Probing large-scale structure with large samples of X-ray selected AGN: I Baryonic acoustic oscillations

We investigate the potential of large X-ray-selected AGN samples for detecting baryonic acoustic oscillations (BAO). Though AGN selection in X-ray band is very clean and efficient, it does not provide redshift information, and thus needs to be complemented with an optical follow-up. The main focus of this study is (i) to find the requirements needed for the quality of the optical follow-up and (ii) to formulate the optimal strategy of the X-ray survey, in order to detect the BAO. We demonstrate that redshift accuracy of $\sigma_0=10^{-2}$ at $z=1$ and the catastrophic failure rate of $f_{\rm fail}\lesssim 30\%$ are sufficient for a reliable detection of BAO in future X-ray surveys. Spectroscopic quality redshifts ($\sigma_0=10^{-3}$ and $f_{\rm fail}\sim 0$) will boost the confidence level of the BAO detection by a factor of $\sim 2$. For meaningful detection of BAO, X-ray surveys of moderate depth of $F_{\rm lim}\sim {\rm few~} 10^{-15}$ erg/s/cm$^2$ covering sky area from a few hundred to $\sim$ten thousand square degrees are required. The optimal strategy for the BAO detection does not necessarily require full sky coverage. For example, in a 1000-day long survey by an eROSITA type telescope, an optimal strategy would be to survey a sky area of $\sim 9000$ deg$^2$, yielding a $\sim 16\sigma$ BAO detection. A similar detection will be achieved by ATHENA+ or WFXT class telescopes in a survey with a duration of 100 days, covering a similar sky area. XMM-Newton can achieve a marginal BAO detection in a 100-day survey covering $\sim 400$ deg$^2$. These surveys would demand a moderate-to-high cost in terms the optical follow-ups, requiring determination of redshifts of $\sim 10^5$ (XMM-Newton) to $\sim 3\times 10^6$ objects (eROSITA, ATHENA+, and WFXT) in these sky areas.