Variations of the quasar radio spectra with period 130 h⁻¹ Mpc
It is known that the spatial distribution of galaxies and quasars is structured at a scale LS = 130 h⁻¹Mpc. The same scale can be present at a spatial distribution of the physical characteristics of quasars. The search of period ≈ LS was conducted in the radiospectral indices of quasars in a centime...
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| Cite this: | Variations of the quasar radio spectra with period 130 h⁻¹ Mpc / M. Khodyachikh // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 71-74. — Бібліогр.: 10 назв. — англ. |
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| citation_txt | Variations of the quasar radio spectra with period 130 h⁻¹ Mpc / M. Khodyachikh // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 71-74. — Бібліогр.: 10 назв. — англ. |
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| description | It is known that the spatial distribution of galaxies and quasars is structured at a scale LS = 130 h⁻¹Mpc. The same scale can be present at a spatial distribution of the physical characteristics of quasars. The search of period ≈ LS was conducted in the radiospectral indices of quasars in a centimetre range. The Veron-Cetti & Veron catalogue [10] was used as source. In the power spectra of series of spectral indices and proper distances of quasars the peak corresponding to the expected period confidently emerges. 0.23 ± 0.03 estimation of the parameter of density was obtained by the method of smoothing the period in different ranges of z at the varying parameter of density in the flat model of Universe. Interpretation of argument of periodicity, as proper distance, results in a geocentrism. The conformable time is proportional to proper distance and is also a good approximation of the argument of periodicity when the parameter of density equals to 0.23. At the temporal character of the exposed periodicity the centred position of the observer is not required. In such interpretation the exact expression for the argument of periodicity is unknown. The proper distance or the conformable time is introduced by its true values with an accuracy not worse than 1%.
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VARIATIONS OF THE QUASAR RADIO SPECTRA
WITH PERIOD 130 h−1 Mpc
M. Khodyachikh
Kharkiv National University, Kharkiv, Ukraine
4 Svoboda Sq., Kharkiv, Ukraine
e-mail: khod@astron.kharkov.ua
It is known that the spatial distribution of galaxies and quasars is structured at a scale LS =
130h−1 Mpc. The same scale can be present at a spatial distribution of the physical characteristics
of quasars. The search of period � LS was conducted in the radiospectral indices of quasars in
a centimetre range. The Veron-Cetti & Veron catalogue [10] was used as source. In the power
spectra of series of spectral indices and proper distances of quasars the peak corresponding to
the expected period confidently emerges. 0.23 ± 0.03 estimation of the parameter of density was
obtained by the method of smoothing the period in different ranges of z at the varying parameter of
density in the flat model of Universe. Interpretation of argument of periodicity, as proper distance,
results in a geocentrism. The conformable time is proportional to proper distance and is also
a good approximation of the argument of periodicity when the parameter of density equals to 0.23.
At the temporal character of the exposed periodicity the centred position of the observer is not
required. In such interpretation the exact expression for the argument of periodicity is unknown.
The proper distance or the conformable time is introduced by its true values with an accuracy not
worse than 1%.
INTRODUCTION
In the sharply-directed deep surveys of the sky Broadhurst et al. [1] have found out large-scale coherent periodic
distribution of galaxies with an extension 1800h−1 Mpc in a direction of galactic poles. In power spectra of
different sets of the galaxies clusters and superclusters the peak corresponding to a characteristic length of
large-scale structure by the Universe LS ([2]; the survey [4]) emerged repeatedly. The usually used value
LS � 130h−1 Mpc corresponds to its estimation based on the data [1] with z < 0.3 at density parameter
Ωm � 0.2 (ΩΛ = 0). At large redshifts the similar scale was detected in the spacing of quasars in the field
of 1.8 < z < 2.4 [8]. Einaste et al. [3] have revealed three-dimensional moderately regular net structure with
a step of � 120h−1 Mpc consist of rich clusters and voids. They consider that there should be a process
obscure till now producing regular spatial net on big scales. Suppose, that this hypothetical process results in
the change of quasars luminosities. Then at a spacing of luminosities of quasars there should also be a periodic
structure. Thus, the energy distribution in their spectra, that is spectral indexes should also change. Owing
to the large dispersion of luminosities of quasars, the detection of their variations is inconvenient. That is why
the analysis of spectral indexes of quasars was carried out. If our suppositions really take place, it is necessary
to expect the appearance of a peak in a power spectrum of the relation of spectral indexes on proper distance
at the frequency corresponding to LS.
METHOD
Normalized on a single dispersion the sample power spectra (SPS) of the centered series yk, xk we shall designate
S(ω), where ω = 2πP−1 is an angular frequency corresponding to the period P . For the decrease of a minor-lobe
level SPS were calculated with a window application. The weighing was performed with Hann function w(xk).
The length of implementation is L = X2 − X1, where X1 and X2 are boundary values of a xk series. While
SPS estimating, the sample was divided into s segments with equal number of objects. SPS were calculated
for each segment. At the frequencies of interest an averaged periodogram Pω and its error σP were calculated.
As the criterion of signal presence at ω frequency the value pω = (Pω−1)/σP was used. Since SPS are normalized
on a single dispersion, mathematical expectation (Pω − 1) is equal to zero.
As radial coordinate was derived the proper distance d(Ωm, ΩΛ, z), where Ωm and ΩΛ are the parameter of
density and dimensionless cosmological constant. Usually, at the analysis of cosmological periodicities the SPS
for the distribution of quasars on argument ln (1 + z) or lg (1 + z) are calculated. Working with arbitrary
c© M. Khodyachikh, 2004
71
argument f(Ωm, ΩΛ, z) it is necessary to account for the change of peak frequencies with the change of a view
and parameters of a function f(Ωm, ΩΛ, z). Let us introduce the scaled argument
d(Ωm, ΩΛ, z) = f(Ωm, ΩΛ, z)D(Ωm, ΩΛ, z1), (1)
where
D(Ωm, ΩΛ, z1) = ln (1 + z1)/f(Ωm, ΩΛ, z1). (2)
With such argument peak frequency in SPS changes unsignificantly at variation parameters. The calculations
were performed at ln (1 + z1) = 1.5 (z1 = 3.482).
SPS AND AVERAGED PERIODOGRAMS
The sample was built under the data of the Veron-Cetty & Veron catalogue [10], in which the radioflows sν at
wavelengths of 6 and 11 cm and their spectral indexes α(sν ∝ ν−α) for 1246 quasars are adduced. The relation
between mean α and ln (1 + z) was determined by a least-squares method:
ᾱ = (0.45 ± 0.09) − (0.18 ± 0.05) ln (1 + z). (3)
The zi, αi values will derive from an initial series. They can be converted to the series xi = ri(Ωm, ΩΛ, zi),
yi = αi − ᾱ at given parameters Ωm, ΩΛ. Spectral analysis of this series is carried out below.
We suppose that there is a period P = LS at spectral indexes of quasars. Let us estimate the frequency
of a corresponding peak in SPS. The local value LS is determined by observations of galaxies distribution
within the interval 0 < z < zp at definite parameters Ωm, ΩΛ. Following [1] at zp � 0.3 and Ωm = 0.2
(ΩΛ = 0), the value LS = 130h−1 Mpc [2]. When parameters Ωm and ΩΛ are changed the value LS will change
proportionally to the proper distance d(Ωm, ΩΛ, zp). When ΩΛ = 0 and Ωm = 0, 0.4 the values LS = 131.9 and
128.3h−1 Mpc, respectively. Let us consider only flat model ΩΛ = 1−Ωm when the values Ωm = 0.30 and 0.23,
approximately corresponding to limiting estimates of density parameter [9] at a level 1σ. In a flat model when
Ωm = 0.3 the lengths are notably more: LS = 140.2h−1 Mpc. The frequency of an anticipated peak in SPS
equals to ω = 140 when P = LS. Having put value Ωm = 0.23, we shall find ω = 151. The boundary values of
the series Xk = ln (1 + zk) are equal to X1 = 0 and X2 = 1.7.
Figure 1. The SPS Sω of relation spectral indices and scaled distance when the parameter of density Ωm = 0.30 and
Ωm = 0.23. Averaged SPS on five segments of Pω periodogram (dot-dashed line), pω = (Pω-1)/σP for frequencies, where
pω > 1 (solid line)
In Fig. 1 the part of interest of the SPS of xi, yi series is routined when Ωm = 0.30 and 0.23. There is
an expected peak within the range of the anticipated frequencies.
72
The sample of radioloud quasars is not full. A non-uniformity in distribution of quasars can result in
the appearance of false peaks. The spectral window W (ω) was calculated. As W (ω) < 0.01 at ω < 10 , it is
impossible to explain the appearance of a peak in SPS by any heterogeneities in the distribution of quasars, in
particular by the effects of selection.
While spectral estimation the sample of quasars was divided into s segments with identical quantity of
objects ns = N/s. In the sample the quasars are arranged as of right ascension increases. In k-th segment
the quasars with numbers i = k+s(j−1) in the basic sample were taken, where j takes the values in the ranges
from 1 up to ns. While such division of the sample the distribution of quasars in each segment on redshifts and
on the sky was obtained close to that of in the basic sample. The spectral resolution of the Pω periodogram
is not worse than in the SPS. In Fig. 1 the results of estimation are shown when the sample divided into five
segments. Maximum Pω is seen near the frequencies of SPS peaks. The Pω value exceeds the background by
2.2σp (Ωm = 0.23). The estimation performed confirms the presence of periodicity at spectral indices of quasars.
ESTIMATE OF PARAMETER OF DENSITY
Let arbitrary option value Ωm be equal to Ωm. At the change of parameter Ωm the ratio of scales (frequen-
cies of peaks and periods, corresponding to them) at different intervals z and the peak height Sω will vary.
The frequencies of a peak ω in various intervals z at arbitrary value Ωm will differ. Their dispersion change
is depending on Ωm. When Ωm = Ωm the value σω should be minimized. The SPS in the range of small z
(X < 0.85) and large z (X > 0.85) are routined. The SPS were calculated with application of Hann weighing
function. The frequencies of peaks in two intervals z are close on value when Ωm = 0.21 and considerably differ
at other Ωm. As follows from this preliminary analysis, the relation of a peak characteristics to parameter of
density confidently emerges. It is possible to be use for Ωm estimates.
Increasing quantity of intervals more reliable estimates can obtain. In area X from 0 up to 1.7 the ΔX
intervals were calculated with the shift in 0.2 both as four intervals with ΔX = 1.1 and as five intervals with
ΔX = 0.9. For a set of values Ωm in each interval the SPS were calculated with weighting function and
the frequencies of peak ωi maximum and their dispersion were determined. Minimum value of σω equals to
σm = 0.58 when ΔX = 0.9 and σω = 0.30 when ΔX = 1.1. In Fig. 2 the relation of value σω to parameter Ωm
by normalized on these value σω is routined on parameter Ωm. A parameter estimate equals to Ωm = 0.23±0.03
at ΔX = 1.1 and Ωm = 0.22 ± 0.04 at ΔX = 0.9 when a level is 2σ. The value σm is increased rapidly with
decreasing width of the ΔX interval, therefore, the estimate is more reliable when the ΔX = 1.1.
Figure 2. σω peak frequencies in different intervals ln (1 + z) versus parameter Ωm when the width of interval is 1.1
(upper curve) and 0.9. The values σω are normalized by minimum value and are routined on parameter Ωm
An estimation of density parameter was carried out without using the values LS and P . The equality of
these values is obtained when Ωm = 0.23.
DISCUSSION OF RESULTS
The exact expression for argument of periodicity is not known. The proper distance d(Ωm, z) or scaled distance
r(Ωm, z) was used as the first approaching of the periodicity argument r0(Ωm, z). Suppose it has the form
r0(Ωm, z) = r(Ωm, z)[1+ e(t)]. For variable t we shall choose the simplest combination t = r(1.5− r), providing
e = 0 at r = 0 and r = 1.5 in decomposing e = a1t + a2t
2. Maximum values Sω in SPS are achieved at
Ωm = 0.21. With updated argument r0(Ωm, z) should receive the large Sω. Maximizing a peak Sω(a1, a2)
73
the estimates were made: a1 = 0.001± 0.006 and a2 = 0.001± 0.014. A variable t < 0.57 in the whole range r.
At a level 1σ the value |e| < 0.01, i.e., the scaled distance r(Ωm, z) is introduced by its true values r0(Ωm, z)
with an accuracy not worse than 1%. The proper distance d and conformal time η are linearly dependent.
Therefore, the argument of periodicity is interpreted ambiguously. Our estimate of density parameter is made
if we suppose, that periodicity argument is proper distance. The interpretation of the argument, as proper
distance, results in geocentrism. The conformal time η is also the argument of periodicity. At temporary
nature of the detected periodicity centered position of the observer is not required. Periodic variations in
spectral indexes of quasars are probably due to temporary changes of quasars activity. Then, the similar
variations should appear both in luminosities of quasars and in their visible spatial density. The periodicities in
radioluminosities of quasars were found in works [5, 6]. The periodicities in distribution of quasars depending
on proper distances were investigated in work [7]. Thus, the estimate of density parameter Ωm = 0.22 ± 0.02
was obtained that is the relation between the argument of periodicity and z was approximately the same, as
well as in spectral indexes. Our estimation of density parameter will agree with the value Ωm = 0.27± 0.04 [9]
obtained in the analysis of the WMAP whole results and other astronomical data.
[1] Broadhurst T. J., Ellis R. S., Koo D. C., Szalay A. S. Large-scale distribution of galaxies at the Galactic poles //
Nature.–1990.–343.–P. 726–728.
[2] Broadhurst T., Jaffe A. H. Using the comoving maximum of the galaxy power spectrum to measure cosmological
curvature // [astro-ph/9904348].–1999.
[3] Einasto J., Einasto M., Gottlo ber S., et al. A 120 Mpc periodicity in the three-dimensional distribution of galaxy
supercluster // Nature.–1997.–385.–P. 139–141.
[4] Guzzo L. Large-scale structure at the turn of the millennium // [astro-ph/9911115].
[5] Khodyachikh M. F. The Habble radiodiagrams for quasars at 6 and 11 cm // Kinematics and Physics of Celestial
Bodies.–1988.–4.–P. 53–58.
[6] Khodyachikh M. F. The cosmological periodicities in radio fluxes of quasars // Sov. Astron. Zh.–1990.–67.–
P. 218–221.
[7] Khodyachikh M. F. Cosmological periodicities in the full and selective samples of quasars // Grav., Cosmology and
Relativ. Astrophys.: Kharkiv Conf.–2003.–P. 55.
[8] Roukema B. F., Mamon G. A. Tangentional large scale structure as a standard ruler: curvature parameters from
quasars // Astron. and Astrophys.–2000.–358.–P. 395–408.
[9] Spergel D. M, Verde L., et al. First-year Wilkinson Microwave Anisotropy Probe (WMAP) // Astrophys. J. Suppl.
Ser.–2003.–148.–P. 175–194.
[10] Veron-Cetty M.-P., Veron P. A catalogue of quasars and active nuclei // ESO Scientific Report.–2000.–N 1.–408 p.
74
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| id | nasplib_isofts_kiev_ua-123456789-79606 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0233-7665 |
| language | English |
| last_indexed | 2025-12-07T15:49:24Z |
| publishDate | 2005 |
| publisher | Головна астрономічна обсерваторія НАН України |
| record_format | dspace |
| spelling | Khodyachikh, M. 2015-04-03T15:11:53Z 2015-04-03T15:11:53Z 2005 Variations of the quasar radio spectra with period 130 h⁻¹ Mpc / M. Khodyachikh // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 71-74. — Бібліогр.: 10 назв. — англ. 0233-7665 https://nasplib.isofts.kiev.ua/handle/123456789/79606 It is known that the spatial distribution of galaxies and quasars is structured at a scale LS = 130 h⁻¹Mpc. The same scale can be present at a spatial distribution of the physical characteristics of quasars. The search of period ≈ LS was conducted in the radiospectral indices of quasars in a centimetre range. The Veron-Cetti & Veron catalogue [10] was used as source. In the power spectra of series of spectral indices and proper distances of quasars the peak corresponding to the expected period confidently emerges. 0.23 ± 0.03 estimation of the parameter of density was obtained by the method of smoothing the period in different ranges of z at the varying parameter of density in the flat model of Universe. Interpretation of argument of periodicity, as proper distance, results in a geocentrism. The conformable time is proportional to proper distance and is also a good approximation of the argument of periodicity when the parameter of density equals to 0.23. At the temporal character of the exposed periodicity the centred position of the observer is not required. In such interpretation the exact expression for the argument of periodicity is unknown. The proper distance or the conformable time is introduced by its true values with an accuracy not worse than 1%. en Головна астрономічна обсерваторія НАН України Кинематика и физика небесных тел MS1: Decameter Radioastronomy Variations of the quasar radio spectra with period 130 h⁻¹ Mpc Article published earlier |
| spellingShingle | Variations of the quasar radio spectra with period 130 h⁻¹ Mpc Khodyachikh, M. MS1: Decameter Radioastronomy |
| title | Variations of the quasar radio spectra with period 130 h⁻¹ Mpc |
| title_full | Variations of the quasar radio spectra with period 130 h⁻¹ Mpc |
| title_fullStr | Variations of the quasar radio spectra with period 130 h⁻¹ Mpc |
| title_full_unstemmed | Variations of the quasar radio spectra with period 130 h⁻¹ Mpc |
| title_short | Variations of the quasar radio spectra with period 130 h⁻¹ Mpc |
| title_sort | variations of the quasar radio spectra with period 130 h⁻¹ mpc |
| topic | MS1: Decameter Radioastronomy |
| topic_facet | MS1: Decameter Radioastronomy |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79606 |
| work_keys_str_mv | AT khodyachikhm variationsofthequasarradiospectrawithperiod130h1mpc |