Non-equilibrium ionization states and cooling rates of photoionized enriched gas

Evgenii O. Vasiliev 0 0 Institute of Physics, Southern Federal University , Stachki Ave. 194, Rostov-on-Don 344090 , Russia A B S T R A C T Non-equilibrium (time-dependent) cooling rates and ionization state calculations are presented for low-density gas enriched with heavy elements (metals) and photoionized by external ultraviolet/X-ray radiation. We consider a wide range of gas densities and metallicities and also two types of external radiation field: a power-law and an extragalactic background spectra. We have found that both cooling efficiencies and ionic composition of enriched photoionized gas depend significantly on the gas metallicity and density, the flux amplitude and the shape of ionizing radiation spectrum. The cooling rates and ionic composition of the gas in non-equilibrium photoionization models differ strongly (by a factor of several) from those in photoequilibrium due to overionization of the ionic states in the non-equilibrium case. The difference is maximal at low values of the ionization parameter and similar in magnitude to that between the equilibrium and non-equilibrium cooling rates in the collisionally controlled gas. In general, the non-equilibrium effects are notable at T 106 K. In this temperature range, the extent of mismatch between the two ionic states and their ratios between the photoequilibrium and the photo-non-equilibrium models reach a factor of several. The net result is that the time-dependent energy losses due to each chemical element (i.e. the contributions to the total cooling rate) differ significantly from the photoequilibrium ones. We advocate the use of non-equilibrium cooling rates and ionic states for gas with near-solar (and above) metallicity exposed to an arbitrary ionizing radiation flux. We provide a parameter space (in terms of temperature, density, metallicity and ionizing radiation flux), where the non-equilibrium cooling rates are to be used. More quantitatively, the non-equilibrium collisional cooling rates and ionization states are a better choice for the ionization parameter log U 5. The difference between the photoequilibrium and the photo-non-equilibrium decreases with the ionization parameter growth, and the photoequilibrium can be used for ionization parameter as high as log U 2 for Z 102 Z and log U 0 for Z Z . Thus, the non-equilibrium calculations should be used for the ionization parameter range between the above-mentioned values. In general, where the physical conditions favour collisional ionization, the non-equilibrium (photo)ionization calculations should be conducted. - Recent observations of heavy elements (metals) in the intergalactic medium (IGM) give rich information about star formation and the enrichment history of the Universe (Madau et al. 1996; Pettini 1999; Schaye et al. 2003; Nicastro et al. 2005; Simcoe et al. 2006; Danforth & Shull 2008). In order to understand these observations, it is necessary to know which processes are responsible for the observed ionic composition and thermal state of the IGM. In the absence of ionizing background radiation, these processes are controlled by collisions and determined by gas metallicity and temperature. However, when galaxies and quasars form, they produce strong ionizing photons (Haardt & Madau 1996, 2001; Miniati et al. 2004; Faucher-Giguere et al. 2009). Therefore, photoionization and photoheating are to be taken into account. Calculations of the cooling rates of astrophysical plasma in the collisional ionization equilibrium (CIE) were performed by many authors (House 1964; Cox & Tucker 1969; Raymond, Cox & Smith 1976; Shull & van Steenberg 1982; Gaetz & Salpeter 1983; B ohringer & Hensler 1989; Sutherland & Dopita 1993; Landi & Landini 1999; Benjamin, Benson & Cox 2001; Bryans et al. 2006). However, calculations of the time-dependent ionization of metals and associated radiative cooling showed significant deviations from the CIE states (Kafatos 1973; Shapiro & Moore 1976; Edgar & Chevalier 1986; Schmutzler & Tscharnuter 1993; Sutherland & Dopita 1993; Gnat & Sternberg 2007). In some conditions, ionizing radiation can be important for the thermal and ionization states of primordial and enriched gas. Efstathiou (1992) showed that the presence of UV radiation can strongly suppress the cooling rate of primordial gas. In the photoionization equilibrium case, Wiersma, Schaye & Smith (2009) came to a similar conclusion for enriched gas exposed to the external ionizing radiation. It is obvious that ionizing radiation forces the ionic composition of gas to settle on to photoequilibrium. However, during transition from a pure collisional to a photoequilibrium case the non-equilibrium effects are expected to play a role. In general, numerical simulations of metal ionization states in the IGM should take into account the effects of ionizing background. However, this requires tracing a huge number of metal species and their ionization states, as well as complex calculations of the cooling and heating rates of the enriched photoionized gas. Therefore, simulations often consider either a limited number of metal ionization states or cooling rates of collisionally ionized gas. For instance, Raga, Mellema & Lundqvist (1997) studied a radiative bow shock using a limited ionization and cooling network, and Yoshikawa & Sasaki (2006) used the CIE cooling rates to study the ionic composition of a warm-hot intergalactic medium. Hughes & Singh (1994) presented a comprehensive non-equilibrium ionization analysis of the supernova remnant. Recently, self-consistent calculations were successfully performed in one dimension. Gnat & Sternberg (2004) studied the metals photoionization structures of pressure-supported gas clouds in dark matter minihaloes and lately Gnat & Sternberg (2009) considered the ionic composition of gas in post-shock cooling layers behind fast radiative shock waves. More recently, threedimensional non-equilibrium modelling of the interstellar medium were performed by de Avillez & Breitschwerdt (2010a,b). They considered the evolution of the turbulent magnetized interstellar medium taking into account the time-dependent ionization of 10 main chemical elements. Here, we study how a non-equilibrium state affects the ionic composition and cooling rates of an enriched photoionized gas, and analyse a parameter space (i.e. temperature, density, metallicity and ionizing radiation flux) where the effects of the non-equilibrium state should be taken into account. In the last decade studies of the intergalactic gas became very intensive. Among the most interesting observations are the conclusions about the total mass of baryons in the Universe and its metal fraction. Fukugita & Peebles (2004) have estimated the cosmic baryon budget and found that less than 10 per cent of the total baryonic content in the Universe is locked in the form of collapsed objects (stars, galaxies, groups). More recently, Danforth & Shull (2008) found that approximately 50 per (...truncated)