HALO7D-X: Milky Way Halo Accretion Survey

• HALO7D-X is a survey of the Milky Way’s outer stellar halo that captures seven-dimensional chemo-kinematic data to trace its accretion history.
• It integrates archival HST imaging, Gaia astrometry, and Keck spectroscopy to precisely measure positions, motions, and chemical abundances of distant halo stars.
• Mock observations with Bullock and Johnston models demonstrate its capability to distinguish progenitor mass functions and accretion timelines despite limited sensitivity to orbital circularity.

Searching arXiv for the specified HALO7D-X paper and closely related survey/method references. HALO7D-X is a survey of the Milky Way stellar halo designed to constrain the Galaxy’s accretion history through combined phase-space and chemical measurements of distant halo stars (Apfel et al., 7 Jul 2025). The survey targets the outer stellar halo at Galactocentric radii $> 15$ kpc and is intended to recover the fossil record of halo assembly by measuring seven-dimensional chemo-kinematic information: sky position, proper motions, line-of-sight velocity, distance, $[\mathrm{Fe/H}]$, and $[\alpha/\mathrm{Fe}]$ (Apfel et al., 7 Jul 2025). Its observing strategy combines archival Hubble Space Telescope imaging, Gaia astrometry, and follow-up Keck spectroscopy, and its inference strategy is calibrated on mock observations of the Bullock and Johnston stellar halo simulations. In the survey design study, the observables are shown to be sensitive to the mass distribution and accretion timeline of stellar-halo progenitors, but not to their orbital circularity (Apfel et al., 7 Jul 2025).

1. Survey definition and scientific scope

HALO7D-X is explicitly designed to investigate the accretion history of the Milky Way by observing faint halo stars with $18 < G < 21.5$ mag (Apfel et al., 7 Jul 2025). The survey uses Hubble Space Telescope and Gaia data to determine sky position and proper motions, while Keck spectroscopy provides line-of-sight velocity, distance, $[\mathrm{Fe/H}]$, and $[\alpha/\mathrm{Fe}]$ (Apfel et al., 7 Jul 2025). The underlying premise is that the long dynamical times in the stellar halo preserve coherent signatures of accreted populations in kinematics and chemistry, even after substantial phase mixing. This motivates a survey design centered on sparse but information-rich lines of sight rather than contiguous wide-area mapping.

The scientific objective is not merely to catalog halo stars, but to connect observed chemo-dynamical distributions to progenitor properties in hierarchical assembly. In the design study, the target quantities are the mass spectrum and accretion timeline of the dwarf galaxies that contributed to the stellar halo (Apfel et al., 7 Jul 2025). Orbital circularity is also tracked in the simulations, but the mock-survey analysis indicates that the planned observations are not sensitive to that parameter. This suggests that HALO7D-X is optimized for recovering coarse-grained merger history rather than the full orbital morphology of individual accretion events.

A central feature of the survey concept is the use of simulated halos as a forward model. Rather than inferring accretion history directly from first principles, the survey compares real Milky Way data to mock observations of simulated halos constructed to match the same selection function, observables, and measurement uncertainties (Apfel et al., 7 Jul 2025). The design therefore integrates observational planning with a probabilistic classification problem over a library of halo assembly histories.

2. Observational design and measurement program

The HALO7D-X footprint consists of 30 lines of sight made up of multiple HST archival fields and optimized for Keck DEIMOS spectroscopy (Apfel et al., 7 Jul 2025). The final footprint comprises 371 HST fields, and each line of sight averages at least 15 halo stars with $18 < G < 21.5$ (Apfel et al., 7 Jul 2025). The survey geometry is therefore a set of distributed pencil beams rather than a contiguous survey region. A plausible implication is that the design prioritizes broad sampling of halo phase-space over local spatial completeness.

The archival-field selection applies several filters to pre-existing HST exposures taken before the Gaia DR2 cut-off of 2016 May 23. The fields were required to satisfy $|b_{\rm Ecl}| > 5^\circ$, $|b_{\rm Gal}| > 5^\circ$, declination from $-30^\circ$ to $[\mathrm{Fe/H}]$0, imaging with WFC3/UVIS or ACS/WFC in F555W, F606W, F775W, F814W, or F850LP, individual exposure times of 50–500 s, and $[\mathrm{Fe/H}]$1, with no bright extended sources (Apfel et al., 7 Jul 2025). Nearby pointings within $[\mathrm{Fe/H}]$2, corresponding to the DEIMOS mask size, were grouped into candidate lines of sight, followed by visual screening to remove problematic regions such as the Magellanic Clouds (Apfel et al., 7 Jul 2025).

Proper motions are obtained by combining HST multi-epoch imaging with Gaia DR2 positions in a common reference frame using the method of McKinnon et al. (2023) (Apfel et al., 7 Jul 2025). For baselines of at least 4 yr, this yields proper-motion errors $[\mathrm{Fe/H}]$3–$[\mathrm{Fe/H}]$4 smaller than Gaia alone at $[\mathrm{Fe/H}]$5, reaching $[\mathrm{Fe/H}]$6 mas yr$[\mathrm{Fe/H}]$7 at $[\mathrm{Fe/H}]$8 (Apfel et al., 7 Jul 2025). Keck II/DEIMOS spectroscopy uses the 600ZD or 1200G grating at central wavelength $[\mathrm{Fe/H}]$9 Å, with $[\alpha/\mathrm{Fe}]$0–6000 and slit widths $[\alpha/\mathrm{Fe}]$1–$[\alpha/\mathrm{Fe}]$2 (Apfel et al., 7 Jul 2025). Exposure times of $[\alpha/\mathrm{Fe}]$3–3 hr per mask are designed to reach $[\alpha/\mathrm{Fe}]$4 per resolution element at $[\alpha/\mathrm{Fe}]$5 (Apfel et al., 7 Jul 2025).

The principal measurement targets are summarized below.

Observable	Source or method	Target performance
Sky position (RA, Dec)	HST archival pointings	ACS/WFC or WFC3/UVIS
Proper motions $[\alpha/\mathrm{Fe}]$6	HST multi-epoch imaging + Gaia DR2	$[\alpha/\mathrm{Fe}]$7 mas yr$[\alpha/\mathrm{Fe}]$8 at $[\alpha/\mathrm{Fe}]$9
Line-of-sight velocity $18 < G < 21.5$0	Keck II/DEIMOS spectroscopy	$18 < G < 21.5$1 km s$18 < G < 21.5$2
Distance	Spectro-photometric modeling plus Gaia parallax prior	$18 < G < 21.5$3
$18 < G < 21.5$4	Keck spectroscopy	$18 < G < 21.5$5 dex
$18 < G < 21.5$6	Keck spectroscopy	$18 < G < 21.5$7 dex

The spectroscopy also yields stellar parameters and distance moduli via pipelines such as MINESweeper (Cargile et al. 2020) (Apfel et al., 7 Jul 2025). In aggregate, the survey is described as targeting $18 < G < 21.5$8–600 distant halo stars across the 30 lines of sight (Apfel et al., 7 Jul 2025).

3. Simulated-halo framework and mock-catalog construction

The design study evaluates HALO7D-X with mock observations of the Bullock and Johnston stellar halo models, referred to as “B & J halos” (Apfel et al., 7 Jul 2025). These are eleven $18 < G < 21.5$9CDM-motivated hybrid simulations in which the host-galaxy potential, including disk, bulge, and smooth halo, evolves analytically while each accreted satellite’s dark matter is evolved with an $[\mathrm{Fe/H}]$0-body code (Apfel et al., 7 Jul 2025). Stars are painted onto dark-matter particles through a leaky-box chemical model tuned to match Local Group dwarfs (Apfel et al., 7 Jul 2025). The resulting simulation suite provides a controlled set of accretion histories with associated chemo-dynamical observables.

The mock stellar catalogs are generated with the Galaxia code, which smooths or interpolates the B & J star particles into individual stars with $[\mathrm{Fe/H}]$1, $[\mathrm{Fe/H}]$2, $[\mathrm{Fe/H}]$3, $[\mathrm{Fe/H}]$4, and apparent magnitudes (Apfel et al., 7 Jul 2025). For each simulated halo, 360 Solar-placement angles on the disk are used, each producing 30 simulated lines of sight. Along each line of sight, modeled as $[\mathrm{Fe/H}]$5 deg$[\mathrm{Fe/H}]$6, all stars with $[\mathrm{Fe/H}]$7 are selected to mimic HALO7D-X (Apfel et al., 7 Jul 2025).

Observational uncertainties are incorporated by smoothing each simulated star into a multivariate normal whose covariance is chosen to match expected errors, and then distributing its weight over nearby grid cells in observable space (Apfel et al., 7 Jul 2025). This produces a survey-specific representation of each halo in a discretized observable space. The data for a given line of sight are then represented by cell-count vectors $[\mathrm{Fe/H}]$8, where $[\mathrm{Fe/H}]$9 is the total number of cells in the five-dimensional grid (Apfel et al., 7 Jul 2025).

The progenitor satellites in the simulations are parameterized by $[\alpha/\mathrm{Fe}]$0, denoting stellar mass, lookback accretion time, and orbital circularity (Apfel et al., 7 Jul 2025). These latent assembly variables are not observed directly by HALO7D-X. Instead, the survey attempts to infer them indirectly by identifying which mock halos generate observable distributions most similar to the Milky Way. This suggests a model-selection or mixture-classification formulation rather than continuous parameter estimation from a generative physical model.

4. Statistical inference and halo discrimination

The likelihood formalism in the design study treats each line of sight as a multinomial draw over observable-space cells (Apfel et al., 7 Jul 2025). Let $[\alpha/\mathrm{Fe}]$1 denote the origin-halo index $[\alpha/\mathrm{Fe}]$2 among the 11 B & J halos. For a given observed line of sight $[\alpha/\mathrm{Fe}]$3, simulated halo $[\alpha/\mathrm{Fe}]$4, Solar angle $[\alpha/\mathrm{Fe}]$5, and simulated line of sight $[\alpha/\mathrm{Fe}]$6, the likelihood is

$[\alpha/\mathrm{Fe}]$7

that is, a multinomial $[\alpha/\mathrm{Fe}]$8, where $[\alpha/\mathrm{Fe}]$9 is the probability of cell $18 < G < 21.5$0 (Apfel et al., 7 Jul 2025). Marginalizing over simulated lines of sight and Solar placements, and multiplying over all observed lines of sight, gives

$18 < G < 21.5$1

To infer halo fractions, the analysis introduces a Dirichlet prior on the halo-fraction vector $18 < G < 21.5$2,

$18 < G < 21.5$3

leading to the posterior

$18 < G < 21.5$4

In this formulation, a high value of $18 < G < 21.5$5 indicates that the observed halo most closely resembles simulated halo $18 < G < 21.5$6 (Apfel et al., 7 Jul 2025). For the eventual Milky Way application, the real survey data will be converted into count vectors $18 < G < 21.5$7 in the same five-dimensional cells, and the posterior halo-fraction vector $18 < G < 21.5$8 will be evaluated against the 11 simulation models (Apfel et al., 7 Jul 2025).

The study also defines a clustering metric used to optimize the ordering of halos in the confusion matrix:

$18 < G < 21.5$9

where $|b_{\rm Ecl}| > 5^\circ$0 is the distance of confusion-matrix cell $|b_{\rm Ecl}| > 5^\circ$1 from the diagonal, $|b_{\rm Ecl}| > 5^\circ$2 its median posterior probability, and $|b_{\rm Ecl}| > 5^\circ$3 its uncertainty (Apfel et al., 7 Jul 2025). This metric is used to expose structure in the inter-halo confusion pattern rather than to estimate astrophysical parameters directly.

5. Sensitivity to accretion-history parameters

The mock-survey analysis shows that HALO7D-X is sensitive to the mass distribution and accretion timeline of stellar-halo progenitors (Apfel et al., 7 Jul 2025). With the final design of 30 lines of sight and 15 stars per line of sight, the median posterior for the correct halo exceeds $|b_{\rm Ecl}| > 5^\circ$4, and the probability that the correct halo has the maximum posterior fraction is $|b_{\rm Ecl}| > 5^\circ$5 (Apfel et al., 7 Jul 2025). Varying the number of lines of sight from 5 to 30 and the number of stars per line of sight from 5 to 100 confirms that both dimensions materially improve halo discrimination (Apfel et al., 7 Jul 2025).

A more specific inference target is the epoch by which a halo accumulated half of its stellar mass, together with the relative dominance of its most massive progenitors. From the mock tests, HALO7D-X can distinguish $|b_{\rm Ecl}| > 5^\circ$6 mass-accretion times at the level of $|b_{\rm Ecl}| > 5^\circ$7 Gyr and mass-spectrum differences $|b_{\rm Ecl}| > 5^\circ$8 of order unity, including cases such as distinguishing $|b_{\rm Ecl}| > 5^\circ$9 from $|b_{\rm Gal}| > 5^\circ$0 (Apfel et al., 7 Jul 2025). Real-data uncertainties in proper motion, $|b_{\rm Gal}| > 5^\circ$1, $|b_{\rm Gal}| > 5^\circ$2, and distance are described as comparable to or smaller than the smoothing scales used in the simulated-halo probability density functions, motivating the expectation of similar performance on Milky Way data (Apfel et al., 7 Jul 2025).

By contrast, the survey is not sensitive to progenitor orbital circularity (Apfel et al., 7 Jul 2025). The cumulative distributions of satellite circularity in the simulated halo groups show no clear separation, and the small pencil beams cannot distinguish stream versus plume morphology (Apfel et al., 7 Jul 2025). This is an important limitation: the survey can recover broad assembly chronology and progenitor mass hierarchy, but not the detailed orbital family of the accreted satellites. A common misconception would be to treat seven-dimensional chemo-kinematic information as sufficient for full orbital-history reconstruction; the design study indicates that this is not the case for the HALO7D-X geometry.

6. Grouping of simulated halos and implications for the Milky Way

A notable result of the design analysis is that the 11 simulated halos separate into three groups, denoted A, B, and C, based on the similarities in the distributions of the survey observables (Apfel et al., 7 Jul 2025). The grouping is obtained by converting the $|b_{\rm Gal}| > 5^\circ$3 confusion matrix of median posterior fractions into a two-dimensional heat map and reordering the halos using the clustering metric $|b_{\rm Gal}| > 5^\circ$4 (Apfel et al., 7 Jul 2025). These groups are also distinct in the mass distribution and accretion timeline of their progenitor satellites, linking observable-space similarity to assembly-history similarity.

The three groups are defined in the design summary as follows.

Group	Assembly pattern	Progenitor characteristics
A	Built early	$|b_{\rm Gal}| > 5^\circ$5 mass accreted $|b_{\rm Gal}| > 5^\circ$6 Gyr ago; many low-mass satellites with $|b_{\rm Gal}| > 5^\circ$7
B	Assembled more steadily	$|b_{\rm Gal}| > 5^\circ$8 mass by 10–10.5 Gyr ago; fewer, larger progenitors with $|b_{\rm Gal}| > 5^\circ$9 a few $-30^\circ$0
C	Dominated by one very massive event	$-30^\circ$1; most mass in a single satellite

The existence of these groups means that HALO7D-X is not only a classifier over individual simulation instances, but also a tool for coarser inference over assembly channels (Apfel et al., 7 Jul 2025). For the Milky Way application, high posterior weight on models within one group would suggest that the Galaxy’s halo is either early built-up, steadily assembled, or dominated by one major merger (Apfel et al., 7 Jul 2025). This suggests a hierarchical interpretation in which robust inference may first emerge at the group level before being sharpened at the level of individual simulated halos.

The article’s design logic therefore links observable-space clustering to formation-history clustering. That connection is central to the survey’s scientific rationale: by identifying similarities in observables among halos, the analysis aims to identify similarities in their accretion histories (Apfel et al., 7 Jul 2025).

7. Position within Galactic-halo studies

HALO7D-X occupies a specific niche within stellar-halo research. It is neither a full-sky astrometric survey nor a purely spectroscopic census, but a hybrid program that combines archival HST baselines, Gaia DR2 astrometry, and targeted Keck/DEIMOS spectroscopy to produce seven-dimensional chemo-kinematic constraints for distant halo stars (Apfel et al., 7 Jul 2025). Its line-of-sight architecture reflects the practical availability of HST archival fields and the multiplexing constraints of DEIMOS, while its statistical framework is designed around direct comparison to simulated stellar halos.

The survey’s use of the Bullock and Johnston models, Galaxia-generated mock stars, multinomial cell-count likelihoods, and a Dirichlet prior over model fractions makes it a forward-modeling experiment in Galactic archaeology rather than a purely descriptive observational program (Apfel et al., 7 Jul 2025). Its intended deliverable is an inference about the Milky Way’s progenitor mass function and accretion timeline, derived through similarity to simulated halos rather than direct recovery of all merger parameters. The design study concludes that the survey can recover two fundamental aspects of the Galaxy’s hierarchical formation history: the progenitor mass function and the accretion timeline (Apfel et al., 7 Jul 2025).

Within that scope, HALO7D-X is best understood as a sparse, high-information survey of the outer halo optimized for assembly-history discrimination. Its principal strength lies in connecting chemo-kinematic observables to merger chronology and progenitor mass hierarchy; its principal limitation is the inability of the planned pencil-beam sampling to constrain orbital circularity or stream-versus-plume morphology (Apfel et al., 7 Jul 2025).