The effect of photoionization on the cooling rates of enriched, astrophysical plasmas

Robert P. C. Wiersma 1 Joop Schaye 1 Britton D. Smith 0 0 Center for Astrophysics & Space Astronomy, Department of Astrophysical & Planetary Sciences, University of Colorado , Boulder, CO 80309 , USA 1 Leiden Observatory, Leiden University , P.O. Box 9513, 2300 RA Leiden , the Netherlands A B S T R A C T Radiative cooling is central to a wide range of astrophysical problems. Despite its importance, cooling rates are generally computed using very restrictive assumptions, such as collisional ionization equilibrium and solar relative abundances. We simultaneously relax both assumptions and investigate the effects of photoionization of heavy elements by the metagalactic ultraviolet (UV)/X-ray background and of variations in relative abundances on the cooling rates of optically thin gas in ionization equilibrium. We find that photoionization by the metagalactic background radiation reduces the net cooling rates by up to an order of magnitude for gas densities and temperatures typical of the shock-heated intergalactic medium and protogalaxies (104 K T 106 K, / 100). In addition, photoionization changes the relative contributions of different elements to the cooling rates. We conclude that photoionization by both the ionizing background and heavy elements needs to be taken into account in order for the cooling rates to be correct to an order of magnitude. Moreover, if the rates need to be known to better than a factor of a few, then departures of the relative abundances from solar need to be taken into account. We propose a method to compute cooling rates on an element-by-element basis by interpolating pre-computed tables that take photoionization into account. We provide such tables for a popular model of the evolving UV/X-ray background radiation, computed using the photoionization package CLOUDY. 1 I N T R O D U C T I O N Dissipation of energy via radiative cooling plays a central role in many different astrophysical contexts. In general, the cooling rate depends on a large number of parameters, such as the gas density, temperature, chemical composition, ionization balance and the radiation field. In the absence of radiation, however, the equilibrium ionization balance depends only on the temperature. In that case, the cooling rate in the low-density regime, which is dominated by collisional processes, is simply proportional to the gas density squared, for a given composition. Thus, the cooling rates for a plasma in collisional ionization equilibrium (CIE) can be conveniently tabulated as a function of the temperature and composition (metallicity) of the gas (e.g. Cox & Tucker 1969; Raymond, Cox & Smith 1976; Shull & van Steenberg 1982; Gaetz & Salpeter 1983; Boehringer & Hensler 1989; Sutherland & Dopita 1993; Landi & Landini 1999; Benjamin, Benson & Cox 2001; Gnat & Sternberg 2007; Smith, Sigurdsson & Abel 2008); and such tables are widely used for a large variety of problems. Although it is convenient to ignore radiation when calculating cooling rates, radiation is generally important for the thermal and ionization state of astrophysical plasmas. For example, Efstathiou (1992) investigated the effect of the extragalactic ultraviolet (UV) background on the cooling rates for gas of primordial composition (in practice, this means a pure H/He plasma) and found that including photoionization can suppress the cooling rates of gas in the temperature range T 104 105 K by a large factor. Although the effects of radiation are often taken into account for gas of primordial composition, photoionization of heavy elements is usually ignored in the calculation of cooling rates (but see Leonard 1998; Cen et al. 2001; Benson et al. 2002). In this paper, we will investigate the dependence of cooling rates of gas enriched with metals on the presence of ionizing radiation, focusing on the temperature range T 104 108 K and optically thin plasmas. We will show that, as is the case for gas of primordial composition (Efstathiou 1992), photoionization can suppress the metallic cooling rates by a large factor. Moreover, the suppression of the cooling rate is significant up to much higher temperatures than for the primordial case. We will also investigate the relative contributions of various elements to the cooling rates. If the relative abundances are similar to solar, then oxygen, neon and iron dominate the cooling in the temperature range T 104 107 K. However, we will show that the relative contributions of different elements to the cooling rate are sensitive to the presence of ionizing radiation. Although we will illustrate the results using densities and radiation fields that are relevant for studies of galaxy formation and the intergalactic medium (IGM), the conclusion that photoionization significantly reduces the cooling rates of enriched gas is valid for a large variety of astrophysical problems. For example, for T 105 K and 106 K the reduction of metal-line cooling rates is significant as long as the dimensionless ionization parameter1 U 103 and 101, respectively. We will focus on the temperature range 104 108 K because gas in this temperature range is usually optically thin and because the effects of photoionization are generally unimportant at higher temperatures. Tables containing cooling rates and several other useful quantities as a function of density, temperature, redshift and composition, appropriate for gas exposed to the models for the evolving metagalactic UV/X-ray background of Haardt & Madau (2001), are available on the following web site: http://www.strw.leidenuniv.nl/WSS08/. The web site also contains a number of videos that illustrate the dependence of the cooling rates on various parameters. This paper is organized as follows. In Section 2, we present our method for calculating element-by-element cooling rates including photoionization and we compare the limiting case of CIE to results taken from the literature. Section 3 shows how metals and ionizing radiation affect the cooling rates. Section 4 demonstrates the importance for the low-redshift shock-heated IGM, which is thought to contain most of the baryons. In this section, we also illustrate the effect of changing the intensity and spectral shape of the ionizing radiation. We investigate the effect of photoionization on the relative contributions of individual elements in Section 5 and we summarize and discuss our conclusions in Section 6. Throughout this paper, we use the cosmological parameters from Komatsu et al. (2008): ( m, , b, h) = (0.279, 0.721, 0.0462, 0.701) and a primordial helium mass fraction XHe = 0.248. Densities will be expressed both as proper hydrogen number densities nH and density contrasts b/ b 1, where b is the cosmic mean baryon density. The two are related by nH 1.9 107 cm3 (1 + )(1 + z)3 2 M E T H O D All radiative cooling and heating rates were computed by running large grids of photoionization models using the publicly available photoionization package CLOUDY2 (ver (...truncated)