Predicting dark matter particle mass, size, and properties from energy cascade and two-thirds law in dark matter flow 后印本

摘要: Dark matter can be characterized by the mass and size of its smallest constituents, which are challenging to directly probe and detect. After years of null results in the search for thermal WIMPs, a different prospective might be required beyond the standard WIMP paradigm. We present a new approach to estimate the dark matter particle mass, size, density, and many other relevant properties based on the nature of flow of dark matter. A comparison with hydrodynamic turbulence is presented to reveal the unique features of self-gravitating collisionless dark matter flow, i.e. an inverse mass and energy cascade from small to large scales with a scale-independent rate of energy cascade $\varepsilon_u\approx -4.6\times 10^{-7}m^2/s^3$. For the simplest case with only gravitational interaction involved and in the absence of viscosity in flow, the energy cascade leads to a two-thirds law for pairwise velocity that can be extended down to the smallest scale, where quantum effects become important. Combining the rate of energy cascade $\varepsilon_u$, the Planck constant $\hbar$, and the gravitational constant $G$ on the smallest scale, the mass of dark matter particles is found to be around $0.9\times10^{12}GeV$ with a size around $3\times10^{-13}m$. Since the mass scale $m_X$ is only weakly dependent on $\varepsilon_u$ as $m_X \propto (-\varepsilon_u\hbar^5/G^4)^{1/9}$, the estimation of $m_X$ should be robust for a wide range of possible values of $\varepsilon_u$. If gravity is the only interaction and dark matter is fully collisionless, mass of around $10^{12}GeV$ is required to produce the given rate of energy cascade $\varepsilon_u$. In other words, if mass has a different value, there must be new interaction beyond gravity. This work suggests a heavy dark matter scenario produced in the early universe ($\sim 10^{-14}s$). Potential extension to self-interacting dark matter is also presented.