Dependences of QSO Lya absorption line statistics on cosmological parameters

We have performed high-resolution hydrodynamic simulations of the Lya forest in a variety of popular cold dark matter dominated cosmologies, including a low density and a vacuumdominated model. The ̄uctuation amplitude of these models is chosen to match the observed abundance of galaxy clusters at low redshift. We assume that the intergalactic medium is photoionized and photoheated by a uniform ultraviolet background with the required amplitude to give the observed mean hydrogen absorption. We produce simulated spectra, analyse them by ®tting Voigt pro®les and compare line statistics with those obtained from high-resolution observations. All models give column density distributions in good agreement with observations. However, the distribution of line widths (the b-parameter distribution) re ̄ects differences in the temperature of the intergalactic medium between the models, with colder models producing more narrow lines. All the models with a low baryon density, Qbh 2 ˆ 0:0125, are too cold to produce a b-parameter distribution in agreement with observations. Models with a higher baryon density, Qbh 2 ˆ 0:025, are hotter and provide better ®ts. Peculiar velocities contribute signi®cantly to the line widths in models with low matter density, and this improves the agreement with observations further. We brie ̄y discuss alternative mechanisms for reconciling the simulations with the observed b-parameter distributions. Key words: hydrodynamics ± quasars: absorption lines ± cosmology: theory ± large-scale structure of Universe. 1 I N T R O D U C T I O N Neutral hydrogen in the intergalactic medium produces a forest of Lya absorption lines blueward of the Lya emission line in quasar spectra (Bahcall & Salpeter 1965; Gunn & Peterson 1965). Hydrodynamic simulations of hierarchical structure formation in a cold dark matter (CDM) dominated universe have been shown to be remarkably successful in reproducing a variety of properties of the observed forest (Cen et al. 1994; Zhang, Anninos & Norman 1995; Miralda-Escude et al. 1996; Hernquist et al. 1996; Wadsley & Bond 1996; Zhang et al 1997; Theuns, Leonard & Efstathiou 1998a; Theuns et al. 1998b; Dave et al. 1998; Bryan et al. 1998). The simulations show that the weaker Lya lines (neutral hydrogen column density NH i #10 14 cm) are predominantly produced in the ®lamentary and sheet-like structures that form naturally in this structure formation scenario. Higher column density lines occur where the line of sight intersects a halo. These models assume that the intergalactic medium (IGM) is photoionized and photoheated by ultraviolet (UV) light from quasars. The characteristic break in the rate of evolution of the number of lines below a redshift ,1:7, as observed by the Hubble Space Telescope, can then be explained by the decrease in the intensity of this ionizing background, itself a consequence of the rapid decline in quasar numbers towards lower redshifts (Theuns et al. 1998a; Dave et al. 1998). While the ®rst simulations showed good agreement with the observed line statistics, more detailed studies at higher numerical resolution in a standard CDM universe produced a larger fraction of narrow lines than are observed (Theuns et al. 1998b; Bryan et al. 1998). Theuns et al. suggested that an increase in temperature of the IGM might broaden the absorption lines suf®ciently to improve the agreement with observations. A higher gas temperature leads to more thermal broadening and in addition increases the Jeans mass. At low redshifts, the temperature of the gas responsible for the majority of Lya lines is determined by the balance between adiabatic cooling and photoheating. This causes the gas temperature to be a function of density, and this `equation of state' is well approximated by a power law, T ˆ T0…1 ‡ d† , where d is the gas overdensity (Hui & Gnedin 1997). T0 can be made higher by Mon. Not. R. Astron. Soc. 303, L58±L62 (1999) q 1999 RAS *Present address: Max-Planck-Institut fuÈr Astrophysik, Karl-Schwarzschild-Strasse 1, D-85740 Garching, Germany. increasing the photoheating rate, or by heating the gas for longer by increasing the age of the universe. The ®rst can be achieved by increasing the baryon density Qbh , the latter by decreasing the matter density Qm. Using some simplifying assumptions, Hui & Gnedin (1997) obtain the scaling T0 ~ ‰Qbh =…Qmh 2 † 1=2 Š 1=1:7 : …1† Increasing Qbh 2 by a factor 2 and using Qm ˆ 0:3 instead of 1 increases T0 by a factor $2, which might be suf®cient to obtain agreement with observations. In this Letter we use high-resolution hydrodynamic simulations to investigate the dependence of the b-parameter distribution on cosmological parameters, for a given reionization history. This complements the work of Haehnelt & Steinmetz (1998), who quanti®ed the dependence of the b-parameter distribution on the reionization history, for a critical density universe. 2 S I M U L AT I O N We have simulated six different cosmological models, characterized by their total matter density Qm, the value of the cosmological constant QL, the rms of mass ̄uctuations in spheres of 8h ÿ1 Mpc, j8, the baryon density Qbh 2 and the present-day value of the Hubble constant, H0 ˆ 100h km s Mpc. The parameters for these models are summarized in Table 1. Note that the Sb, Ob and Lb models have a baryon density slightly higher than the value Qbh 2 ˆ 0:0193 6 0:0014, advocated by Burles & Tytler (1998) from measurements of the deuterium abundance in quasar spectra. Rauch et al. (1997) required a similarly high value Qbh 2 $ 0:017 in order to make the measured ̄ux decrement of the Lya forest consistent with the observed intensity of ionizing photons from quasars. We model the evolution of a periodic, cubical region of the universe of comoving size 2.5hMpc. The code used is based on a hierarchical P3M implementation (Couchman 1991) for gravity and smoothed particle hydrodynamics (SPH, Lucy 1977; Gingold & Monaghan 1977, see e.g. Monaghan 1992 for a review) for hydrodynamics. It is a hybrid between the hydra code of Couchman, Thomas & Pearce (1995) and the apmsph code, which were described in detail in Theuns et al. (1998b). In particular, we use the apmsph method for consistently computing SPH densities for particles in underdense regions. These simulations use 64 particles of each species, so the SPH particle masses are 1:65 ́ 10 …Qbh =0:0125†…h=0:5†M( and the CDM particles are more massive by a factor QCDM=Qb. This resolution is suf®cient to simulate linewidths reliably (Theuns et al. 1998; note that numerical convergence will be even better in the hotter simulations). The simulations of Bryan et al. (1998) indicate that the absence of long waves will produce a small, but for our purposes unimportant, underestimate of the widths of the absorption pro®les. All our simulations were run with the same initial phases to minimize cosmic variance when comparing the different models. We assume that the IGM is ionized and photoheated by an imposed uniform background of UV photons that originate from quasars, as computed by Haardt & Madau (1996). This ̄ux is redshift dependent, due to the evolution of the quasar luminosity function. Haardt & Madau (1996) give two ®ts to the hydrogen ionization rate GH i as a function of redshift. We have used their q0 ˆ 0:5 ®t for the critical density models and their q0 ˆ 0:1 ®t for the open ones. This amplitude of the ̄ux is indicated as HM in the GH i column of Table 1. In addition, for the low Qbh 2 models, we have divided the ionizing ̄ux by two, indicated as HM/2 . The dependence on q0 re ̄ects small differences in the completeness corrections of the observed quasar luminosity functions and is relatively unimportant for the simulations described here. The detailed expressions for the heating and cooling rates as a function of temperature and ionizing ̄ux are taken from Cen (1992) with some minor modi®cations (Theuns et al. 1998). Our analysis differs slightly from that in Theuns et al. in that we do not impose thermal equilibrium but solve the rate equations to track the abundances of H i , H ii and He i , He ii and He iii . We assume a helium abundance of Y ˆ 0:24 by mass. We have used cmbfast (Seljak & Zaldarriaga 1996) to compute the linear matter transfer function for each model. The amplitude of the transfer function is normalized to the observed abundance of galaxy clusters at z ˆ 0 using the ®ts j8 ˆ 0:52Q ÿ0:46‡0:1Qm m for QL ˆ 0 and j8 ˆ 0:52Q ÿ0:52‡0:13Qm m for QL ˆ 1 ÿ Qm, as computed by Eke, Cole & Frenk (1996). Cosmological dependences of QSO Lya statistics L59 q 1999 RAS, MNRAS 303, L58±L62 Table 1. Models simulated. Name Qm QL j8 Qbh 2 h GH i 1 S 1 0 0.50 0.0125 0.5 HM/2 2 O 0.3 0 0.85 0.0125 0.65 HM/2 3 L 0.3 0.7 0.90 0.0125 0.65 HM/2 4 Sb 1 0 0.50 0.025 0.5 HM 5 Ob 0.3 0 0.85 0.025 0.65 HM 6 Lb 0.3 0.7 0.90 0.025 0.65 HM Figure 1. Comparison between observed and simulated column density distributions at mean redshifts of 3 (top panel) and 2 (bottom panel). The data in the top panel are from Kim et al. (1997, hereafter KHCS, Å z ˆ 3:35) and Hu et al. (1995, hereafter HKCSR, Å z ˆ 2:9) and in the bottom panel from KHCS (Å z ˆ 2:3) and from Petitjean et al. (1993, hereafter PWRCL, Å z ˆ 2:0). The different models are indicated in the panel.