Decaying Cold Dark Matter Model and Small-Scale Power

TL;DR

The paper addresses the tension that LCDM faces on small scales, such as overly concentrated halos and excessive dwarf galaxies. It proposes a ΛDCDM model where half of the CDM decays into relativistic products by $z=0$, causing adiabatic halo expansion that lowers inner densities while preserving the successes of LCDM; analytic relations show how halo radii, concentrations, and rotation curves evolve, and the model is shown to be COBE- and cluster-normalized with enhanced power at $z>2$. A fiducial parameter set yields a decay lifetime $τ ≈ 1.44 t_0$, higher initial power on small scales, and distinct observational signatures, including evolving cluster gas fractions and a population of dark or ultra-low surface brightness dwarf galaxies. The work argues that this approach reconciles small-scale tensions without abandoning LCDM’s successes and outlines concrete tests—primarily cluster gas fraction evolution via X-ray/SZ observations and searches for dark galaxies—that could falsify or support the model.

Abstract

The canonical cosmological constant dominated cold dark matter model (LCDM) may possess too much power on small scales at z=0, manifested as central over-concentration of dark matter and over-abundance of dwarf galaxies. We suggest an alternative model, LDCDM, where one half of the cold dark matter particles decay into relativistic particles by z=0. The model successfully lowers the concentration of dark matter in dwarf galaxies as well as in large galaxies like our own at low redshift, while simultaneously retaining the virtues of the LCDM model. The model solves the problem of over-production of small dwarf galaxies in the LCDM not by removing them but by identifying them with failed, "dark" galaxies, where star-formation is quenched due to dark matter evaporation and consequent halo expansion. A dramatic difference between the LDCDM model and other proposed variants of the LCDM model is that the small-scale power at high redshift (z>2) in the LDCDM model is enhanced compared to the LCDM model. A COBE-and-cluster normalized LDCDM model can be constructed with the following parameters: H0=60km/sec/Mpc, lambda0=0.60, Omega_{0,CDM}=0.234, Omega_{0,b}=0.044, n=1.0, and sigma8=1.06. A clean test of this model can be made by measuring the evolution of gas fraction in clusters. The prediction is that the gas fraction should decrease with redshift and is smaller by 31% at z=1 than at z=0. X-ray and Sunyaev-Zel'dovich effect observations should provide such a test.

Figures (1)

• Figure 1: shows the rotation curves (thick) and mass profiles (thin) for the initial (solid; $\Lambda$CDM ) and final (dashed; $\Lambda$DCDM ) halo, both having the NFW profile but different virial radii ($r_{200}$). Both x and y axes have arbitrary units. The initial concentration of $c_i=30$ is used for this illustration, although the relative effect is quite insensitive to the value of $c_i$. The long vertical bars indicate the core radius for the initial ( $\Lambda$CDM ; solid) and final ( $\Lambda$DCDM ; dashed) halo. The short vertical bars indicate the virial radius ($r_{200}$) for the initial ( $\Lambda$CDM ; solid) and final ( $\Lambda$DCDM ; dashed) halo. The final radius of maximum rotation velocity is larger than the initial radius of maximum rotation velocity by a factor of $2$. The rotation velocity at virial radius is reduced by about $20\%$ ($V_{200,f}\sim 0.8 V_{200,i}$) and the maximum rotation velocity reduced by about $40\%$ ($V_{max,f}\sim 0.6 V_{max,i}$). The mass of a halo within a fixed proper radius in the $\Lambda$DCDM model is reduced by a factor of $\sim 8.0$ in the inner region and a factor of $\sim 1.6$ in outer region.