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PAC in DESI. II. Galaxy-halo connection into the $10^{6}{\rm M}_{\odot}$ frontier

By applying the Photometric object Around Cosmic webs (PAC) method to DESI Y1 and DECaLS data, this study constrains the stellar-mass-to-halo-mass relation down to $10^{8.0}\,h^{-1}{\rm M}_{\odot}$ , revealing a rising star-formation efficiency in low-mass haloes that suggests central red dwarf galaxies formed prior to reionization and were subsequently quenched by the UV background.

Original authors: Kun Xu, Carlos S. Frenk, Y. P. Jing, Shaun Cole, Sownak Bose, J. Aguilar, S. Ahlen, D. Bianchi, D. Brooks, F. J. Castander, T. Claybaugh, A. de la Macorra, P. Doel, J. E. Forero-Romero, E. Gaztañaga

Published 2026-04-01

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Kun Xu, Carlos S. Frenk, Y. P. Jing, Shaun Cole, Sownak Bose, J. Aguilar, S. Ahlen, D. Bianchi, D. Brooks, F. J. Castander, T. Claybaugh, A. de la Macorra, P. Doel, J. E. Forero-Romero, E. Gaztañaga, S. Gontcho A Gontcho, G. Gutierrez, C. Hahn, R. Joyce, S. Juneau, R. Kehoe, T. Kisner, M. Landriau, L. Le Guillou, M. Manera, R. Miquel, J. Moustakas, S. Nadathur, W. J. Percival, F. Prada, I. Pérez-Ràfols, G. Rossi, L. Samushia, E. Sanchez, D. Schlegel, J. H. Silber, D. Sprayberry, G. Tarlé, B. A. Weaver, H. Zou

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 ocean made of dark matter. Floating in this ocean are "haloes"—bubbles of dark matter that act as the nurseries for galaxies. For a long time, astronomers have been trying to figure out the rules of this nursery: How much dark matter does it take to make a galaxy? And how efficiently does that dark matter turn into stars?

This paper is like a detective story where the authors are trying to solve a mystery about the smallest, faintest galaxies (dwarf galaxies) that have been hiding in plain sight.

Here is the breakdown of their investigation, explained in simple terms:

1. The Problem: The "Local Void" and the "Faint Signal"

Imagine you are trying to study the average size of fish in a lake. But, you happen to be standing in a tiny, empty patch of the lake where there are almost no fish. If you only look at your immediate surroundings, you might conclude, "Fish are very rare here!" and get the wrong idea about the whole lake.

The Issue: Our solar system is sitting in a "Local Void"—a region of space that is emptier than average. This makes it hard to study dwarf galaxies because there just aren't many of them nearby to count.
The Old Way: Astronomers usually try to take a "spectrum" (a detailed chemical fingerprint) of every galaxy to measure it. But this is like trying to catch every single fish in the ocean with a tiny net; it's too slow and misses the tiny ones.
The New Trick (PAC): The authors used a clever method called PAC (Photometric Objects Around Cosmic webs). Instead of trying to catch every fish, they used a "sonar" approach. They took a list of galaxies they could identify clearly (the spectroscopic ones) and looked at the blurry, fuzzy neighbors around them (the photometric ones). By measuring how these fuzzy neighbors cluster around the clear ones, they could infer the properties of the tiny, faint galaxies without needing to take a detailed spectrum of every single one.

2. The Discovery: The "Upturn" in Efficiency

The team used supercomputer simulations (like a video game of the universe) to compare their observations with theory. They were looking for the Stellar Mass–Halo Mass Relation (SHMR). Think of this as a rulebook that says: "If you have a bucket of dark matter this big, you should get a galaxy of this size."

The Expectation: Scientists thought that as the buckets of dark matter got smaller, the galaxies inside them would get smaller very quickly. It was like a dimmer switch that just kept turning down.
The Surprise: They found a "glitch" in the dimmer switch. When they looked at the smallest buckets of dark matter (around $10^{10}$ $1 0^{10}$ times the mass of our sun), the efficiency of making stars actually went up.
- The Analogy: Imagine you are baking cookies. You expect that if you have a tiny bit of dough, you'll get a tiny, sad cookie. But the authors found that for the tiniest amounts of dough, the oven was actually super-efficient, baking surprisingly large, fluffy cookies.
- The Result: Small dark matter haloes were making stars much more efficiently than anyone thought possible.

3. The Mystery of the "Red Dwarfs"

The paper also noticed something strange about the color of these small galaxies.

The Observation: Most of these tiny galaxies are red and dead (they stopped making stars long ago).
The Puzzle: Usually, small galaxies are blue and active. Why are these tiny ones red and dead?
The Solution: The authors propose a time-travel theory. They think these galaxies formed very early in the universe's history, before a cosmic event called "Reionization" (a giant wave of UV radiation from the first stars).
- The Story: Before the UV wave hit, these tiny dark matter haloes were super-efficient factories, churning out stars quickly. Then, the UV wave hit, acting like a cosmic "off switch," killing the star formation instantly.
- The Result: We are left with "zombie" galaxies: tiny, red, and dead, but they contain more stars than current computer models say they should be able to hold.

4. The "Cosmic Weight Limit"

Finally, the authors asked: "How small can a dark matter halo get and still exist?"

They put a "minimum weight limit" on their computer models and saw how badly the model broke.
They found that if dark matter haloes smaller than about 100 million times the mass of our sun existed, the data would look very different.
The Verdict: The data strongly suggests that dark matter haloes must exist down to this size. This puts a strict limit on theories about what dark matter actually is (ruling out some theories that say dark matter is too "warm" to form such small clumps).

Summary

In short, this paper used a clever "sonar" trick to peek at the smallest galaxies in the universe. They discovered that:

Small dark matter haloes are surprisingly good at making stars (an efficiency "upturn").
These tiny galaxies are mostly red and dead because they were born early and then "quenched" by the universe's first radiation.
Dark matter clumps must exist down to a specific small size, giving us a new clue about the nature of dark matter itself.

It's like realizing that the tiniest, most fragile bubbles in a soda can actually hold more fizz than the big ones, and that they were all popped by a giant wave a long time ago.

1. Problem Statement

Understanding the formation of dwarf galaxies is critical for testing Dark Matter (DM) models and the physics of cosmic reionization. However, constructing spectroscopic samples complete down to low stellar masses ( $M_* \lesssim 10^8 M_\odot$ ) is increasingly difficult due to observational limitations. Furthermore, the existence of the "Local Void" complicates studies of dwarf galaxies in an average cosmological environment, as local underdensities bias measurements.

Previous studies using the Photometric objects Around Cosmic webs (PAC) method (specifically SDSS PAC IV) constrained the Stellar Mass–Halo Mass Relation (SHMR) down to halo masses of $\sim 10^{10} h^{-1} M_\odot$ . This paper aims to push this frontier further, utilizing the deeper DESI Year 1 Bright Galaxy Survey (BGS) and DECam Legacy Survey (DECaLS) to probe stellar masses down to $10^{6.4} M_\odot$ and constrain the SHMR to even lower halo masses.

2. Methodology

Data Sources

Spectroscopic Tracers: DESI Year 1 Bright Galaxy Survey (BGS) Bright sample ( $r < 19.5$ ), covering $\sim 5349$ deg $^2$ overlapping with DECaLS.
Photometric Targets: DECaLS photometric catalogue (Data Release 9), providing deep imaging ( $g, r, z$ bands) down to $r \sim 23.3$ .
Simulations: The Jiutian hybrid simulation suite (specifically Jiutian-1G and Jiutian-300 runs) using Planck18 cosmology. These simulations utilize the HBT+ subhalo finder and a specific treatment for "orphan" galaxies (subhaloes that become numerically unresolved but whose central galaxies persist) to ensure accurate subhalo abundance tracking down to $\sim 50$ particles.

The PAC Method

The authors employ the PAC method to measure the excess surface density $\bar{n}_2 w_p(r_p)$ of photometric objects around spectroscopic tracers.

Mechanism: It calculates the angular cross-correlation function (ACCF) between the spectroscopic sample (known redshifts) and the photometric sample (unknown redshifts).
Selection: By performing Spectral Energy Distribution (SED) fitting on the photometric catalogue at the redshift of each spectroscopic source, the authors select photometric galaxies within specific stellar mass bins.
Advantage: This allows the construction of a statistically complete sample of low-mass galaxies without needing individual spectroscopic redshifts for every target, bypassing the spectroscopic bottleneck.

Modeling Framework

Subhalo Abundance Matching (SHAM): The authors model the $\bar{n}_2 w_p(r_p)$ measurements using a SHAM framework.
Separation of Centrals and Satellites: Unlike previous works that often assumed a single SHMR for all galaxies, this study models central ( $P_c$ ) and satellite ( $P_s$ ) SHMRs separately.
Parametrization:
- Non-parametric: Uses 43 anchor points for centrals and 34 for satellites, interpolated linearly with a monotonicity prior.
- Parametric: A modified Behroozi et al. (2013) function with an additional term ( $f_{low}$ ) to capture low-mass upturns.
Covariance Handling: Due to the high dimensionality (349 stellar mass bins $\times$ 10 radial bins), the authors use a Jackknife resampling method combined with Principal Component Analysis (PCA) and Singular Value Decomposition (SVD) to compress the data vector and stabilize the covariance matrix inversion.

3. Key Contributions

Extension to the $10^6 M_\odot$ Frontier: Successfully constrained the SHMR down to halo masses of $\sim 10^{8.0} h^{-1} M_\odot$ and stellar masses of $10^{6.4} M_\odot$ , a regime previously inaccessible to spectroscopic surveys.
Discovery of a Low-Mass Upturn: Identified a clear "upturn" in the central SHMR at halo masses $M_h \sim 10^{10.0} h^{-1} M_\odot$ , indicating that Star Formation Efficiency (SFE) increases toward lower masses, contrary to standard expectations where SFE drops due to reionization suppression.
Robustness Checks: Systematically tested the results against:
- Mass-dependent scatter in the SHMR.
- Reionization-induced suppression of the Halo Occupation Fraction (HOF) using H I and H $_2$ cooling models.
- Galaxy Assembly Bias (GAB).
- Alternative cosmologies (Planck18 vs. WMAP9).
Minimum Halo Mass Constraints: Derived strict upper limits on the minimum mass of dark matter haloes required to host the observed galaxies.

4. Key Results

SHMR Structure:
- Centrals: Exhibit a distinct upturn at $M_h \sim 10^{10} h^{-1} M_\odot$ , suggesting higher SFE in small haloes than previously modeled.
- Satellites: The satellite SHMR is less constrained at low masses due to the small virial radii of low-mass centrals (falling below the analysis scale cut of $0.16 h^{-1}$ Mpc).
- Scatter: The scatter in the SHMR is found to be larger for satellites ( $\sigma_s \approx 0.37$ ) than for centrals ( $\sigma_c \approx 0.22$ ).
Galaxy Stellar Mass Function (GSMF):
- The derived GSMF is consistent with DESI PAC I but systematically higher by $\sim 15\%$ .
- Red Dwarf Dominance: Combining with DESI PAC I color data, the authors find that red dwarf galaxies are predominantly central galaxies, not satellites. This challenges the notion that low-mass red galaxies are primarily quenched satellites.
Systematics and Tensions:
- Assembly Bias: Even under the extreme assumption of maximal assembly bias ( $\rho=1$ ), the inferred SHMR remains robust, though the satellite SHMR is slightly overestimated. Assembly bias alone cannot explain the $\sim 15\%$ GSMF tension.
- Cosmology: Switching from Planck18 to a WMAP9-like cosmology ( $\Omega_m \approx 0.268$ ) reduces the GSMF tension. A hypothetical cosmology with $\Omega_m \approx 0.216$ and $\sigma_8 \approx 0.87$ (effectively mimicking $z=0$ structure growth at $z=0.1$ ) removes the tension entirely, suggesting potential issues with the assumed cosmology or effective redshift determination.
Minimum Halo Mass Limits:
- The data imposes a $3\sigma$ upper limit of $M_{lim} = 10^{8.38} h^{-1} M_\odot$ .
- The data imposes a $5\sigma$ upper limit of $M_{lim} = 10^{8.71} h^{-1} M_\odot$ .
- This implies dark matter haloes must exist down to at least these masses to host the observed population.

5. Significance and Implications

Reionization Physics: The results motivate a hypothesis where Star Formation Efficiency (SFE) was significantly higher in low-mass haloes prior to reionization. This allowed relatively massive galaxies to form in small haloes before being quenched by the UV background, resulting in the observed population of central red dwarfs. This contradicts current galaxy formation models which typically predict much lower stellar masses for such systems.
Dark Matter Constraints: The derived lower limits on halo mass ( $10^{8.38} - 10^{8.71} h^{-1} M_\odot$ ) provide stringent constraints on warm dark matter (WDM) and other non-cold dark matter models that suppress the formation of small haloes.
Environmental Bias: The discrepancy between this work (average environment) and previous studies (Local Void) highlights the strong environmental dependence of early-formed red galaxies, likely due to halo assembly bias.
Future Outlook: The study demonstrates the power of the PAC method for probing the faint end of the galaxy population. Future Stage-IV imaging surveys (LSST, Euclid, Roman) will extend these measurements to even lower masses and break degeneracies between SHMR slope and scatter using higher-order statistics.

In summary, this paper successfully extends the galaxy-halo connection into the $10^6 M_\odot$ regime, revealing a surprising upturn in star formation efficiency at low masses and providing robust constraints on the minimum mass of dark matter haloes, while highlighting potential tensions in current cosmological models and galaxy formation prescriptions.