An accurate measure of the size of dark matter halos using the size of galaxies

The physically motivated definition of galaxy size proposed recently, linked to the farther location of the in situ star formation, considerably reduces the scatter of the galaxy mass-size relation and provides a viable method to infer the galaxy stellar mass from its size. We provide a similar relation correlating the size of galaxies with the size of their dark matter haloes by leveraging the small scatter of the aforementioned relation. We analysed the simulated galaxies of the two main cosmological volumes of the EAGLE simulations and computed the size of the galaxies and their mass when mimicking the observational analysis. For central galaxies, we computed the relation between galaxy size and halo size. We show that the simulated galaxies reproduce the observed stellar mass-size relation’s normalisation and slope. The scatter of this relation, 0.06 dex, matches the intrinsic scatter measured in observation. We then computed the correlation between galaxy size and halo size and found that the relation is steeper than when using the half-mass radius as a measure of size, with the scatter (0.1 dex) being a factor of two smaller than the observed relation. As well, the galaxy-to-halo mass relation derived from the simulations provides a factor of two better scatter than the observed scatter. This opens the possibility of measuring the size of dark matter haloes with greater accuracy (less than 50%, i.e. around six times better than using the effective radius) by using only deep imaging data.

💡 Research Summary

The paper investigates a physically motivated definition of galaxy size, R₁, defined as the projected radius at which the stellar surface density reaches 1 M⊙ pc⁻². This definition, introduced by Trujillo et al. (2020), is linked to the outermost radius where gas can efficiently collapse and form stars, and it dramatically reduces the scatter in the stellar mass–size relation to about 0.06 dex, far better than traditional metrics such as the effective radius (Rₑ).

Using the two flagship cosmological hydrodynamical simulations of the EAGLE project—a 100 Mpc³ reference run and a higher‑resolution 25 Mpc³ recalibrated run—the authors analyse galaxies at z = 0. They compute R₁ by rotating each galaxy to align with its stellar angular momentum vector, then constructing azimuthally averaged stellar surface‑density profiles in circular annuli. Because the particle mass (~10⁶ M⊙) makes direct surface‑density maps noisy at the 1 M⊙ pc⁻² threshold, interpolation of the averaged profile is used to locate R₁. Galaxy stellar mass (M★) is measured within the radius where the g‑band surface brightness reaches 29 mag arcsec⁻² (R₂₉,g), ensuring consistency with observational procedures. The half‑mass radius (R₅₀) is also recorded as a proxy for the traditional effective radius.

The simulated M★–R₁ relation reproduces the observed normalization, slope (≈ M★ ∝ R₁³), and intrinsic scatter (0.06 dex), confirming that the simulation’s sub‑grid physics (star formation threshold, feedback, etc.) yields realistic galaxy sizes. The authors then explore the correlation between galaxy size and halo size, defining halo radius R₂₀₀ as the radius enclosing a mean density 200 times the critical density. They find that R₁ correlates with R₂₀₀ more tightly than R₅₀ does: the R₁–R₂₀₀ relation is steeper (slope ≈ 0.9 versus ≈ 0.6 for R₅₀) and exhibits a scatter of only 0.1 dex, roughly half the scatter reported for observational samples. Likewise, the stellar‑to‑halo mass relation derived from the simulations shows a scatter about a factor of two smaller than that inferred from current observations.

These results imply that, given a measurement of R₁ from deep imaging, one can infer the host halo’s radius (and thus its mass) with an uncertainty of less than 50 %, i.e., about six times more precise than methods based on the effective radius. The authors discuss limitations: the analysis is restricted to z ≈ 0 because the surface‑density threshold may evolve with redshift; low‑mass galaxies near the resolution limit and morphologically disturbed systems sometimes fail to yield a reliable R₁; and the method assumes that the star‑formation threshold used in the simulations (based on Schaye 2004) holds universally.

In conclusion, the study provides a robust, simulation‑backed framework for estimating dark‑matter halo sizes from purely photometric galaxy size measurements. This opens the possibility of exploiting forthcoming deep, wide‑field surveys (e.g., LSST, Euclid, Roman) to map halo properties across large volumes without requiring spectroscopic or lensing data, thereby offering a powerful new tool for testing galaxy formation models and the connection between baryons and dark matter.