Influence of the continuum determination method on the mean transmission in the Lyα forest
Determination of the initial flux, or continuum, in the quasar spectra prior to its absorption by the intergalactic Hi is nontrivial problem and it affects the precision of the mean transmission in the Lyα forest, F(z). The results of comparison of the F(z) values obtained using different methods of...
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| Цитувати: | Influence of the continuum determination method on the mean transmission in the Lyα forest / O. Torbaniuk // Advances in Astronomy and Space Physics. — 2016. — Т. 6., вип. 1. — С. 34-40. — Бібліогр.: 51 назв. — англ. |
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irk-123456789-1199482017-06-11T03:03:27Z Influence of the continuum determination method on the mean transmission in the Lyα forest Torbaniuk, O. Determination of the initial flux, or continuum, in the quasar spectra prior to its absorption by the intergalactic Hi is nontrivial problem and it affects the precision of the mean transmission in the Lyα forest, F(z). The results of comparison of the F(z) values obtained using different methods of the continuum determination are presented in this paper. This analysis was conducted using the most complete compilation of the F(z) data from the literature. It was found that the values of the F(z) obtained with the manually determined continuum are systematically higher than those obtained from extrapolated continuum. The difference varies from 5% at z = 2 up to 33% at z = 4.5, respectively. 2016 Article Influence of the continuum determination method on the mean transmission in the Lyα forest / O. Torbaniuk // Advances in Astronomy and Space Physics. — 2016. — Т. 6., вип. 1. — С. 34-40. — Бібліогр.: 51 назв. — англ. 2227-1481 DOI:10.17721/2227-1481.6.34-40 http://dspace.nbuv.gov.ua/handle/123456789/119948 en Advances in Astronomy and Space Physics Головна астрономічна обсерваторія НАН України |
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Determination of the initial flux, or continuum, in the quasar spectra prior to its absorption by the intergalactic Hi is nontrivial problem and it affects the precision of the mean transmission in the Lyα forest, F(z). The results of comparison of the F(z) values obtained using different methods of the continuum determination are presented in this paper. This analysis was conducted using the most complete compilation of the F(z) data from the literature. It was found that the values of the F(z) obtained with the manually determined continuum are systematically higher than those obtained from extrapolated continuum. The difference varies from 5% at z = 2 up to 33% at z = 4.5, respectively. |
| format |
Article |
| author |
Torbaniuk, O. |
| spellingShingle |
Torbaniuk, O. Influence of the continuum determination method on the mean transmission in the Lyα forest Advances in Astronomy and Space Physics |
| author_facet |
Torbaniuk, O. |
| author_sort |
Torbaniuk, O. |
| title |
Influence of the continuum determination method on the mean transmission in the Lyα forest |
| title_short |
Influence of the continuum determination method on the mean transmission in the Lyα forest |
| title_full |
Influence of the continuum determination method on the mean transmission in the Lyα forest |
| title_fullStr |
Influence of the continuum determination method on the mean transmission in the Lyα forest |
| title_full_unstemmed |
Influence of the continuum determination method on the mean transmission in the Lyα forest |
| title_sort |
influence of the continuum determination method on the mean transmission in the lyα forest |
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Головна астрономічна обсерваторія НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/119948 |
| citation_txt |
Influence of the continuum determination method on the mean transmission in the Lyα forest / O. Torbaniuk // Advances in Astronomy and Space Physics. — 2016. — Т. 6., вип. 1. — С. 34-40. — Бібліогр.: 51 назв. — англ. |
| series |
Advances in Astronomy and Space Physics |
| work_keys_str_mv |
AT torbaniuko influenceofthecontinuumdeterminationmethodonthemeantransmissioninthelyaforest |
| first_indexed |
2025-07-08T16:58:35Z |
| last_indexed |
2025-07-08T16:58:35Z |
| _version_ |
1837098774667722752 |
| fulltext |
In�uence of the continuum determination method
on the mean transmission in the Lyα forest
O.Torbaniuk
∗
Advances in Astronomy and Space Physics, 6, 34-40 (2016) doi: 10.17721/2227-1481.6.34-40
© O.Torbaniuk, 2016
Main Astronomical Observatory of the NAS of Ukraine, 27 Akademika Zabolotnoho Str., Kyiv 03680, Ukraine
Determination of the initial �ux, or continuum, in the quasar spectra prior to its absorption by the intergalactic
Hi is nontrivial problem and it a�ects the precision of the mean transmission in the Lyα forest, F̄ (z). The results
of comparison of the F̄ (z) values obtained using di�erent methods of the continuum determination are presented in
this paper. This analysis was conducted using the most complete compilation of the F̄ (z) data from the literature.
It was found that the values of the F̄ (z) obtained with the manually determined continuum are systematically
higher than those obtained from extrapolated continuum. The di�erence varies from 5% at z = 2 up to 33% at
z = 4.5, respectively.
Key words: quasars: absorption lines, methods: data analysis, statistical, large-scale structure of Universe
introduction
The Lyα forest in the spectra of distant quasars
traces the thermal and radiative history of the Uni-
verse, as well as the evolution of underlying matter
distribution over a wide range of scales and redshifts.
It is possible due to relation of the Lyα opacity of the
intergalactic neutral hydrogen H i to its density and
other physical parameters. As a measure of opacity
the value F = e−τ named the transmission is used;
here τ is the optical depth. Fluctuations of this value
δF provide an invaluable information about the den-
sity �uctuations on the smallest scales, available for
observations [7, 12, 23, 28, 32, 34].
These studies mainly involve the following steps:
(i) determination of the continuum level and nor-
malization the spectrum onto it, (ii) determination
of the mean transmission F̄ , which is a function of
the redshift, (iii) calculation of the transmission �uc-
tuations and their two-point statistics (transmission
autocorrelation function ξF (∆v) and the �ux power
spectrum PF (k)). The last step is not simple from
the math point of view, but it is well understood and
unambiguous. The �rst two steps, involving the data
processing, are much more ambiguous and encounter
some problems.
One of them is related to the choice of absorption-
free regions within the Lyα-forest. Directly it is
possible only in the case of high-resolution spectra,
when continuum is usually �tted manually and in-
terpolated with spline-polynomials (see e. g. [4, 12,
14, 31]). In the case of median-resolution spectra
it is di�cult to select unabsorbed regions, there-
fore indirect techniques based on some assumptions
about the quasar spectrum shape are applied. In
the present paper we tried to compile the most com-
plete sample of the F̄ values from the literature and
analyse the di�erence between those obtained with
di�erent methods of continuum determination.
compilation of
the F̄ (z) measurements
Our compilation of the F̄ (z) measurements from
the literature is presented in Figure 1. Short descrip-
tion of these data, including the continuum determi-
nation method, is shown in Table 1. Here we use
the term �continuum� for the whole intrinsic spec-
trum, including emission lines. There are two main
classes of methods that are used for this purpose (see,
e. g. review in [20, 47]). One class deals with ex-
trapolation of continuum on wavelengths longer than
1215Å, another class does not use information out-
side the Lyα forest. Both of these techniques have
several modi�cations and own pros and cons, some
of them are noted by the authors of the papers men-
tioned in Table 1.
For example, in [31] for a sample of eight high
resolution quasar spectra with low signal-to-noise ra-
tio F̄ (z) was determined in three redshift bins. For
this work continuum was obtained manually by com-
mon interpolation of the regions free from absorp-
tion lines using spline or Chebyshev polynomials.
Authors noted some possible sources of continuum
errors related to this procedure, e. g. underestima-
tion of continuum at low redshifts (z ∼ 2) due to
large shallow �ux depressions and its overestimation
at high redshifts (z > 4) because of the high density
of absorption lines that prevents accurate reproduc-
∗el.torbaniuk@gmail.com
34
Advances in Astronomy and Space Physics O.Torbaniuk
tion of continuum.
Similar problem with high-redshift quasars was
also noticed in [22], where authors used own mea-
surements of three quasar spectra with combination
of spectra from [16, 24, 27, 30, 33, 40]. The values of
τeff were calculated at redshift range ∼ 1.5− 4.4. In
addition a compilation of low redshift (z < 1.5) data
from the HST [1, 17, 18, 35] was used. In [21] the
authors obtained the redshift dependence of the τeff
at 1.5 < z < 4, which is well described by a single
power law τeff(z) = 0.0032(1+z)3.37±0.20. This gives
the value of τeff(z ≈ 0) at least four times lower than
that from HST observations.
The tendency of systematic underestimation of
the zeroth or �rst-order contribution to the contin-
uum by usual manual �tting methods with multiple
splines or other high-order polynomials was also dis-
cussed by [38]. They noted, that such continuum
underestimates results because of small number of
pixels at low �ux decrement, therefore they adopted
the highest �ux value in each individual simulated
spectrum as the value of the continuum. Such simple
approximation allows to limit from the top the e�ect
of continuum �tting while measuring the �ux decre-
ment. This technique was applied by authors for
�tting continuum in seven HIRES spectra from [39],
for other 14 UVES spectra from this work contin-
uum was �tted manually according to procedure de-
scribed in [22]. Using combined sample of 21 spectra
and after removal of pixels contaminated by metal
lines they found the best �t to τeff(z): log τeff =
log τ0 + α [(1 + z)/4] with log τ0 = −0.44 ± 0.01,
α = 3.57± 0.20.
In [14] the authors have found that their esti-
mations of the quasar continuum obtained by cu-
bic spline interpolation are systematically biased low,
with the magnitude of the bias increasing from < 1%
at z = 2 up to 12% at z = 4. Authors noted that
this bias can be accounted for using mock spectra.
More complicated automatic algorithms in addi-
tion to simple interpolation by some polynomials
over the unabsorbed regions are applied to high-
resolution spectra , e. g. the CANDALF software de-
veloped by R.Baade and used in [19] for a sample
of high-resolution low-redshift quasars. Such soft-
ware determines continuum simultaneously with the
line �tting procedure. Similar idea of adjustment of
the continuum level with absorption lines �tting was
used in [20].
For low and medium-resolution spectra the con-
tinuum �tting procedure is more complicated due to
a smaller number of unabsorbed parts that can be
seen by eye. In this case some special algorithms are
used instead of manual search for unabsorbed parts.
One of such techniques was proposed in [9] and ap-
plied in [8] using LRIS spectra from [50]. The itera-
tive algorithm consists of multiple �tting of spectrum
point by third-order polynomial and rejecting points
lying below 2σ from the �t.
All the methods of continuum determination
within the Lyα-forest region that take into account
the longer wavelength part of spectrum are based on
the idea, that the whole shape of the UV-bump is a
result of some general physical processes. The �rst
steps in this direction were made in pioneer work by
Press, Rybicki & Schneider [37]. They obtained τ(z)
using 29 spectra of SSG sample extrapolating con-
tinuum shortward of the Lyα emission line in a form
∼ C1/2λ
1/2+C1λ. Such extrapolation is useful when
the number of unabsorbed pixels in the Lyα forest is
too low for high-precision interpolation, that can be
caused by either low spectral resolution or low trans-
mission level at high redshifts even in high-resolution
spectra.
To avoid this problem for high-redshift quasars
the authors of [44] extrapolated continuum in the
Lyα region in a sample of 15 spectra at 4 < z < 6
with the power law ∼ λ−1.25. Changing the spec-
tral index from −0.75 and −2 they found, that for
this range there is a ±18% range in the spectrum
normalization at 1075Å. The same continuum ex-
trapolation, but with spectral index −1.5, was also
applied for four high-redshift quasars in [5]. The
data from [44] plotted in Fig. 1 are those averaged
over six redshift bins from a combined sample of their
own spectra and those from [5]. The same extrap-
olation was used by [43] for moderate-resolution
ESI data with redshift above 4.5, while in other
HIRES and ESI spectra continuum was �tted man-
ually. Comparing the two methods in the redshift
range 4.0�4.5 authors have found that the ratio of
continuum values for these cases is 0.84±0.18, which
gives a relatively small correction to the transmission
values. Note, that the value of spectral index used
in [5, 43, 44] is lower than that found, e. g. in [49]
for a part of quasar composite spectrum redward of
1215Å, but it is more close to values found for a part
of the spectrum blueward of the Lyα emission line
from the HST and FUSE UV-spectra of the near-
est quasars in [41, 46, 51]. On the other hand, for
a sample of the 19 most distant quasars with z up
to 6.42 the authors of [13] used the spectral slope
of α = 1.5, which is similar to that of [49], which
describes the mean quasar continuum in the range
of ∼1300�5000Å. Extrapolation of the continuum
was also used for high-resolution spectra at high red-
shifts, e. g. for sample of 15 spectra at 4 < z < 6 with
the power law continuum ∼ λ−1.25 in [44].
More general method based on quasar spectra
similarity, and hence involving composite spectra,
was proposed for medium-resolution spectra in [6]
and used for a sample of 1061 SDSS quasars. In
this case the part of a composite spectrum in the
Lyα forest region is considered as a multiple of in-
trinsic quasar spectrum (unabsorbed continuum and
emission lines) and the mean transmission F̄ (z′) at
given redshift z′. It is clear, that such consideration
35
Advances in Astronomy and Space Physics O.Torbaniuk
su�ers from degeneracy between F̄ (z′) and ampli-
tude of continuum, thus the authors had to �x one
of them and adopted the unasborbed continuum to
be described by a power law extrapolated according
to [37]. Later, the same technique was used by [36]
for a sample of 2dF spectra. Similar consideration
of spectra as a sum of power-law continuum, extrap-
olated from longer wavelength region, and several
emission lines was used in [11] for a sample of SDSS
quasars, but in this case the spectral index was esti-
mated spectrum-by-spectrum. It was noticed, how-
ever, that such extrapolation yields the values of F̄ ,
which are ∼ 8% smaller than those obtained from
high-resolution spectra (e. g. [11]; see also discussion
in [42, 48]). This discrepancy evidences for overesti-
mation of the continuum level in the case of extrap-
olation.
More complicated method was proposed in [32].
Instead of using composite spectra the authors of [32]
worked with a whole sample of individual spec-
tra. Applying the principal component analysis they
found the mean intrinsic spectrum, mean transmis-
sion and mean generalized calibration vector, a func-
tion de�ned by them to include calibration errors and
mean absorption by metal lines with λ > 1300Å, and
also their �uctuations.
Recently, [3] introduced a novel technique, which
exploits the same idea as in [6], but unlike [6] the
authors of [3] used composite spectra to measure
the overall shape of the mean �ux evolution with-
out �tting continua. To break the degeneracy be-
tween F̄ (z′) and continuum amplitude the authors
derived only the ratio of the mean transmission at
di�erent redshifts to its value at z ∼ 2 and then
normalized the results to measurements made from
high-resolution data. To account for di�erences in
shape of individual spectra, they adjusted the con-
tinuum slope to some reference composite spectrum.
However, the authors of [3] point out signi�cant vari-
ations of the Lyα emission line between the compos-
ite spectra with di�erent redshift, and relate these
variations to redshift errors caused by the line asym-
metry due to absorption of its blue side.
Another method of predicting quasar continuum
within the Lyα forest region proposed in [45] uses
the same idea of correlation of the quasar spec-
tral shape in di�erent parts of spectrum, but do
not postulate the constant spectral index over the
whole spectrum. Instead of simple extrapolation,
the authors applied principal component analysis for
50 low-redshift spectra from the HST and proposed
to reconstruct continuum in the range from 1020 to
1216Å knowing the spectral shape in the range of
1216�1600Å using their relation between the weights
of principal components for these regions. The rea-
soning for such method are the correlations between
the unabsorbed �ux in these two wavelength regions,
found by the authors in the HST spectra. The
authors tested their method on HST spectra and
found an average absolute �ux error of 9%, with a
range of 3%�30%.
the method of comparison
All the data compiled in Fig. 1 and described
in the previous section were presented as sets
{z, ∆z, τeff , σup
τ , σlow
τ } or {z,∆z, F̄ , σup
F , σlow
F },
that depend on the results form presented in particu-
lar article: in one case authors presented the e�ective
optical depth τeff and in other � mean transmission
F̄ . Here ∆z is the redshift range in which the value
of F was averaged, σup
τ , σlow
τ and σup
F , σlow
F are the
upper and lower errors of the corresponding values.
For further analysis the all data were recalculated in
terms of the F̄ , and for each value of F̄ we found
the arithmetic mean error of σF from the upper and
lower values.
After this uni�cation two subsamples of the mean
transmission values with redshifts range z > 1 were
compiled. In this redshift range the F̄ (z) dependence
can be described by a power law. The �rst subsam-
ple includes only the results obtained with manual
methods of the continuum �tting using absorption-
free regions of spectrum selected �by eye� and inter-
polated by polynomials (splines, Chebyshev polyno-
mials, etc.). Mainly, the �rst subsample includes the
results from [10, 14, 16, 21, 22, 20, 24, 30, 31, 33, 39,
40, 43, 47, 50]. In [10] and [47] the continuum was
additionally �xed using the simulated spectra.
The second subsample includes data obtained
with extrapolated continuum (as a power law from
redward part of spectra with di�erent values of the
spectral index [5, 11, 36, 44, 43]).
It should be noted that the data from [14, 39, 47]
are presented taking into account absorption of
metals that also exist in the intergalactic medium.
Determination of the shape of the metal absorption is
di�cult. Typically, separate search of metals lines in
high-resolution spectra, where metal lines are much
smaller than the Hydrogen lines, is produced. Unfor-
tunately, in medium or low resolution spectra such
procedure is not possible and �statistical� method of
the metals impact subtraction is applied. It consists
of a determination of the transmission level of the in-
tergalactic medium in the redward part of the spec-
trum, free from absorption of neutral hydrogen, and
further subtracting from the value of transmission in
the Lyα-forest, which is actually the sum of trans-
mission in the Lyα-line and transmission in lines of
metals. Since the contribution of the metal absorp-
tion is about 1-2% it can be neglected in present
studies of the comparison of methods of continuum
�tting. In fact, we started with a calculation with-
out the data from [14, 39, 47], but since the di�erence
between F̄ (z) obtained with and without those data
appeared to be about 1-2%, we decided to those data
to our �nal sample.
36
Advances in Astronomy and Space Physics O.Torbaniuk
The data from both subsamples were �tted by
the dependence F̄theor(z) = e−τeff(z), where τeff(z) =
α(1 + z)β , α and β are free parameters. The values
of parameters were determined using the method of
maximum likelihood [29], i. e. maximizing of the
function L ∼ exp
(
−χ2/2
)
, where
χ2 =
∑
i
[
F̄i − F̄theor(zi)
]2
/σ2
F,i.
results and discussion
The best-�t values of α and β parameters along
with the marginalized 1σ-errors are given in Ta-
ble 2. In Fig. 2 the best-�t with 1σ-errors inter-
val and 1,2,3σ contours for likelihood function are
shown.
From Fig. 2 it can be seen that the values of F̄
from the �rst subsample (manual �tting of the con-
tinuum) are systematically higher than that from the
second subsample and this di�erence increases from
5% at z = 2 to 33% at z = 4.5. Unfortunately,
comparison of these methods is impossible on high
redshift, since unabsorbed part in the Lyα forest
at z ≳ 4 cannot be selected due to the high den-
sity of absorption lines (the so-called �Gunn-Peterson
trough� at z ∼ 5− 6).
There are few main reasons of the such di�er-
ence between obtained values of the mean transmis-
sion. Firstly, the interpolated unabsorbed parts of
the spectrum are usually chosen �by eye� without
any studies of the form of emission line pro�les and
other physical parameters. For example, some in-
tensive emission line may be absorbed so its �ux is
equal to the average �ux in the �pure� continuum,
that leads to an underestimation of �true� continuum
level. Secondly, the extrapolation does not include
the emission lines therefore continuum is chosen as
the �average� with lines or �pure� continuum extrap-
olated from the redward region from Lyα line with
higher spectral index than in the Lyα-forest region.
It is interesting to compare the current result with
those from [3]. Its authors use a method which is
actually a �mix� of both continuum �tting proce-
dures. Their results are shown in Fig. 2 with dia-
monds. One can see that values of F̄ (z) from [3] are
consistent with our �t for the �rst subsample because
the authors of [3] normalized their values onto some
mean value F̄ (z) at z = 2 from high-resolution spec-
tra. But on higher redshifts these values are more
close to our �t for the second subsample. Since [3]
tried to reproduce the full shape of the initial quasar
spectra in the Lyα-region, this result, probably, in-
dicates that continuum obtained by extrapolation is
closer to the real one than that obtained by man-
ual �tting procedure. Certainly, this claim requires
independent veri�cation.
acknowledgement
The author is thankful to Dr. Ganna Ivashchenko
and Dr. Irina Vavilova for their invaluable help
and fruitful discussions. This work has been sup-
ported by the Target Programme of Space Research
of the NAS of Ukraine for 2013-2016 and by the Swiss
National Science Foundation grant SCOPE IZ7370-
152581.
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38
Advances in Astronomy and Space Physics O.Torbaniuk
Table 1: Description of the data plotted in Fig. 1. The number of spectra in the sample and the point of obtained
F̄ (z) are designated as n and p, respectively. KPE stands for the Echelle spectrograph at Kitt Peak Observatory,
MMT is Multiple Mirror Telescope, UCLES/AAT is the University College of London Echelle Spectrograph at the
Anglo-Australian Telescope, HIRES is the High Resolution Echelle Spectrometer at the Keck telescope, LRIS is the
Low Resolution Imaging Spectrometer at the Keck II telescope, UVES is the UV-Visual Echelle Spectrograph at the
VLT telescope, Kast is the double spectrograph on the Shane 3m telescope at Lick observatory, HET is Hooby-Eberly
Telescope, KP is Kitt Peak 4m MARS spectrograph, MIKE is the Magellan Inamori Kyocera Echelle spectrograph on
Magellan; GHRS, FOS and STIS are spectrometers on the HST; 2QZ is the Two-degree Field QSO Redshift Survey.
The rows marked with [K01] and [K02] are those, for which the values of τeff were took not from original papers, but
from [22] or [21], respectively. [22] estimated τeff from the spectra generated arti�cially using the line list provided
in original papers, except [40]. The continuum approximation technique described in [38], [48] are denoted by [R97],
[T04].
n p R = λ/∆λ origin zf continuum source
29 � ∼ 300 SSG sample 2.5�4.3 extrap. Press et al. (1993) [37]
13 13 180, 1300 FOS 0�0.95 manually Bahcall et al. (1993) [1] / [K02]
4 3 36000 HIRES 2.74�3.20 manually Hu et al. (1995) [16] / [K01]
1 1 ∼ 45000 HIRES 3.4�4.0 manually Lu et al. (1996) [30] / [K01]
3 7 ∼ 650 FOS 0.52�1.72 manually Impey et al. (1996) [18] / [K02]
1 1 6000-16000 KPE, MMT 1.67�2.10 manually Kulkarni et al. (1996) [27] / [K01]
1 1 ∼ 38000 HIRES 2.50�2.81 manually Kirkman et al. (1997) [24] / [K01]
10 11 ∼ 1500 GHRS 0.006�0.223 manually Impey et al. (1999) [17] / [K02]
1 1 35000 UCLES/AAT 1.92-2.17 manually Outram et al. (1999) [33] / [K01]
15 4 ∼ 16000 GHRS 0�0.07 manually Penton et al. (2000) [35] / [K02]
8 3 ∼ 45000 HIRES 2.1�4.4 manually McDonald et al. (2000) [31]
9 3 37500-45000 HIRES 1.85�4.43 manually Schaye et al. (2000) [40] / [K01]
3 3 ∼ 45000 UVES 1.54�2.33 manually Kim et al. (2001) [22]
4 4 ∼ 4700 ESI 5.40�6.16 α = −1.5 Becker et al. (2001) [5]
15 6 ∼ 5300 ESI 4.09�5.51 α = −1.25 Songaila et al. (2002) [44]
8 10 ∼ 45000 UVES 1.5�3.6 manually Kim et al. (2002) [21]
21 42 ∼ 45000 UVES, HIRES 1.65�4.45 manual. / [R97] Schaye et al. (2003) [39]
1061 � ∼ 2000 SDSS 1.65�4.45 extrap.+lines (comp.) Bernardi et al. (2003) [6]
27 3 ∼ 45000 UVES (LUQAS) 2�3 manually Viel et al. (2004) [50]
50 60 5300, 36000 ESI, HIRES 2.0�6.3 man. / α = −1.25 Songaila et al. (2004) [43]
77 10 1200 Kast/Lick 1.64�2.36 b-spline, corrected Tytler et al. (2004) [47]
24 9 ∼ 45000 HIRES 2.2�3.2 [T04] Kirkman et al. (2005) [26]
19 98 2600 ESI, MMT, HET, KP 4.92�6.25 α = −1.5 Fan et al. (2006) [13]
9 1 30000�50000 STIS, UVES, HIRES 0.5�1.9 CANDALF Janknecht et al. (2006) [19]
3492 3 ∼ 2000 SDSS 2.4�3.9 extrap.+lines Desjacques et al. (2007) [11]
74 8 1300 FOS 0�1.6 [T04] Kirkman et al. (2007) [25]
18 21 ∼ 45000 UVES (LUQAS) 1.6�3.6 manually Kim et al. (2007) [20]
86 12 7000�50000 ESI, HIRES, MIKE 2.0�4.2 3-spline, corrected Faucher-Giguere et al. (2008) [14]
40 17 ∼ 45000 UVES 1.7�4.7 3-spline, corr. Dall'Aglio et al. (2008) [10]
655 3 500�2000 2QZ 2.1�2.5 extrap.+lines (comp.) Polinovskiy et al. (2010) [36]
6065 28 ∼ 2000 SDSS DR7 2.15�4.85 � Becker et al. (2013) [3]
18 3 ∼ 45000 UVES 2.1�2.9 � Garzilli et al. (2012) [15]
Table 2: The optimal values of the parameters α, β for two subsamples with 1σ-errors.
continuum α, ×10−3 β χ2 d.o.f
manually 3.85± 0.10 3.232± 0.019 68.1 121
extrapolation 4.15± 0.02 3.368± 0.003 70.8 27
39
Advances in Astronomy and Space Physics O.Torbaniuk
Fig. 1: Compilation of the mean transmission data as a function of redshift from literature. See
explanation in Table 1 and in the text.
Fig. 2: The optimal approximation with 1σ-error for the �rst (green) and second (yellow) subsamples,
and the 1,2,3σ-level of maximum likelihood function. Diamonds are the results of [3].
40
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