Lyα EMISSION FROM COSMIC STRUCTURE. I. FLUORESCENCE

The machinery we develop includes three parts. First, we apply self-shielding corrections given the distribution of SPH particles, either from the output of cosmological simulations or from model structures. Then, the distributions of gas density, temperature, velocity, and emissivity, represented by SPH particles, are put onto a grid. Finally, we apply the Monte Carlo Lyα radiative transfer algorithm of ZM02 to the grid and obtain Lyα images and spectra. The ZM02 algorithm can be applied to systems with arbitrary geometry and arbitrary distributions of gas density, temperature, and velocity. It is modified to work in conjunction with the gas distribution prepared by the first two parts of the machinery. We give a brief review of the ZM02 algorithm below and describe the first two parts of the machinery in detail in the next two subsections.

In the ZM02 Monte Carlo algorithm, for each photon, the scattering process is generally described by three steps: (1) the initial position of each Lyα photon is generated based upon the emissivity distribution in the gas while its initial direction is randomly drawn; (2) the optical depth, τ, through which the photon will travel before scattering is drawn from an exponential distribution exp(−τ), and the spatial location for the scattering at this optical depth is determined along the initial direction from the neutral hydrogen distribution (density, temperature, and velocity) and the scattering cross section; and (3) the thermal velocity of the scattering atom is determined, and the new frequency and direction of the photon are calculated. In general, we use the term "scattering" to refer to this process of absorption and re-emission. In the rest frame of the absorbing atom, the Lyα photon is re-emitted with an unchanged frequency, except for the recoil effect (which the code accounts for but is negligibly small for our applications). The calculation of scattering is performed in the rest frame of the atom and the frequency and direction of the scattered photon are transferred back to the laboratory frame. When calculating the photon-free path, the bulk motion (fluid velocity) of the medium is taken into account by using the frequency in the fluid frame to compute the (thermally broadened) scattering cross section. With the new frequency and direction, steps (2) and (3) are repeated until the photon escapes the system.

To generate the image of the Lyα emission, a fixed direction of observation is chosen, and the output of the computation is stored in a 3D array containing the observed Lyα spectrum at each projected spatial position. At each photon scattering, the probability that the photon escapes along the chosen direction of observation is calculated, and this probability is added to the pixel in the 3D array corresponding to the projected position and frequency of the photon. The scattering of Lyα photons can be divided into two regimes. Around the line center, the scattering cross section has a thermal core with high amplitude, and at large frequency offsets, the cross section follows the Lorentz wing. For Lyα scatterings in a medium with high optical depth, the frequency of a Lyα photon changes back and forth around the line center ("core" scatterings) with little change in its spatial position, until it suffers a scattering that leads to a large frequency jump that shifts it out of the core regime. To avoid spending excessive computational time performing the core scatterings with little spatial diffusion, we introduce a numerical acceleration scheme to skip the core scatterings. In the fluid frame, if the absolute value of the frequency offset from the line center ν₀ is within q times (σ/c)ν₀ before scattering, where σ is the 1D thermal velocity dispersion of the hydrogen atoms and q is a positive number, we draw a frequency offset directly from a distribution to assign the frequency after scattering. This distribution is a Gaussian distribution of width (σ/c)ν₀ with the central ±q(σ/c)ν₀ part excluded. The photon then travels with this new frequency until the next scattering. In our applications, the acceleration scheme is invoked only if the line-center optical depth across the grid cell (see Section 2.3) exceeds 10³. We take q = 3 and find that choosing it to be smaller does not affect the final spectra. We also tested the effect of using the acceleration scheme advocated by Tasitsiomi (2006), which assumes an optical-depth dependent core width. We find that adopting that scheme does not have noticeable effects in the results of our application here, and we therefore use our constant core width approach.

As discussed in Section 1, we apply our machinery to analytically specified, isolated gas clouds and to gas distributions extracted from SPH simulations. The only difference between our two configurations (in terms of code operation) is the setup of the gas particle properties. Once these are determined from the cosmological or analytic density field, we proceed in exactly the same manner for both cases. We describe our procedure for determining the gas properties below.

In the SPH technique, the density field is represented by discrete particles with an extent determined by a 3D kernel or smoothing length (Monaghan & Lattanzio 1985). The smoothing lengths of the particles are chosen to overlap a fixed number of particles to ensure accurate representation of the fluid. Each particle has an associated temperature and velocity that capture the (continuous) properties of the fluid.

In our cosmological SPH simulation, particles are exposed to a uniform photoionizing background in the approximation that all of the gas is optically thin (Katz et al. 1996). In reality, however, some of the gas is optically thick and should be self-shielded. Accounting for the self-shielding effect is particularly important for the Lyα emission signature, a signature that critically depends on the recombination rate and, therefore, on the distribution of ionized and neutral gas. We introduce an algorithm to perform the self-shielding correction a posteriori to the neutral fractions of particles of gas experiencing illumination by either the uniform UV background or a local ionizing source.

We note that because of this self-shielding correction, if simulation temperatures were directly adopted, they would also be too high in general, but specifically in dense regions. We make the following correction for this effect: for particles with hydrogen number densities n_H>1 × 10⁻³ cm⁻³ and temperatures T < 5 × 10⁴ K, we set the particle temperature to T_corr = 10⁴ K (we refer readers to Appendix C for details motivating this choice). Particles with temperatures in excess of T = 5 × 10⁴ K have been shock-heated, and these high temperatures are thought to be more robust, so we do not modify them. We calculate neutral fractions using these revised temperatures including photo- and collisional ionization of the gas. We do not alter the simulation temperatures when running the scattering calculation. We discuss the effects of adopting the simulation temperatures directly in Appendix C. The self-shielding correction is performed directly on the particles, rather than on a grid, to retain the full resolution in the SPH gas distribution.

For all of our calculations, we adopt a power-law spectrum for the ionizing background. To make predictions for fluorescence in the presence of both the UVB and a local ionizing source, we have run additional cases in which we have placed a bright quasar at different locations relative to the gas distribution. We assume that the quasar also has a power-law ionizing spectrum and emits isotropically.

We correct for the effect of self-shielding on a particle-by-particle basis by computing for each particle the optical depth contributed by all particles that lie within three smoothing lengths, h_s, of the sightline from each particle along the six principal directions (±x, ± y, and ±z) of the box (plus the additional quasar direction when the quasar is present). For computational convenience, we use the equivalent Gaussian form of the kernel for our calculations; however, the simulation is run with a cubic spline kernel. The contribution of a particle's density to the optical depth outside of three smoothing lengths is negligible. Because we are primarily interested in the transition layers between optically thick and thin regimes in a given structure, we must further correct the optical depth to account for the density gradient across a particle. We describe our procedure and tests for this in detail in Appendix A for the interested reader; including the density gradient makes a critical difference to the accuracy of the result. The average of the attenuated UVB intensity over the six directions is adopted as the mean intensity at the center of the particle. At this position, the neutral hydrogen fraction is determined through photoionization equilibrium. For the case of illumination by a quasar, which can be put at any reasonable position, the attenuated ionizing flux from the quasar's direction is also calculated and added to the photoionization term for the neutral hydrogen determination. Since each particle's neutral fraction changes via this procedure, we carry it out iteratively until achieving a fractional convergence of 10⁻² between the old and new neutral fractions for the most discrepant particle in the region. The code for the self-shielding correction can thus deal with the general case of photoionization from UVB and/or a local ionizing source.

For particles with ionizing τ ∼ 1 we are particularly sensitive to the resolution of our underlying simulation. We correct the optical depths for particles as described in Appendix A. This correction ensures an accurate representation of both the density field and the neutral fractions of particles throughout the box. However, in the case of quasar-induced illumination, the resolution of our simulations is simply not sufficient as detailed in Appendix A. These calculations should be regarded as lower limits to the possible detectable emission. For the purposes of applying the Lyα transfer code, we represent the corrected gas distributions from particles with a regular grid as we describe below.

To conveniently apply the scattering code, we resample the SPH output at a fixed redshift onto a 3D grid. In each grid cell, the quantities to be determined from the particle distribution are the neutral hydrogen density, the emissivity, the temperature, and the fluid velocity.

For the neutral density ρ_cell and emissivity _cell in a cell, we determine the fraction of neutral mass and Lyα luminosity of each particle that falls into the cell according to the SPH profile of each particle and add contributions from all relevant particles. We have

$$\begin{equation} \rho _{\rm cell} =\frac{\sum _{i=1}^{N_p} m_{{\rm neut},i} K_i}{V_{\rm cell}} \end{equation} \tag{ 3 }$$

and

$$\begin{equation} \epsilon _{\rm cell} =\frac{\sum _{i=1}^{N_p} l_i K_i}{V_{\rm cell}}, \end{equation} \tag{ 4 }$$

where N_p is the number of particles contributing to the cell under consideration, V_cell is the volume of the cell, m_neut,i and l_i are the neutral hydrogen mass and Lyα luminosity of the i-th particle, and K_i is the fraction of the particle that overlaps the cell based on its SPH kernel (Equation (14) of Katz et al. 1996). The luminosity of a particle is determined from the emissivity at the particle position (defined as 0.66 times the ionization rate at the location of the particle) and its volume.

Only the distribution of neutral hydrogen is important for Lyα scattering. Therefore, for the temperature or fluid velocity in each cell, we calculate the neutral-mass-weighted average, that is

$$\begin{equation} Q_{\rm cell} =\frac{\sum _{i=1}^{N_p} m_{{\rm neut},i} K_i Q_i}{\sum _{i=1}^{N_p} m_{{\rm neut},i} K_i}, \end{equation} \tag{ 5 }$$

where Q is either the temperature T or one of the three components (v_x, v_y, v_z) of the bulk velocity. The bulk velocity of each particle is the sum of its peculiar and the Hubble flow velocity ${\bf v}_{H} = H{\bf {r}}$ (referenced to the center of the box).

To perform the Lyα scattering calculation, we must represent the emissivity with a finite number of photons and then "launch" these photons in the gas distribution. We could do this in a variety of ways: for example, we could launch photons with a number in proportion to , or launch a single photon per cell and weight these photons by . We choose an intermediate course to efficiently sample the emissivity distribution while minimizing computation time. We map the emissivity, , of a cell to the number, N_γ, of photons launched from the cell through the monotonic function G(),

$$\begin{equation} G(\epsilon) = \left\lbrace \begin{array}{@{}ll} f \epsilon /\epsilon _{\rm crit}, & {\rm {if}}\ \epsilon /\epsilon _{\rm crit} \le N_{\rm tr},\\ f N_{\rm tr} \log _{N_{\rm tr}}(\epsilon /\epsilon _{\rm crit}), & {\rm {if}}\ \epsilon /\epsilon _{\rm crit} > N_{\rm tr}. \end{array} \right. \end{equation} \tag{ 6 }$$

The values of _crit and f determine the number of photons launched given the gas distribution and grid size. In practice, we choose _crit such that we draw a sufficient number of photons for a fiducial grid resolution (e.g., 32³) with f = 1. We scale f in proportion to the grid resolution, N_grid, as N⁻³_grid for other resolutions. After exploring several schemes for photon launching, we choose this one with N_tr = 10 for convenience and speed of computation, i.e., precision of recovery of the Lya image with minimal computing time. Adopting this scheme, the total number of photons launched from the entire grid is approximately independent of the grid resolution. We note that the two-dimensional (2D) spatial resolution of the Lyα image is always matched to the 3D resolution of the grid.

We weight the photons such that we recover the correct luminosity for each cell. The number N_γ of launched photons from each cell is forced to be an integer. If G() ⩾ 1, we round it to the nearest integer N_γ = [G()] and assign a weight V_cell/N_γ. If G() < 1 for a cell, we draw a uniform random deviate between 0 and 1. If the random deviate is greater than G(), no photon is launched from the cell. If it is smaller than G(), a single photon is launched with a weight of V_cell/G(). That is, for these undersampled cells [G() < 1], the single photon drawn carries the luminosity corresponding to 1/G() cells of similar emissivity.

We first examine a z = 3 SIS exposed to a uniform ionizing background. In our calculations, we assume a UVB intensity of the form I_ν = 3 × 10⁻²²(ν_L/ν)erg s^-1 cm⁻² Hz⁻¹ sr⁻¹, where ν_L is the frequency at the Lyman limit. This is close to the spectrum computed by, e.g., Haardt & Madau (1996) in shape and over the frequency range that matters, and is consistent with recent measurements of the cosmic UVB (e.g., Kirkman et al. 2005). We further assume a ΛCDM cosmology with Hubble constant H₀ = 65 km s⁻¹, Ω_m = 0.3, and Ω_Λ = 0.7. The sphere has total mass of 10¹¹ M_☉ and a 5% gas fraction. The virial radius R_vir = 37.4  kpc and virial velocity V_vir = 107 km s⁻¹ are set by the total halo mass (e.g., Padmanabhan 1993). The velocity dispersion (from both thermal and turbulent contributions) of the system is set to be 51 km s⁻¹. The cloud is rotating with a flat rotation curve with a circular velocity equal to V²_c = V²_vir − 2σ². We ignore the ellipticity this rotation would induce. We set the temperature of the sphere to be 2 × 10⁴ K throughout. For gas in high-density shielded regions, the cooling times are very short and the gas is likely to have the indicated low temperature given the available cooling and heating processes. The density of the sphere is represented by particles of fixed mass and with smoothing lengths chosen to enclose 12 neighboring particles. We distribute the mass according to the SPH kernel.

As a key component, our self-shielding code should calculate the correct value for the neutral fraction of each particle. This determines the photoionization rate, and therefore, the emission rate of Lyα photons. In the top panel of Figure 1, we show the neutral fraction, X$_{{\rm H}\,\mathsc {i}}$, of particles in the sphere as a function of radius. The effect of self-shielding is clear in this diagram. The black points show the optically thin case, in which we have exposed each particle in the cloud to the same ionizing flux (corresponding to a photoionization rate of 9.5 × 10⁻¹³ s^-1). The blue points show the neutral fraction of particles after we have applied our self-shielding correction. At the center of the cloud, the gas becomes completely neutral owing to the shielding layer, which is recombining rapidly enough to keep the inner cloud completely neutral: no photoionizing photons are able to penetrate to this depth. This shielding layer is very thin—it is effectively a skin of about only 2 kpc separating nearly completely ionized from completely neutral gas. It is from this thin layer, in addition to the extended emission from the larger optically thin regions, from which Lyα emission emerges. Our results for the "SPH" version of the SIS are in good agreement with the results of ZM02 (shown by the red line in the figure). Of interest for absorption line studies is the projected neutral hydrogen column density of this cloud, which is shown in the middle panel of Figure 1. If there were a quasar directly behind this system, it would be considered a damped Lyα system (DLA) over the ∼10 kpc central region. We will return to this column-density distribution below. The fluorescent emissivity of Lyα photons at each position is computed as 66% of the photoionization rate.

Zoom In Zoom Out Reset image size

Once we have determined the emissivity, neutral density, temperature, and velocity at each location in the gas distribution, we put these quantities on a uniform grid with length 2R_vir on a side and run our radiative transfer code. We first ensure that our grid resolution is fine enough to resolve the self-shielding layer in our cloud. We show in the bottom panel of Figure 1 the neutral density profile of the sphere (directly from the particles) and compare it to the density profile generated from grids with resolutions of 32³, 64³, and 128³. The SPH smoothing lengths of the particles are 0.7 kpc on average, while the smoothing length in the transition region (from optically thin to thick) is 0.25 kpc. There is a slight offset between the particle distribution and the gridded distribution; however, this is simply due to the subtle difference between the density as determined at a given particle's position in the sphere and the density as determined from the sum of overlapping particle mass profiles. This figure demonstrates that the 128³ grid recovers the density profile with sufficient accuracy for our calculations, and we adopt it for subsequent calculations of the SIS.

In Figure 2, we show the results of the radiative transfer calculation for the isothermal sphere described above. The upper left panel in this figure shows the projected Lyα emissivity map, which we obtain by integrating the Lyα emissivity along the line of sight and assuming that Lyα photons isotropically escape the cloud without scattering. In this sense, it is a "column emissivity per solid angle" map. This emissivity image is the surface brightness one would measure if the Lyα photons underwent no scattering and streamed directly out of the cloud over the 4π solid angle from where they were physically produced. This is similar to what one would observe if seeing this object in non-resonant line radiation such as Hα or Hβ, although of course these would be at much lower intensities. The lower left panel shows the emergent scattered Lyα image. A comparison of the true (i.e., scattered) Lyα image to the "column emissivity" map, illustrates the effects of spatial diffusion of the photons. Note the graininess in the Lyα image at low surface brightness is due to the finite number of photons we run. With respect to the emissivity map, Lyα emission seen in the scattered image shows spatial diffusion caused by the scattering, although the effect is small.

Zoom In Zoom Out Reset image size

The right-hand panels of Figure 2 show the 2D spectra of the cloud. These spectra are generated by orienting a wide slit (over the entire cloud) along the x-axis (upper right panel) and y-axis (lower right panel). The rotation curve for the sphere is clearly seen in the lower-right panel. Since the sphere is set to rotate around the x-axis, there is no effect of rotation in the upper-right panel, which shows the characteristic double-peaked Lyα profile. For clarity, we show the 1D spectrum of the whole cloud in Figure 3. The velocity profile becomes more apparent in the 1D diagram. It is clear from these figures that the photons are escaping the cloud primarily by substantial shifts from the line-center frequency, so that the scattering cross section becomes sufficiently low to allow the photon to escape. The peaks are separated by ≈ 7 Å, which corresponds approximately to the width given by ±4σ × λ_Lyα/c, where σ is the 1D thermal velocity dispersion (Gould & Weinberg 1996). ZM02 also present the Lyα images and spectrum for this case, and we find the agreement is, as expected, excellent. The brightest pixel in the Lyα image corresponds to a surface brightness of ∼6.0 × 10⁻²⁰ erg s^-1 cm⁻² arcsec⁻², which is 30% higher than expected under the "simple mirror" approximation (GW96) from our adopted ionizing background at the redshift of the SIS in the absence of heating (Equation (5) of GW96). As we show in Appendix A, this is in accordance with the expectations from an exact solution for this system based on ZM02. The excess flux over the simple mirror expectation arises from a simple limb-brightening effect. Even so, at these flux levels detecting such a system is a challenge for modern 10 m class telescopes. The maximum source surface brightness should be compared with the B-band sky brightness of ∼ 2.9 × 10⁻¹⁷ erg s^-1 cm⁻² arcsec⁻² Å⁻¹, corresponding to B = 22.2 mag arcsec^-2. At the specified redshift, z = 3, this relatively bright region has size ∼10 kpc that would correspond to a diameter of ∼13. For our adopted UVB at this redshift, detecting this object with a signal-to-noise ratio (S/N) of 1 would require approximately 100 hr on a 10 m telescope assuming a 10 Å filter, 30% telescope efficiency, and 80% atmospheric transparency. The detectability is not, however, this remote. For this calculation, we have ignored two important effects: (1) heating of the gas from high-energy photoelectrons and (2) cooling radiation. We have not explicitly included the first effect in our calculation, but one can estimate its magnitude from Equation (13) of GW96: it would basically double the observed surface brightness. We address the second effect more completely in Paper II, as its amplitude is entirely dependent on the adopted temperature of the gas that, in this case, is physically motivated but otherwise arbitrarily chosen.

Zoom In Zoom Out Reset image size

Even given more optimistic estimates for the surface brightness, it remains a major observational undertaking to detect Lyα emission caused by the UVB alone—for example, larger structures of size 10 arcsec² could be detected in ∼26 hr with a 10 m telescope should they exist at these redshifts. More promising at present is the possibility of detecting Lyα emission from clouds exposed to an enhanced ionizing field. We turn our attention to this case.

We now investigate the case of a singular isothermal cloud, constructed as described above, that is irradiated by a local bright quasar. The UVB + quasar case is of particular interest because of the potential surface brightness enhancement and therefore detectability of these systems. It is timely to analyze this case because of the recent detection of Lyα fluorescence in a DLA system irradiated by a bright quasar (Adelberger et al. 2006). As noted previously, our code for performing the self-shielding correction is equipped to deal with an anisotropic radiation field to study anisotropically irradiated gas fields, novel with respect to the cases studied in ZM02. We place the quasar at (x, y, z) = (−500, 0, 0) kpc (physical) from the center of the sphere. The quasar is assumed to emit isotropically and have a power-law continuum shortward of 912 Å of $L_\nu =L_{\nu _L}(\nu /\nu _L)^{\alpha }$, where α is taken to be −1.57 in accord with observations (Telfer et al. 2002). We assume a specific 912 Å luminosity, $L_{\nu _L}$ at the Lyman limit ν_L of 1.0 × 10³¹ erg s^-1 Hz⁻¹ (Liske & Williger 2001) unless otherwise specified. When we turn on the quasar and examine the resulting neutral fraction for particles near the y = z = 0 line, we see in the bottom panel of Figure 4 that the quasar has indeed ionized the outer edges of the cloud facing it, as expected from this configuration. At the cloud, the quasar intensity corresponds to an enhancement in ionizing photon flux per unit area above the UVB of approximately 60.

Zoom In Zoom Out Reset image size

In the top panel of Figure 4, we show a particle representation of the cloud near the z = 0 plane, where particles are color-coded according to their relative neutral fractions, i.e., their neutral fractions in the presence of the quasar relative to their neutral fractions when exposed to the UVB alone. The blue points in the diagram show those particles that have been most strongly affected by the quasar. The quasar has the most dramatic effect on the nearly neutral innermost particles and particles on direct sightlines to the quasar radiation. Particles on the opposite side of the cloud from the QSO experience a less dramatic reduction of their neutral fractions because the quasar radiation is attenuated or entirely blocked from view by the central optically thick structure. The half-moon illumination caused by the quasar is apparent from this figure. In fact, it looks more like a keyhole, but the highly ionized outer layers of the cloud contribute very little to the Lyα surface brightness owing to their low density. We now explore how this translates into Lyα emissivity and, ultimately, scattered radiation.

Based on the properties of the quasar, we can determine order-of-magnitude expectations for the surface brightness of Lyα emission for the case in which the DLA acts simply as a "mirror," converting 66% of the quasar's ionizing radiation into Lyα fluorescence.⁹ At the distance of the cloud, these photons should emerge as:

$$\begin{eqnarray} \Gamma _{\rm mirror} &=& \frac{0.66\ r_{\rm SS}^2\ \dot{N}_{\rm ionizing}}{4 d_{q}^2},\\ \dot{N}_{\rm ionizing} &=& \int _{\nu _L}^{\infty } \frac{L_{\nu }}{h\nu } d\nu, \end{eqnarray} \tag{ 7 }$$

where r_SS is the self-shielding radius of the cloud, d_q is the cloud–quasar distance, and the prefactor of 0.66 comes from the fraction of ionizing photons that eventually cascade to the Lyα transition (Gould & Weinberg 1996, GW96). For the systems we examine, d_q is 500  kpc and r_SS depends on the quasar flux as we show below. For the quasar spectrum we adopt, the peak surface brightness should go roughly as ${\sim} 1.01 \times 10^{-17} [(1+z)/4]^{-4} [L_{\nu _L,31}][ d_q/(500 {\; {\rm kpc}})]^{-2}\;{\rm erg\ s^{-1}\ cm^{-2}\ arcsec^{-2}}$, where $L_{\nu _L,31}$ is the quasar luminosity at the Lyman limit in units of 10³¹ erg s^-1 Hz⁻¹. Figure 5 shows the Lyα images and spectra when we include the radiation field of the quasar. We see in the upper left-hand panel that the effect of the quasar on the Lyα emission is to produce a half-moon region of high surface brightness gas. The half-moon illumination reflects the higher ionization rate and, therefore, a higher recombination rate in the portion of the cloud facing the quasar. This should be compared with the uniform emission shown in Figure 2 for the case in which the only source of illumination is the UVB. In the Lyα image itself, this half-moon shape is preserved. Such a feature serves as a diagnostic of this configuration because it implies either a specially arranged gas density distribution, or an anisotropic illumination similar to the case discussed here. The spectra are also modified in the presence of the quasar. The amplitude of emission is higher as expected, and the peak separation is smaller than the case with UVB illumination alone.

Zoom In Zoom Out Reset image size

The brightest feature in the QSO-irradiated cloud is 53 times brighter than the brightest feature seen from exposure to the UVB alone. The quasar itself contributes ∼200 times more ionizing flux than the UVB alone at the center of the cloud. Since the UV-absorbing and Lyα emitting surface is finite and curved, as opposed to an infinite flat surface, Lyα photons are emitted into 2π–4π steradians. This geometric effect leads to a factor of 2–4 reduction in the surface brightness with respect to the expectation from an infinite flat "mirror." The calculated increased surface brightness relative to the UVB-only case is in line with this expectation, given the strength of the quasar radiation field.¹⁰ As we show in Appendix A, the reason for any small discrepancy is that the neutral fraction profile is not being faithfully represented in our 100,000 particle case. When we run this case with 500,000 particles, we get closer to the expected value, but even this is not fully adequate. Since high-resolution cosmological simulations typically have at most 1,000,000 particles in their most well-resolved structures, current SPH simulations are simply unable to faithfully capture the steep transition from optically thick to thin that occurs in these systems. In the limit of a very bright quasar, this half-moon shape is eliminated as the ionizing flux propagates further into the cloud. We illustrate this effect in Figure 6 in which we show a sequence of surface brightness and neutral column-density images as the quasar luminosity $L_{\nu _L}$ at the Lyman limit is increased from 0 (the UVB-only case) in the leftmost panel, and then from 1.02 × 10²⁹ to 1.02 × 10³² erg s^-1 Hz⁻¹. We show the impact of the quasar on the projected neutral column density of the system in the bottom panels of Figure 6. The sequence of neutral column density shows that, as expected, the neutral layers are progressively blasted away, leaving only a very small, dense core in the case of very strong quasar illumination.

Zoom In Zoom Out Reset image size

There are three features to note in these figures that, in conjunction, can provide constraints on the physical situation of individual optically thick systems when observed. The first is simply the Lyα surface brightness. Given the quasar luminosity and distance, it is straightforward to calculate how bright (in the absence of dust) the optically thick cloud will glow. Depending on the impinging flux, this anisotropic illumination will create a half-moon or a "pac-man" type structure. The second is the frequency distribution of the photons. Most importantly, fluorescence will manifest itself as a double-peaked profile with a peak separation approximately equal to 8σ where σ is the cloud's velocity dispersion, as demonstrated here. In the absence of other bulk flows, the peak separation, together with an estimate of the object's size, directly constrains the mass of the object. Rotation within the cloud will be apparent in the spectrum depending on the orientation of the slit to the rotation axis of the cloud. In the case we show in Figure 5, a "double" rotation curve can be clearly seen in the 2D Lyα spectrum. The third diagnostic is the size of the "absorber." For a given impinging flux, halo mass, and density profile, there is a specific size over which the cloud will appear as a Lyman limit system or DLA. Combining emission observations with absorption line studies to measure the column density, one can set limits on this size and thereby set constraints on simple models such as those presented here. In Section 5, we demonstrate how these diagnostics work together by comparing these simple models in detail to a recently discovered system (Adelberger et al. 2006).

We have selected a 1.5 Mpc (physical) region and a smaller 200 kpc (physical) region from the L5 simulation as well as a 1.8 Mpc (physical) region from the L22 simulation for which we make predictions for fluorescent Lyα emission. We show the total gas density and temperature from these simulations in Figure 7. Irradiating these gas structures with a uniform ionizing background,¹¹ we determine the neutral fractions for all of the particles within these sub-regions of the simulations using the well-tested algorithms of our self-shielding correction, which we describe in Section 2.2. Since we now have an arbitrary geometry and gas density distribution, we can only compare our particle neutral fractions before and after we correct them for the effects of self-shielding: we do not have a simple reference such as a self-shielding radius. We show in Figure 8 the resultant neutral fraction distribution after we perform the self-shielding correction on the SPH particles compared to the case in which all particles are exposed to a uniform UVB for the L5 simulation. The effect of the self-shielding is seen clearly by the shift toward higher neutral fractions in dense regions, with a substantial number of particles becoming completely neutral. We note that there is almost no change in the low density regions that are optically thin to Lyα.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

To preserve the high resolution achievable with SPH simulations, we would ideally have grid sizes that were smaller than the smallest smoothing lengths in the box. The smallest physical scale resolved in this simulation (i.e., the smallest particle smoothing length) is 0.07[0.38] kpc for the L5[L22] simulation. For a 1.5[1.8] Mpc region, this would correspond to an unrealistically high-resolution grid of (2.1 × 10⁴)³[(4.7 × 10³)³] cells. However, because they are shielded, extremely dense regions play no role in generating photons, and the requirement of grid resolution should be much less stringent in these regions. For our applications, the boundaries of any dense region will simply act as "mirrors" for the incoming photons. We, therefore, need to resolve dense regions as a whole, not individual particles inside them. We have tested the effect of grid resolution and based upon these experiments, have adopted a resolution of 300³ cells (corresponding to 5 kpc and 6 kpc spatial resolution for the large regions of the L5 and L22 boxes, respectively) to make our predictions. We adopt a spatial resolution of 128³ cells (corresponding to 1.6 kpc resolution) for the small sub-sub-region of the L5 box. The details of these tests can be found in Appendix B.

We first examine the 200 kpc sub-sub-region of the L5 simulation that contains multiple optically thick structures. To explicitly examine the effect of frequency diffusion, we generate a Lyα map with the radiative transfer turned off, which is the same as the emissivity map. The top panels of Figure 9 show the unscattered Lyα image and 2D spectrum extracted along the y-direction. The bottom panels in this figure show the image and spectrum from the full radiative transfer calculation. The connection between gas density and emission is striking in this zoomed region as one can see by comparing the upper left panel of Figure 7 with the Lyα image in the bottom left panel of Figure 9. Very dense knots of gas produce a substantially higher emission signature in both images and spectra.

Zoom In Zoom Out Reset image size

A comparison of the top and bottom panels of Figure 9 directly shows the effect of the resonant scattering. The image in the scattered case is smeared compared to the non-scattered case owing to the spatial diffusion of the photons. The differences between these images shows the modest amount of spatial diffusion that occurs in these systems. The comparison between the 2D spectra for both cases shows that photons diffuse primarily in frequency space, in contrast to a spatial random walk. In the non-scattered image, each blob gives rise to a narrow bright line near line center in the 2D spectrum in contrast to the characteristic broad double-peaked line profiles. The peculiar velocity and Hubble flow in the gas cause frequency shifts away from zero. When we examine the scattered image, however, we see that each structure now gives rise to a more diffuse line profile in frequency. While this realistic case is more complex than the idealized cases presented in Section 3, we can still see the fingerprints of resonant scattering on this scale. With the appropriate scaling, the top panel of Figure 9 could represent an image in an optically thin recombination line such as Hα. Taking the ratio of the top and bottom panels yields an estimate of the relative morphology for lines that are optically thin and thick, respectively. While in high-emissivity locations, the difference is modest, in low-emissivity regions the difference between, e.g., an Hα image and a Lyα image would be quite substantial.

We now examine the larger regions of the L5 and L22 simulations in which blobs of the size shown in Figure 9 are only a small portion. We show in Figure 10 the Lyα images and 2D spectra generated from the large L5 and L22 simulation regions shown in Figure 7 (with different surface brightness scale). We show the results for both simulation boxes in Figure 10 to facilitate comparison between the z = 2 (top panels) and z = 3 (bottom panels) cases from the L22 and L5 simulations, respectively. In contrast to the isothermal sphere case and owing to the highly disturbed gas density and velocity structure, we do not have clean diagnostics of characteristic radii and analytic expectations for the separations of spectral features. However, a comparison of the panels of Figure 10 and the bottom panels of Figure 7 shows that the emission primarily originates from dense knots of material, as one would expect, since the emission comes from the rapidly recombining skins of optically thick cores, which should occur in regions of high density. Since we have adopted the same UVB for both redshifts, the difference in emission intensity between the images is caused primarily by the cosmological surface brightness dimming, which is ∝(1 + z)⁻⁴.

Zoom In Zoom Out Reset image size

The 2D spectra are quite complex as can be seen in the right panels of Figure 10. As we showed in detail in Figure 9, each blob of optically thick gas gives rise to a disturbed version of the characteristic double-peaked profile. Since we have a large number of such blobs, the resultant spectra are a superposition of many of these profiles, each modified by the fluid velocity field and the geometry (e.g., the frequency distribution may not be symmetric about the line center). The profiles shift with respect to each other because of the Hubble flow and the peculiar velocity of the gas. The complex structure seen in the 2D spectra is, therefore, generically expected owing to transfer effects. It is also worth noting that, as one approaches sufficiently low surface brightness limits, the "forest" of Lyman limit systems illuminated by the UVB emerges. That is, many systems become visible at a similar surface brightness level—once this threshold in surface brightness is achieved, the filamentary structure is evident, i.e., once one Lyman limit system is observable, many others are also visible.

In Figure 11, we show several 1D spectra from blobs of gas in different regions of the structure in the L5 box. This is analogous to obtaining a narrow-band image for a particular field and follow-up spectroscopy of the identified sources. Solid lines in the figure show the post-transfer spectra and dotted lines show the "unscattered" spectra. The overall double peaks owing to the transfer of photons are clear in some cases (e.g., A3 and A1) but unlike the isothermal case, they are not symmetric owing to the bulk velocity of the gas in the simulations. While comparison of any individual system requires detailed modeling, characteristic line-widths and morphologies from large-volume calculations such as these could be derived. Observational campaigns to obtain deep narrow-band imaging and follow-up spectroscopy are currently underway and comparison with calculations such as these will prove helpful for understanding the origin of the Lyα emission. We discuss the requirements for observing such fields in Section 5.

Zoom In Zoom Out Reset image size

Similar to the case discussed in Section 3.2, we now place a bright quasar with $L_{\nu _L}=1.0\times 10^{32}\;{\rm erg\;s^{-1}\;Hz^{-1}}$ (10 times brighter than for the previous SIS case) in the center of our cosmological sub-regions to examine the effect on the Lyα emission strength and morphology and to show the expectations for observing a field containing a bright quasar. The quasar will have little effect on the emission from gas that is already highly ionized by the UVB, but will have a substantial effect on the emission from the dense optically thick clumps that are not already significantly ionized by the UVB. We see this in Figure 12 where we show the resulting Lyα image and 2D spectra for the L22 (top panels) and L5 (bottom panels) simulations including a quasar. Comparing with Figure 10 one can see that in the dense knots, the emission is brighter by more than an order of magnitude relative to the UVB-only case. We note that even in the outer reaches of this system, there is a substantial relative increase in the surface brightness—the quasar is sufficiently powerful to reach the edges of this region.

Zoom In Zoom Out Reset image size

In Figure 13, we quantify the shift to higher surface brightness in the distribution of pixels in the resulting Lyα map caused by the QSO illumination. In the UVB-only case, the brightest pixels were set by the intensity of the UVB. Now, the brightest pixels are determined by the quasar flux impinging on the densest regions. The faintest pixels come from low column-density material that is highly ionized. There is, therefore, little difference at low emissivities between the UVB and UVB+QSO case since these systems already emit near maximum. The brightest systems are those that are able to remain optically thick in the presence of the vastly increased ionizing flux of the quasar. The UV photon enhancement caused by the additional ionizing flux of the quasar is ≈ 500(d_q/1 Mpc)⁻². In our calculations, the brightest pixel is now ∼2 × 10⁻¹⁷ erg s^-1 cm⁻² arcsec⁻², a factor of ∼400 over the UVB-only case. The enhancements in the average pixel surface brightness relative to the UVB-only case are shown in Figure 13. On average, the resultant enhancement over the UVB is more modest. This is due to the geometry of the emission which can result in a factor of 2–4 suppression of the expected Lyα surface brightness.

Zoom In Zoom Out Reset image size

Most striking is that the presence of the quasar highlights the morphology of the densest knots in the large-scale density distribution. This is the "meatball" topology of Lyα emission referred to in GW96. The quasar brings the contrast between the emissions from optically thick and optically thin sources into sharp relief since only the densest knots are able to reprocess the increased ionizing radiation. The lower surface brightness material, which appears spatially extended and fluffy, becomes sinewy in the presence of the quasar. This corresponds to material that was previously partly neutral, and has become fully ionized in the quasar's radiation field. Hence, its fluorescent emissivity has decreased since the fluorescent emissivity of the gas is proportional to the photoionization rate, which is small for gas with very low neutral fractions.

The 2D spectra for the QSO case also highlights the densest systems. The brightest knots have narrower frequency distributions compared with their counterparts in the UVB-only case. The QSO has completely photoionized many low-emissivity structures, eliminating their contribution in both the image and the spectra. The highest column-density systems are relatively smaller and brighter and, because the quasar radiation has generally lowered the neutral column density of the gas, the spectral pattern is narrower in frequency since the photons undergo smaller frequency diffusion at lower column-densities. The double-peaks of the highest density systems become much more prominent in the presence of the quasar's radiation. For relatively isolated blobs, one can see clearly the double-peaked spectral feature associated with the object in the 2D spectrum (e.g., the systems located at (X, Y) = (0.8, 0.3) and (0.8, 1.3)).

Fluorescent Lyα emission in quasar fields should have a very different morphology as a function of luminosity compared to fluorescence from the UVB alone. Bright knots of emission from high column density dominate over the general emission from the IGM.

What are the realistic prospects for observing Lyα emission from the IGM from the ground and from space? A useful figure of merit is the amount of observing time required to reach a fixed S/N. We gain some insight into the practical difficulty of this problem by considering the simple mirror approximation as cast by GW96, who obtained the following expression for S/N as a function of observing time:

$$\begin{eqnarray} \mbox{S}/\mbox{N} & = & \xi \frac{\Phi _{\rm obs}}{(1+z)^{1/2}} \left[ \frac{\pi ^{1/2} D^2 f T \Delta \Omega }{16 (\sigma /c) \phi _{\rm sky} \lambda _{ \rm{Ly}\alpha }} \right]^{1/2} \\ && \sim 7.5 \left(\frac{1+z}{3.2}\right)^{-3.5} \left(\frac{f}{0.25}\right)^{1/2}\left(\frac{D}{10\,{\rm m}} \right) \left(\frac{T}{20\,{\rm hr}} \right)^{1/2} \nonumber \\ && \times \left(\frac{\Delta \Omega }{10\,{\rm arcsec^2}} \right)^{1/2} \left(\frac{\sigma }{35\;{\rm km\; s^{-1}}} \right)^{-1/2}, \end{eqnarray} \tag{ 9 }$$

where T is the integration time, D is the telescope diameter, f is the telescope efficiency, ϕ_sky is the flux from the sky, Φ_obs is the source flux, σ is the velocity dispersion of the source, ξ is the atmospheric transmission, and ΔΩ is the source size. In Equation (9), we have assumed ξ = 0.9 and ϕ_sky = 1.85 × 10⁻²(γ s^-1 m⁻² arcsec⁻² Å⁻¹), corresponding to a B-band surface brightness B = 22.2. The strong (1 + z) scaling in Equation (9) arises from the redshift dependence of Φ_obs, assuming that the UVB intensity is constant with redshift. Using their values for the ionizing background, telescope setup and source size, they inferred that the IGM Lyα fluorescence from the UVB would be marginally detected in ∼20 hr.

However, this prediction may be optimistic in several respects. The lower amplitude and flatter shape of the UVB we adopt cause our value of Φ_obs to be lower than the GW96 value by a factor of 3.11, which leads to an increase in observation time by a factor of 9.7. The typical source sizes for the brightest fluorescent sources in the simulation are not 10 arcsec², but rather more like $4\;\rm arcsec^2$, causing a factor of 2.5 increase in observing time. This already implies typical observing programs of 500 hr instead of the 20 hr GW96 obtained for marginal detection. GW96 also adopted a matched filter that is approximately 3 times narrower than even a very narrow 10 Å filter, causing another factor of 3 increase in observing time. GW96 further assume that sources have a Gaussian profile and that observations would reach a frequency resolution of ∼1 Å. These observations would be very powerful for detecting low-level Lyα emission. If the source sizes in our simulation and our adopted UVB intensity are correct, then, in the presence of the terrestrial night sky, it will require ∼1500 hr exposures to detect the typical sources of fluorescence from the uniform UVB with current ground-based telescopes.

This probably explains why fluorescence from the general IGM has been difficult to detect with the large 100 hr programs currently completed (Rauch et al. 2008). In space, the sky background is 1 mag fainter and integration times can be longer. Future dedicated space-based and ground-based facilities will be ideal for detecting the glow of the IGM. In the near term, however, observations in quasar fields where the ionizing flux can easily be 1500 times the uniform UVB are feasible in only hours on 10 m class telescopes. As we showed in Section 4, the morphology of emission near quasars highlights the "forest" of Lyman limit systems.

We now simulate observational maps of Lyα fluorescent emission from our cosmological simulations.

To mimic narrow-band Lyα observations, we add a background of sky photons and Poisson noise to our theoretical predictions for a specific observational setup. We fix the telescope aperture, integration time, narrow-band filter width, and telescope efficiency to make "exposures" of our theoretical structures. We subtract the background from these frames—simply taken to be the minimum pixel count—to create "sky-subtracted" images from our predicted Lyα images. We then convert our image files to standard observational image format and use the Source Extractor program (Bertin & Arnouts 1996) to identify sources from our image, just as would be done for an observed narrow-band image. We use a 10 Å filter on a 10 m telescope aperture with 30% efficiency and integration times of 10 and 1500 hr to generate our observed maps.

In Figures 14 and 15, we show the maps created by this procedure for our simulated results at redshifts 2 and 3, respectively. The left panels in these figures show the UVB only cases. Right panels in the figures show the case of UVB+QSO. The difficulty of observing fluorescence is clear from the top panels of these figures, which show the resulting maps after 10 hr of integration. The middle panels show 1500 hr observations and the bottom panels show the "perfect" case (equivalent to an infinite exposure time) at the same resolution as the images to assist with identifying the features. While fluorescence from the UVB alone is not observable in 10 hr, and only marginally detected after 1500 hr at z = 2 and not at all at z = 3, the quasar-illuminated structures glow brightly and with high significance after a single night of observation.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

With minimum high-resolution volumes of (5.555 h⁻¹ Mpc)³, we can begin to examine the statistics of fluorescent sources in our models. Such statistics can be compared to observations from large Lyα surveys (e.g., Matsuda et al. 2006; Steidel et al. 2000; Cantalupo et al. 2007; Rauch et al. 2008). We leave a more complete statistical analysis of large simulation volumes to future work, but we demonstrate here the types of measurements we can make from our simulated data. We first look at the distribution of sources from the Source Extractor software applied to the observed maps from the UVB+QSO case presented in Figures 14 and 15. Sources are defined within the SExtractor software as being 5σ detections.

Figures 16 and 17 present results of this analysis for the 1.5 Mpc (physical) sub-region of the L5 simulation, for the 10 and 1500 hr cases, respectively. The top panels in these figures show the differential distribution of sources as a function of Lyα flux. The bottom panels show the fluxes of identified sources as a function of radial distance from the quasar, which is located at the center of the box. In the "quasar field," the distribution of fluxes is substantially skewed toward higher values, which results from the increased photoionization of optically thick systems in the sub-region.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

In the 10-hr field, ten sources are detected, with fluxes in the range ∼ 2 × 10⁻¹⁹–2 × 10⁻¹⁸ erg s⁻¹ cm⁻². There is only a marginal trend of flux with distance from the quasar. One might naively expect a d⁻² falloff in flux, but sources further from the QSO can remain self-shielded to a larger radius and therefore present a larger reflecting area. For a population of isothermal spheres, like those in Section 3, one can show that the expected falloff in flux is d^−2/3, shown by the dashed line, which approximately describes the overall trend of points. Because of the smaller reflecting area of sources at smaller radii, we expect that our fixed grid resolution smears out the brightest sources near the quasar. Therefore, the radial falloff may be even flatter than d^−2/3. Given the slowness of the radial trend, we expect observable sources beyond the 750 h⁻¹ kpc radius of the volume we have analyzed. The 1500-hr map contains 76 detected sources, down to fluxes ∼3 × 10⁻²⁰ erg s⁻¹ cm⁻², and it again shows only a weak trend of source flux with distance from the quasar. In future work, we will examine larger simulation volumes to determine the nature of this distance dependence robustly.

In this section, we compare a simple model of Lyα fluorescence with observations to investigate the origin of the emission. Our method has already been applied to constrain the emission mechanism for emission seen in a DLA absorption trough seen in close proximity to a background quasar (a "proximate DLA;" Hennawi et al. 2009), and here we show the application to a case with different geometry.

Adelberger et al. (2006) observed a DLA with column density $N_{\rm H\,\mathsc {i}}=(2.5 \pm 0.5) \times 10^{20}\;{\rm cm^{-2}}$ at z = 2.842 in the spectrum of a background quasar Q1549-D10. The absorber is at a projected angular separation θ_Q = 49'' (corresponding to 380 kpc) from the bright (G ∼ 16) quasar HS1549+1919, which has the same redshift as the DLA. Extended Lyα emission with a double-peaked spectrum is observed at θ_l = 15 (corresponding to a physical size of ∼11 kpc proper) offset from the absorber. The extended Lyα emission region has an apparent AB magnitude of G = 26.8 ± 0.2 mag, and the line has an equivalent width of Δλ_EW = 275 ± 75 Å in the G band, which is ∼1000 Å wide. The emission line has a peak separation of ∼ 8 Å and a line flux of 2.1 × 10⁻¹⁷ erg s^-1 cm⁻², which yields an inferred surface brightness of ∼1 × 10⁻¹⁶ erg s^-1 cm⁻² arcsec⁻², assuming that the emission region has diameter of 05. The AB magnitude at 912 Å estimated for the foreground quasar is m₉₁₂ = 16.7, which corresponds to a luminosity at the Lyman limit of $L_{\nu _L}=1.34 \times 10^{32}$ erg s⁻¹ Hz⁻¹. From these observables we can calculate the expected Lyα flux owing to fluorescence induced by the quasar's impinging radiation. Recall that in the "mirror" approximation, a fraction η = 0.66 of the ionizing photons impinging on an optically thick cloud get re-radiated as Lyα photons. For a given background and quasar intensity, the observed surface brightness should be given by the following expression:

$$\begin{equation} \pi \times SB=\frac{h\nu _\alpha \eta }{(1+z)^4} \times \left[ \pi \int \frac{I_\nu d\nu }{h\nu } + \int \frac{L_\nu d\nu }{h\nu } \frac{ {\rm cos}\theta }{4\pi d^2} \right], \end{equation} \tag{ 11 }$$

where ϕ is the angle between the foreground and background quasars such that d = d_⊥/sin ϕ, and θ is the angle between the mirror normal and the line of sight. Substituting the observed values into Equation (11), we obtain a value for the surface brightness of 5.3 × 10⁻²⁰ (background) + 2.7 × 10⁻¹⁶cos θsin²ϕ (quasar) erg s⁻¹ cm⁻² arcsec⁻². This matches the observed value for a plausible geometric factor of 0.3 = cos θsin²ϕ. Approximating the absorber as an isothermal sphere, we can compare our more sophisticated numerical results described in Section 3.2 directly to this system.

We can also compare our results described in Section 3.2 to this absorber, modeled as an SIS. We assume the quasar radiates isotropically to compute its luminosity from the observed flux. The highest predicted Lyα surface brightness in our image is 3.75 × 10⁻¹⁷ erg s^-1 cm⁻² arcsec⁻²—a factor of ∼7 cos θsin²ϕ below the analytic mirror prediction and ∼2.2 below the observed value of 0.84 × 10⁻¹⁶ erg s^-1cm⁻² arcsec⁻². For our system, while we know ϕ exactly, θ is uncertain, and we take an average value of θ = 60 degrees for our system. Our calculation is therefore a factor of ∼3 below the expectation for the mirror under these assumptions. This is compatible with the expected losses due to geometry (e.g., Lyα photons leak out of the system and are therefore emitted over a solid angle larger than 2π). We show a comparison of the surface brightness for both the analytic and numerical predictions and the observations in Table 1, for reference.

For this high incident quasar flux, the optically thick regions of the cloud are eroded by photoionization, resulting in a decreased region of high enough column density to act as an efficient fluorescent surface. For the density profile we have adopted, the bright emission region itself becomes nearly coincident with the high column-density absorber and not offset from the absorber (as in the lower flux half-moon illuminated cases). This can be seen in Figure 18 where we show the Lyα image, neutral column-density distribution, and 1D spectrum for comparison with the observations. The most significant differences between our predictions and the observations are the large absorber size and the spatially offset high Lyα surface brightness. This places some tension on our simple model for this system. To obtain a large surface brightness and maintain a high neutral fraction over 10 kpc scales, a large, dense sheet rather than a centrally concentrated ball may be required.

Zoom In Zoom Out Reset image size

This individual system provides an exciting glimpse into what is possible by combining detailed observations of Lyα fluorescence and the type of predictions that are now possible. Variations in density profile, temperature structure, and velocity structure give rise to distinct signatures, with the appropriate data allowing us to discriminate between different physical mechanisms for powering the observed Lyα emission. Combining such modeling with larger samples of quasar-absorber pairs (e.g., Hennawi et al. 2006a; Adelberger et al. 2006), one should be able to directly constrain the ensemble physical properties of the densest regions of the IGM.

In order to make the best use of the predictions presented here, one would like to exploit both spatial and spectral information. Currently, one can already compare our Lyα maps and 1D spectra to observations obtained in deep long-slit spectroscopic or narrow-band surveys with follow-up slit spectroscopy (e.g., Rauch et al. 2008; C. C. Steidel et al. 2010, in preparation). Blue-sensitive integral field units (or tunable narrow-band filters) on large telescopes will have the capability to make channel maps of Lyα emission around structures, identified in imaging or spectroscopic surveys, at a given redshift that can be directly compared to the kinds of predictions that we are making here. We show such a configuration in Figure 19, which presents a series of frequency-slices through our z = 3 cosmological calculation of fluorescence around a bright quasar. As the filter is tuned past Lyα at the appropriate redshift, the "forest" of optically thick absorbers comes into view and then fades away.

Zoom In Zoom Out Reset image size