[Paper Review] Reconstruction of HI power spectra with radio-interferometers to study dark energy

R. Ansari, J.M. Le Goff+6 more|ArXiv.org|Jul 23, 2008

Radio Astronomy Observations and Technology5 references15 citations

TL;DR

This paper proposes using radio interferometers to map neutral hydrogen (HI) 21 cm emission across redshifts 0.5–3 to reconstruct the HI power spectrum and detect Baryon Acoustic Oscillations (BAO) as standard rulers for probing dark energy. By simulating interferometric observations with cylinder and dish arrays, it demonstrates that a 4-year packed-cylinder array survey can constrain the dark energy equation of state with 6% precision on $w_0$ and 25% on $w_a$, rivaling optical surveys like SDSS-III and WFMOS.

ABSTRACT

Among the tools available for the study of the dark energy driving the expansion of the Universe, Baryon Acoustic Oscillations (BAO) and their effects on the matter power spectrum are particularly attractive. It was recently proposed to study these oscillations by mapping the 21cm emission of the neutral hydrogen in the redshift range $0.5

Motivation & Objective

• To assess the feasibility of using radio interferometers to reconstruct the HI power spectrum for cosmological studies.
• To evaluate the precision of BAO scale measurements using HI 21 cm emission in the redshift range $0.5 < z < 3$.
• To compare the sensitivity of different interferometer configurations—packed and unpacked arrays of cylinders or dishes—to constraints on dark energy parameters.
• To quantify the impact of instrumental noise and foreground subtraction on the detectability of BAO wiggles in the HI power spectrum.
• To determine the cosmological parameter constraints achievable with a 4-year survey using HI intensity mapping, particularly on $w_0$ and $w_a$.

Proposed method

• A simplified procedure is developed to reconstruct the HI power spectrum in Fourier space from interferometric visibility data, assuming a small sky patch near the zenith.
• The noise power spectrum $P_{\text{noi}}(k)$ is derived based on the baseline distribution and system temperature, accounting for thermal and electronic noise in the array.
• The HI power spectrum is modeled as a scaled version of the large-scale structure (LSS) matter power spectrum, with a redshift-dependent bias and HI fraction $f_{\text{HI}}(z)$.
• Foreground subtraction is modeled as a smooth spectral component (Galactic, extragalactic, CMB) that can be removed via polynomial or spectral fitting, assuming it does not contaminate the BAO scales.
• Cosmological parameter constraints are derived using Fisher matrix analysis, combining BAO data with Planck priors on $\Omega_m$, $\Omega_b$, $h$, $\sigma_8$, $n_s$, and $\tau$.
• The dark energy equation of state is parameterized as $w(z) = w_0 + w_a \cdot z/(1+z)$, and the Fisher matrix is computed from the uncertainties in transverse and radial BAO peak positions.

Experimental results

Research questions

• RQ1 Can radio interferometers reconstruct the HI power spectrum with sufficient signal-to-noise to detect Baryon Acoustic Oscillations at $z \sim 1.5$?
• RQ2 What is the impact of interferometer configuration—cylinders vs. dishes, packed vs. unpacked—on the noise power spectrum and BAO scale precision?
• RQ3 How do instrumental and cosmic variance limits affect the detectability of BAO wiggles in the HI power spectrum?
• RQ4 What precision can be achieved on dark energy parameters $w_0$ and $w_a$ using HI intensity mapping compared to optical surveys?
• RQ5 How does the inclusion of Planck priors improve the constraints on $w_0$ and $w_a$ from BAO measurements in the HI power spectrum?

Key findings

• A 4-year survey with a packed array of north-south oriented cylinders achieves a 6% precision on $w_0$ and 25% on $w_a$, with a Figure of Merit (FoM) of 119 at 95% confidence level.
• The packed-cylinder array configuration yields a 69.1 FoM, outperforming the unpacked cylinder array (10.1 FoM) and packed-dish array (13.6 FoM), due to better baseline coverage and reduced noise.
• With only cosmic variance and no instrumental noise, the FoM reaches 136, indicating that the main limitation in realistic surveys is instrumental noise, not fundamental limits.
• The Fisher matrix analysis shows that combining HI intensity mapping BAO data with Planck priors significantly improves constraints on $w_0$ and $w_a$.
• The HI 21 cm power spectrum at $z=1.5$ has a mean brightness temperature of 0.00033 K, which is three orders of magnitude below extragalactic radio sources, but foregrounds can be subtracted via spectral fitting.
• The BAO peak at $k \sim 0.03$ h/Mpc is detectable with a signal-to-noise ratio sufficient to constrain $w_0$ at the 10% level, even with realistic noise levels.