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Peer-reviewedCC BY 4.0The Astrophysical Journal

A Universal Relation between Primordial Density-potential Cross-correlation Coefficient and Spin Factor Distribution

  • Jun-Sung Moon1
  • Jounghun Lee2
  • Juhan Kim3
  1. 1Institute of Astronomy and Astrophysics
  2. 2Seoul National University
  3. 3Korea Institute for Advanced Study
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Abstract

Recent studies have revealed that the key properties of visible galaxies like their optical sizes, stellar ages, star formation rates, and morphologies are closely linked with the angular momenta of their host dark matter (DM) halos. According to the linear tidal torque theory (LTTT), the halo angular momentum, as a conserved quantity, is directly proportional to the primordial spin factor, τ , defined as the degree of misalignment between the principal axes of the initial density and potential Hessian matrices, which were found by numerical experiments to follow a Gamma distribution, fully characterized by its mean and variance. In this study, we heuristically develop an analytic expression for the mean and variance of τ in terms of the initial density-potential cross-correlation coefficient, q . Analyzing a dataset from the Multiverse simulations performed for both of the flat ΛCDM and w CDM cosmologies, we prove that this analytic expression is universally valid in describing how the mean and variance of τ change with q , regardless of the smoothing scales for both of the cosmologies. Given the prior finding that the τ -distribution can be reconstructed from the observable galaxy size distribution, this universal analytic expression may allow us to determine q from the same observable via the mean and variance of τ . We discuss a possibility of constraining the early Universe physics from the reconstructed q via our heuristic model, without suffering from cosmological degeneracies.

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Cite

BibTeXRIS
BibTeX
@article{moon2026universal,
  title = {{A Universal Relation between Primordial Density-potential Cross-correlation Coefficient and Spin Factor Distribution}},
  author = {Jun-Sung Moon and Jounghun Lee and Juhan Kim},
  journal = {The Astrophysical Journal},
  year = {2026},
  month = oct,
  doi = {10.3847/1538-4357/aea098},
  url = {https://iopscience.iop.org/article/10.3847/1538-4357/aea098},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - A Universal Relation between Primordial Density-potential Cross-correlation Coefficient and Spin Factor Distribution
AU  - Jun-Sung Moon
AU  - Jounghun Lee
AU  - Juhan Kim
PY  - 2026
DA  - 2026/10/14
JO  - The Astrophysical Journal
DO  - 10.3847/1538-4357/aea098
UR  - https://iopscience.iop.org/article/10.3847/1538-4357/aea098
AB  - Recent studies have revealed that the key properties of visible galaxies like their optical sizes, stellar ages, star formation rates, and morphologies are closely linked with the angular momenta of their host dark matter (DM) halos. According to the linear tidal torque theory (LTTT), the halo angular momentum, as a conserved quantity, is directly proportional to the primordial spin factor, τ , defined as the degree of misalignment between the principal axes of the initial density and potential Hessian matrices, which were found by numerical experiments to follow a Gamma distribution, fully characterized by its mean and variance. In this study, we heuristically develop an analytic expression for the mean and variance of τ in terms of the initial density-potential cross-correlation coefficient, q . Analyzing a dataset from the Multiverse simulations performed for both of the flat ΛCDM and w CDM cosmologies, we prove that this analytic expression is universally valid in describing how the mean and variance of τ change with q , regardless of the smoothing scales for both of the cosmologies. Given the prior finding that the τ -distribution can be reconstructed from the observable galaxy size distribution, this universal analytic expression may allow us to determine q from the same observable via the mean and variance of τ . We discuss a possibility of constraining the early Universe physics from the reconstructed q via our heuristic model, without suffering from cosmological degeneracies.
SN  - 0004-637X
SN  - 1538-4357
ER  -