Lyman-αforest constraints on decaying dark matter

Abstract

We present an analysis of high-resolution $N$-body simulations of decaying dark matter cosmologies focusing on the statistical properties of the transmitted Lyman-$\ensuremath{\alpha}$ ($\mathrm{Ly}\ensuremath{\alpha}$) forest flux in the high-redshift intergalactic medium (IGM). In this type of model a dark matter particle decays into a slightly less massive stable dark matter daughter particle and a comparably light particle. The small mass splitting provides a nonrelativistic kick velocity ${V}_{k}=c\ensuremath{\Delta}M/M$ to the daughter particle resulting in free-streaming and subsequent damping of small-scale density fluctuations. Current $\mathrm{Ly}\ensuremath{\alpha}$ forest power spectrum measurements probe comoving scales up to $\ensuremath{\sim}2--3{h}^{\ensuremath{-}1}\text{ }\text{ }\mathrm{Mpc}$ at redshifts $z\ensuremath{\sim}2--4$, providing one of the most robust ways to probe cosmological density fluctuations on relatively small scales. The suppression of structure growth due to the free-streaming of dark matter daughter particles also has a significant impact on the neutral hydrogen cloud distribution, which traces the underlying dark matter distribution well at high redshift. We exploit $\mathrm{Ly}\ensuremath{\alpha}$ forest power spectrum measurements to constrain the amount of free-streaming of dark matter in such models and thereby place limits on decaying dark matter based only on the dynamics of cosmological perturbations without any assumptions about the interactions of the decay products. We use a suite of dark-matter-only simulations together with the fluctuating Gunn-Peterson approximation to derive the $\mathrm{Ly}\ensuremath{\alpha}$ flux distribution. We argue that this approach should be sufficient for our main purpose, which is to demonstrate the power of the $\mathrm{Ly}\ensuremath{\alpha}$ forest to constrain decaying dark matter models. We find that Sloan Digital Sky Survey 1D $\mathrm{Ly}\ensuremath{\alpha}$ forest power spectrum data place a lifetime-dependent upper limit ${V}_{k}\ensuremath{\lesssim}30--70\text{ }\text{ }\mathrm{km}/\mathrm{s}$ for decay lifetimes $\ensuremath{\lesssim}10\text{ }\text{ }\mathrm{Gyr}$. This is the most stringent model-independent bound on invisible dark matter decays with small mass splittings. For larger mass splittings (large ${V}_{k}$), $\mathrm{Ly}\ensuremath{\alpha}$ forest data restrict the dark matter lifetime to ${\ensuremath{\Gamma}}^{\ensuremath{-}1}\ensuremath{\gtrsim}40\text{ }\text{ }\mathrm{Gyr}$. We leave the calibration of IGM properties using high-resolution hydrodynamic simulations for future work, which might become necessary if we consider data with higher precision such as the Baryon Oscillation and Spectroscopic Survey (BOSS) $\mathrm{Ly}\ensuremath{\alpha}$ data. Forthcoming BOSS data should be able to provide more stringent constraints on exotic dark matter, mainly because the larger BOSS quasar spectrum sample will significantly reduce statistical errors.