[Paper Review] The dark matter profile of the Milky Way inferred from its circular velocity curve

Xiaowei Ou, Anna–Christina Eilers+2 more|arXiv (Cornell University)|Mar 22, 2023

Galaxies: Formation, Evolution, PhenomenaPhysics and Astronomy13 citations

TL;DR

This study computes the Milky Way’s circular velocity curve out to ~30 kpc using spectrophotometric parallaxes from APOGEE DR17, Gaia DR3, and other photometry, and shows a best-fit cored Einasto dark matter profile with a relatively low virial mass.

ABSTRACT

In this paper, we construct the circular velocity curve of the Milky Way out to $\sim 30$ kpc, providing an updated model of the dark matter density profile. We derive precise parallaxes for 120,309 stars with a data-driven model, using APOGEE DR17 spectra combined with Gaia DR3, 2MASS, and WISE photometry. At outer galactic radii up to 30 kpc, we find a significantly faster decline in the circular velocity curve compared to the inner parts. This decline is better fit with a cored Einasto profile with a slope parameter $0.91^{+0.04}_{-0.05}$ than a generalized Navarro-Frenk-White (NFW) profile. The virial mass of the best-fit dark matter halo profile is only $1.81^{+0.06}_{-0.05} imes10^{11}$ $M_{\odot}$, significantly lower than what a generalized NFW profile delivers. We present a study of the potential systematics, affecting mainly large radii. Such a low mass for the Galaxy is driven by the functional forms tested, given that it probes beyond our measurements. It is found to be in tension with mass measurements from globular clusters, dwarf satellites, and streams. Our best-fit profile also lowers the expected dark matter annihilation signal flux from the galactic centre by more than an order of magnitude, compared to an NFW profile-fit. In future work, we will explore profiles with more flexible functional forms to more fully leverage the circular velocity curve and observationally constrain the properties of the Milky Way's dark matter halo.

Motivation & Objective

• Redetermine the Milky Way circular velocity curve to large radii (up to ~30 kpc) with improved parallax precision.
• Infer the dark matter density profile by fitting baryonic+dark matter models to the observed curve.
• Assess systematic uncertainties and compare DM profile fits (Einasto vs. gNFW).
• Evaluate implications for local DM density, annihilation signals, and Milky Way mass estimates.

Proposed method

• Construct a data-driven spectrophotometric parallax model using APOGEE DR17 spectra and Gaia DR3 plus photometry (Gaia, 2MASS, WISE).
• Select red giant branch tracers with APOGEE log g between 0.0 and 2.2 and cross-match with Gaia DR3.
• Train a linear model in log parallax as a function of photometric and 8575 APOGEE spectral features with L1 regularization to identify informative features.
• Propagate spectrophotometric parallaxes into Galactocentric coordinates and velocities, and derive the circular velocity via Jeans’ equation under axisymmetry.
• Model the tracer density with an exponential profile and estimate the radial velocity dispersion also as an exponential, then compute vc(R) from equation vc^2 = <v_phi^2> - <v_R^2> [1 + dln nu/dlnR + dln< v_R^2>/dlnR].
• Fit two DM halo models (gNFW and Einasto) to the circular velocity data using emcee MCMC, comparing fits via chi-squared and posterior convergence.

Experimental results

Research questions

• RQ1 What does the Milky Way circular velocity curve look like out to ~30 kpc with updated parallaxes and tracer selection?
• RQ2 Which dark matter density profile (Einasto vs. generalized NFW) best reproduces the outer decline of the measured circular velocity curve?
• RQ3 What are the implied Milky Way halo properties (M200, r200, c200, local DM density) under the preferred DM model, and how do they compare with previous estimates?
• RQ4 How significant are the systematic uncertainties (e.g., tracer density, solar parameters, asymmetric drift) in shaping the outer Galactic rotation curve?
• RQ5 What are the implications of the inferred DM profile for DM detection signals from the Galactic center and for Galactic formation history?

Key findings

• The circular velocity declines steadily with radius, from ~234 km/s at R≈7.9 kpc to ~173 km/s at R≈27.3 kpc, with a noticeably faster outer decline.
• An Einasto DM profile provides a substantially better fit to the data than a generalized NFW profile, with a median alpha ≈ 0.91 and a reduced chi-squared ≈ 2.97.
• The best-fit DM halo implies a virial mass M200 ≈ 1.81 × 10^11 Msun and a virial radius r200 ≈ 119 kpc, significantly lower than typical NFW-based inferences.
• The local DM density is inferred to be ρ_DM,⊙ ≈ 0.447 GeV cm^-3 for Einasto, and the corresponding J-factor is ~15.8 × 10^22 GeV^2 cm^-5 for θ<15°, both reflecting a cored inner profile.
• Systematic uncertainties are modest (1–5%) up to R≈22 kpc but can reach ~15% at larger radii due to neglected asymmetric drift corrections; nonetheless the outer velocity decline persists across systematics.
• The inferred cored DM profile reduces the expected dark matter annihilation flux from the Galactic center by more than an order of magnitude relative to an NFW-based fit.