The detectability of baryonic acoustic oscillations in future galaxy surveys

TL;DR

This study assesses the detectability of BAO in the galaxy power spectrum using ultra-large N-body simulations (BASICC) and a GALFORM-based semi-analytic galaxy model to explore nonlinear growth, redshift-space distortions, and bias. It presents a robust, general method to extract the BAO scale via a ratio of the measured spectrum to a smooth reference, and quantifies how the recovered scale translates into constraints on the dark energy equation of state parameter $w$, including realistic assessments of sampling variance. The authors find that BAO provides an unbiased estimate of the sound horizon, with sampling variance dominating errors even in giant volumes; constraints on $w$ from BAO alone are feasible but not at the 1% level for near-future surveys unless an all-sky spectroscopic program (e.g., SPACE) is available. The results highlight the dependence of BAO sensitivity on tracer selection, the necessity of accurate modeling of nonlinearities and biases, and the substantial gains expected from next-generation surveys for cosmology.

Abstract

We assess the detectability of baryonic acoustic oscillations (BAO) in the power spectrum of galaxies using ultra large volume N-body simulations of the hierarchical clustering of dark matter and semi-analytical modelling of galaxy formation. A step-by-step illustration is given of the various effects (nonlinear fluctuation growth, peculiar motions, nonlinear and scale dependent bias) which systematically change the form of the galaxy power spectrum on large scales from the simple prediction of linear perturbation theory. Using a new method to extract the scale of the oscillations, we nevertheless find that the BAO approach gives an unbiased estimate of the sound horizon scale. Sampling variance remains the dominant source of error despite the huge volume of our simulation box ($=2.41 h^{-3}{\rm Gpc}^{3}$). We use our results to forecast the accuracy with which forthcoming surveys will be able to measure the sound horizon scale, $s$, and, hence constrain the dark energy equation of state parameter, $w$ (with simplifying assumptions and without marginalizing over the other cosmological parameters). Pan-STARRS could potentially yield a measurement with an accuracy of $Δs/s = 0.5-0.7 % $ (corresponding to $Δw \approx 2-3% $), which is competitive with the proposed WFMOS survey ($Δs/s = 1% $ $Δw \approx 4 % $). Achieving $Δw \le 1% $ using BAO alone is beyond any currently commissioned project and will require an all-sky spectroscopic survey, such as would be undertaken by the SPACE mission concept under proposal to ESA.

Figures (19)

• Figure 1: A test of the choice of starting redshift used in the N-body simulations. The upper panel compares the power spectrum measured at $z=15$ in the BASICC when the simulation is started at $z=63$ (dashed red curve) and at $z=127$ (solid blue curve). The power spectra plotted in the upper panel have been divided by the linear perturbation theory prediction for the dark matter power spectrum at $z=15$. The lower panel shows the ratio between the power spectrum measured from the simulation started at redshift 63 to that measured from the run which started at redshift 127.
• Figure 2: The power spectrum of the dark matter in real-space measured at the starting redshift of the BASICC, $z=63$ (red points). The corresponding prediction of linear perturbation theory is shown by the green (solid) line. The blue (dot-dashed) curve shows the power spectrum of the unperturbed glass-like distribution of particle positions. The dashed line shows the Poisson noise expected for the number density of dark matter particles used in the BASICC. The noise of the initial particle distribution is much less than Poisson. The arrow marks the position of the Nyquist frequency of the FFT grid.
• Figure 3: The fractional error in the power spectrum of the dark matter (top panel) and in the power spectrum of haloes more massive than $1.8 \times 10^{13}\, h^{-1}\,M_{\odot}$ (bottom panel), estimated using the low resolution simulations from the dispersion of $P(k)$ around the ensemble mean. The smooth black curves show the error predicted by the analytical expression given in Eq. \ref{['eq:err']}. The red points show the scatter from the ensemble of low resolution simulations. The arrow in the bottom panel shows the wavenumber for which $\bar{n}P(k=0.2 h {\rm Mpc}^{-1})=1$.
• Figure 4: Upper panel: the fraction of 'resolved galaxies' in the high resolution N-body simulation as a function of magnitude, at different output redshifts (as given by the key in the lower panel). The magnitude is in the observer-frame $R$-band; to obtain an apparent $R$-band magnitude, the distance modulus corresponding to the redshift should be added to the plotted magnitude. The vertical lines mark the magnitude at which the galaxy sample is 100% complete at each redshift. Lower panel: the cumulative luminosity function of galaxies brighter than a given $R$-band magnitude, for different redshifts as given in the key. The vertical lines show the 100% completeness limits at each redshift and the horizontal lines indicate the associated space density of galaxies.
• Figure 5: The growth of the power spectrum of density fluctuations in the dark matter, as measured in real-space. The smooth curves show the predictions of linear perturbation theory at the redshifts indicated by the key. The power spectra measured in the low resolution ensemble at $z=0$ are plotted to show the sampling variance for a simulation box of side $1340\,h^{-1}\,$Mpc. The smallest wavenumber plotted corresponds to the fundamental mode in the simulation, $2 \pi /L = 0.0469\,h^{-1}\,$Mpc. The maximum wavenumber shown is $0.67$ times the Nyquist frequency of the FFT grid, chosen to avoid any aliasing effects.