method.
• The method is insensitive to selection functions and completeness, as it relies on direct acceleration measurements rather than velocity moments.
• Radial accelerations from Gaia’s Radial Velocity Spectrometer are expected to be less constraining than angular accelerations, though they may improve with future sensitivity.