🔭 astrophysics

The stellar and dark matter distributions in early-type galaxies measured by stacked weak gravitational lensing

Using stacked weak gravitational lensing data from the Hyper Suprime-Cam Subaru Strategic Program, this study reveals that luminous early-type galaxies with stellar masses around $10^{11}M_\odot$ exhibit non-zero dark matter core radii and a bottom-heavy initial mass function, suggesting stronger feedback effects than predicted by current hydrodynamical simulations and providing new direct constraints on the stellar-to-halo mass relation.

Original authors: Momoka Fujikawa, Masamune Oguri

Published 2026-05-01

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CC BY 4.0

Original authors: Momoka Fujikawa, Masamune Oguri

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, invisible web made of "dark matter." Most of the time, this web is so thin and spread out that we can't see it. But sometimes, it clumps together to form massive halos around galaxies, acting like a heavy, invisible blanket that holds the stars together.

For decades, scientists have had a debate about what this "blanket" looks like right in the center of a galaxy.

The Big Debate: A Sharp Spike or a Soft Pillow?
According to the standard theory of how the universe works (called the Cold Dark Matter model), the center of this dark matter blanket should be incredibly dense, like a sharp, needle-like spike. This is called a "cusp."

However, some observations suggest the center is actually flat and smooth, like a soft pillow. This is called a "core." This disagreement is known as the "core-cusp problem."

The New Experiment: The "Stacking" Technique
In this paper, researchers Momoka Fujikawa and Masamune Oguri decided to settle this debate by looking at a specific type of galaxy: bright, red, early-type galaxies (think of them as the "elderly" galaxies of the universe).

They used a powerful telescope in Japan (the Subaru Telescope) to look at thousands of these galaxies. Since they couldn't see the dark matter directly, they used a trick called weak gravitational lensing.

The Analogy: Imagine looking at a streetlight through a slightly warped glass window. The light bends. If you look at many streetlights through many slightly warped windows, you can figure out exactly how the glass is warped, even if you can't see the glass itself.
The Trick: The "glass" here is the dark matter. The "streetlights" are distant background galaxies. The gravity of the foreground galaxies bends the light from the background ones. By measuring how much the light bends, they can weigh the dark matter.

Because the signal from a single galaxy is too faint to see the details in the very center, the team used a technique called stacking. They took data from hundreds of thousands of galaxies and piled them on top of each other. This is like taking a blurry photo of a single person and combining it with 10,000 other photos of similar people to create one super-sharp, high-definition image.

What They Found
By peering into the centers of these galaxies (down to about 10,000 light-years from the center), they found something surprising:

The "Pillow" Effect: For galaxies with a specific mass (around 100 billion times the mass of our Sun), the dark matter didn't look like a sharp spike. Instead, it looked like a soft core with a flat center.
The "Feedback" Hypothesis: Why is there a soft core? The researchers suggest that the stars inside the galaxy acted like a powerful feedback mechanism. Imagine a party where the music (stars) gets so loud and energetic that it pushes the furniture (dark matter) away from the center, creating a flat, open space.
Stronger Than Expected: The "push" they observed seems stronger than what current computer simulations of the universe predict. It's as if the party was even rowdier than the models thought it would be.

A New Way to Weigh Galaxies
The paper also did something unique: they weighed the stars and the dark matter halo at the same time using only this lensing trick.

The Result: They found that for a given amount of dark matter, there are more stars than we previously thought.
The Implication: This suggests that the "Initial Mass Function" (a rulebook for how stars are born) might be "bottom-heavy." In simple terms, these galaxies might be churning out more small, dim stars than we expected, rather than just big, bright ones. This is like finding a factory that produces twice as many tiny screws as the blueprints predicted.

The Bottom Line
This study shows that by stacking thousands of faint signals, we can map the invisible dark matter in the centers of galaxies. They found that for certain galaxies, the dark matter center is flat, not spiky, likely because the stars inside pushed it away. This suggests our understanding of how galaxies form and how stars are born needs a little adjustment to account for this extra "push."

1. Problem Statement

The standard $\Lambda$ CDM cosmological model predicts that Cold Dark Matter (CDM) halos possess a "cuspy" central density profile, typically described by the Navarro-Frenk-White (NFW) profile where density scales as $\rho \propto r^{-1}$ near the center. However, this prediction conflicts with observations of dwarf galaxies and some early-type galaxies, which often exhibit "cored" profiles with nearly constant central densities (the core-cusp problem).

While strong gravitational lensing and stellar dynamics have been used to study these profiles, they often suffer from degeneracies between the stellar Initial Mass Function (IMF) and the dark matter fraction, or are limited to specific high-mass systems. Furthermore, previous weak lensing studies have generally focused on outer halo regions, lacking the resolution to probe the inner density profiles ( $\sim$ 10 kpc) of early-type galaxies systematically. This study aims to resolve the central dark matter distribution and stellar mass of early-type galaxies using stacked weak gravitational lensing, a method complementary to strong lensing and dynamics, to test if baryonic feedback creates cores and to constrain the Stellar-to-Halo Mass Relation (SHMR) without relying on spectral energy distribution (SED) fitting.

2. Methodology

Data Source

Lens Sample: Photometric Luminous Red Galaxies (LRGs) from the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP). The sample covers $\sim$ 1200 deg $^2$ with redshifts $0.05 \le z \le 1.25$ and stellar masses $M_\star \ge 10^{10.3} M_\odot$ .
Source Sample: Background galaxies from the HSC-SSP three-year shear catalog ( $\sim$ 430 deg $^2$ ).
Redshift Selection: The analysis focuses on lens redshifts $0.4 < z < 0.6$ to maximize the lensing signal and minimize photometric redshift uncertainties and surface brightness issues.
Systematics Control: The authors employ a $P(z)$ cut method to mitigate the dilution effect from foreground galaxies, ensuring only background sources with high probability of being behind the lens are used. Intrinsic shape noise is the dominant error source; cosmic shear noise is neglected.

Modeling Approach

The study utilizes a two-component model to fit the differential surface mass density profile ( $\Delta\Sigma$ ):

Stellar Component: Modeled using the Hernquist profile ( $\rho \propto r^{-1}(r+a)^{-3}$ ), where the scale radius $a$ is linked to the effective radius $r_e$ .
Dark Matter Component: Modeled using an empirical cored power-law profile. This allows for a central core radius ( $r_c$ ) and a power-law slope ( $\gamma$ ) in the outer region. The model is defined as:
$\rho_{DM}(r) \propto \frac{1}{(r^2 + r_c^2)^{(1+\gamma)/2}}$
Note: This is an empirical model chosen for its analytical tractability and flexibility within the inner fitting range, rather than a specific physical simulation output.

Fitting Strategy

Inner Profile Fitting: The model is fitted to the inner region ( $0.013 < r < 0.1$ Mpc/ $h$ ). Parameters include the fitted stellar mass ( $M_{\star,fit}$ ), normalization ( $A$ ), slope ( $\gamma$ ), and core radius ( $r_c$ ). The stellar mass is treated as a free parameter to account for IMF uncertainties and systematic errors in photometric mass estimates.
Outer Profile Fitting: The outer region ( $0.04 < r < 3$ Mpc/ $h$ ) is fitted with a model including a central NFW component, a satellite component, and a 2-halo term to constrain the total halo mass ( $M_{NFW}$ ).
Comparison: The inner dark matter profile is compared against the extrapolation of the outer NFW profile to identify deviations (cores).

3. Key Contributions

First Systematic Stacked Weak Lensing Analysis: This is the first study to systematically probe the inner density profiles ( $\sim$ 10 kpc) of early-type galaxies using stacked weak lensing, extending the reach of weak lensing beyond the traditional outer halo regime.
Direct SHMR Constraint: The authors provide a new constraint on the Stellar-to-Halo Mass Relation (SHMR) where both stellar mass and halo mass are derived directly from weak lensing measurements, independent of SED fitting assumptions.
IMF Constraint: By comparing lensing-derived stellar masses with photometric estimates (assuming a Salpeter IMF), the study offers constraints on the stellar Initial Mass Function (IMF).

4. Key Results

Central Dark Matter Distributions

Core Detection: For most stellar mass bins, the core radius ( $r_c$ ) is consistent with zero. However, for two specific bins ( $10^{10.7} M_\odot < M_\star < 10^{11.1} M_\odot$ ), the data strongly prefers non-zero core radii (inconsistent with zero at $>3\sigma$ ).
Deviation from NFW: In the bins with detected cores, the central dark matter density is significantly lower than the extrapolated NFW profile (deviating by $>3\sigma$ ). In other mass bins, the profiles are consistent with NFW within $\sim 2\sigma$ .
Negative Correlation: A negative correlation is found between the core radius ( $r_c$ ) and the density slope ( $\gamma$ ); a larger core implies a steeper dark matter slope to compensate for the lower central density.

Dark Matter Fractions and Feedback

Low Dark Matter Fractions: In the mass bins where cores are detected, the dark matter fraction within $5r_e$ ( $f_{DM}(<5r_e)$ ) is significantly lower than predictions from hydrodynamical simulations (EAGLE and TNG-100).
Feedback Implication: The observed low dark matter fractions suggest that baryonic feedback effects are stronger than currently predicted by state-of-the-art simulations. This feedback likely expels dark matter from the center, creating the observed cores.

Stellar-to-Halo Mass Relation (SHMR) and IMF

Stellar Mass Discrepancy: The stellar masses derived from weak lensing ( $M_{\star,fit}$ ) are systematically higher (by a factor of $\sim$ 2 at $M_\star \gtrsim 10^{11} M_\odot$ ) than those derived from photometric SED fitting assuming a Salpeter IMF.
IMF Conclusion: To reconcile the higher lensing masses with the halo masses, the study concludes that the stellar IMF in massive early-type galaxies must be more "bottom-heavy" (richer in low-mass stars) than the Salpeter IMF. This aligns with findings from strong lensing and stellar kinematics but is confirmed here via weak lensing.
SHMR Consistency: When the IMF is adjusted to match the lensing results, the derived SHMR is consistent with previous empirical relations (e.g., Behroozi et al. 2019).

5. Significance

Resolution of Small-Scale Challenges: The detection of cores in specific mass ranges provides observational evidence supporting the role of baryonic feedback in solving the core-cusp problem, though the effect appears stronger than current simulations predict.
Methodological Advancement: The paper demonstrates that stacked weak lensing is a viable and powerful tool for probing the inner structure of galaxies, complementing strong lensing and dynamics. It breaks the degeneracy between stellar mass and dark matter fraction without relying on assumptions about the IMF used in photometric mass estimation.
Cosmological Implications: The results suggest that current hydrodynamical simulations may underestimate the efficiency of feedback mechanisms in early-type galaxies. Additionally, the confirmation of a bottom-heavy IMF in massive galaxies has implications for galaxy formation models and the interpretation of stellar populations at high redshift.

In summary, this work leverages the depth and area of the HSC-SSP data to reveal that early-type galaxies with intermediate stellar masses ( $\sim 10^{11} M_\odot$ ) possess cored dark matter distributions, implying stronger feedback than simulated, and that their stellar populations are likely dominated by low-mass stars, deviating from the standard Salpeter IMF.