Lyman-$\alpha$ forest constraints on decaying dark matter

We present an analysis of high-resolution $N$-body simulations of decaying dark matter cosmologies focusing on the statistical properties of the transmitted Lyman-$\alpha$ ($\mathrm{Ly}\alpha$) 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 $V_k=c\Delta M/M$ to the daughter particle resulting in free-streaming and subsequent damping of small-scale density fluctuations. Current $\mathrm{Ly}\alpha$ forest power spectrum measurements probe comoving scales up to $\sim 2–3h^{-1}\mathrm{Mpc}$ at redshifts $z\sim 2–4$, 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 $\mathrm{Ly}\alpha$ 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 $\mathrm{Ly}\alpha$ flux distribution. We argue that this approach should be sufficient for our main purpose, which is to demonstrate the power of the $\mathrm{Ly}\alpha$ forest to constrain decaying dark matter models. We find that Sloan Digital Sky Survey 1D $\mathrm{Ly}\alpha$ forest power spectrum data place a lifetime-dependent upper limit $V_k\lesssim 30–70\mathrm{km}/\mathrm{s}$ for decay lifetimes $\lesssim 10\mathrm{Gyr}$. This is the most stringent model-independent bound on invisible dark matter decays with small mass splittings. For larger mass splittings (large $V_k$), $\mathrm{Ly}\alpha$ forest data restrict the dark matter lifetime to ${\Gamma }^{-1}\gtrsim 40\mathrm{Gyr}$. 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) $\mathrm{Ly}\alpha$ 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.

Figure 1

Ratio of DDM 3D matter power spectrum relative to CDM in the relevant parameter range. In the left panel we show a comparison of power spectrum difference generated from a modified CAMB code (dashed lines) with that from DDM $N$-body simulations with decay parameters $V_k=200\mathrm{km}/\mathrm{s}$ and ${\Gamma }^{-1}=10\mathrm{Gyr}$ at redshift $z=2.2$, 3.0, and 4.2 (bottom to top). The right panel shows the same comparison with $V_k=100\mathrm{km}/\mathrm{s}$ and ${\Gamma }^{-1}=1\mathrm{Gyr}$. The light blue shaded areas indicate the upper limit on $k$ for SDSS $\mathrm{Ly}\alpha$ forest data and VHS data.

Figure 2

Comparison of the SDSS 1D $\mathrm{Ly}\alpha$ forest power spectra [45] as a function of redshift from $z=4.2$ (top diamond point set with $1\sigma$ error bar) to 2.2 (bottom diamond point set) in steps of 0.2 with predictions from our numerical simulations. For each redshift bin the solid lines are from the best-fit CDM model simulations, while the dash-dotted lines are from DDM simulations with the decay parameter value marked in each panel. $V_k$ is the recoil kick velocity, and ${\Gamma }^{-1}$ is the decay lifetime.

Figure 3

Comparison of DDM parameter $1\sigma$ exclusion contours from 29 (solid region on the right) and [28] (two solid region on the left between $V_k\sim 9–100$ km/s) to those that are derived from current $\mathrm{Ly}\alpha$ forest data. The, diagonally hatched region is the $1\mathrm{\text{−}}\sigma$ exclusion region from the VHS data set [47] together with WMAP 7 data [50] and the SDSS galaxy 3D power spectrum [6]. The line horizontally hatched regions shows the $1\mathrm{\text{−}}\sigma$ exclusion contours from the SDSS 1D $\mathrm{Ly}\alpha$ forest power spectrum [45]. The two solid region on the left depict those regions of parameters space that may strongly alter interpretations of the small-scale problems facing CDM and a significant portion of these regions is independently ruled out by our $\mathrm{Ly}\alpha$ forest analysis (see text for details).

Figure 4

1D marginalized posterior probabilities for the cosmological and astrophysical parameters that we consider in our analysis of SDSS $\mathrm{Ly}\alpha$ forest data. Cosmological and astrophysical parameters are inferred using a Taylor expansion of the flux power spectrum of the fiducial model to first order, based on our simulation suite, and performing MCMC analysis over the full parameter space.