Using the redshift evolution of the Lyman-$\alpha$ effective opacity as a probe of dark matter models

Abstract

Lyman-$\alpha$ forest data are known to be a good probe of the small scale matter power. In this paper, we explore the redshift evolution of the observable effective optical depth ${\tau }_{\mathrm{eff}}(z)$ from the Lyman-$\alpha$ data as a discriminator between dark matter models that differ from the $\Lambda$CDM model on small scales. We consider the thermal warm dark matter (WDM) and the ultra-light axion (ULA) models for the following set of parameters: the mass of ULA, $m_a\simeq 10^{-24}–5\times 10^{-22}\mathrm{eV}$ and WDM mass, $m_{\mathrm{wdm}}=0.1–4.6\mathrm{keV}$. We simulate the line-of-sight HI density and velocity fields using semi-analytic methods. The simulated effective optical depth for the alternative dark matter models diverges from the $\Lambda$CDM model for $z\gtrsim 3$, which provides a meaningful probe of the matter power at small scales. Using likelihood analysis, we compare the simulated data with the high-resolution Lyman-$\alpha$ forest data in the redshift range $2<z<4.2$. The analysis yields the following 1$\sigma$ bounds on dark matter masses: $m_{\mathrm{wdm}}>0.7\mathrm{keV}$ and $m_{\mathrm{a}}>2\times 10^{-23}\mathrm{eV}$. To further test the efficacy of our proposed method, we simulate synthetic data sets compatible with the $\Lambda$CDM model in the redshift range $2\le z\le 6.5$ and compare with theory. The 1$\sigma$ bounds obtained are significantly tighter: $m_{\mathrm{wdm}}>1.5\mathrm{keV}$ and $m_{\mathrm{a}}>7\times 10^{-23}\mathrm{eV}$. Although our method provides an alternative way of constraining dark matter models, we note that these bounds are weaker than those obtained by high-resolution hydrodynamical simulations.

arXiv commentaccepted for publication in JCAP

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