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

TL;DR

This study tests whether the physically motivated galaxy-size definition $R_1$, the radius where the stellar surface density reaches $1~M_\,\mathrm{pc}^{-2}$, remains tightly correlated with dark matter halo properties when applied to cosmological simulations. Using two EAGLE volumes, the authors show that the observed $M_\star$–$R_1$ relation is reproduced with $\approx0.06$ dex scatter, and that $R_1$ correlates with halo size $R_{200}$ with $\approx0.10$ dex scatter, much tighter than the traditional $R_{50}$–$R_{200}$ relation. The extended double-power-law fits yield precise predictions for halo size and mass from $R_1$, implying halo radii can be inferred with less than ~50% uncertainty from deep imaging alone, a factor of ~6 improvement over using $R_{50}$-based estimates. The work also finds a tight stellar-to-halo mass relation with $\approx0.11$ dex scatter, about half that reported in prior studies, supporting the practical utility of $R_1$ for measuring dark matter haloes. Overall, the results demonstrate that a physically motivated, image-based galaxy size metric can substantially tighten inferences about dark matter halo properties and enhance the use of deep imaging in constraining galaxy–halo connections.

Abstract

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.

Figures (6)

• Figure 1: From left to right, projected density maps and radial profiles of stellar mass, stellar luminosity, and gas star formation rate for a simulated spiral galaxy of stellar mass $3.8\times 10^{10}~\mathrm{M}_\odot$ selected from the recalibrated simulation. The vertical dashed, solid, and dot-dashed lines mark the positions of $R_{50}$, $R_1$, and $R_{29,g}$, respectively. For this star forming galaxy, $R_1$ is a better measure of the size of the galaxy for its proximity to the edge (truncation radius) of the disc. The edge of the disc coincides with a net drop in the star formation rate surface density, the starting hypothesis for the new definition of galaxy size.
• Figure 2: Correlation between $R_1$ and stellar mass for all galaxies in the sample (orange symbols). The median values in each bin are plotted together with the 16% and 84% quantiles (shaded area). For bins with fewer than ten galaxies, single galaxies are plotted as small dots. The orange solid line depicts the double power-law fit for $M_\star>10^{8.6}~\mathrm{M}_\odot$ (extrapolated below that mass). We show the relation between $R_{50}$ and stellar mass for all galaxies in the sample in purple. For visual comparison, the galaxies in the sample of Trujillo2020 are represented with small dots, both $R_1$ and $R_{50}$. The distribution of the residuals around the best-fit linear relation for all galaxies is shown in the inset. The distribution has been fitted with a Gaussian (solid line) with a dispersion of $\sigma_{\Delta\log_{10}R_1}=0.06~\mathrm{dex}$.
• Figure 3: Correlation between $R_1$ and $R_{200}$ for central galaxies. Median (dots and solid lines) and 16% and 84% quantiles (shaded areas) are shown. We quote in the legend the average of the scatter for the entire sample of central galaxies and with respect to the analytic fit as well as the dispersion around the mean. The purple line and shaded area are the relation between $R_{50}$ and $R_{200}$ and its 16% and 84% quantiles. The dotted line is the linear correlation proposed by Kravtsov2013 for early-type galaxies, $R_{50}=0.015R_{200}$, with a scatter of $0.2~~\mathrm{dex}$ (shaded area). The top x-axis gives the corresponding halo mass, $M_{200}$.
• Figure 4: Correlation between $M_{200}$ and $M_\star$ for central galaxies. Median (dots and solid lines) and 16% and 84% quantiles (shaded areas) are shown. We quote in the legend the average of the scatter for the entire sample of central galaxies and with respect to the analytic fit, together with dispersion around the mean. We plot in the inset the distribution of residuals for the analytic fitting function and all the galaxies in the sample.
• Figure 5: Left panel. Relation between size and stellar mass for all galaxies in the two simulations. Dots and diamonds are the median values in bins of halo mass, and the shaded areas indicate the 16% and 84% quantiles. Single dots are for individual galaxies, in bins containing fewer than ten galaxies. The vertical lines mark the minimum masses considered for the two simulations in the computation of the analytic fits. Middle panel. Relation between stellar mass, $M_\star$, and halo mass, $M_{200}$, for all central galaxies in the two simulations. Symbols are as in the left panel. The vertical lines mark the lower halo mass limit of the samples extracted from the two simulations and employed in the computation of the $R_1$--$R_{200}$ relation. Right panel. Same as the middle panel, but for the $R_1$--$M_{200}$ relation.