Variations of the energy spectra of solar X-ray flares: interconnection with the photospheric, chromospheric, and magnetic activity of the Sun (1972−2001)

The problem of flare energy distribution of the Sun is strongly related to the power-law energy spectra of flares on the UV Ceti-type stars. In a preliminary study (1972–1993), the X-ray flare integral energy spectrum (IES) was represented by a unique power law of N ~ E−b with index b = 0.76. Later...

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Published in:	Кинематика и физика небесных тел
Date:	2005
Main Author:	Kasinskii, V.
Format:	Article
Language:	English
Published:	Головна астрономічна обсерваторія НАН України 2005
Subjects:	MS2: Physics of Solar Atmosphere
Online Access:	https://nasplib.isofts.kiev.ua/handle/123456789/79614
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Cite this:	Variations of the energy spectra of solar X-ray flares: interconnection with the photospheric, chromospheric, and magnetic activity of the Sun (1972−2001) / V. Kasinskii // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 105-109. — Бібліогр.: 5 назв. — англ.

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spelling	Kasinskii, V. 2015-04-03T15:26:59Z 2015-04-03T15:26:59Z 2005 Variations of the energy spectra of solar X-ray flares: interconnection with the photospheric, chromospheric, and magnetic activity of the Sun (1972−2001) / V. Kasinskii // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 105-109. — Бібліогр.: 5 назв. — англ. 0233-7665 https://nasplib.isofts.kiev.ua/handle/123456789/79614 The problem of flare energy distribution of the Sun is strongly related to the power-law energy spectra of flares on the UV Ceti-type stars. In a preliminary study (1972–1993), the X-ray flare integral energy spectrum (IES) was represented by a unique power law of N ~ E−b with index b = 0.76. Later it was shown that the exponent index b varies with the cycle phase, that is with the Wolf number. The purpose of this paper is to investigate the temporal variations in the power-law spectrum of soft X-ray flares over the three solar cycles (1972–2001). A more extensive statistic (56 000 flares) allows us to revise earlier results and to derive new ones. Not only b-index undergoes variations associated with a 11-year cycle but the limiting energy of flares (log Em) as well. The three-cycle-averaged b is 0.666, with variations in the range 0.50 < b < 0.80. The results may be useful for study of flare activity on red dwarf stars. The author is grateful to Prof. Ya. Yatskiv for official invitation to the MAO-2004 Conference, Kyiv, Ukraine, July 15–17, 2004. en Головна астрономічна обсерваторія НАН України Кинематика и физика небесных тел MS2: Physics of Solar Atmosphere Variations of the energy spectra of solar X-ray flares: interconnection with the photospheric, chromospheric, and magnetic activity of the Sun (1972−2001) Article published earlier
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
title	Variations of the energy spectra of solar X-ray flares: interconnection with the photospheric, chromospheric, and magnetic activity of the Sun (1972−2001)
spellingShingle	Variations of the energy spectra of solar X-ray flares: interconnection with the photospheric, chromospheric, and magnetic activity of the Sun (1972−2001) Kasinskii, V. MS2: Physics of Solar Atmosphere
title_short	Variations of the energy spectra of solar X-ray flares: interconnection with the photospheric, chromospheric, and magnetic activity of the Sun (1972−2001)
title_full	Variations of the energy spectra of solar X-ray flares: interconnection with the photospheric, chromospheric, and magnetic activity of the Sun (1972−2001)
title_fullStr	Variations of the energy spectra of solar X-ray flares: interconnection with the photospheric, chromospheric, and magnetic activity of the Sun (1972−2001)
title_full_unstemmed	Variations of the energy spectra of solar X-ray flares: interconnection with the photospheric, chromospheric, and magnetic activity of the Sun (1972−2001)
title_sort	variations of the energy spectra of solar x-ray flares: interconnection with the photospheric, chromospheric, and magnetic activity of the sun (1972−2001)
author	Kasinskii, V.
author_facet	Kasinskii, V.
topic	MS2: Physics of Solar Atmosphere
topic_facet	MS2: Physics of Solar Atmosphere
publishDate	2005
language	English
container_title	Кинематика и физика небесных тел
publisher	Головна астрономічна обсерваторія НАН України
format	Article
description	The problem of flare energy distribution of the Sun is strongly related to the power-law energy spectra of flares on the UV Ceti-type stars. In a preliminary study (1972–1993), the X-ray flare integral energy spectrum (IES) was represented by a unique power law of N ~ E−b with index b = 0.76. Later it was shown that the exponent index b varies with the cycle phase, that is with the Wolf number. The purpose of this paper is to investigate the temporal variations in the power-law spectrum of soft X-ray flares over the three solar cycles (1972–2001). A more extensive statistic (56 000 flares) allows us to revise earlier results and to derive new ones. Not only b-index undergoes variations associated with a 11-year cycle but the limiting energy of flares (log Em) as well. The three-cycle-averaged b is 0.666, with variations in the range 0.50 < b < 0.80. The results may be useful for study of flare activity on red dwarf stars.
issn	0233-7665
url	https://nasplib.isofts.kiev.ua/handle/123456789/79614
citation_txt	Variations of the energy spectra of solar X-ray flares: interconnection with the photospheric, chromospheric, and magnetic activity of the Sun (1972−2001) / V. Kasinskii // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 105-109. — Бібліогр.: 5 назв. — англ.
work_keys_str_mv	AT kasinskiiv variationsoftheenergyspectraofsolarxrayflaresinterconnectionwiththephotosphericchromosphericandmagneticactivityofthesun19722001
first_indexed	2025-11-25T03:53:45Z
last_indexed	2025-11-25T03:53:45Z
_version_	1850505769761374208
fulltext	VARIATIONS OF THE ENERGY SPECTRA OF SOLAR X-RAY FLARES: INTERCONNECTION WITH THE PHOTOSPHERIC, CHROMOSPHERIC, AND MAGNETIC ACTIVITY OF THE SUN (1972–2001) V. Kasinskii Irkutsk State University of Railways 15 Chernyshevski Str., 664074 Irkutsk, Russia e-mail: vkasin@sgd.iriit.irk.ru The problem of flare energy distribution of the Sun is strongly related to the power-law energy spectra of flares on the UV Ceti-type stars. In a preliminary study (1972–1993), the X-ray flare integral energy spectrum (IES) was represented by a unique power law of N ∼ E−b with index b = 0.76. Later it was shown that the exponent index b varies with the cycle phase, that is with the Wolf number. The purpose of this paper is to investigate the temporal variations in the power-law spectrum of soft X-ray flares over the three solar cycles (1972–2001). A more extensive statistic (56 000 flares) allows us to revise earlier results and to derive new ones. Not only b-index undergoes variations associated with a 11-year cycle but the limiting energy of flares (log Em) as well. The three-cycle-averaged b is 0.666, with variations in the range 0.50 < b < 0.80. The results may be useful for study of flare activity on red dwarf stars. INTRODUCTION A statistical study of the active UV Ceti-type flare stars showed that time-integrated flare energy at the optical wavelength can be represented by a power function ∼ E−b with a wide variety of b-indices 0.5 < b < 0.9 [2]. The Sun behaves as an UV Ceti star whose exponent of the energy spectrum for flare optical radiation in all spectral lines of hydrogen series is b = 0.80 [5]. Based on X-ray (1–8 Å) flux data for 1972–1993, the flare integral energy spectrum was calculated with mean < b >= 0.76 ± 0.03 (37 000 flares) [4]. The IES approximation gives the linear dependence of log E = 30.9−1.35 logN , where N is the accumulated number of flares with energy E > Em. The study of IES of flares shows clear variations in the spectral index b with the phase of the 11-year cycle [4]. The correlation coefficient between the Wolf number W and the b-index is 0.6–0.8. These results need to be supported by a new data set related to the end of the 22nd cycle and to the beginning of the 23rd cycle (1994–2001). DATA REDUCTION AND RESULTS To obtain the flare energy E, the X-ray flux FX (erg cm−2 s−1) have to be integrated over the duration of the individual flare T and over the hemisphere from the flare site to the Earth by the formula E = � 2πR2 au ∫ T 0 FXdt, (1) where Rau is the distance from the Sun to the Earth. The X-ray flux FX data were taken from the site of National Oceanic and Atmospheric Administration – US Space Enviroment Center (1972–2001). In the earlier work the above integral was calculated by the triangle approximation of the flare profile, 1/2FmaxT , which was sufficient for the massive calculations for more than 1000 flares per year. This study somewhat takes into account the light curves of F (t). To estimate the flare energy E, a new technique was adopted by dividing the phase of rise and decay of F (t). There exists a wide scope of flare light curves, but their main feature is a sharp increase in F (t) from the time of onset t0 to the maximum of flare tmax and a farther exponential decay of F from tmax to te to the end of flare. Therefore, the flux F (t) was time integrated by taking into account the beginning, the phase of maximum and the end of flare. Next step, the amount of flux was spatially integrated over the hemisphere 2πR2 au, where Rau = 1 AU. Assuming for the raise phase the “triangle” approximation of c© V. Kasinskii, 2004 105 Eq. (1) and for decay part the exponential approximation that is te corresponds to the e times decay of F (t) we have the empirical estimation formula for E: E = 1028Fmax[ 4.22 (tmax − t0) + 2.53 (te − tmax)], (2) where F is in ergs per square centimetre per second, t is in seconds, and E is in ergs. The individual E values from Eq. (2) fits the range of energy 1024 < E < 1032 in accordance with the previous data. Thereupon, the accumulated number of flares with energy E > Em was approximated by the power-like function: N(Em) = ∫ Em n(E)dE ∼ CE−b. (3) A dependence similar to Eq. (2) means that, if E is plotted versus N , one obtains on a “log–log” scale a linear dependence: log E = log Em − 1 b log N. (4) Table 1 presents the example of energy spectra parameters for 1978–2001. The data for 1972–1977 are approximate since the values of b-index were calculated using small statistics. The high limiting energy of one flare for 30 years is estimated as log Em = 32.5 (1989) while the mean energy for one flare is < log Em >= 31.01 in the “log” scale. It is smaller than the upper limit of the radiant energy of 5 · 1032 erg, reported by some authors [5]. Table 1. The parameters of the power-law energy spectrum in X-ray solar flares Year log Em b N/year W log N25 1978 31.6 0.60± 0.03 1134 92 4.24 1979 31.6 0.64± 0.03 1469 155 4.28 1980 31.6 0.69± 0.01 2463 156 4.60 1981 31.9 0.684± 0.005 4005 140 4.84 1982 32.3 0.631± 0.005 3852 116 4.64 1983 31.8 0.71± 0.01 2583 67 3.95 1984 31.8 0.58± 0.01 2176 46 3.95 1985 30.1 0.68± 0.03 1065 18 3.45 1986 30.3 0.62± 0.04 916 13 3.39 1987 30.4 0.68± 0.03 1389 29 3.96 1988 31.6 0.64± 0.02 2367 100 4.24 1989 32.5 0.60± 0.01 2610 158 4.56 1990 31.5 0.72± 0.01 2630 142 4.68 1991 32.2 0.659± 0.005 3324 145 4.08 1992 31.6 0.67± 0.01 2816 90 4.40 1993 31.1 0.69± 0.01 2429 56 4.04 1994 30.3 0.69± 0.02 1612 22 3.63 1995 29.2 0.72± 0.03 1124 16 3.45 1996 29.2 0.63± 0.07 510 9 3.03 1997 30.4 0.66± 0.03 1138 22 3.57 1998 31.1 0.68± 0.01 2244 62 4.32 1999 30.9 0.76± 0.01 2421 95 4.52 2000 30.9 0.80± 0.01 2260 130 4.76 2001 31.4 0.72± 0.01 2730 134 4.60 As an example, Figure 1 shows the power spectrum in X-ray flares for the 1984 year, N = 4005 flares. As follows from Fig. 1, the flares of intermediate energies give a linear relation between log E and log N . As regards the fainter flares (approximately 1026 erg), however, a sharp “break” appears in the spectrum. The energy Ebreak is near the flare detection threshold, and the break, therefore, is due to observational selection [2]. The IES parameters b and log Em are mutually poorly correlated, r ≤ 0.37. They can be taken, therefore, as two independent parameters of the power spectrum. Their physical meanings are different. While the former may be defined as the “slope of spectrum”, the latter defines the “limit of energy” intersected by the line on the log E axis. 106 �� Figure 1. The power energy spectrum of flares in X-rays (N = 4005). The slope of the straight line gives b value of 0.684 As it is seen from Table 1, besides b and log Em there is another important parameter, that is log N25. The latter defines the “number of flares” with energy level 1025 erg intersected by the line (4) on the logN axis. Energy level 1025 defines the number of microflares that could be observed every year if the power-law spectrum model (3) is correct. Microflares have excited considerable interest in different areas of solar physics. In particular, the existence of small, frequent energy releases suggests mechanism for coronal and chromospheric heating. Microscopic magnetic reconnection processes are suspected to exist virtually anywhere on solar surface, and this could reveal them as tiny X-ray flares [3]. As it can be seen from Table 1 (last column), the number of microflares correlated well with the Wolf number. The importance of microflares parameter log N25 becomes more clear if we take it along with energy pa- rameter log Em as two independent parameters of power-law IES. Their product reflects the square of IES in the logarithmic scale: IE = 1 2 (log Em · log N25). (5) The Eq. (7) defines the “integral” of IES that is the proliferation of energy and numbers of flares over the double logarithmic scale. The summary cross-correlations for the five parameters of IES with the Wolf number (W ) at the zero, one, and 11 years are given in Table 2. As it is expected, W and number of flares (N) are well correlated at zero and 11-year time-lag. More interesting is the fact that mutual W– N correlation is higher at the lag +1 year. This lag of +1 year is also observed in the correlation maximum of index b with respect to Wolf number (Table 2, last column). An analogous phase shift between the spectral index b and an average flare energy release have been found at red dwarf star EV Lac by the authors [1]. This fact comprises the problem and needs further investigation. Table 2. Cross-correlations of IES parameters with W in X-ray solar flares Wolf N , flares log E · log N log N25 log Em b W (0) 0.70 0.88 ± 0.10 0.87 0.80 0.30 ± 0.20 W (1) 0.92 0.870± 0.10 0.83 0.63 0.51 ± 0.20 W (11) 0.79 0.75 ± 0.15 0.60 0.73 0.48 ± 0.24 Table 2 also shows that the spectral index b is the lowermost correlated parameter with the sunspot (W ) and flare (N) activity. Therefore, it is reasonable to assume that the logarithmic integral of linear IES (5) is more important physical parameter than the index b. It is significant that all the parameters mentioned in 107 �� Figure 2. The modulation of the logarithmic integral of IES (circles) by the Wolf numbers (squares) for 1976–2001 with the 1/4 of a year resolution Table 2 have shown rather high correlation with the Wolf number at the lag +11 years – W (11). This fact reflects the 11-year modulation of all activity processes on the Sun. A large amount of flares per year (≥ 1000) allows us to calculate the IES with more time resolution of 1/4 of a year. The comparison of W (t) with logarithmic integral of IES are presented in Fig. 2 with time resolution of one quarter of a year. Both curves show a good correlation, revealing a significant 11-year modulation at a level of 0.87 (see Table 2). RELATION OF IES PARAMETERS WITH OTHER SOLAR INDICES So far we have considered the relation of IES parameters and Wolf number which may be considered as the main index of sunspots 11-year activity cycle. The other indices, in one way or another, related to the Wolf num- ber (W ). The other commonly used index strongly connected with W is the radio flux at ν = 2800 MHz (wavelength λ = 10.7 cm) or F10.7. For completeness of approach from the Solar Geophysical Data (SGD) we have taken the yearly rows of F10.7 cm, number of active regions NAO, and number of optical flares NHα. They may be considered as the coronal, photospheric, and chromospheric indices of solar activity. The correlation of these indices with power index b was done. The correlation coefficient maximum of r∼ 0.65–0.55 falls on +1 year lag related to the time of F10.7, NAO, and NHα. A significant 11-year modulation of b by the indices is also revealed. It is remarkable that there is no observed time-lag difference between three indices and b(t). They are all synchronized in time with respect to power index b. Therefore, F10.7, NAO, and NHα indices may be called “Wolf-similar” despite a physical difference between them. At the same time it underlines the fact that the time-lagging of 1 year of b relative to all three indices is as important as it is for EV Lac star [1]. In the recent time a new specific index – NOAA Mg II – has appeared. Index NOAA Mg II gives the ratio of intensity “center-to-limb” h and k lines of Mg II (280 nm). Therefore, the Mg II-index represents an essential measure of chromospheric activity. In Fig. 3 a smoothed correlation of Mg II-index and logarithmic integral of IES (5) are displayed. Data time resolution is three months. One can see that Mg II-index is positively correlated with the integral of IES. Particularly, near sinusoidal 11-year correlation with maximum r = 0.84 (point 42) takes place. The maximum correlation does not seem to be lagging with respect to Mg II-index in the beginning of the period. The main conclusions are the following. 1. The integral energy spectrum of solar flares has a power-law form. The three-cycle-averaged index of power spectrum in soft X-rays is b = 0.666 ± 0.005. The range of variations of b; 0.509 < b < 0.805 is in reasonable agreement with the corresponding index of red dwarf stars [2]. 2. The exponent b undergoes variations with the 11-year cycle phase, and correlates with the Wolf number W , number of flares N , chromospheric Mg II-index, radio flux index F10.7, and other indices. The exponent b increases from the epoch of minimum (0.637) to the epoch of maximum b = 0.715± 0.005. 108 � �� Figure 3. The correlation of chromospheric Mg II-index and logarithmic integral of IES with a time resolution of 1/4 of a year. A strong 11-year correlation (0.84) can be seen at point 42 3. The 11-year cyclic variation of IES parameters, the b-index, limiting energy and of flares log Em and logarithmic integral of IES (log Em · log N25) may serve as a fundamental dependence for revealing a similar activity on the red dwarf (UV Cet) stars. Acknowledgements. The author is grateful to Prof. Ya. Yatskiv for official invitation to the MAO-2004 Conference, Kyiv, Ukraine, July 15–17, 2004. [1] Alekseev I., Gershberg R. E. The activity of red dwarf star EV Lac heating in Crimea in 1986–1995 // The Earth and the Universe, Aristotel Univ.–Thessaloniki: Ziti Ed., 1997.–P. 44–57. [2] Gershberg R. Flare red dwarf stars: news from Crimea // Uspekhi Phis. Nauk.–1998.–168, N 8.–P. 892–898. [3] Hudson H. S. Solar flares, microflares, nanoflares, and coronal heating // Solar Phys.–1991.–133.–P. 357–369. [4] Kasinsky V., Sotnikova S. T. Solar flares energy spectrum over the 11-year cycle, and the similarity between solar and stellar flares // Astron. and Astrophys. Transactions.–1997.–12.–P. 313–314. [5] Kurochka L. Energy distribution of 15 thousand solar flares // Astron. Zh.–1987.–64, N 2.–P. 443–446. 109

Variations of the energy spectra of solar X-ray flares: interconnection with the photospheric, chromospheric, and magnetic activity of the Sun (1972−2001)

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