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Stellar Wind of Components of Detached Binary Systems 分离双星系统组分的恒星风
IF 0.7 4区 物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS Pub Date : 2025-09-29 DOI: 10.1134/S1063772925702038
A. V. Tutukov, A. V. Sobolev

The paper is devoted to the consideration of the role of the donor stellar wind in the matter exchange between the components of detached binary systems. A classification of close binary systems with interacting components is proposed. A list of potential donors and accretors of such systems, including X-ray binary and symbiotic stars, is given. Analytical tasks have been completed to evaluate the conditions and efficiency of interaction through the stellar wind, a criterion was found for maintaining the self-induced stellar wind of X-ray binaries, and a condition for the formation of an accretion disk during accretion of stellar wind matter by a compact accretor. Three-dimensional gas dynamic models of component interaction are constructed for the five initial velocities of the stellar wind using the example of Sco X-1 type systems. The simulation results are illustrated by pictures of streamlines, temperature distribution, and wind gas densities in the orbital and frontal planes. Model focusing of the donor wind flow by the accretor is confirmed by the observed phase X-ray light curve of Vela X-1.

本文研究了在分离双星系统组分之间的物质交换中,施主星风的作用。提出了一种具有相互作用分量的紧密双星系统的分类方法。这类系统包括x射线双星和共生恒星,给出了潜在的供体和吸积体清单。完成了通过恒星风相互作用的条件和效率的分析任务,找到了维持x射线双星自致恒星风的判据,以及紧致吸积体吸积恒星风物质过程中形成吸积盘的条件。以Sco X-1型系统为例,建立了五种初始速度的恒星风组分相互作用的三维气体动力学模型。模拟结果由轨道面和锋面的流线图、温度分布图和风气密度图说明。通过观测到的船帆X-1的相位x射线光曲线证实了吸积体对供体气流的模型聚焦。
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引用次数: 0
A Two-Planet Problem with an Arbitrary Inclination of a Pair of Orbits. Secular Evolution of the Kepler-117 Exosystem 具有任意轨道倾角的两行星问题。开普勒-117系外系统的长期演化
IF 0.7 4区 物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS Pub Date : 2025-09-29 DOI: 10.1134/S1063772925702026
B. P. Kondratyev, V. S. Kornoukhov

A new method is used to study a current version of the two-planet problem on the secular evolution of planetary orbits with small eccentricities and mutual inclinations, having an arbitrary orientation relative to the main (picture) plane. A model has been developed that describes a wide class of exoplanetary systems with an inclination angle of orbits different from (pi {text{/}}2.) The orbits of the planets are modeled by the Gaussian rings, the perturbing function is represented by the mutual gravitational energy of these rings in the form of a series up to terms of second order of smallness. To describe the evolution of orbits, instead of osculating Keplerian elements, a new set of variables is introduced: the unit vector ({mathbf{R}}) of normal to the plane of the ring and two Poincaré variables (left( {p,q} right);) for eight independent variables, a system of differential equations is obtained and analytically solved. The method is applied to study the secular evolution of the two-planet system Kepler-117 (KOI-209) with non-resonant orbits of exoplanets. It has been established that in this system the oscillations of the same components of the orientation vector ({mathbf{R}}) for each of the orbits, as well as the values (left( {e,i,{{Omega }}} right),) occur strictly in antiphase. The eccentricities of both orbits oscillate with the period ({{T}_{kappa }} approx 182.3;{text{years}},) and the inclinations of the orbits and the longitudes of the ascending nodes change in the libration mode with the same period ({{T}_{g}} approx {text{174}}.5;{text{years}}.) The lines of the orbital apsides rotate unevenly counterclockwise with the periods of secular rotation ({{T}_{{{{g}_{2}}}}} approx 178.3;{text{years}}) (for a light planet), and ({{T}_{{{{g}_{1}}}}} approx 8140;{text{years}}) (for a more massive planet).

一种新的方法被用于研究当前版本的两行星问题,即相对于主平面具有任意方向的小偏心和互倾角的行星轨道的长期演化。建立了一个模型,描述了轨道倾角不同于(pi {text{/}}2.)的一类系外行星系统。行星的轨道由高斯环建模,扰动函数由这些环的相互引力能以一系列的形式表示,直到二阶小。为了描述轨道的演化,我们不再使用开普勒元素,而是引入了一组新的变量:环平面法向的单位向量({mathbf{R}})和八个自变量的两个poincarcar变量(left( {p,q} right);),得到了一个微分方程组并进行了解析求解。应用该方法研究了系外行星轨道非共振的双行星系统Kepler-117 (KOI-209)的长期演化。已经确定,在该系统中,每个轨道的方向矢量({mathbf{R}})的相同分量的振荡以及值(left( {e,i,{{Omega }}} right),)严格地发生在反相中。两个轨道的离心率都以({{T}_{kappa }} approx 182.3;{text{years}},)为周期振荡,轨道的倾角和升交点的经度在振动模式中以相同的周期变化({{T}_{g}} approx {text{174}}.5;{text{years}}.)轨道两侧的线沿长期旋转周期逆时针旋转不均匀({{T}_{{{{g}_{2}}}}} approx 178.3;{text{years}})(对于轻行星),({{T}_{{{{g}_{1}}}}} approx 8140;{text{years}})(对于质量较大的行星)。
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引用次数: 0
Second-Degree Local Integral for Rotating Systems. Part II 旋转系统的二阶局部积分。第二部分
IF 0.7 4区 物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS Pub Date : 2025-09-29 DOI: 10.1134/S1063772925702014
F. T. Shamshiev

The study of the existence of the quadratic local integral in stationary two-dimensional potential fields that was initiated in the first part of the work, is continued. New mathematical relationships that deepen the understanding of the structure of functions describing the behavior of potential fields under arbitrary mass distribution have been proposed. The rotation of the coordinate system to simplify the equations and emphasize key features of the functional dependencies has been employed. Particular attention has been paid to arbitrary functions defining the potential and its derivatives under specific conditions. Their properties and possible solutions have been analyzed. Besides, linear differential equations with polynomial and periodic solutions have been studied. Theoretical results, which can be used for further analysis of quadratic integrals and for clarifying the differences between polynomials and other types of functions in broader mathematical models, have been formulated. The paper is partially based on a report presented at the Modern Stellar Astronomy 2024 conference.

本文继续研究了平稳二维势场中二次局部积分的存在性。提出了新的数学关系,加深了对描述任意质量分布下势场行为的函数结构的理解。坐标系的旋转简化了方程,强调了函数依赖的关键特征。特别注意在特定条件下定义势及其导数的任意函数。分析了它们的性质和可能的解决方法。此外,还研究了多项式解和周期解的线性微分方程。理论结果,可用于二次积分的进一步分析和澄清多项式和其他类型的函数在更广泛的数学模型之间的区别,已经制定。这篇论文部分基于2024年现代恒星天文学会议上发表的一份报告。
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引用次数: 0
Reasons for the Slow Apsidal Rotation of the Massive Eclipsing Star V1141 Cas 大质量食星V1141 Cas侧转缓慢的原因
IF 0.7 4区 物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS Pub Date : 2025-09-29 DOI: 10.1134/S1063772925701999
A. S. Volkova, I. M. Volkov, S. A. Naroenkov

High-precision photometric measurements of the unexplored eclipsing star V1141 Cas (P = 6.909d, (V{{ = 12.02}^{m}}), (e = 0.37), Sp B1 V) have shown that the apsidal rotation velocity, ({{dot {omega }}_{{{text{obs}}}}} = 0.127^circ )/yr, is two times slower than the theoretical value under the synchronism condition, ({{dot {omega }}_{{{text{theor}}}}} = 0.235^circ )/yr. The physical parameters of the component stars were obtained: ({{T}_{1}} = 23,500 pm 400) K, ({{M}_{1}} = 8.4 pm 0.5{kern 1pt} {{M}_{ odot }}), ({{R}_{1}} = 4.24 pm 0.08{kern 1pt} {{R}_{ odot }}), ({{T}_{2}} = 22,000 pm 400) K, ({{M}_{2}} = 7.0 pm 0.5{kern 1pt} {{M}_{ odot }}), and ({{R}_{2}} = 3.38 pm 0.08{kern 1pt} {{R}_{ odot }}). The age of the system is determined to   be 7.5 million years with a solar chemical composition. The measured photometric parallax, (pi =0.00031^{primeprime} pm 0.00004^{primeprime} ), is very close to the Gaia value. The interstellar extinction, ({{A}_{{text{V}}}} = {{2.2}^{m}}), is 40 percent higher than the survey’s data.

对未探测的食星V1141 Cas (P = 6.909d, (V{{ = 12.02}^{m}}), (e = 0.37), Sp B1 V)的高精度光度测量表明,在同步条件下,其侧旋速度({{dot {omega }}_{{{text{obs}}}}} = 0.127^circ ) /yr比理论值({{dot {omega }}_{{{text{theor}}}}} = 0.235^circ ) /yr慢2倍。得到各组成恒星的物理参数:({{T}_{1}} = 23,500 pm 400) K、({{M}_{1}} = 8.4 pm 0.5{kern 1pt} {{M}_{ odot }})、({{R}_{1}} = 4.24 pm 0.08{kern 1pt} {{R}_{ odot }})、({{T}_{2}} = 22,000 pm 400) K、({{M}_{2}} = 7.0 pm 0.5{kern 1pt} {{M}_{ odot }})、({{R}_{2}} = 3.38 pm 0.08{kern 1pt} {{R}_{ odot }})。该系统的年龄被确定为750万年,具有太阳的化学成分。测得的光度视差(pi =0.00031^{primeprime} pm 0.00004^{primeprime} )非常接近盖亚值。星际灭绝,({{A}_{{text{V}}}} = {{2.2}^{m}}),比调查数据高出40%。
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引用次数: 0
Transient Narrow High-Velocity Absorptions in the Stationary Spectra of SS 433 ss433固定光谱中的瞬态窄高速吸收
IF 0.7 4区 物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS Pub Date : 2025-09-29 DOI: 10.1134/S1063772925701987
A. V. Dodin, K. A. Postnov, A. M. Cherepashchuk, A. M. Tatarnikov

We report on the discovery of rare emergence (31 nights from 363 nights of observations) of narrow absorption features in hydrogen and helium lines in stationary SS 433 spectra with velocities ranging from ‒650 to –1900 km/s. The components arise independently of the appearance of P Cygni line profiles which are frequently observed in the SS 433 stationary spectra with terminal velocities ranging from –200 to ( sim {kern 1pt} - {kern 1pt} 2500) km/s. The characteristic rising time of the transient absorptions is about one day and the decay time is about two days. The phenomenology of the absorptions suggests their origin due to hydrodynamic instabilities of wind outflows from a supercritical accretion disk in SS 433.

我们报告了在静止的SS 433光谱中,在速度范围从-650到-1900 km/s的氢和氦谱线中罕见地出现(在363个夜晚的观测中有31个夜晚)窄吸收特征。这些成分独立于天鹅座P线轮廓的出现,这些轮廓在SS 433固定光谱中经常观察到,终端速度范围从-200到( sim {kern 1pt} - {kern 1pt} 2500) km/s。瞬态吸收的特征上升时间约为一天,衰减时间约为两天。吸收的现象学表明,它们的起源是由于SS 433中超临界吸积盘的风流出物的流体动力不稳定性。
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引用次数: 0
On the Encounter Rate of Open Star Clusters 关于疏散星团的相遇率
IF 0.7 4区 物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS Pub Date : 2025-09-29 DOI: 10.1134/S1063772925702002
A. D. Grinenko, D. A. Kovaleva

Probable past and future close encounters of open clusters with known characteristics over 64 m-illion years have been calculated by integrating the orbits of cluster centers in the Galactic potential using the galpy package. It has been shown that in the Galactic neighborhood of the Sun, pairwise cluster encounters at distances comparable to or smaller than their sizes occur at a characteristic rate of 35–40 events per 1 Myr. Close encounters between open clusters with a significant age difference occur at a rate of 15 events per Myr. It can be expected that in the Galaxy as a whole, such events occur an order of magnitude more frequently per unit time. Thus, dynamical interactions between stellar ensembles of different ages may not be too rare and could influence the properties of stellar populations. A pair of clusters with similar ages: HSC 1428 and Gulliver 22 was identified as a likely physically bound binary cluster system. A forecast of expected close encounters over the next 32 Myr has been provided for 490 pairs of clusters. Currently, 29 pairs of clusters are at their closest approach. The paper has been partially based on a report presented at the Modern Stellar Astronomy 2024 conference.

在过去和未来,已知特征超过6400万年的疏散星团可能会发生近距离接触,这是通过使用星系包将星团中心的轨道整合到银河系势中来计算的。已经证明,在太阳附近的银河系中,在与太阳大小相当或小于太阳大小的距离上发生的成对星团相遇的特征率为每1迈r 35-40次。具有显著年龄差异的开放群集之间的近距离接触发生率为每个最高当量15次。可以预期,在整个银河系中,这样的事件在单位时间内发生的频率要高出一个数量级。因此,不同年龄的恒星群之间的动态相互作用可能不会太罕见,并可能影响恒星群的性质。一对年龄相似的星团:HSC 1428和格列佛22被确定为一个可能的物理束缚的二元星团系统。已经为490对星团提供了未来32年的预期近距离接触预报。目前,29对星团正处于最接近的位置。这篇论文部分基于2024年现代恒星天文学会议上发表的一份报告。
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引用次数: 0
Analysis of Recovery Phase Characteristics for Different ICME Polarities (1995–2015) 1995-2015年不同ICME极性恢复相位特征分析
IF 0.7 4区 物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS Pub Date : 2025-09-29 DOI: 10.1134/S1063772925600207
W. Alotaibi, B. Badruddin, M. Derouich

Interplanetary coronal mass ejections (ICMEs) are among the main drivers of major geomagnetic storms. The recovery phase of such storms, characterized by a return of geomagnetic indices to pre-disturbance levels, is primarily governed by the decay of the ring current and the cessation of solar wind energy input. This study examines how the characteristics of the recovery phase, specifically the exponential decay time constant ((tau )) of key geomagnetic indices, depend on the polarity configuration of the interplanetary magnetic field (IMF) of the ICMEs. A total of 163 ICME-driven storms from 1995 to 2015 were analyzed using hourly OMNI data. The recovery phase of each storm was modeled with an exponential decay to extract (tau ) for the Disturbance Storm Time (Dst) index, Planetary amplitude (ap) index, and Auroral Electrojet (AE) index. Events were categorized into eleven distinct IMF polarity and flux rope configurations to evaluate polarity-dependent recovery behavior. Correlation analyses were also conducted to assess the relationship between (tau ) of geomagnetic indices and various solar wind parameters, including IMF ({{B}_{z}}), solar wind speed, and coupling functions. Results reveal significant differences in recovery durations across ICME polarity groups. The SN polarity exhibited the fastest Dst recovery ((tau = 18.68 pm 0.80) h), whereas SNS and ({{F}^{ + }}) configurations exhibited the slowest recoveries ((tau = 43.95 pm 1.27) and (50.97 pm 1.58) h, respectively). For the ap and AE indices, the fastest recovery occurred in NSN ((tau = 4.02 pm 0.46) h) and SNN ((tau = 4.33 pm 0.61) h) configurations, while prolonged recovery was associated with (Fr) (ap) and NSS (AE) events ((tau > 29.90) h). Events dominated by northward magnetic fields recovered significantly faster than those with prolonged southward IMF orientations. Strong statistical coupling was found between (tau )(Dst) and (tau )(ap) ((r = 0.87)), while (tau )(AE) was most sensitive to (n{{E}_{y}}) ((r = - 0.52)). Additionally, configurations with small rotation angles (({{F}^{ - }})) recovered more rapidly than those with complex rotations (({{F}^{ + }})), reflecting the role of magnetic structure in sustaining energy input. These findings enhance predictive models of magnetospheric recovery by linking IMF polarity and flux rope topology to the timescales of geomagnetic relaxation.

行星际日冕物质抛射(ICMEs)是主要地磁风暴的主要驱动因素之一。这种风暴的恢复阶段,以地磁指数恢复到扰动前的水平为特征,主要是由环电流的衰减和太阳风输入的停止所控制的。本研究探讨了恢复阶段的特征,特别是关键地磁指数的指数衰减时间常数((tau ))如何依赖于ICMEs的行星际磁场(IMF)的极性配置。利用每小时OMNI数据分析了1995年至2015年间163次由icme驱动的风暴。利用指数衰减模型模拟每一场风暴的恢复阶段,提取出扰动风暴时间(Dst)指数、行星振幅(ap)指数和极光电喷射(AE)指数(tau )。事件分为11种不同的IMF极性和通量绳配置,以评估极性依赖的恢复行为。对地磁指数(tau )与IMF ({{B}_{z}})、太阳风速度、耦合函数等太阳风参数之间的关系进行了相关分析。结果显示,ICME极性组的恢复持续时间有显著差异。SN极性的Dst恢复最快((tau = 18.68 pm 0.80) h),而SNS和({{F}^{ + }})构型的Dst恢复最慢(分别为(tau = 43.95 pm 1.27)和(50.97 pm 1.58) h)。ap和AE指标中,NSN ((tau = 4.02 pm 0.46) h)和SNN ((tau = 4.33 pm 0.61) h)配置恢复最快,(Fr) (ap)和NSS (AE)事件((tau > 29.90) h)恢复时间较长。由北向磁场主导的事件的恢复速度明显快于由北向磁场主导的事件。(tau ) (Dst)和(tau ) (ap) ((r = 0.87))之间存在较强的统计耦合,而(tau ) (AE)对(n{{E}_{y}}) ((r = - 0.52))最敏感。此外,旋转角度小的构型(({{F}^{ - }}))比旋转角度复杂的构型(({{F}^{ + }}))恢复得更快,这反映了磁性结构在维持能量输入方面的作用。这些发现通过将IMF极性和通量绳拓扑结构与地磁弛豫的时间尺度联系起来,增强了磁层恢复的预测模型。
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引用次数: 0
The Probable Quadruple Systems GI Cep and V548 Cyg 可能的四重系统GI Cep和V548 Cyg
IF 0.7 4区 物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS Pub Date : 2025-09-15 DOI: 10.1134/S1063772925701951
A. I. Khaliullina

Orbital-period variations of the eclipsing binaries GI Cep and V548 Cyg are analyzed. The period variations in both systems can be described as a superposition of secular decrease and two cyclic variations of the period. The rate of decrease of the period dP/dt = 3.73 × 10–7 day/yr for GI Cep and 2.38 × 10–7 day/yr for V548 Cyg. A superposition of two types of cyclic variations is observed for GI Cep and V548 Cyg: with periods 14.4 years and 33.7 years for GI Cep, and 5.4 and 43.8 years for V548 Cyg. The observed cyclic variations in the period of GI Cep can occur due to the presence of a third body in the system or due to the magnetic activity of the secondary component. The system can be triple or quadruple. The hypothesis of magnetic activity is not suitable for V548 Cyg. Apparently, this is quadruple system.

分析了双星GI Cep和V548 Cyg的轨道周期变化。这两个系统的周期变化可以描述为长期减少和周期的两个周期变化的叠加。GI Cep周期dP/dt减少率为3.73 × 10-7天/年,V548 Cyg为2.38 × 10-7天/年。在GI Cep和V548 Cyg中观测到两种类型周期变化的叠加:GI Cep的周期为14.4年和33.7年,V548 Cyg的周期为5.4年和43.8年。在GI Cep周期中观测到的循环变化可能是由于系统中存在第三个体或由于次级组分的磁活动而发生的。系统可分为三组或四组。磁活动的假设不适合V548 Cyg。显然,这是一个四重系统。
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引用次数: 0
Characteristics of Super-Earths and Mini-Neptunes 超级地球和迷你海王星的特征
IF 0.7 4区 物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS Pub Date : 2025-09-15 DOI: 10.1134/S1063772925701926
G. A. Morozov, E. S. Belenkaya

More than half of currently known stars have nearby exoplanets with size between Earth and Neptune, called super-Earths and mini-Neptunes. The California–Kepler Survey (CKS) studied data from NASA’s Kepler mission and revealed a bimodal distribution of planets with (R < 3.5{kern 1pt} {{R}_{{text{E}}}}) by radius (({{R}_{{text{E}}}}) is the radius of the Earth). It occurred that there was a lack of planets with radii (1.5{kern 1pt} {{R}_{{text{E}}}} < R < 2{{R}_{{text{E}}}}). The CKS did not take into account data from other missions and exoplanets discovered by non-transit methods. All data from this mission were limited to 2022. This article examines the distribution of super-Earths and mini-Neptunes, taking into account all data on exoplanets known by 2024 from the NASA catalog. Mini-Neptunes and super-Earths with known radii were selected. There were 937 such planets, including 366 planets with known mass. Since the radius of a planet can only be determined by the transit method, the distribution by radii is built using the data of transit planets, but, unlike CKS, not only the data of the Kepler mission are taken. The data for the remaining distributions are selected regardless of the method of their detection and the telescope used. We show that the current data are best fitted by a double-peaked Gaussian distribution, which describes two populations of planets: rocky (hereinafter super-Earths) and exoplanets with gas envelopes (exoplanets surrounded by hydrogen–helium atmospheres, but consisting mainly of heavy elements—ice and rock, hereinafter mini-Neptunes). The magnitude of the gap between populations at present is analyzed. It is shown that the gap is filled evenly on both sides; in CKS, the first peak is significantly smaller than the second, that is, there were fewer super-Earths than mini-Neptunes. Perhaps more super-Earths have been discovered recently, which is why there was a shortage of them in the CKS. The composition of some exoplanets was determined using theoretical models of the dependence of mass on radius.

目前已知的恒星中,有一半以上的恒星附近有大小介于地球和海王星之间的系外行星,被称为超级地球和迷你海王星。加州-开普勒巡天(CKS)研究了美国宇航局开普勒任务的数据,揭示了半径为(R < 3.5{kern 1pt} {{R}_{{text{E}}}}) (({{R}_{{text{E}}}})是地球的半径)的行星的双峰分布。似乎没有半径为(1.5{kern 1pt} {{R}_{{text{E}}}} < R < 2{{R}_{{text{E}}}})的行星。CKS没有考虑其他任务的数据和通过非过境方法发现的系外行星。该任务的所有数据仅限于2022年。本文研究了超级地球和迷你海王星的分布,并考虑了2024年之前美国宇航局目录中已知的所有系外行星数据。半径已知的迷你海王星和超级地球被选中。有937颗这样的行星,包括366颗已知质量的行星。由于行星的半径只能通过凌日法确定,因此半径分布是使用凌日行星的数据来建立的,但是,与CKS不同的是,不仅采用了开普勒任务的数据。其余分布的数据选择与它们的探测方法和使用的望远镜无关。我们表明,目前的数据最适合双峰高斯分布,它描述了两类行星:岩石(以下简称“超级地球”)和有气体包层的系外行星(系外行星被氢氦大气包围,但主要由重元素——冰和岩石组成,以下简称“迷你海王星”)。分析了目前人口差距的大小。结果表明,间隙在两侧均匀填充;在CKS中,第一个峰值明显小于第二个峰值,也就是说,超级地球的数量少于小海王星。也许最近发现了更多的超级地球,这就是为什么中国缺少超级地球的原因。一些系外行星的组成是用质量依赖于半径的理论模型确定的。
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引用次数: 0
Nature of Quasi-Periodic Radiative Pulsations in the Rope Flux Models of Flares 耀斑绳通量模型中准周期辐射脉动的性质
IF 0.7 4区 物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS Pub Date : 2025-09-15 DOI: 10.1134/S106377292570194X
A. A. Solov’ev

Rope flux models of solar flares associate the phenomenon of quasi-periodic pulsations of flare radiation with a parametric catastrophe that occurs when the top of a twisted magnetic loop enters the corona. A sharp decrease in external pressure leads to the longitudinal magnetic field of a force-free flux rope tending to zero on the magnetic surface where the current changes sign, and the density of the azimuthal current and the force-free parameter begin to grow indefinitely near this surface, approaching a break. The current velocity of electrons here will inevitably exceed the speed of ion sound, and plasma instability will arise. Scattering of electrons on ion-acoustic plasmons will sharply decrease the plasma conductivity and cause rapid, flare dissipation of the magnetic energy of the rope, i.e., decrease in the amplitude of the field and currents and expansion of the rope cross-section. This is how the first peak of the flare radiation will be formed. In this case, the torque applied to each section of the rope will be greatly weakened in the energy release region. In equilibrium, the torque should be the same along the entire length of the loop, so there will be a transfer of the azimuthal flux by Alfvén waves from the loop legs to the top. Alignment of the torque along the rope axis will return the rope to its original state, after which the second peak of the flare radiation is formed, and the process is repeated several times until the reserve of free magnetic energy associated with the currents in the entire loop decreases significantly. The oscillations of the rope cross-section accompanying the peaks of its radiation represent a specific type of fluctuations of a system with time-varying rigidity: in them the magnetic field intensity, providing the restoring force, changes greatly. Calculation of such oscillations allows achieving not only qualitative but also quantitative correspondence between the theoretical results and observational data.

太阳耀斑的绳通量模型将耀斑辐射的准周期脉动现象与一种参数突变联系起来,这种突变发生在扭曲磁环的顶部进入日冕时。外部压力的急剧减小导致无力磁通绳的纵向磁场在电流变化符号的磁表面上趋于零,并且在该表面附近的方位电流密度和无力参数开始无限增长,接近于断裂。这里电子的电流速度将不可避免地超过离子声的速度,等离子体的不稳定性将会出现。电子在离子声等离子体激元上的散射会使等离子体电导率急剧降低,并引起绳索磁能的快速、耀斑耗散,即磁场和电流的振幅减小以及绳索截面的扩大。这就是耀斑辐射的第一个峰值将如何形成。在这种情况下,施加在绳索各部分上的扭矩在能量释放区域将大大减弱。在平衡状态下,转矩沿环的整个长度应该是相同的,因此将有一个方位角通量由阿尔夫萨芬波从环腿转移到顶部。沿绳轴方向的转矩对齐将使绳恢复到原来的状态,之后形成耀斑辐射的第二个峰值,这个过程重复几次,直到整个回路中与电流相关的自由磁能储备显著减少。绳索横截面的振荡伴随其辐射的峰值,代表了具有时变刚度的系统的一种特定类型的波动:在这种情况下,提供恢复力的磁场强度变化很大。这种振荡的计算不仅可以在理论结果和观测数据之间实现定性的,而且可以实现定量的对应。
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