Power spectra of convective motions in the solar photosphere
We reproduced the convective velocity field and the temperature structure of the solar photosphere using neutral iron line λ ≈ 639.3 nm profiles from the observations with high spatial resolution taken around the centre of the solar disc in the non-perturbed region. We obtained power spectra of vert...
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| Zitieren: | Power spectra of convective motions in the solar photosphere / O.A. Baran // Advances in Astronomy and Space Physics. — 2013. — Т. 3., вип. 2. — С. 89-93. — Бібліогр.: 17 назв. — англ. |
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Baran, O.A. 2017-06-07T18:14:21Z 2017-06-07T18:14:21Z 2013 Power spectra of convective motions in the solar photosphere / O.A. Baran // Advances in Astronomy and Space Physics. — 2013. — Т. 3., вип. 2. — С. 89-93. — Бібліогр.: 17 назв. — англ. 2227-1481 https://nasplib.isofts.kiev.ua/handle/123456789/119618 We reproduced the convective velocity field and the temperature structure of the solar photosphere using neutral iron line λ ≈ 639.3 nm profiles from the observations with high spatial resolution taken around the centre of the solar disc in the non-perturbed region. We obtained power spectra of vertical velocity and temperature variations at different photospheric levels in order to separate and study convective motions on different spatial scales. In the lower photosphere the main power is localized on the granular scales with a peak at scales of about 1-1.5 Mm (for the velocity variations) and 1.5 2 Mm (for the temperature variations) and it decreases with height. In the higher layers of the solar photosphere the peaks of the spectra of long-lived structures (T > 20 min) are slightly shifted to the larger scales (≈ 3 Mm at the height h = 400 km), but still present granulation. So, a separate regime of mesogranulaton at scales 5-10 Mm distinct from granulation by a power gap has not been found. Mesostructures appear as a part of a broad distribution of granular scales without further distinction from granulation. The authors are grateful to Dr. N. G. Shchukina for kindly proving the results of observations and to Dr. R. I. Kostyk for data reduction. en Головна астрономічна обсерваторія НАН України Advances in Astronomy and Space Physics Power spectra of convective motions in the solar photosphere Article published earlier |
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Power spectra of convective motions in the solar photosphere |
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Power spectra of convective motions in the solar photosphere Baran, O.A. |
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Power spectra of convective motions in the solar photosphere |
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Power spectra of convective motions in the solar photosphere |
| title_fullStr |
Power spectra of convective motions in the solar photosphere |
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Power spectra of convective motions in the solar photosphere |
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power spectra of convective motions in the solar photosphere |
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Baran, O.A. |
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Baran, O.A. |
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2013 |
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English |
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Advances in Astronomy and Space Physics |
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Головна астрономічна обсерваторія НАН України |
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Article |
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We reproduced the convective velocity field and the temperature structure of the solar photosphere using neutral iron line λ ≈ 639.3 nm profiles from the observations with high spatial resolution taken around the centre of the solar disc in the non-perturbed region. We obtained power spectra of vertical velocity and temperature variations at different photospheric levels in order to separate and study convective motions on different spatial scales. In the lower photosphere the main power is localized on the granular scales with a peak at scales of about 1-1.5 Mm (for the velocity variations) and 1.5 2 Mm (for the temperature variations) and it decreases with height. In the higher layers of the solar photosphere the peaks of the spectra of long-lived structures (T > 20 min) are slightly shifted to the larger scales (≈ 3 Mm at the height h = 400 km), but still present granulation. So, a separate regime of mesogranulaton at scales 5-10 Mm distinct from granulation by a power gap has not been found. Mesostructures appear as a part of a broad distribution of granular scales without further distinction from granulation.
|
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2227-1481 |
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https://nasplib.isofts.kiev.ua/handle/123456789/119618 |
| citation_txt |
Power spectra of convective motions in the solar photosphere / O.A. Baran // Advances in Astronomy and Space Physics. — 2013. — Т. 3., вип. 2. — С. 89-93. — Бібліогр.: 17 назв. — англ. |
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AT baranoa powerspectraofconvectivemotionsinthesolarphotosphere |
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2025-11-26T23:38:13Z |
| last_indexed |
2025-11-26T23:38:13Z |
| _version_ |
1850781644105973760 |
| fulltext |
Power spectra of convective motions in the solar photosphere
O.A.Baran∗
Advances in Astronomy and Space Physics, 3, 89-93 (2013)
© O.A.Baran, 2013
Astronomical Observatory, Ivan Franko National University of Lviv, Kyryla i Mefodia str., 8, 79005, Lviv, Ukraine
We reproduced the convective velocity �eld and the temperature structure of the solar photosphere using neutral
iron line λ ≈ 639.3 nm pro�les from the observations with high spatial resolution taken around the centre of the
solar disc in the non-perturbed region. We obtained power spectra of vertical velocity and temperature variations
at di�erent photospheric levels in order to separate and study convective motions on di�erent spatial scales. In the
lower photosphere the main power is localized on the granular scales with a peak at scales of about 1�1.5Mm (for
the velocity variations) and 1.5�2Mm (for the temperature variations) and it decreases with height. In the higher
layers of the solar photosphere the peaks of the spectra of long-lived structures (T > 20min) are slightly shifted
to the larger scales (≈ 3Mm at the height h = 400 km), but still present granulation. So, a separate regime of
mesogranulaton at scales 5�10Mm distinct from granulation by a power gap has not been found. Mesostructures
appear as a part of a broad distribution of granular scales without further distinction from granulation.
Key words: solar convection, granule, mesogranule
introduction
Convection is responsible for many interesting
phenomena on the Sun and the study of the solar
convection is important in various aspects of solar
research. It is generally agreed that the granulation
and the supergranulation are two di�erent scales of
the solar convection in the photosphere. The scales
of granulation are about 0.5�2Mm [13], the super-
granulation � 20�70Mm [12]. The granulation can
be observed through both intensity and velocity mea-
surements, while the supergranulation can be found
only in velocity measurements (intensity �uctuations
at such scales are very faint [3, 14]). However, a
scale between the granulation and supergranulation
(5�10Mm), �rst identi�ed as the mesogranulation by
November et al. [9], is still a controversy. There
has been a heated debate as to the nature of meso-
granulation, and about whether mesogranulation is
a distinct scale of convection or not [1, 10, 11, 17].
The most recent observational results showed that
the statistical properties and behaviour of mesogran-
ulation structures are consistent with the results of
spatial and temporal averaging of random data, so it
is very likely that mesogranulation is a ghost feature
of surface convection generated by averaging proce-
dures [8].
The power spectra of solar granulation computed
by Espagnet et al. [2] and displayed in a logP�log k
scale were used for a comparison with the theory
of convective turbulence. These spectra are �tted
by two straight lines of corresponding slopes −17/3
and −5/3, and this fact provides some strong ar-
guments to believe that granules are turbulent ed-
dies and present some convective characteristics. As
well Rieutord et al. [13] o�er some theoretical guide-
lines to explain their spectra. They interpret the
combined presence of k−17/3 and k−10/3 power laws
for the intensity and vertical velocity at small sub-
granulation scales down to 0.4Mm as a �signature
of buoyancy-driven turbulent dynamics in a strongly
thermally di�usive regime�; in the mesogranulation
range and up to the scale of 25Mm, they �nd a k2
spectral power law for the vertical velocity and in
the 2.5�10.0Mm mesoscale range intensity �uctua-
tions also follow a k2 power law.
The aim of the present work is to represent the
power spectra of the vertical velocity and the temper-
ature variations of the photosphere convection using
pro�les with high spatial resolution and to determine
the horizontal scale dependence of such variations at
di�erent heights in the solar photosphere. We try to
�nd out whether the mesogranulation is just a part
of the smooth spatial power spectrum, or it has en-
ergy excess in power spectra like the granulation and
supergranulation.
observations and data processing
Here, we use the results of observations by
N. Shchukina of the neutral iron spectral line with
λ ≈ 639.3 nm taken in August 2001 on the 70-cm
German Vacuum Tower Telescope (VTT) located on
the Canary Islands (Spain). The observations were
taken around the centre of the solar disc in the non-
perturbed region [6]. The image tremor on the in-
put slit of the spectrograph did not exceed 0.5 arcsec,
so the spatial resolution was equal to 350 km. The
data set consists of time sequence (947 images, obser-
vation duration 2.6 h) of 512 pro�les in total corre-
∗lesiaab@gmail.com
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Advances in Astronomy and Space Physics O.A.Baran
sponding to the extent of 64 400 km over the surface
of the Sun.
Fig. 1: The vertical velocity distribution in the solar
photosphere .
Fig. 2: The distribution of the temperature variations
in the solar photosphere.
The reconstruction of the parameters of the in-
homogeneous atmosphere was carried out by the so-
phisticated technology developed by Stodilka, who
solved the inverse NLTE problem of radiative trans-
fer using modi�ed response functions and Tikhonov's
stabilizers [15, 16]. In contrast to the previous stud-
ies [4, 5], which used the method of λ-metre to ob-
tain intensity and velocity distributions at a certain
height in the solar atmosphere, we reproduced the
altitude distribution of vertical velocity (Fig. 1) and
temperature variations (Fig. 2) in the solar photo-
sphere (along two spatial coordinates: its depth, h,
and the coordinate along the spectrograph slit, X).
Since we are interesting only in properties of the
photosphere convection, the acoustic waves were re-
moved using k − ω �ltration: the �eld of Fourier
transform of w < vs · kx (vs is the speed of sound)
corresponds to the convective motions (shaded ver-
tical in Fig. 3).
Fig. 3: k − ω-�ltration of the velocity and temperature
variations in the solar photosphere.
Besides we separated convective motions with
periods T < 10min, corresponding to short-lived
granules and convective motions with periods T >
20min, corresponding to convective structures with
a lifetime longer then average granules � mesogran-
ules, if they exist (shaded obliquely in Fig. 3). Then
we calculated power spectra of the vertical velocity
and temperature �uctuations for the whole convec-
tion and for the short-lived and long-lived convective
structures in order to compare them later.
results
The power spectrum of the convective motions at
a certain height depends on the spatial and temporal
frequency, in our investigation we calculate spectra
summed by temporal frequency.
Assuming that there is no preferred direction,
which comes true for the quiet solar atmosphere, we
calculate spatial power spectra for two-dimensional
images from those for one-dimensional images using
the equation [1]:
P2(k) = 2πkP1(k).
Thus obtained (and normalized to unity at the height
h = −25 km) power spectra of vertical velocity and
temperature variations of the solar convection at the
heights h = 0, 200, 400 km are shown in Fig. 4�5.
We got such spectra for di�erent layers of the so-
lar photosphere up to the height h = 550 km. Simi-
larly, we calculated the power spectra of convective
motions with periods T < 10min (for short-lived
granules) and T > 20min (for long-lived convective
structures (or mesogranules?)) in order to compare
them.
In previous studies [2, 13] it was found that the
spectra seem to follow P (k) = kα with speci�c α
for di�erent spacial range and the possible physical
origin of the slope coe�cients is discussed. In our
90
Advances in Astronomy and Space Physics O.A.Baran
work we have to detect the general changes of spectra
with height, thereby we approximate the entire curve
of the power spectrum. We revised a class of func-
tions and best approached the dependence P (k) =
Akαe−βk selecting coe�cients for each spectrum in-
dividually. Thus approximated power spectra of ver-
tical velocity and temperature variations of the so-
lar convection at the heights h = 0, 200, 400 km are
shown in Fig. 4�5 (thick line). The power spectra
of convective motions with periods T < 10min and
T > 20min are approximated similarly. The re-
sults of our approximation of power spectra of con-
vection with di�erent range of temporal frequencies
selected by us (all convection, convection motions
with period T < 10min and convective motions with
T > 20min) are presented in Fig. 6�7. By analyzing
these lines we found the following:
(i) All the power spectra of convective veloci-
ties are maximal in the lower layers (Fig. 6, bottom)
with power peaks at spatial frequencies correspond-
ing to the average granular scales λ ≈ 1.5Mm for
T > 20min and λ ≈ 1Mm for T < 10min. The
power spectra decrease with height (Fig. 6, middle)
up to the higher layers of the solar photosphere.
The spectrum of long-lived structures (T > 20min)
changes most rapidly with height and in the high
layers (Fig. 6, top) its maximum is slightly shifted
to the smaller spatial frequencies corresponding to
the larger granular scales: λ ≈ 3Mm at height
h = 400 km.
(ii) All the power spectra of convective temper-
ature variations are maximal in the lower layers
(Fig. 7, bottom) with power peaks at spatial frequen-
cies corresponding to the granular scales λ ≈ 2Mm
for T > 20min and λ ≈ 1.5Mm for T < 10min.
At the height h ≈ 200 km (Fig. 7, middle) the power
spectrum decreases (through the temperature sign
reversal in this layers). Note, that the tempera-
ture �uctuations reach a minimum at higher or lower
heights depending on sizes of the convective cells (the
larger the size, the higher the reversal takes place
[7]). In the higher layers of the solar photosphere
(Fig. 7, top) the power spectra of temperature varia-
tions increase again and the peak of the spectrum of
long-lived structures (T > 20min) is slightly shifted
to the smaller spatial frequencies (λ ≈ 3Mm at the
height h = 400 km), but still presents granulation.
As can be seen, the behaviour of long-lived cells
(representing mesogranules) is similar to the be-
haviour of short-lived cells (representing granules).
conclusions
In the present study we used the results of the
high spatial resolution observations of the quiet solar
photosphere to compute the power spectra of verti-
cal velocity and temperature variations of the pho-
tosphere convection. Analyzing the power spectra of
vertical velocity and temperature variations of the
solar convection we have not seen apparent energy
excess at the scale of mesogranulation proposed in
some early works.
Based on a comparison of the approximated
power spectra of vertical velocities and temperature
variations of all convection, short-lived granules and
the convective structures with a lifetime longer than
the average duration of existence of granules, our re-
sults may be summarised as the following: the power
spectra of long-lived convective motions vary with
height similar to those of short-lived convective mo-
tion. So, speci�c di�erences in vertical velocity and
temperature variations of long-lived and short-lived
granules are not found: the variations decrease with
height for convection of both small and large tempo-
ral periods; the temperature sign reversal takes place
(with only a small di�erence in heights where it oc-
curs); in the higher layers of the solar photosphere
the power spectra of vertical velocity and tempera-
ture variations of long-lived (T > 20min) structures
are slightly shifted to the smaller spatial frequencies,
but still present granulation.
Thereby we have con�rmed that the main power
of the convective motions is distributed on the gran-
ular scales and mesostructures appear as a part of a
broad distribution of granular scales without further
distinction from granulation.
acknowledgement
The authors are grateful to Dr.N.G. Shchukina
for kindly proving the results of observations and to
Dr.R. I. Kostyk for data reduction.
references
[1] ChouD.-Y., ChenC.-S., OuK.-T. & WangC.-C. 1992,
ApJ, 396, 333
[2] EspagnetO., MullerR., RoudierT. & MeinN. 1993,
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[7] KostikR., KhomenkoE. & ShchukinaN. 2009, A&A,
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91
Advances in Astronomy and Space Physics O.A.Baran
Fig. 4: The power spectra of the vertical velocity vari-
ations in the solar photosphere at heights h = 0, 200,
400 km.
Fig. 5: The power spectra of the temperature variations
in the solar photosphere at heights h = 0, 200, 400 km.
[14] RieutordM. & RinconF. 2010, Living Reviews in Solar
Physics, 7, 2
[15] StodilkaM. I. 2002, J. of Physical Studies, 6, 435
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19, 4, 334
[17] StrausTh., Deubner F.-L. & FleckB. 1992, A&A, 256,
652
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Advances in Astronomy and Space Physics O.A.Baran
Fig. 6: The approximated power spectra of the vertical
velocity variations in the solar photosphere at heights
h = 0, 200, 400 km: solid line - all convection, dashed
line - convective motions with T > 20 min, dotted line -
convective motions with T < 10 min.
Fig. 7: The approximated power spectra of the tempera-
ture variations in the solar photosphere at heights h = 0,
200, 400 km: solid line - all convection, dashed line - con-
vective motions with T > 20 min, dotted line - convective
motions with T < 10 min.
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