Abstract
The galaxy correlation function serves as a fundamental tool for studying cosmology, galaxy formation and the nature of dark matter. It is well established that more massive, redder and more compact galaxies tend to have stronger clustering in space1,2. These results can be understood in terms of galaxy formation in cold dark matter (CDM) halos of different mass and assembly history. Here we report an unexpectedly strong large-scale clustering for isolated, diffuse and blue dwarf galaxies, comparable to that seen for massive galaxy groups but much stronger than that expected from their halo mass. Our analysis indicates that the strong clustering aligns with the halo assembly bias seen in simulations3 with the standard ΛCDM cosmology only if more diffuse dwarfs formed in low-mass halos of older ages. This pattern is not reproduced by existing models of galaxy evolution in a ΛCDM framework4,5,6, and our finding provides clues for the search of more viable models. Our results can be explained well by assuming self-interacting dark matter7, suggesting that such a scenario should be considered seriously.
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Data availability
The stellar mass and star formation rate for SDSS galaxies used in this paper are publicly available at https://wwwmpa.mpa-garching.mpg.de/SDSS/DR7/. The galaxy size and Sérsic index data can be downloaded at http://sdss.physics.nyu.edu/vagc/. The galaxy group catalogue is publicly available at https://gax.sjtu.edu.cn/data/Group.html. The ALFALFA H i sample can be downloaded at https://egg.astro.cornell.edu/alfalfa/data/. The simulation data are available through the IllustrisTNG public data release71 at https://www.tng-project.org/ for the runs used in this paper, and for L-Galaxies implemented on the runs. The ELUCID simulation data are available upon request. Source data are provided with this paper.
Code availability
The code for the semi-analytic method based on the isothermal Jeans model is publicly available at https://github.com/JiangFangzhou/SIDM. The codes used in this paper are available at https://github.com/ChenYangyao/dwarf_assembly_bias.
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Acknowledgements
We thank F. Jiang, L. Gao, J. Wang, Q. Guo, X. Yang, Y. Zu, R. Li, D. Yang, C. Gao and K. Wang for comments. This work is supported by the National Natural Science Foundation of China (NSFC, numbers 12192224, 12273037 and 11890693). H.W. acknowledges support from CAS Project for Young Scientists in Basic Research, grant number YSBR-062. Y.R. acknowledges support from the CAS Pioneer Hundred Talents Program (Category B), as well as the USTC Research Funds of the Double First-Class Initiative. Y.C. acknowledges support from China Postdoctoral Science Foundation (grant number 2022TQ0329). We acknowledge the science research grants from the China Manned Space Project with CMS-CSST-2021-A03 and Cyrus Chun Ying Tang Foundations. The work is also supported by the Supercomputer Center of University of Science and Technology of China, and the Tsinghua Astrophysics High-Performance Computing platform of Tsinghua University. H.W. acknowledges the hospitality of the International Centre of Supernovae (ICESUN), Yunnan Key Laboratory at Yunnan Observatories Chinese Academy of Sciences.
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All authors made substantial contributions to this paper; all authors read and commented on the document. Z.Z., Y.C. and Y.R. contributed equally to this work, and Y.C. and Y.R. are co-first authors of this paper. H.W. conceived of the original idea, initiated the project and led the analysis. H.M. contributed to the writing and interpretation of results. X.L. contributed to the analysis of observational data. H.L. contributed to the analysis of simulation data.
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Extended data figures and tables
Extended Data Fig. 1 Dwarf galaxy sample selection.
a, b, c, Distributions of dwarf properties. Green dots represent the finally selected dwarfs. Red dots show the dwarfs with 0.1(g − r) > 0.6 and blue dots show the dwarfs with 0.1(g − r) < 0.6 and n > 1.6. d, Redshift distributions of dwarf galaxy samples with different Σ*. Shaded region shows the redshift distribution for control samples, fctl(z), used in the z-matching method.
Extended Data Fig. 2 2PCCFs for the main samples.
The first and third rows show the 2PCCFs for dwarfs with different surface density. And the second and fourth rows show the 2PCCF ratios relative to compact dwarfs. The top two rows show the results using the z-weighting method, while the bottom two rows present those for the z-matching method. The error bars for both the 2PCCFs and the 2PCCF ratios represent the 16th and 84th percentiles of 100 bootstrap samples. The shaded region indicates the radial interval used for fitting and best-fit relative bias. The error bars for relative bias represent the 16th and 84th percentiles of the posterior distribution.
Extended Data Fig. 3 Number density n(z) as a function of redshift for different Σ*.
n(z) is normalized by that of the lowest-z bin (n0). a, n(z) for low-mass (\(7.5 < \log \,{M}_{* }/{{\rm{M}}}_{\odot }\le 8.5\)) and massive (\(8.5 < \log \,{M}_{\ast }/{{\rm{M}}}_{\odot } < 9\)) dwarfs separately. For massive dwarfs, the SEs become large only when z > 0.04. For less-massive dwarfs, the SEs are significant even at z ~ 0.02. For given M*, the impact of the SEs depends only weakly on Σ*, as is expected from the small redshift concerned here. At z > 0.04, there is no low-mass dwarf with Σ* > 7 M⊙pc−2. b, n(z) for red (0.3 < 0.1(g − r) < 0.6) and blue (0.1(g − r) < 0.3) dwarfs separately. Dwarfs with different colors exhibit similar behavior, indicating that the SEs are insensitive to galaxy color. This is because our galaxies have already been restricted to a relatively narrow color range.
Extended Data Fig. 4 Relative biases obtained based on different dwarf subsamples.
Here the samples are divided by z (a), M* (b), color (c), Right Ascension (R.A., d), and Sérsic n (e), respectively, and the relative biases versus Σ* are shown for subsamples. In e, the main sample is exactly the sample used in the main text. The n > 1.6 sample consists of isolated dwarf galaxies with n > 1.6 and 0.1(g − r) < 0.6. The no n-cut sample includes the main sample and n > 1.6 sample. Note that the three curves are normalized to different compact samples that may have different clustering strength. f, Relative bias as a function of n for no n-cut dwarf sample. The relative bias is normalized to the subsample with the largest n. Only results using the z-weighting method are shown here. The results from the z-matching method are very similar and thus not presented. Markers with error bars are median values with 16th–84th percentiles of relative biases obtained from the posterior distribution of MCMC fitting.
Extended Data Fig. 5 2PCCFs with satellite contamination.
Blue and red solid curves represent the 2PCCFs for diffuse and compact dwarf galaxies, respectively, while dotted curves show the impact of different levels of satellite contamination on these dwarfs. Satellite contamination can notably amplify small-scale clustering, while it moderately enhances large-scale clustering for compact dwarfs and leaves the large-scale clustering unchanged for diffuse dwarfs. Note that the wine and cyan dotted lines show the results including all compact and diffuse satellite dwarfs, respectively. Thus, satellite contamination cannot explain the strong large-scale clustering observed in isolated diffuse dwarfs. Error bars represent 16th–84th percentiles of bootstrap samples.
Extended Data Fig. 6 Comparison of halo masses of dwarf galaxies derived from different methods.
a–d, halo mass versus M* for dwarf samples with different Σ*. Symbols with error bars show the halo mass obtained by using the HI kinematics versus M* and their uncertainties. The error bars for halo mass represent 1-σ uncertainties, while the error bars for M*, taken from ref. 52, represent 16th and 84th percentiles of the likelihood distribution. Teal shadow region shows the SHMR14 and its 1σ uncertainty. Cyan symbols show the results for UDGs taken from ref. 44. These UDGs have spatially-resolved HI kinematics maps, therefore their halo mass measurements are more reliable than ours. As can be seen, these UDGs follow the same trend as our diffuse dwarfs.
Extended Data Fig. 7 HI mass (MHI) verses M* for dwarf galaxy samples with varying Σ*.
The colored lines represent the median relationships of different samples.
Extended Data Fig. 8 Numerical simulations for dwarf galaxies and dwarf-host halos at z = 0.
a, b, 2PCCF of dwarf-host halos (1010.5≤Mh/M⊙ < 1011 M⊙; backsplash excluded) in the DMO simulation TNG300-1-Dark71, shown for the total sample and subsamples with different ranges of zf (a) and λ (b). Fractions of halos in subsamples are equal to those of subsamples of observed dwarf in the massive sample (see Fig. 3). c, PDF and median of halo concentration (c) for halo (sub)samples in a. Halo concentrations of UDG analogues simulated by NIHAO5 are shown by grey shaded area (minimum to maximum) and error bar (mean and standard deviation). Their concentration, cDM, is evaluated from the halos in the DMO counterpart of the hydro, compatible with ours. d, e, f, 2PCCF of central star-forming (sSFR ⩾ 10−11yr−1) dwarfs in galaxy-formation models: L-Galaxies86 (run on TNG100-1-Dark35,71, d), TNG100-136 (e) and TNG50-187 (f), shown for subsamples with different ranges of Σ*, and for the total sample (black). Dwarfs here include those with 108.5 ⩽ M*/M⊙ < 109 for L-Galaxies and TNG100-1, and 108 ⩽ M*/M⊙ < 109 for TNG50-1. Reference sample includes all galaxies (central or satellite, star-forming or quiescent) above the lower mass limit of the dwarf sample. In a, b, d–f, grey markers linked by curves from thin to thick are the 2PCCFs of massive halos with given ranges of mass in that simulation. Each upper panel shows wp, while each lower panel shows the ratio of wp to that of total. Markers with error bars for 2PCCFs show median values with 16th–84th percentiles estimated from bootstrap samples.
Supplementary information
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This file includes 7 methodological chapters and 1 table, including sample selection criteria, redshift control method, parametric uncertainty quantification, environmental characterization of dwarfs, H i kinematics-based halo mass estimation, abundance matching procedures and model assumption validation.
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Zhang, Z., Chen, Y., Rong, Y. et al. Unexpected clustering pattern in dwarf galaxies challenges formation models. Nature 642, 47–52 (2025). https://doi.org/10.1038/s41586-025-08965-5
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DOI: https://doi.org/10.1038/s41586-025-08965-5
