Models Based on Cosmological Simulations

Tasitsiomi 2006 present results from a zoom-in simulation of an individual halo (stellar mass 10¹⁰ M⊙) with an effective resolution of 29 pc at 𝑧∼8 in a small cosmological volume. They include the transfer of Lyman-𝛼 photons, but no continuum radiation and no dust. The source of the Lyman-𝛼 photons is assumed to be predominantly recombination after ionization by Lyman continuum photons from young, hot stars.

They inject the Lyman-𝛼 photons spatially distributed in the cells that have an

Figure 3.10: Left: spectrum of the emitter studied by Tasitsiomi 2006, with (dotted) and without (solid line) attenuation by the neutral IGM. The dashed line shows the spectrum with attenuation of IGM only in the blue part of the spectrum, the long-dashed line indicates the rest-frame line center. Right: surface brightness map of the emitter. Reproduced by the permission of the AAS (Figure 10 in Tasitsiomi 2006)

intrinsic luminosity above a certain threshold to reduce computation time. They calculate the emerging spectrum integrated over all lines of sight, and find it to be nearly symmetric and double-peaked with hints of a slightly enhanced blue peak resulting from gas streaming into the halo as explained in the first section of this chapter. We show the spectrum emerging from the emitter in figure 3.10 (solid line).

To simulate observations of an object at this redshift, one has to correct for the effect of the neutral hydrogen between the object and the observer. Before complete reionization, this is called the Gunn-Peterson trough (Gunn & Peterson 1965) known from quasar spectra (e.g Becker et al. 2001). Effectively, it scatters all photons bluewards of the line center out of the line of sight since the Hubble flow will shift these photons in resonance with the neutral IGM after traveling some distance from the emitter. Partially, this will also occur for the red side of the spectrum due to the (thermal) motions of the intervening gas. The attenuated spectrum is shown in figure 3.10 (dotted line). Tasitsiomi 2006 note that the effect of the inflowing gas on the shape of the spectrum is probably quite low because the column densities are so high that a velocity shift of a few hundred km/s does not significantly reduce the optical depth for blue photons.

Laursen et al. 2009 present a set of 9 zoom-in simulations¹of halos taken from

Figure 3.11: Surface brightness map for one of the emitters studied by Laursen et al. 2009.

Left: excluding dust effects. Right: including dust effects. Reprinted with permission (c) AAS (Figure 4 in Laursen et al. 2009)

1 We skip the discussion of Laursen & Sommer-Larsen 2007 since Laursen et al. 2009 directly extends this work. Laursen & Sommer-Larsen 2007 present calculations for one LAE without dust.

3.3 Towards Realistic LAEs 53

Figure 3.12: Spectra of the emitters studied in Laursen et al. 2009 for both a dust-free case (dotted) and including dust (solid lines). Reprinted with permission (c) AAS (Figure 10 in Laursen et al. 2009)

a cosmological volume with stellar masses of 6×10⁶ - 3×10¹⁰ M⊙ and effective resolutions of 491 to 137 pc at 𝑧 = 3.6. They do not only include Lyman-𝛼 photons from recombination, but also from gravitational cooling and the UV background.

However, 90% of the Lyman-𝛼 photons are generated by recombination of Lyman-continuum photons emitted by young stars. In figure 3.12, we show the resulting spectra from all nine studied emitters, both including effects of dust on the radiative transfer (solid lines) and excluding it (dotted lines). They find the counter-intuitive result that while the dust cross section for Lyman-𝛼 photons is independent of frequency, the effect of dust on the emerging spectrum is not: Dust tends to remove

more flux far away from the line center than near the line center. The reason is the interplay of the absorption by dust with the scattering on neutral hydrogen. Photons that diffuse far out into the wings are those residing in dense environments where the optical depth emerging from hydrogen is high. These photons are therefore the ones that are scattered often and have large path lengths, which makes them subject to severe attenuation. On the other hand, photons escaping at the line center are typically located in low-density environments and escape after fewer scatterings, rendering absorption less probable. Additionally, dust is mostly present near the dense regions where it was produced. In figure 3.11, we show a surface brightness plot of the emerging Lyman-𝛼 radiation of a single emitter without (left) and with dust (right) for illustration. They find an escape fraction of Lyman-𝛼 of about unity for the two emitters with less than 10¹⁰ M^⊙ dynamical mass, and about 30% escape fraction above this mass, with a trend to lower escape fraction for higher mass.

Additionally, Laursen et al. 2009 find a dependency of flux on orientation of up to a factor of 4.

Yajima et al. 2012 present simulations of a cosmological volume with a resolution of 342 pc and simulate radiative transfer for the 10 most massive galaxies at six redshifts between 3.1 and 10.2 with stellar masses of about 10¹⁰M⊙ at 𝑧= 3.1. They include Lyman-𝛼 from both recombination and collisional excitation, continuum radiation, ionizing radiation, and dust. The Lyman-𝛼 emissivity here is derived from the ionization state due to the ionizing radiation transport. They find varying EWs (∼ 67-21 Å) and increasing escape fractions (∼ 0.13-0.6) with decreasing redshift, indicating an evolution of the emitters. The Lyman-𝛼 luminosity, however, does evolve only by a factor of 2. Their spectra are typically single-peaked and slightly bluer than the intrinsic Gaussian spectrum, which they consider to be due to strong ionization near the sources and large outflow velocities.

For completeness, we also mention here the work by Barnes et al. 2011 that focuses on Damped Lyman-𝛼 absorbers (DLAs) as a source of extended Lyman-𝛼 emission, employing a cosmological zoom-in simulation of 3 objects at a resolution of 514 pc (𝑧∼3). They only follow Lyman-𝛼 photons (modeled as central point source) and do not include dust. They find the absorption region of the objects to be generally smaller than the Lyman-𝛼 emission region, with the central source illuminating neutral clouds further outside. Additionally, they find a dependency of the Lyman-𝛼 properties on angle of observation.

It is worth noting that while the publications above partially comment on anisotropic

3.3 Towards Realistic LAEs 55

escape (e.g Barnes et al. 2011; Laursen et al. 2009; Yajima et al. 2012), they do not focus on it. To investigate the effects of anisotropies in the ISM and disentangling them from effects of the circumgalactic medium (CGM) and IGM, one can use simulations of isolated galaxies.