Annu. Rev. Astron. Astrophys. 1998. 36: 267-316
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3.3. Absorption Line Widths

By measuring the line widths we may hope to gain insights into the temperature and kinematics of Lyalpha clouds. High resolution spectra showed that many low column density (NHI < 1015cm-2) Lyalpha lines do indeed show widths (b (= sqrt2 sigma) ~ 10 - 45 kms-1) that are consistent with photoionization temperatures (Chaffee et al. 1983; Carswell et al. 1984; review by Carswell 1988), though some lines appear to be as wide as 100 kms-1. Median Doppler parameters are around bmed ~ 30-35 kms-1, with a largely intrinsic scatter about the mean with standard deviation ~ 15 kms-1 (Atwood et al 1985; Carswell et al. 1991; Rauch et al. 1992). The Doppler parameters may decrease with increasing redshift. Williger et al (1994) have found an excess of lines with lower Doppler parameters b ~ 20kms-1 at z approx 4.

Occasionally, a correlation between Doppler parameter and column density has been noted (Carswell et al. 1984, Hunstead et al. 1988). However, the reality of this effect has been subject to a debate which culminated in the so-called "b-N controversy" (Hunstead & Pettini 1991; Webb & Carswell 1991; Peacock 1991), when Pettini et al. (1990) suggested that (when looked at with high enough resolution) Lyalpha lines had much lower Doppler parameters (mostly b ltapprox 22 kms-1) than previously thought. There also appeared to be a strong positive correlation between Doppler parameter b and column density N. These results were not confirmed by an analysis of another QSO spectrum with an identical observational setup (Carswell et al. 1991). The controversy was resolved when it was realized that the presence of noise in a spectrum can distort weak line profiles and lead to underestimates of the average b values of low column density lines. The problem is exacerbated by a detection bias against weak broad lines, which are more difficult to find against a noisy continuum and tend to end up below the detection threshold. The combination of these effects accounts for both the presence of spuriously low Doppler parameters and the apparent b - N correlation seen in these datasets (Rauch et al 1992, 1993).

RECENT KECK RESULTS     Data taken at similar resolution but with much higher signal to noise ratio with the Keck telescope's HIRES instrument have basically confirmed the earlier 4m results. Hu et al. (1995) found the Doppler parameter distribution at z ~ 3 to be well represented by a Gaussian with a mean of 28 kms-1 and width sigma = 10 kms-1, truncated below a cutoff bc = 20 kms-1. With increasing redshift, there seems to be a genuine trend to lower Doppler parameters. The finding by Williger et al (1994) of evolution in b appears confirmed: Median Doppler parameters for relatively strong lines (13.8 < log N(HI) < 16.0) change from 41 kms-1 (< z > ~ 2.3; Kim et al. 1997) to 31 kms-1 (< z > ~ 3.7; Lu et al 1996), with lower cutoffs dropping from 24 to 15 kms-1 over the same redshift range. The locus of the Pettini et al (1990) narrow lines in the b - N diagram is virtually empty (Hu et al 1995), as expected in data with such a high S/N ratio. Kirkman & Tytler (1997) obtain similar results for the Doppler parameters in their Keck data at even better S/N ratios, but they question the significance of the change with redshift, and find a lower, mean b of 23 kms-1 (< z > ~ 2.7) with a lower cutoff bc=14 kms-1 at logN(HI) = 12.5. However, at logN(HI) = 13.8 their minimum b at 19 kms-1 is very close to the result of Kim et al. 1997, so the analyses may well be consistent. It is conceivable that the discrepancies at lower column densities arise once more from the noise bias discussed above which may affect any dataset as long as there continues to be a supply of weaker and weaker lines crossing the detection threshold with increasing S/N ratio. The differences might lie in a different understanding of what constitutes "statistically acceptable fits" or "detectable lines". A dataset spanning a large redshift range, with - most importantly - a homogeneous S/N ratio would be desirable.

THE TEMPERATURE OF THE IGM FROM LINE PROFILES ?     Though narrow lines (b < 15 kms-1) are apparently very rare or even absent, this should not be interpreted as indicating a minimum temperature of the Lyalpha absorbing gas. The issue is more complex; in analogy with other astrophysical situations there are reasons for which a correlation might be expected between the temperature (or velocity dispersion) and the density (or column density) of the gas. Typical photoionization equilibrium temperatures should be in excess of 30000 K (e.g., Donahue & Shull 1991), but temperatures as low as 20000 K can be attained through inverse Compton cooling and a decrease of the ionizing spectrum at the HeII edge (Giallongo & Petitjean 1994). If photo-thermal equilibrium is abandoned, adiabatic expansion cooling can lower the temperatures further while maintaining high ionization, as suggested by Duncan et al (1991). Currently favored theories of Lyalpha clouds that are the result of cold dark matter-based gravitational collapse do predict a b - N correlation with temperatures for low column density clouds even below 104 K, as a consequence of adiabatic expansion and inefficient photoheating at low densities, while the larger column densities are heated as a result of compression during collapse. However, inspite of the low temperatures the Doppler parameters of the weak lines are predicted to be large because of bulk motion: Nature, in a random act of unkindness, has endowed these cool clouds with a large size so that the Hubble expansion dominates the line broadening. Yet, it may be worth trying to track down the residual influence of the gas temperature on the line profiles. The lower column density systems are at gas densities where the cooling time (for processes other than expansion cooling) exceeds a Hubble time. Therefore, the gas retains a memory of the temperature after reheating is complete (Miralda-Escudé & Rees 1994; Meiksin 1994; Hui & Gnedin 1997), and the process of reheating may have left a record in the Doppler parameter distribution (Haehnelt & Steinmetz 1998).

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