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Measurements of the ionization fraction

(Weinberg, "Gravitation and Cosmology"):

The Lyman-α line of hydrogen, at 1215 Å is produced by the transition from 1s to 2p state. Normally, this wavelength does not penetrate the earth's atmosphere. But if if the source is red-shifted between 1.5 < z < 6, then it is visible in the 3000 Å to 7000 Å transperency window. A larger window is of course possible from space.

The Lyman-α absorption coefficent is . This is very convenient, since it leads to typical optical depth of order 0 < τ < 2. Also, suppression of absorption by stimulated emission is prevented by the high energy of the transition, corresponding to about 10 ev = 118,000 K.

Quasars show Lyman-α as an emission line. Hence, suppression of photons blueward of the line indicates absorption by neutral hydrogen at . The absorption eats into the quasar continuum.

FZH04a: Develop a model of reionization in which HII regions develop around regions of high overdensity. Show how to construct power spectra of the resulting HI field and how to relate that to the HII region morphology.

LOFAR will be able to probe reionization (ZS04). LOFAR should be able to measure the thickness of ionization fronts around hard sources. ZS04 looked at Pop III starburst and Miniquasar spectra and show that the thickness is different. LOFAR can resolve the Miniquasar front.

Along with the Lyα forest, there are other "forests" for other transitions, some in entirely different regimes of the EM spectrum. Nicastro05 reports the detection of an x-ray forest are due to highly ionised resonant line absorption. He-like oxygen and H-like nitrogen are visible in the spectrum of Mkn 421. The column density for both are on the order of 10¹⁵cm ^{− 2} and are in systems at z = 0.011 and 0.027. The inferred temperatures () are different from associated Lyα systems () suggesting a multiphase WHIM.

Reionization also effects the CMB signal. Via the kinetic SZ effect, structure in the reionization pattern imprints its signature on the CMB. The effect on the power spectrum is sensitive to the sources (McQuinn05). Pop III stars lead higher power than other sources.

When the upcoming low-frequency radio observatories like Low Frequency Array (LOFAR), the Mileura Widefield Array (MWA) and eventually the Square Kilometer Array (SKA) come online, they will be able to observe the 21cm line of neutral hydrogen at high redshift. Since the 21cm line is so narrow, it will be able to follow the depletion of HI through the period of ionization. Obviously these will constrain the models of reionization. Fluctuations in the brightness temperature (radio-head jargon for intensity) maps will be describable by a power spectrum which is a function of frequency ν∼(1 + z)21cm. At redshifts high enough that the baryons are entirely neutral, the powerspectrum will be strongly correlated with the powerspectrum of the density fluctuations. Bulk flows will affect the powerspectrum in a manner similar to the 'fingers of god'. As HII regions grow, holes will develop in the map. Consequently, the powerspectrum will develop a peak at the scale of the mean size of these voids. Clearly, the shapes of these voids and their affect on the power spectrum will be dependent the distribution of sources, the sharpness of the edges of the HII regions (and consequently the shape of the source spectra), and the relation of the background density to the source distribution through effects like shadowing by dense (i.e. damped) systems. Unfortunately, the foreground signal at the ∼ 1m wavelengths is several orders of magnitude brighter than the expected signal. Fortunately, the foreground signal is expected to be smooth, while the high-redshift signal is expected to be high frequency. Hence, subtracting the smooth component should retrieve the high-redshift signal.

Polarisation of the 21cm signal is produced by the same mechanism that induces polarisation in the CMB signal (BL05): Thomson scattering. Since Thomson scattering is off of free electrons, the polarisation signal probes the HII regions prior to overlap and the free electron optical depth after overlap. The foreground signal is expected to be polarised. Differencing might still be possible.

Lyα photons will be absorbed if the gas is neutral. The statistics of high-redshift Lyα sources put limits on the ionization volume fraction. Using conservative estimates of the number density of sources and the size of the Stromgren spheres around the sources, MR05 find a lower limit to the ionized volume fraction of 20-50% at z = 6.5.

GRBs

Totani06 uses the IR spectrum of the afterglow of the z=6.29 GRB050904 to conclude that the IGM was mostly ionized (x_HI < 0.6 (95% CF)) by z=6.3. They used the Lyα damping wing for their analysis.

The unabsorbed afterglow spectrum of GRB 050904: , with α = -1.25. (Haislip et al. (2006), Tagliaferri et al. (2005)). β = -1.36 ± 0.06 (t < 1 day); -0.82 ± 0.15 (1 day < t < 2.6 days); -2.4 ± 0.4 (t > 2.6 days) (Tagliaferri et al. (2005)).

There was hope that GRB spectra may be able to probe the H fraction at high redshifts. GRB050904 was a z=6.29 GRB whose Lyα forest was measured ( Haislip et al. (2006), Kawai et al. (2005), Tagliaferri et al. (2005), and Totani06 ). Half the GRB detected by swift are "dark bursts": x-ray bright but optically undetected afterglows. The previous studies looked at the damping wing red-ward of Lyα in the observed infrared spectrum. McQuinn07 revisited the fitting and note that the constraints on x_H are weak for the same reason I found when fitting damping wings to QSO data: a low ionization fraction is indistinguishable from a high ionization fraction with a few pockets of very low ionization.

Apparently GRBs, being time-variable, permit quantification of the time evolution of the IGM via multiple samplings of the LOS (Starling et al. 2005, Vreeswijk et al. 2007). I really don't understand this. The evolution during our lifetime is surely insignificant.

GSFC07 looked at the size of the largest gaps in the IR spectra of the GRBs and decided they are sensitive to the reionization history. They also examined the spectrum of GRB050904 and concluded that at z∼6. If reionization occurs later, then the gaps are larger and more numerous. Seems pretty sensible. But then they refer to the multiple samplings (taken only hours or days apart) to probe the evolution. Again, I don't understand this. Surely it is identical to varying the threshold for measuring the gap widths in the highest S/N spectrum (the earliest, usually). And they really don't test for cosmic variance.

There is a curiously beneficial selection effect in GRBs. If you take an IR spectrum of a GRB a fixed amount of time after detection of the burst, the fact that high-z GRBs are subject to time dilation means they will be observed in the IR sooner and, hence, at a brighter phase, conveniently offsetting (partially) the dimming due to the larger distance. It is found that GRBs only dim as (1+z)^-1 when the IR spectra are taken.

Etittley 12:43, 9 October 2007 (BST)

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Bibliography

GSFC07: Gallerani, Salvaterra, Ferrara, & Choudhury: "Testing Reionization with Gamma Ray Burst Absorption Spectra" 0710.1303

McQuinn07: McQuinn, Lidz, Zaldarriaga, Hernquist, & Dutta: "Probing the Neutral Fraction of the IGM with GRBs during the Epoch of Reionisation" 0710.1018

Totani06: Totani et al: "Implications for Cosmic Reionization from the Optical Afterglow Spectrum of the Gamma-Ray Burst 050904 at z=6.3" 2006PASJ...58..485T