Scaling relations in the phase-space structure of dark matter haloes

Journal Article · 17 March 2025 · Monthly Notices of the Royal Astronomical Society

DOI: https://doi.org/10.1093/mnras/staf447 · OSTI ID:2545950

Gross, Axel  ^[1]; Li, Zhaozhou  ^[2]; Qian, Yong-Zhong  ^[1]

---

1. University of Minnesota, Minneapolis, MN (United States)
2. The Hebrew University, Jerusalem (Israel)

We present new scaling relations for the isotropic phase-space distribution functions (DFs) and energy distributions of simulated dark matter haloes. These relations are inspired by those for the singular isothermal sphere with density profile $$\rho (r)\propto r^{-2}$$, for which the DF satisfies $$f(E) \propto r_{\mathrm{max}}^{-2}(E)$$ and the energy distribution satisfies $$\mathrm{ d}M/\mathrm{ d}E \propto r_{\mathrm{max}}(E)$$, with $$r_{\mathrm{max}}(E)$$ being the radius where the gravitational potential equals energy $$E$$. For the simulated haloes, we find $$f(E)\propto r_{\mathrm{max}}^{-2.08}(E)$$ and $$\mathrm{ d}M/\mathrm{ d}E \propto r_{\mathrm{max}}(E)$$ across broad energy ranges. In addition, the proportionality coefficients depend on the gravitational constant and the parameters of the best-fitting Navarro–Frenk–White density profile. These scaling relations are satisfied by haloes over a wide mass range and provide an efficient method to approximate their DFs and energy distributions. Understanding the origin of these relations may shed more light on halo formation.

• Research Organization: University of Minnesota, Minneapolis, MN (United States)
• Sponsoring Organization: Israel Science Foundation; USDOE
• Grant/Contract Number: FG02-87ER40328
• OSTI ID: 2545950
• Journal Information: Monthly Notices of the Royal Astronomical Society, Journal Name: Monthly Notices of the Royal Astronomical Society Journal Issue: 3 Vol. 538; ISSN 1365-2966; ISSN 0035-8711
• Publisher: Oxford University PressCopyright Statement
• Country of Publication: United States
• Language: English