Abstract
Recent studies point out that there exists some rough scaling relations for dark matter and some tight connections between dark matter and baryons. However, most of the relations and tight connections can only be found in galaxies, but not in galaxy clusters. In this article, we consider a new expression that can characterize the properties of dark matter-baryon interplay for both galactic and galaxy cluster scales. By using the archival observational data of galaxies and galaxy clusters, we show that the value {boldsymbol{K}}{boldsymbol{=}}{bar{{boldsymbol{n}}}}_{{boldsymbol{D}}}{bar{{boldsymbol{n}}}}_{{boldsymbol{B}}}{{boldsymbol{r}}}_{{boldsymbol{o}}}{boldsymbol{V}}{boldsymbol{/}}{{boldsymbol{v}}}^{{bf{4}}} is almost a constant and scale independent within the optical radius ro, where {bar{{boldsymbol{n}}}}_{{boldsymbol{D}}} is the average dark matter number density, {bar{{boldsymbol{n}}}}_{{boldsymbol{B}}} is the average baryon number density, v is the characteristic velocity and V is the interacting volume. This would be the first universal relation between dark matter and baryons on both galactic and galaxy cluster scales. We anticipate this result to be a starting point to explain the small-scale problem and the scaling relations for dark matter in galaxies. The constant K discovered may reveal some underlying global interaction between dark matter and baryons.
Highlights
It is commonly believed that dark matter particles exist in galaxies and galaxy clusters
Based on the assumption of collisionless behavior of dark matter particles, computer simulations show that dark matter density would follow the Navarro-Frenk-White (NFW) profile[5], which is usually regarded as a universal density profile for dark matter
This profile only gives good agreement with the data of galaxy clusters[6] and some galaxies[7,8], but not for dwarf galaxies[9,10]. It does not have any universal relation for dark matter which is true for both galactic and galaxy cluster scales
Summary
The effect of dark matter-baryon interplay inside an ‘interacting region’ would depend on the average dark matter number density nD, average baryon number density nB and the volume of the interacting region V which depends on the optical radius ro. The Tully-Fisher relation relates the total baryonic mass with tviecloroctitaytiaosnMcuB r=ve(s4r7ise±to6)aMco nksmta−n4t s−4 v′4 19, where v′ is v′ quickly within ro, the asymptotic we assume that circular velocity. Recent studies show that the data of some elliptical galaxies fall on the spiral baryonic Tully-Fisher relation if one assumes a certain value of mass-to-luminosity ratio[33]. The above deduction method can only be applied for galaxies It is because there is no Tully-Fisher relation for galaxy clusters. EthteempproedrautcutrρeDTrsoifs not a constant for galaxy hot gas in galaxy clusters, which can be given by Virial relation v ≈ 3kT /mp. Where S0 is the central surface brightness, rc is the core radius and β is a fitted parameter These parameters can be used to construct the density profile of hot gas[36]: ρB ρB0 1.
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