4. Lyman alpha statistics

A statistically well-defined sample of Ly lines in the region between the Ly and Ly emissions ( 5191 Å) can be obtained from Table 2. The Ly lines affected by the proximity effect ( Mpc from the QSO; see Bajtlik et al. 1988; Lu et al. 1991) and those associated with metal systems (indicated as MLy) are excluded from the sample.

 
Figure 2:   Plot of the Doppler parameter b vs. the logarithmic column density for the Ly lines listed in Table 2.

The distribution of lines in the plane is shown in Fig. 2 (click here). The lack of lines at the top left corner can be ascribed to an observational bias: as already shown by GCFT, the selection criterion tends to miss lines with low column density and large Doppler width.

The dataset can be considered virtually complete (for typical b values) for .

A considerable fraction of the lines with belongs to complex saturated systems. As a consequence, the deblending choices and therefore the fitting parameters may be not always unique. A considerable improvement can be obtained when the simultaneous fit of the saturated Ly and the corresponding Ly line is possible. Unfortunately, due to the high density of Ly lines at these redshifts, Ly absorptions with an uncontaminated profile are rare and the uncertainty for most of the lines in the right region of the diagram  2 (click here) cannot be removed.

Simulations carried out by Fontana & Ballester (1995) show that, for isolated, unsaturated lines at , the parameters given by the fitting procedure are quite close to the "true'' value, with a small and symmetric scatter around it. At column densities larger than 10^14.5 cm^-2 the Ly lines are saturated and b and N correlate strongly, increasing the uncertainties.

By comparing our list of lines with that published by GCFT, we have verified on real data how the diagram changes when the average s/n ratio is almost doubled, checking the trends expected on the basis of simulations.

To carry out a meaningful comparison, we have considered only the isolated Ly lines in common between the two line lists, at wavelengths Å. In this range the s/n per resolution element is . The lines are listed in Table 3 (click here).

Figure 3 (click here) shows the individual trajectory of each absorption line in the plane . GCFT parameter values are indicated by the solid black circles and our values correspond to the end of the adjoining line.

Saturated lines tend to move keeping approximately constant the equivalent width value, as observed in the simulations (Fontana & Ballester 1995). Often they correspond to complex features. If the improved s/n is not sufficient for a proper deblending, but the better definition of the wings forces a fit with a lower b parameter, then they move toward higher column densities.

Lines with low column density in regions with low s/n ratio have poorly defined profiles and are very sensitive to the continuum level. The s/n increase, together with a choice of a slightly lower continuum with respect to GCFT, has induced a migration from high b values and small column densities toward smaller Doppler widths.

   

Present work GCFT sample

# b b

1 4783.51 13.47 35.62 4783.72 13.72 47.09

2 4808.53 14.91 33.13 4808.30 14.62 41.59

3 4818.06 15.74 39.26 4817.86 14.80 56.55

4 4829.85 14.50 25.84 4829.67 14.16 38.82

5 4841.99 13.73 36.72 4841.83 13.65 30.28

6 4843.75 13.82 20.23 4843.61 13.73 22.10

7 4864.48 13.31 33.41 4864.25 13.73 56.34

8 4868.72 13.95 28.22 4868.49 13.86 45.75

9 4881.81 13.11 27.04 4881.50 13.41 20.62

10 4883.56 13.59 45.18 4883.55 13.59 32.21

11 4885.29 13.17 29.13 4885.17 13.33 29.11

12 4892.98 13.79 32.84 4892.90 13.80 31.03

13 4896.47 14.14 28.48 4896.26 14.23 27.78

14 4926.34 13.51 51.57 4926.28 13.37 13.32

15 4929.33 13.69 26.21 4929.10 13.71 27.53

16 4930.68 13.61 25.96 4930.46 13.63 28.94

17 4950.41 13.44 38.58 4950.44 13.54 52.10

18 4958.86 13.77 24.59 4958.70 13.91 37.90

19 4989.55 13.30 24.55 4989.60 13.39 23.47

20 4994.34 13.84 21.08 4994.23 13.81 22.55

21 5001.80 13.00 20.12 5001.91 13.24 24.82

22 5003.64 12.94 14.17 5003.67 13.36 32.17

23 5010.85 13.14 33.86 5010.40 13.38 35.23

24 5020.79 13.30 19.94 5020.84 13.35 13.48

25 5041.69 14.04 26.85 5041.48 13.98 25.82

26 5050.05 13.89 23.05 5049.84 13.79 18.03

27 5051.05 13.86 23.62 5050.83 13.80 29.00

28 5055.37 13.75 24.71 5055.22 14.03 34.67

29 5062.65 13.52 22.96 5062.51 13.66 27.73

30 5065.30 14.46 27.59 5065.08 14.29 33.37

31 5073.73 13.36 26.76 5073.34 13.22 8.26

32 5099.63 13.10 28.88 5099.25 13.44 62.69

33 5118.56 13.91 24.91 5118.41 13.99 26.83

34 5119.60 13.45 18.90 5119.37 13.56 16.25

35 5143.81 14.19 27.28 5143.64 14.26 29.70

36 5150.82 13.32 36.15 5150.61 13.35 31.57

37 5155.51 12.83 18.10 5155.42 12.84 25.19

38 5162.33 12.85 27.16 5162.03 12.94 32.15

39 5167.94 13.03 31.53 5167.80 13.22 34.33

40 5170.47 13.25 19.81 5170.31 13.24 22.54

41 5185.15 13.33 42.25 5184.94 13.43 42.56

Table 3: Isolated lines in common between this sample and that of GCFT

 
Figure 3:   Migration diagram illustrating the effect of improving the s/n ratio on the determination of the absorption lines parameters. The points correspond to the GCFT determination

 
Figure 4:   Doppler parameter distribution for the Ly lines in Table 2, out of 8 Mpc from the quasar PKS 2126-158

The Doppler width distribution of the complete () sample of Ly lines is shown in Fig. 4 (click here).

Using the standard assumption that line broadening is due exclusively to thermal motion, the relation between Doppler parameter and temperature, , (where k is the Boltzmann constant and m is the hydrogen mass) implies that the peak value km s^-1 corresponds to a cloud temperature of K.

The Ly sample contains 21 lines, i.e. , with km s^-1, and 12 lines, i.e. , with km s^-1. Such percentages are almost halved compared with those found in the previous work by GCFT. Nonetheless, it has to be noted that the peak value of the b distribution is roughly the same for the two samples.

The nature of the distribution of Ly clouds Doppler parameters has led in the past to controversies. Pettini et al. (1990) found Ly lines with a median Doppler parameter of 17 km s^-1 and a strong intrinsic correlation between Doppler width and column density. From these results a scenario of very cool, dense and practically neutral clouds emerged, in contrast with previous models. Starting from data with similar resolution, Carswell et al. (1991) following different selection and analysis criteria obtained significantly larger average and median Doppler parameters and, above all, no b-N correlation. Our median b value is intermediate between the results of Pettini et al. and that of Carswell at al. and it agrees with recent result at very high resolution (Hu at al. 1995; Lu et al. 1996).

  
Figure 5: Column density distribution of the Ly lines out of 8 Mpc from the quasar PKS 2126-158. The overplotted solid line represents a power-law distribution, , with (Hu et al. 1995; Giallongo et al. 1996)

The column density distribution of our Ly line sample is shown in Fig. 5 (click here). As shown in Fig. 2 (click here), for values a selection bias is expected: only lines with small Doppler parameters are detectable. This is confirmed by the drop of the column density distribution below this value. The shape of the distribution is in agreement with the power-law fit , with , obtained in the recent works by Hu et al. (1995) and Giallongo et al. (1996).

The number density of lines per unit redshift, in the wavelength interval Å for Ly absorptions with , is in good agreement with the cosmological redshift distribution (Giallongo et al. 1996).