Tomography of the intergalactic medium with multiple QSO absorption spectra

V. D'Odorico1 (dodorico@oats.inaf.it), M. Viel1,2, F. Saitta3, S. Cristiani1,S. Bianchi4, B. Boyle5, S. Lopez6, J. Maza6, P. Outram7

Paper submitted to MNRAS

ResultsWe gathered the largest sample of high resolution UVES spectra of QSO pairs to study the 3-dimensional distribution properties of baryonic matter in the intergalactic medium (IGM) as traced by the transmitted flux in the QSO HI Lyman-α forests. Our sample is formed by 21 QSO pairs evenly distributed between angular separations of ~1 arcmin (comparable with the Jeans length) to 14 arcmin, with Lyman-α forests at a median redshifts z≈1.8.We selected also 8 UVES spectra of single QSOs fro the ESO Large Programme ‘The Cosmic Evolution of the IGM’ (Bergeron et al. 2004) to compute the correlation function along the line of sight and to be used as a control sample for the cross correlation function. We compared the observed sample with a set of mock spectra drawn from a cosmological hydrodynamical simulation (see below).The transmitted flux correlation function is computed with the formula:

ξ(θ, Δ s) = < (F(θ, s) – <F(θ)> )( F(0, s+Δ s) - <F(0)>)>,

where, F is the transmitted flux, <F> is the average transmitted flux in each spectrum, θ is the angular separation between the lines of sight and Δ s is the separation (in velocity or spatial) between two pixels. The main results of our investigation are the following:

1. The clustering properties of matter in the IGM in the direction parallel and transverse to the lines of sight are in very good agreement when the parameters of the concordance cosmology are used to transform the angular distance into velocity separation (Fig. 4). As an implication, peculiar velocities have to be small in the absorbing gas.

2. Matter in the IGM is clustered on scales smaller than ~200 km s-1 or about 3 h-1 comoving Mpc. The regions at lower over density (δ ≤ 6.5) are still clustered but on smaller scales (∆ v ≤ 100 km s-1, Fig. 2).

3. The simulated correlation functions are consistent with the observed analogous quantities at the 3 σ level, although they systematically predict lower clustering at the smaller scales (Fig. 1 and Fig. 3). The agreement becomes better when only the lower density regions are selected for the computation (Fig. 2) or when the effective optical depth of the simulated spectra is fixed to a larger value (marginally consistent with previous extensive observational results on the redshift evolution of the effective optical depth). These are hints of a lack of strong absorption lines in the simulated spectra that needs further investigations.

4. We observed an improved consistency between observations and simulations also when the temperature of the gas in the simulation is increased and, in particular, when a lower γ is adopted in the equation of state of the gas, T = T0 δ

γ-1 (γ=1.1 instead of the standard 1.6). This result suggests a HeII reionisation epoch close to the redshift investigated here.

Fig.1 Comparison of the auto correlation function in velocity space for our sample of observed QSO spectra (solid triangles), for the LP sample of observed QSO spectra (crosses) and for the simulated sample of spectra (empty triangles). Error bars are highly correlated and they are plotted only to give an idea of their extent.

Fig. 2 Same as Fig. 1 for the LP sample of observed QSO spectra (crosses) and for the simulated sample of spectra (empty triangles) but selecting only the pixels with flux value F>0.1. This is equivalent to exclude the lines with column density log N(HI) > 13.96.

Fig. 3 Transverse correlation function for the observed sample of QSO pairs (solid squares) compared with the analogous quantity for the sample of mock spectra (empty squares). Dashed lines represent the correlation function for the two control samples obtained substituting one QSO in each pair with another uncorrelated QSO

Fig. 4 Comparison of the cross correlation function for our sample of QSO pairs (squares) with the auto correlation function computed for the LP QSO sample (crosses) as a function of comoving spatial separation across and along the LOS, respectively.

Sample of observed QSO groups

We used simulations run with the parallel hydrodynamical (Tree SPH) code GADGET-2 (Springel et al. 2001; Springel 2005) with 2x4003 dark matter and gas particles in a box of 120 h-1 comoving Mpc. The cosmological model corresponds to a `fiducial' ΛCDM Universe with parameters Ω0m=0.26, Ω0Λ=0.74, Ω0b=0.0463 and H0=72 km s-1 Mpc-1.

We pierced the simulated box with lines of sight at separations equal to those of the observed QSO pairs for a total of 50 samples exactly reproducing the observed sample of QSO pairs. The mock spectra extent in velocity is about ¼ of the observed one and the pixel size is approximately the same.

The mean HI optical depth in the simulation box is determined by the UV background at the considered redshift. The corresponding observed quantity is the effective optical depth, τeff, which is obtained from the average flux measured in QSO absorption spectra:

< F > = exp(-τeff). The τeff of the simulated spectra can be rescaled to a given value without affecting the density and temperature distributions of the gas (Theuns et al. 1998). So for the spectra reproducing our sample of QSOs we have adopted the average values measured in the observed spectra which are within 1 % of the original values of the simulated spectra. In the computation of the correlation functions, we have used the average fluxes obtained as the mean of the flux values along the LOS as for the observed spectra. We checked that the difference in the resulting correlation functions taking the true values for the average flux is less than 5 %.

Finally, we added to the simulated spectra a Gaussian noise in order to reproduce the observed average signal-to-noise ratios (per pixel).

Sample of simulated spectra

TRIPLET SEXTET

PAIR U

1 arcmin

PAIR A

1.3 arcmin

PAIR Q

5 arcmin

3.8 arcmin

4.9 arcmin

The nature of the Lyman-α forest

It is now more than a decade that thanks to semi analytic and hydro dynamic simulation results (e.g. Cen et al. 1994) the majority of the absorption features observed in Lyman-α forests of high redshift QSO spectra is identified with the fluctuations of the intermediate and low density IGM, arising naturally in the hierarchical process of structure formation. A critical test of the nature of the Lyman-α absorbers as proposed by simulations, comes from the determination of their sizes and spatial distribution. Multiple lines of sight offer an invaluable tool to address the spatial distribution of the absorbers, enabling a more direct interpretation of the observed correlations. The interesting range of separations lies about the Jeans scale of the photoionised IGM (~1 arcmin or ~1.4 h-1 comoving Mpc at z~2). At this scale there should be a transition from a smooth gas distribution, which produces nearly identical absorption features in neighbouring lines of sight, to a correlated density distribution, where the correlation strength decreases with increasing separation of the lines of sight (e.g., Viel et al. 2002). Studies based on the statistics of coincident and anti-coincident absorption lines in adjacent sightlines provided evidence for dimensions of a few hundred kpc(e.g. D'Odorico et al. 1998). The obtained large sizes were conclusive to exclude models of the Lyman-α forest as a population of pressure confined small clouds (e. g., Sargent et al. 1980) or clouds in dark matter mini haloes (e. g., Miralda-Escudé & Rees 1993).

The physics of this highly ionised gas is simple, governed mainly by the Hubble expansion and the gravitational instability. If photoionisation equilibrium is assumed, a mean relation between temperature and over density (δ = ρ/<ρ>), is obtained (Hui & Gnedin 1997): T = T0 δ

γ-1 , where T0 and γ depend on the ionisation history of the Universe (for an early reionisation of HI, γ~1.6). Ricotti, Gendin & Shull (2000) studied the evolution with redshift of the equation of state of the gas and showed that a reionisation of HeII occurring at z ~ 3 would cause a sudden increase in the gas temperature and acorresponding decrease in the value of γ. Observationally, this has been studied mainly by using the distribution of Doppler parameters and column densities of the Lyman-α forest lines (e.g., Schaye et al. 2000; Kim et al. 2002), but also with metal absorptions (e.g., Songaila 1998; Vladilo et al. 2003). Our result supports previous observational evidences of a second reheating of the Universe happening at z~3, most likely due to the reionisation of HeII and it requires confirmation by a larger sample of observed spectra and a set of more refined mock spectra.

The Alcock-Paczynski Test

From the cosmological point of view, one of the most interesting and challenging applications of the kind of calculations carried out in this work is the constraint on the geometry of the Universe (in particular, the estimate of Ω0Λ h

-2) by linking angular separations and redshift differences in the hypothesis that theobserved correlation properties are isotropic.This test, proposed by Alcock & Paczynski (1979), has the great advantage of beingindependent of the evolutionary effects of the observed objects. Its application to the Lyman-α forest (proposed initially by McDonald & Miralda-Escude 1999; Hui, Stebbins & Burles 1999) allows a determination of Ω0Λ in a different redshift range then that traced by the cosmic microwave background (CMB). However, about 13(θ/(1 arcmin))2 QSO pairs with separation < θ (McDonald 2003) are needed to obtain a measure of the cosmological parameters as accurate as those recently produced by the WMAP team (Spergel et al. 2003). This is the long term goal of this project (see Rollinde et al. 2003; Coppolani et al. 2005 for computation of Ω0Λ with sets of low resolution spectra of QSO pairs).

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(1) INAF – Trieste, Italy – (2) Institute of Astronomy, Cambridge, UK – (3) Univ. of Trieste, Italy – (4) INAF -Firenze, Italy – (5) Australia Telescope National Facility, Epping, Australia – (6) Univ. de Chile, Santiago, Chile – (7) Univ. of Durham, Durham, UK

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