Escape fraction of ionizing photons from high-redshift galaxies in cosmological SPH simulations

Hidenobu Yajima 1 Jun-Hwan Choi 0 Kentaro Nagamine 0 0 Department of Physics and Astronomy, University of Nevada , Las Vegas, 4505 S. Maryland Pkwy, Las Vegas, NV 89154-4002, USA 1 Department of Astronomy and Astrophysics, Pennsylvania State University , 525 Davey Lab, University Park , PA 16802, USA Combing the three-dimensional radiative transfer (RT) calculation and cosmological smoothed particle hydrodynamics (SPH) simulations, we study the escape fraction of ionizing photons (f esc) of high-redshift galaxies at z = 3-6. Our simulations cover the halo mass range of Mh = 109-1012 M . We post-process several hundred simulated galaxies with the Authentic Radiative Transfer (ART) code to study the halo mass dependence of f esc. In this paper, we restrict ourselves to the transfer of stellar radiation from local stellar population in each dark matter halo. We find that the average f esc steeply decreases as the halo mass increases, with a large scatter for the lower-mass haloes. The low-mass haloes with Mh 109 M have large values of f esc (with an average of 0.4), whereas the massive haloes with Mh 1011 M show small values of f esc (with an average of 0.07). This is because in our simulations, the massive haloes show more clumpy structure in gas distribution, and the star-forming regions are embedded inside these clumps, making it more difficult for the ionizing photons to escape. On the other hand, in low-mass haloes, there are often conical regions of highly ionized gas due to the shifted location of young star clusters from the centre of dark matter halo, which allows the ionizing photons to escape more easily than in the high-mass haloes. By counting the number of escaped ionizing photons, we show that the star-forming galaxies can ionize the intergalactic medium at z = 3-6. The main contributor to the ionizing photons is the haloes with Mh 1010 M owing to their high f esc. The large dispersion in f esc suggests that there may be various sizes of H II bubbles around the haloes even with the same mass in the early stages of reionization. We also examine the effect of UV background radiation field on f esc using simple, four different treatments of UV background. 1 I N T R O D U C T I O N Observations of cosmic microwave background radiation provides a wealth of information on the cosmic reionization history (e.g. Page et al. 2007; Dunkley et al. 2009). For example, Komatsu et al. (2010) showed that the reionization occurred at z 10.5 assuming an instantaneous reionization scenario. However, the detailed history of reionization and the nature of ionizing sources are not yet fully understood. Since the UV background (UVB) radiation can heat up the interstellar medium (ISM) to 104 K and disturb star formation, UVB coupled with the ionization history of the universe significantly influences the galaxy formation (e.g. Susa & Umemura 2000; Umemura, Nakamoto & Susa 2001; Susa & Umemura 2004; Okamoto, Gao & Theuns 2008; Hasegawa, Umemura & Kitayama 2009). Therefore it is very important to study the UVB intensity and the nature of ionizing sources. Haardt & Madau (1996) pointed out that the UVB is dominated by quasars at z < 4. Using the SDSS sample, Fan et al. (2001) showed that the bright-end slope of the quasar luminosity function at z 4 are considerably steeper than that at lower redshifts, and concluded that the quasars cannot maintain the ionization of IGM at z 4. Subsequently, much argument have been focused on the possibility that the IGM is ionized mainly by the UV radiation from high-redshift (hereafter high-z) star-forming galaxies (e.g. Fan et al. 2006; Bouwens et al. 2007; Gnedin 2008). The key quantity in determining the IGM ionization rate is the escape fraction of ionizing photons (e.g. Razoumov & Sommer-Larsen 2006; Gnedin, Kravtsov & Chen 2008), which is the number ratio of photons escaping from a galaxy to the intrinsically radiated photons by stars. This parameter controls the contribution to the UVB intensity from star-forming galaxies. In this work, we examine the values of f esc in high-z star-forming galaxies. There are several observational constraints on f esc at z 3. Steidel, Pettini & Adelberger (2001) found f esc,rel 0.5 from the composite spectrum of 29 Lyman Break Galaxies (LBGs) at z 3, where f esc,rel is the relative fraction of escaping Lyman continuum (900 ) photons relative to the fraction of escaping non-ionizing UV (1500 ) photons. It is usually defined as (L1500/L900)int exp 9I0G0M , fesc,rel (F 1500/F 900)obs where (F1500/F900)obs, (L1500/L900)int and I9G00M represent the observed 1500 /900 flux density ratio, the intrinsic 1500 /900 luminosity density ratio and the line-of-sight opacity of the IGM for 900 photons, respectively. Equation (1) compares the observed flux density ratio (corrected for the IGM opacity) with the models of UV spectral energy distribution of star-forming galaxies. Giallongo et al. (2002) and Inoue et al. (2005) estimated the upper limit of f esc,rel 0.10.4 for some LBGs at z 3. Shapley et al. (2006) directly detected the escaped ionizing photons from two LBGs in the SSA22 field at z = 3.1, and estimated the average value of f esc,rel = 0.14. Moreover, Iwata et al. (2009) successfully detected the Lyman continuum emission from 10 Ly emitters (LAEs) and seven LBGs within a sample of 198 LAEs and LBGs in the SSA22 field. They showed that the mean value of f esc,rel for the seven LBGs is 0.11 after correcting for dust extinction, and 0.20 if the IGM absorption is taken into account. In the early theoretical works, some authors studied the f esc with ideally modelled galaxies. For example, Dove & Shull (1994) estimated the f esc of Milky Way type galaxy using a semi-analytic method, and reported f esc 0.07. Ricotti & Shull (2000) investigated the dependence of f esc on various physical quantities, such as the collapse redshift and star formation efficiency using a semianalytic method. Wood & Loeb (2000) and Ciardi, Bianchi & Ferrara (2002) studied the effect of inhomogeneous structure of gas on f esc, and showed that f esc increases in clumpy systems by a factor of >2 than in a homogeneous gas distribution. Dove, Shull & Ferrara (2000) investigated the influence of bubbles made by supernovae on f esc using a semi-analytic method. Using numerical simulations, Fujita et al. (2003) studied the effect of supernovae feedback, and reported a high f esc (>0.2) for a disc galaxy with Mh = 1081010 M . Theoretical studies in a more fully cosmological environment can be performed by combining cosmological hydrodynamic simulations of galaxy formation and a three-dimensional radiative transfer calculation. For example, Yajima et al. (2009, hereafter Y09) post-processed the Eulerian hydrodynamic simulation of Mori & Umemura (2006) with RT, and showed that the galaxies in an isolated halo of Mh = 1011 M can have relatively large values of f esc = 0.170.47. Moreover, they found that f esc decreases gradually as (...truncated)