Structure of reionisation (Reionisation)

From Eric's Wiki

The general picture of the structure reionisation is that it proceeded as bubbles of ionised spreading into a mosty-neutral gas with perhaps some degree of ionisation from a diffuse field from the galaxies. As the bubbles grew and merged, the remaining neutral gas was to be found in denser structures such as filaments of halos. These give rise to the lyα absorbers seen in QSO spectra. As such, the lyα absorbers in the "Lyα forest" probe the large-scale structure up to redshifts at which the bubbles merged.

There are several classes of Lyman-α absorber systems:

Forest

Intermediate: Clouds & Lyman-limit

Damped

(From "Allen's Astrophysical Quantities")

Though there are the three distinct classes of absorbers (Lyman-forest systems, Lyman-limit systems, & damped Lyα absorbers), there is no discontinuity in the number densities. The distribution function varies with column density Σ as Σ1.46, steepening moderately as Σ increases.

Lyman-forest systems have N_HI∼10¹⁴cm ^{− 2}. They provide opacity through Lyα scattering. Their optical depths are never deep enough to vary from a simple Gaussian profile. Three important aspects of Lyman-forest systems:

1. The cumulative mass in the clouds is comparable to the mass in higher-surface-density clouds and the mass in galaxies (but the mass in neutral gas is much smaller)
2. The comoving number density decreases with decreasing redshift, indicating the clouds are dispersing
3. The spatial distribution is uniform, unlike the clumpy distribution of large-scale structure. Temperatures are typically K.

Self-shielding prevents the interior of clouds with neutral column densities from being ionised by background radiation. Lyman-limit systems (LLS) are self-shielded absorbers. They are small (Shave 2001) and hence not properly resolved in hydrodynamic simulations (Miralda-Escude et al 1996, Gardner et al 2001, Cen et al 2003, Nagamine et al 2004). The absorption occurs due to photoionisation at or just above 912 Å and hence absorbs light emitted originally at wavelength shorter than 912 Å Since the absorption cross-section falls off as ν ^{− 3}, the absorption-trough can become quickly red-shifted away from the peak in the cross-section.

For (Wolfe et al 1986, Smith et al 1986), damping wings due to resonant Lyα scattering at start dominating the spectra. These systems are called damped Lyα absorbers (DLA) or sometimes Wolfe Clouds. These column densities are comparable to those of present-day spiral galaxies as is the total baryonic mass. The mechanism is essentially the same as the Lyα forest population, but the optical depths are sufficiently deep that the profiles are Voigt instead of Gaussian. Like Lyman-limit systems, they are poorly resolved in simulations leading to an underestimation of their numbers. Damping wings are often not included in simulated spectra because they are wide enough to extend the full width of a typical simulation box. Damped Lyα absorbers are rarer than Lyman-limit systems. (from Peebles, "Principles of Physical Cosmology")

The Lyα forest probes structures on a scale of 1 Mpc at z = 2 to 4. The power spectrum of the transmitted flux fraction is the statistic to use (Croft et al 1998).

BSR04 find correlations in Lyα forest spectra for lines of sight separated by 33" and 35". This implies correlation of structures across 230 to 300 kpc, which isn't huge. They also see CIV at z=3.4 and MgII & Fe II at z=1.68. See references in BSR04 for work on larger separations. Systems have been found on the order of a Mpc in size and possibly up to 30 Mpc.

Linder04: The column densities of clouds and galaxies is strongly peaked at . Damped Lyα systems have . Lymann-limit systems have .

But how about the structure of the clouds? They are certainly not constant density. Which component dominates the column density. Using 1-D hydrodynamical simulations of Lya forest clouds gravitationally confined by dark matter minihalos, including metagalactic radiation field, Meiksin94 found three domains: 1) quasi-hydrostatic core, 2) nonhydrostatic zone in thermal equilibrium, 3) a cosmological accretion layer. Most of the column density is in the intermediate zone.

Gaps in the absorption Gunn-Peterson troughs of luminous sources may exist due to sources within the absorption region. An overdense region of HI will act as an absorber. Within the overdense region, there will be galaxies that will excavate HII regions. These HII regions will produce gaps in the absorption trough. Since the growing HII regions will eventually destroy the HI in the overdense region, there is only a finite length of time in during which this phenomenon will be observed. FHZ04 find that though this period is very short, there will be a small probability of observing this phenomenon. They use a model of reionization in which bubbles of ionised gas form around regions of high overdensity (essentially galaxies) and use the model to predict the probability of finding gaps in the absorption Gunn-Peterson troughs of luminous sources.

In the standard model of the Lyα forest, the IGM is in ionisation equilibrium. The rate of ionisation by UV photons is balanced by the rate of recombination of all species. The recombination rate depends on the temperature of the gas. The gas temperature is a function of the gas density. The temperature-density relation is T = T₀ρ^{γ − 1}. Variations in the mean UV intensity, the mean baryon density, and other parameters that set the normalization of the relation between the option depth are covered by the mean transmitted flux < F > (z). A "nuisiance parameter" arising from the thermal history is the filtering length k_F (Gnedin & Hui 1998). These 4 parameters are free when comparing simulation data to real spectra.

Process not normally included in simulations that affect the Lyα power spectrum. McDonald04 reports the strongest effect is produced by high column density absorbers which add large-scale power, so the slope is underestimated if the effect is ignored. Fluctuations in the field also have an effect. Large-scale flucuations, like around quasars, produce large-scale power. Small-scale fluctuations, like around galaxies, produce small-scale power. Galactic winds effects are less obvious and degenerate with paramaters concerning the temperature of the gas. Though other simulations with galactic winds succeed in reproducing large-scales, they fail in inner Mpc region: observations find little or no absorption but simulations find increased density close to galaxies.

Meiksin & White (2004) show that fluctuations in the radiation field (a few bright sources versus a uniform background) modify the Lyα power spectrum by boosting large-scale power and suppressing power at intermediate scales. The modifications occur at the 10% level, suggesting that observations of the Lyα power spectrum may be able to distinguish between QSO and galaxy dominated radiation fields. They assumed QSO's are uncorrelated with Lyα forest structure.

Croft (2003) finds QSO's lead to a suppression of large-scale power in the Lyα power spectrum since QSOs are likely to form where in high density regions, cancelling by ionisation the contributions of gas in the high-density regions. The finite lifetime of the QSO enhanced the effect by a factor of 2.

The ionisation background attenuation length is between 50 and 500 h ^{− 1} Mpc, comoving. To resolve the Jeans scale, one needs a resolution below 100 h ^{− 1} kpc. Any simulation needs to address this problem.

The HII bubbles formed around proto-galaxies grew until they merged around z∼6. That's the idea if you think QSO's aren't important. The first proto-galaxies (or dwarf galaxies) appeared at z∼20. WL04c use the constraints of "cosmic variance" and "causality" to show that the bubble's were about 10 Mpc (proper) when they merged and the redshift of overlap has a scatter of about σ_z = 0.15z. The "causality" constraint is the light crossing time across bubbles. The "cosmic variance" is the scatter in the formation times of bubbles. The light crossing time increases with time (bubbles grow). The scatter in the formation times of bubbles decreases in time (the bubbles sample a larger volume, decreasing the scatter). Let's clarify this last point. Bubbles merge to form large single bubbles earlier in regions of higher overdensity. Regions of high overdensity will collapse and start forming bubbles earlier. But as the bubbles grow in this manner, they sample the overdensity over a larger region. The variance between overdensities sampled with larger top-hats (bubbles) decreases with increasing top-hat size. Hence, the variance in the average age the original bubbles formed at decreases with time. When the light-crossing time matches the variance in the ages, the bubbles have merged throughout and we see the surface of last neutrality (Surface of Bubble Overlap). Note, the Surface of Lyα Transmission is at a lower redshift because even a small neutral fraction is sufficient to absorb transmission.

The Lyα forest can be used to contrain cosmological models. DN04 give a good description of the various statistics and methods. They all amount to comparison with simulated data, which is usually done with DM-only sims from which gas density and temperatures are derived using power-laws derived from hydrodynamical simulations. I find this part very dubious; but people are quite convinced they can map DM to gas.

Around QSO's (or any source of ionising photons) at z > 6.1, there will be pockets of highly ionised gas (neutral fraction < 1%). This is the proximity effect (Bajtlik et al 1988). The bubble of ionised gas (Strömgren sphere) around the source will grow until the rate of recombination balances the rate of production of ionising photons or the bubble merges with surrounding bubbles. The size of a Strömgren sphere is set both my the environment (the number of atoms to ionise), the lifetime of the source, and the spectrum of the source. The shape of the bubble around a QSO is not likely to be a observed to be a sphere both because the medium into which it is expanding in inhomogeneous and because the difference between the light-travel time from the back and the front of the sphere can be comparable to the expansion time scale (WL04a). However, if the timescales of the QSO are long compared to the recombination timescale, the ionised region will approximate a sphere (Yu04). Estimates of the lifetime of high-redshift QSO's range from yr (Haiman & Cen 2002) to much shorter ages (WBFS03). YL04 find consistency with the observations only if the lifetimes of QSO's are about few yr. But these estimates are dependent on the environment, particularly the ionisation fraction, . Note that f_HI can be either mass-weighted or volume-weighted with the mass-weighted generally greater than the volume weighted because of the elevated recombination rates and self-shielding. The observed Gunn-Peterson troughs indicate the mass-weighted f_HI > 1% (Becker01, Fan02, WBFS03). WL04b & WLBC04 argue it is even greater than 10%. But this is a mean value. Small dense halos will contain the bulk of the high-f_HI gas. Statistical measures of deviation of the bubble from a sphere can constrain cosmological parameters like Ω_Γ.

The absorbers that create to the Lyα forest are held in the minihalo model to be gas gravitationally bound to dark-matter halos (MR93).

In low column density areas (), the gas is at an overdensity of δ = 3 to 30 and is confined in pancakes bounded by shock regions due to infall. At higher column densities, the gas is able to cool (CMOR94).

Simulations associate most of the Lyα forest with warm gas gravitationally bound to the dark matter in filaments (ZAN95, HKWM96, MCOR96, BD97, MW01). About ¼ are due to halos of galaxies or galaxy groups (PMK95). Simulations also permit modelling of the Lyα forest spectrum itself (BGF95, DB96, DHWK97, ZANM97) assuming either a Voigt or a Doppler profile. The simulated spectra (ZANM97)show a power-law column density down to 10¹²cm ^{− 2} but a deficit above 10¹⁶cm ^{− 2}. They also require a softer QSO spectrum (low He II ionising background).

Strong gravitational lensing leads to multiple images of QSOs. The two lines of sight provide information about the sizes of absorbing structures though there are biases (CAZN97).

The probability distribution of gas density (and likely DM density) follows a log-normal form (BD97).

Testing cosmological models with Lyα forest: Cen97 shows the probability distribution of τ in spectra is model-dependent.

Cantalupo05 examines the Fluorescent Lyα emission from HII recombining in already-ionised regions. They use simulations to show that the previous predictions for the amount of emission were too high.

Hydro simulations work well for reproducing the Lyα power spectrum for high redshifts, but not for low (ZDEK05).

The distribution of matter on large scales is largely still in a linear or near-linear growth stage. Hence, Zel'dovich theory applied to an initial power spectrum generates a good approximation to large scale structure, particularly of the voids and filaments. Since Lyα absorption is dominated by matter at an overdensity of one (less dense and the structure is transparent, more dense and it collapses to a small-cross-section halo), the statistics of the Lyα forest are tied to the statistics of the initial power spectrum via Zel'dovich theory. DD05 examine this tie and find structure on scales of 150 kpc h ^{− 1} to 10 Mpc h ^{− 1} are well produced from a CDM spectrum, but below 150 kpc h ^{− 1} there is an apparent deficiency of power in the CDM spectrum.

The scales of reionisation structures is 1 Mpc at the start to 10 Mpc near the end. Variation about this value is due to fluctuations in the matter power spectrum. Similarly, increasing the efficiency of more massive galaxies increases the scale lengths.

Reionisation was probably patchy, with enhanced patchiness if sources clustered with structure and even more if sources were positively biased. There is evidence of strong clustering of QSO's at z=4 to 5 (DBM05).

Lots of damped Lyα systems of z>2.6 have been observed, thanks to SDSS. (PHW05)

During reionisation, the mean free path of photons increased with the scale of the the Stromgren spheres. When the spheres percolated, the MFP was set by the distribution of Ly-limit systems. Also suring percolation, the intensity of the ionising background also grew. The post-ionising optical depth varies on the order of unity at scales of about 100 co-moving Mpc (Becker01, WBFS03) which is expected from analytics (WL05).

During reionisation, dense structures will have shadowed the gas on the opposite side as the source. Some of the structures would be dense enough to radiate away the energy as fast as it is absorbed, and others would be photoevaporated. SIR04 performed simulations of the photoevaporation of minihalos. They distinguish R-type fronts from D-type which occur in denser environments. R-type fronts are generated when the I-front moves faster than twice the speed of sound in the medium. At the transition, the I-front is proceeded by a shock front. ISR05 continued the work, looking at the consumption of photons by the minihalos. They find 2 to 10 photons are absorbed per minihalo atom.

Fluctuations in the background spectrum can be parametrised by η = n_HeII / n_HI. Fluctuations can be produced by a distribution of sources with differing spectral indexes, or radiative transfer (RT) which modifies a source's spectrum depending on the optical depth. MF05b use simulations with RT to show that in regions of high density, the high HeII opacity leads to a decreasing η with density.

Broad line absorbers (BLAs) are broad because of high b values (40 km/s). From simulations, RTB05 find BLAs are due to the small neutral fraction in the warm-hot intergalactic medium (WHIM) which accounts for about 25% of the baryons.

Minihalos are stable self-shielding knots of gas with recombination times shorter than ionisation times. Minihalos act as sinks of photons and hence delay reionisation. Shadowing also alters the Lyα forest statistics. The importance of the delay and shadowing is unknown. Using a subgrid model (i.e. a model below the resolution of a simulation), Ciardi06 look at the extreme cases of minihalo formation, mainly varying their survival. They conclude minihalos can delay reionisation by up to Δz = 2, but, unsurprisingly, the amount is sensitive to the survival model.

Associated with minihalos is the clumping factor, a concept looking for a statistic. Generally, clumping can be equated with the density variance, σ, which is a function of the scale over which the mean and variance are computed. Scale-free parameters are presented in KGH05 that measure either the Ionisation of Recombination clumping factors. C_I = ( < n_HIΓ > / < n_HI > < Γ > ) C_R = ( < R(T)n_en_HII > / < R(T) > < n_e > < n_HII > ). Using simulations, they show that the dependence to clumping is not sensitive to the statistic.

Which ionised first, the low density voids or the high-density structures? Low-density gas requires fewer ionising photons per volume and recombinations are suppressed. But low-density regions are larger and the gas within them accounts for the bulk of the matter in the universe, particularly at high redshift. High-density gas is found in the very overdensities where the sources of ionising radiation are expected. Being closer to the sources, they recieve a higher flux of ionizing radiation. Simulations by Iliev05, lead them to conclude it was an inside job, with the high-density gas being ionised first. But they place their sources in halos, maintaining a constant mass-to-light ratio. It is assumed that there are no sources where there are no halos, which is possibly fine.

Using simulations, ISS05 found that the number of minihalos in an HII region around an ionizing source is almost constant in time. Consequently, minihalos are simply sinks of photons and their effect is degenerate with the escape fraction from the sources.

Lower density structures also impede I-fronts due to enhanced recombinations. Since the amount of clumping increases with time, the amount of resistance also increases with time (ISS05).

What causes the ionisation: local sources or the diffuse ionisation field? Does the answer depend on the nature of the structure? Low density gas will have a low density of sources but be easily ionised by a weak field. High density gas will have a high local density of sources and will require a strong field to overcome the enhanced recombination rates. Hence, low density gas will preferentially be ionised by the diffuse field and high density gas by local sources. Using simulations, KG06 confirm this trend.

Lyman limit systems are found predominantly within the viral radii of (proto-)galaxies, implicating them in galaxy formation. At least, that's the story according to KG06 who examined Lyman limit systems in simulations.

At low redshifts, the Lyα forest can be explained by a uniform UV background with all fluctuations due to structure. Conversely, at , different lines of sight to quasars reveal remarkably different optical depths even though there should be even less structure. An explanation is local fluctuations in the UV background. LBFF06 argue otherwise, suggesting that structure is still the primary source of variation at high redshift. In particular, the rare high-density features dominate the variance. They don't explain why the high-density features make a muck of things at high redshift. But the overall lower level of ionisation may be the cause.

If you put a number of sources in a uniform medium, their ionisation bubbles will grow, merge, and eventually fill space. As you look back at the surface of last absorption, you will see different depths (distances) in every direction, all about a mean depth. This is patchy reionisation. Suppose you start with neutral gas distributed in typical cosmological structures then turn on a uniform ionising field, varying depths will also be seen. This is not patchy reionisation. The depth observed does indeed vary along different lines of sight. How can we distinguish patchy reionisation from structure (LOF05)?

--Etittley 15:39, 24 June 2007 (BST)

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