Estimating accretion times of halo substructures in the Milky Way

TL;DR

This work addresses the Milky Way’s assembly by estimating the accretion times of six halo substructures identified in the solar neighborhood. It employs a two-direction orbital-frequency analysis (Ω_r and Ω_φ) derived from Gaia DR3 data, with radial velocities from Li et al. to compute precise orbits and frequencies, and uses a Bayesian framework to propagate astrometric uncertainties. Accretion times are inferred from the peak of a 2-D power spectrum in (Ω_r, Ω_φ) via t_acc = 2π k_*/(N Δ), with significances assessed against random halo realizations through a high-k tail gamma fit. The results show GL-1 robustly accreted at about $5.59^{+0.07}_{-0.08}$ Gyr ago, while GL-4 and GR-1 yield earlier times that depend on the chosen Galactic potential, underscoring the importance of precise central mass modeling and future high-precision astrometry from Gaia DR4 and next-generation surveys to refine the Milky Way’s accretion history.

Abstract

To unravel the formation history of the Milky Way, we estimate the accretion times of six phase-space substructures in the stellar halo, using the orbital frequencies toward two spatial directions ($r, φ$) in spherical coordinates. These substructures, identified in our previous studies, are located in the solar neighbourhood and therefore have high-precision astrometry from Gaia. The uncertainties of the results are determined using the Monte Carlo method, and the significance is established through comparison with random halo samples. The results for the substructure GL-1 in both directions show good consistency and high significance ($4.4σ$ and $4.5σ$), yielding a combined accretion time of $5.59^{+0.07}_{-0.08}$ Gyr ago. The substructures GL-4 and GR-1, with smaller pericenters, exhibit higher significance in the less massive potential of the Milky Way, implying that the more massive potential may overestimate the central mass, especially the bulge. The accretion times of GL-4 and GR-1 are $4.0 \pm 0.2$ Gyr with a confidence of $3.3σ$, and $2.3 \pm 0.1$ Gyr with a confidence of $3.7σ$, respectively. Further constraints on the accretion times of phase-space substructures require more precise astrometric data, e.g., by Gaia DR4, China Space Station Survey Telescope and Roman space telescope.

Figures (10)

• Figure 1: Distribution of member stars of the six substructures in energy $E$ vs. angular momentum $L_z$ space (left panel) and in $L_\bot = \sqrt{L_x^2 + L_y^2}$ vs. $L_z$ space (right panel). Different substructures are shown in different colors.
• Figure 2: Distributions of halo stars (gray points) and substructure member stars (points in other colors) in the orbital frequency space. Different colors indicate different substructures. The dashed and solid lines represent the two limiting cases of a point mass ($\Omega_\phi = \Omega_r$) and a homogeneous sphere ($\Omega_\phi = \Omega_r/2$), respectively.
• Figure 3: Distributions of the uncertainties in $r$- and $\phi$-direction orbital frequencies for the member stars of the six substructures, with each substructure shown in a different color. The dashed line indicates the 1:1 relation.
• Figure 4: Power spectra of the Fourier transform for substructure GL-1 (left panel) and a random sample (right panel). The axes represent the wavenumbers in the two direction. The black lines mark the regions used to compute the 1-D power spectra.
• Figure 5: Median 1-D power spectra for substructure GL-1 (black solid lines) and random samples (blue solid lines). The $1\sigma$ and $3\sigma$ intervals of the random samples are shown as dark blue and light blue shaded regions, respectively. The $x$-axes represent $2\pi$ times the wavenumbers in the $r$ (top panels) and $\phi$ (bottom panels) directions. The estimated accretion times are marked by black vertical dashed lines, with significances given in the legend. Left and right panels show the results using the eilers19Circular and bovy15Galpy potentials, respectively. Subtitles indicate the substructure name, number of stars, bin width $\Delta$, and applied uncertainty selection.