Constraints on Nonlinearity of the Mass-Concentration Relation

Abstract

We develop a Bayesian generalization of the previous method to constrain a wide variety of mass-concentration (M-C) relations motivated by both theoretical and observational studies. The framework incorporates the intrinsic scatter in concentration, nonlinear weak-lensing (WL) calibration relations, the WL measurement-error covariance, and the underlying parent mass distribution. We employ Hamiltonian Monte Carlo for computational efficiency. Our sample consists of 213 X-ray-selected clusters with WL measurements for the eRASS1, XXL, LoCuSS, and MCXC catalogs at 0<z< 0.9. For each subsample, we account for its specific WL calibration relation and underlying population distribution. We consider a conventional single power-law model, an empirical double power-law model, and four theoretical models calibrated against numerical simulations. The four theoretical M-C models comprise two in which concentration decreases with mass, distinguished by the sign of d^2ln c/d(ln M)^2, and two in which the concentration decreases with increasing mass before turning upward at high masses. Because the mass and redshift ranges of our cluster sample do not extend into the upturn regime predicted by numerical simulations, we distinguish among the models primarily through the curvature of their M-C relations. Regardless of which model is adopted, the inferred M-C relation is in good agreement with the results of recent numerical simulations. We find no statistically significant differences among the models above the 4σ level. However, the result shows a tendency toward a gradual flattening of the mass dependence toward higher masses. Specifically, a monotonically decreasing model with positive curvature is preferred over the single power-law relation and a monotonically decreasing model with negative curvature at the 2σ level and over three double power-law models at the 0.5−1σ level.

Baryonic Imprints on DM Halos: the concentration-mass relation and its dependence on 28 model parameters in the CAMELS suite
Cami Delgado, Dhayaa Anbajagane
arXiv2 Oct 2026PreprintCC BY 4.0Full textCosmology GalaxiesarXiv
Characterizing the hierarchical structure of filaments. I. The origin of the length-mass (L-M) scaling relation
Rahul Patel, Daniel Seifried, Alvaro Hacar
Astronomy & Astrophysics6 Oct 2026Peer-reviewedPublisher termsSolar & stellar physicsCrossref
On the relation between magnetic field strength and gas density in the interstellar medium. II. Density uncertainties and diffuse gas constraints
David Whitworth, Amit Seta, Ralph E. Pudritz +4
The Open Journal of Astrophysics27 Oct 2026Peer-reviewedCC BY 4.0Solar & stellar physicsCrossref
The MAGPI Survey: Emission Line Products Data Release and the Role of Spectroscopic Aperture Covering Fraction on the Balmer Decrement-Stellar Mass Relation
A.J Battisti, E.G.M Muller, E Wisnioski +27
HAL22 Sep 2026PreprintLicence not statedGeneral astronomy General physicsHAL
Two-dimensional weak lensing shear for cluster mass, concentration, ellipticity and miscentering estimation
Calum Murray, Martin Kilbinger, Constantin Payerne
HAL23 Sep 2026PreprintCC BY 4.0Full textCosmology General physicsHALarXiv

Cite

BibTeX RIS

BibTeX

@misc{okabe2026constraints,
  title = {{Constraints on Nonlinearity of the Mass-Concentration Relation}},
  author = {Nobuhiro Okabe},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05662},
  eprint = {2610.05662},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05662},
}

RIS

TY  - UNPB
TI  - Constraints on Nonlinearity of the Mass-Concentration Relation
AU  - Nobuhiro Okabe
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.05662
UR  - https://arxiv.org/abs/2610.05662
AB  - We develop a Bayesian generalization of the previous method to constrain a wide variety of mass-concentration (M-C) relations motivated by both theoretical and observational studies. The framework incorporates the intrinsic scatter in concentration, nonlinear weak-lensing (WL) calibration relations, the WL measurement-error covariance, and the underlying parent mass distribution. We employ Hamiltonian Monte Carlo for computational efficiency. Our sample consists of 213 X-ray-selected clusters with WL measurements for the eRASS1, XXL, LoCuSS, and MCXC catalogs at 0<z< 0.9. For each subsample, we account for its specific WL calibration relation and underlying population distribution. We consider a conventional single power-law model, an empirical double power-law model, and four theoretical models calibrated against numerical simulations. The four theoretical M-C models comprise two in which concentration decreases with mass, distinguished by the sign of d^2ln c/d(ln M)^2, and two in which the concentration decreases with increasing mass before turning upward at high masses. Because the mass and redshift ranges of our cluster sample do not extend into the upturn regime predicted by numerical simulations, we distinguish among the models primarily through the curvature of their M-C relations. Regardless of which model is adopted, the inferred M-C relation is in good agreement with the results of recent numerical simulations. We find no statistically significant differences among the models above the 4σ level. However, the result shows a tendency toward a gradual flattening of the mass dependence toward higher masses. Specifically, a monotonically decreasing model with positive curvature is preferred over the single power-law relation and a monotonically decreasing model with negative curvature at the 2σ level and over three double power-law models at the 0.5−1σ level.
ER  -

Abstract

Related

Cite