Radiative and conductive cooling in a solar flare

We investigate the radiative and conductive cooling in the solar flare observed by RHESSI on 2005 September 13. The radiative and conductive loss energies are estimated from the observations after the flare onset. Consistent with previous findings, the cooling is increased with time, especially the radiation becomes remarkable on the later phase of flare. According our method, about half of thermal energy is traced by RHESSI soft X-rays, while the other half is lost by the radiative (∼38%) and conductive (∼9%) cooling at end of the hard X-rays in this event. The nonthermal energy input of P _nth (inferred from RHESSI hard X-ray spectrum) is not well correlated with the derivative of thermal energy of \fracdE_thdt\frac{\mathrm{d}E_{\mathrm{th}}}{\mathrm{d}t} (required to radiate the RHESSI soft X-ray flux and spectrum) alone. However, after consideration the radiation and conduction, a high correlation is obtained between the derivative of total thermal energy ( \fracdE_th+E_rad+E_conddt\frac{\mathrm{d}E_{\mathrm{th}}+E_{\mathrm{rad}}+E_{\mathrm{cond}}}{\mathrm{d}t}) and nonthermal energy input (P _nth) from the flare start to end, indicating the relative importance of conductive and direct radiative losses during the solar flare development. Ignoring the uncertainties to estimate the energy from the observations, we find that about ∼12% fraction of the known energy is transferred into the thermal energy for the 2005 September 13 flare.     

Small-Scale Flux Emergence Observed Using <Emphasis Type="Italic">Hinode</Emphasis>/SOT

The aim of this paper is to determine the flux emergence rate due to small-scale magnetic features in the quiet Sun using high-resolution Hinode SOT NFI data. Small-scale magnetic features are identified in the data using two different feature identification methods (clumping and downhill); then three methods are applied to detect flux emergence events. The distribution of the intranetwork peak emerged fluxes is determined. When combined with previous emergence results, from ephemeral regions to sunspots, the distribution of all fluxes are found to follow a power-law distribution which spans nearly seven orders of magnitude in flux (10¹⁶ – 10²³ Mx) and 18 orders of magnitude in frequency. The power-law fit to all these data is of the form

The extreme initial kinetic energy allowed by a collapsing turbulent core

We present high-resolution hydrodynamical simulations aimed at following the gravitational collapse of a gas core, in which a turbulent spectrum of velocity is implemented only initially. We determine the maximal value of the ratio of kinetic energy to gravitational energy, denoted here by \((\frac{E_{\mathrm{kin}} }{E_{\mathrm{grav}}} )_{\max}\), so that the core (i) will collapse around one free-fall time of time evolution or (ii) will expand unboundedly, because it has a value of \(\frac{E_{\rm kin}}{E_{\mathrm{grav}}}\) larger than \(( \frac{E_{\mathrm{kin}}}{E_{\mathrm{grav}}} )_{\mathrm{max}}\). We consider core models with a uniform or centrally condensed density profile and with velocity spectra composed of a linear combination of one-half divergence-free turbulence type and the other half of a curl-free turbulence type. We show that the outcome of the core collapse are protostars forming either (i) a multiple system obtained from the fragmentation of filaments and (ii) a single primary system within a long filament. In addition, some properties of these protostars are also determined and compared with those obtained elsewhere.     

Ultra-high energy neutrino fluxes from supermassive AGN black holes

We compute the ultra-high energy (UHE) neutrino fluxes from plausible accreting supermassive black holes closely linking to the 377 active galactic nuclei (AGNs). They have well-determined black hole masses collected from the literature. The neutrinos are produced via simple or modified URCA processes, even after the neutrino trapping, in superdense proto-matter medium. The resulting fluxes are ranging from: (1) (quark reactions)— $J^{q}_{\nu\varepsilon}/(\varepsilon_{d}\ \mathrm{erg}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}\,\mathrm{sr}^{-1})\simeq8.29\times 10^{-16}$ to 3.18×10^?4, with the average $\overline{J}^{q}_{\nu\varepsilon}\simeq5.53\times 10^{-10}\varepsilon_{d}\ \mathrm{erg}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}\,\mathrm{sr}^{-1}$ , where ε _d ～10^?12 is the opening parameter; (2) (pionic reactions)— $J^{\pi}_{\nu\varepsilon} \simeq0.112J^{q}_{\nu\varepsilon}$ , with the average $J^{\pi}_{\nu\varepsilon} \simeq3.66\times 10^{-11}\varepsilon_{d}\ \mathrm{erg}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}\,\mathrm{sr}^{-1}$ ; and (3) (modified URCA processes)— $J^{URCA}_{\nu\varepsilon}\simeq7.39\times10^{-11} J^{q}_{\nu\varepsilon}$ , with the average $\overline{J}^{URCA}_{\nu\varepsilon} \simeq2.41\times10^{-20} \varepsilon_{d}\ \mathrm{erg}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}\,\mathrm{sr}^{-1}$ . We conclude that the AGNs are favored as promising pure neutrino sources, because the computed neutrino fluxes are highly beamed along the plane of accretion disk, peaked at high energies and collimated in smaller opening angle θ～ε _d .     

Nonlinear newtonian theory and the effect of time dilatation

The fact that the energy density ρ_g of a static spherically symmetric gravitational field acts as a source of gravity, gives us a harmonic function \(f\left( \varphi \right) = e^{\varphi /c^2 } \) , which is determined by the nonlinear differential equation $$\nabla ^2 \varphi = 4\pi k\rho _g = - \frac{1}{{c^2 }}\left( {\nabla \varphi } \right)^2 $$ Furthermore, we formulate the infinitesimal time-interval between a couple of events measured by two different inertial observers, one in a position with potential φ-i.e., dt _φ and the other in a position with potential φ=0-i.e., dt ₀, as $${\text{d}}t_\varphi = f{\text{d}}t_0 .$$ When the principle of equivalence is satisfied, we obtain the well-known effect of time dilatation.     

An Analytical Model to Predict the Arrival Time of Interplanetary CMEs

Referring to the aerodynamic drag force, we present an analytical model to predict the arrival time of coronal mass ejections (CMEs). All related calculations are based on the expression for the deceleration of fast CMEs in the interplanetary medium (ICMEs), [(v)\dot]=-\frac115 700(v-V_SW)²\dot{v}=-\frac{1}{15\,700}(v-V_{\mathrm{SW}})^{2} , where V _SW is the solar wind speed. The results can reproduce well the observations of three typical parameters: the initial speed of the CME, the speed of the ICME at 1 AU and the transit time. Our simple model reveals that the drag acceleration should be really the essential feature of the interplanetary motion of CMEs, as suggested by Vršnak and Gopalswamy (J. Geophys. Res. 107, 1019, 2002).     

RHESSI Observations of the Neupert Effect in Three Solar Flares

Previous observations show that in many solar flares there is a causal correlation between the hard X-ray flux and the derivative of the soft X-ray flux. This so-called Neupert effect is indicative of a strong link between the primary energy release to accelerate particles and plasma heating. It suggests a flare model in which the hard X-rays are electron – ion bremsstrahlung produced by energetic electrons as they lose their energy in the lower corona and chromosphere and the soft X-rays are thermal bremsstrahlung from the “chromospheric evaporation” plasma heated by those same electrons. Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) observes in a broad energy band and its high spectral resolution and coverage of the low-energy range allow us to separate the thermal continuum from the nonthermal component, which gives us an opportunity to investigate the Neupert effect. In this paper, we use the parameters derived from RHESSI observations to trace the primary energy release and the plasma response: The hard X-ray flux or spectral hardness is compared with the derivative of plasma thermal energy in three impulsive flares on 10 November 2002 and on 3 and 25 August 2005. High correlations show that the Neupert effect does hold for the two hard X-ray peaks of the 10 November 2002 flare, for the first peaks of the 3 August 2005 flare, and for the beginning period of the 25 August 2005 flare.     

RHESSI Microflares: I. X-Ray Properties and Multiwavelength Characteristics

We study the general X-ray and multiwavelength characteristics of microflares of GOES class A0.7 to B7.4 (background subtracted) detected by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) on 26 September 2003 comparing them with the properties of regular flares. All the events for which X-ray imaging was feasible originated in one active region and were accumulated in areas with intermixed magnetic polarities. During the events’ rise and peak phase, the RHESSI X-ray spectra show a steep nonthermal power-law component (4?γ?10) for energies ??10 keV. Further evidence for the presence of electron beams is provided by the association with radio type III bursts in 5 out of 11 events where AIP radio spectra were available. The strongest event in our sample shows radio signatures of a type II precursor. The thermally emitting flare plasma observed by RHESSI is found to be hot, 11?T?15 MK, with small emission measures, 10⁴⁶?EM?10⁴⁷ cm^?3, concentrated in the flare loop. In the EUV (TRACE 171 Å), the UV (TRACE 1600 Å) and Kanzelhöhe Solar Observatory Hα, impulsive brightenings at both ends of the RHESSI 3?–?6 keV X-ray loop source are observed, situated in opposite magnetic polarity fields. During the decay phase, a postflare loop at the location of the RHESSI loop source is observed in the TRACE 171 Å? channel showing plasma that is cooled from ??10 MK to ≈?1 MK. Correlations between various thermal and nonthermal parameters derived from the RHESSI microflare spectra compared to the same correlations obtained for a set of small and large flares by Battaglia et al. (Astron. Astrophys. 439, 737, 2005) indicate that the RHESSI instrument gives us a spectrally biased view since it detects only hot (T?10 MK) microflares, and thus the correlations between RHESSI microflare parameters have to be interpreted with caution. The thermal and nonthermal energies derived for the RHESSI microflares are \(\bar{E}_{\mathrm{th}}=7\times 10^{27}\) ergs and \(\bar{E}_{\mathrm{nth}}=2\times 10^{29}\) ergs, respectively. Possible reasons for the order-of-magnitude difference between the thermal and nonthermal microflare energies, which was also found in previous studies, are discussed. The determined event rate of 3.7 h^?1 together with the average microflare energies indicate that the total energy in the observed RHESSI microflares is far too small to account for the heating of the active region corona in which they occur.     

Black Hole Dynamic Potentials

In the following paper, certain black hole dynamic potentials have been developed definitively on the lines of classical thermodynamics. These potentials have been refined in view of the small differences in the equations of the laws of black hole dynamics as given by Bekenstein and those of thermodynamics. Nine fundamental black hole dynamical relations have been developed akin to the four fundamental thermodynamic relations of Maxwell. The specific heats C _??,?? and C _J,Q have been defined. For a black hole, these quantities are negative. The ??dA equation has been obtained as an application of these fundamental relations. Time reversible processes observing constancy of surface gravity are considered and an equation connecting the internal energy of the black hole E, the additional available energy defined as the first free energy function K, and the surface gravity ??, has been obtained. Finally as a further application of the fundamental relations, it has been proved for a homogeneous gravitational field in black hole space times or a de Sitter black hole that $C_{\Omega ,\Phi } -C_{J,Q} =\kappa \left[ {\left( {\frac{\partial J}{\partial \kappa }} \right)_{\Omega ,\Phi } \left( {\frac{\partial \Omega }{\partial \kappa }} \right)_{J,Q} +\left( {\frac{\partial Q}{\partial \kappa }} \right)_{\Omega ,\Phi } \left( {\frac{\partial \Phi }{\partial \kappa }} \right)_{J,Q} } \right]$ . This is dubbed as the homogeneous fluid approximation in context of the black holes.     

A Check on the Validity of Magnetic Field Reconstructions

We investigate a method to test whether a numerically computed model coronal magnetic field \({\boldsymbol {B}}\) departs from the divergence-free condition (also known as the solenoidality condition). The test requires a potential field \({\boldsymbol {B}}_{0}\) to be calculated, subject to Neumann boundary conditions, given by the normal components of the model field \({\boldsymbol {B}}\) at the boundaries. The free energy of the model field may be calculated using \(\frac{1}{2\mu _{0}}\int ({\boldsymbol {B}}-{\boldsymbol {B}}_{0})^{2}\mathrm{d}V\), where the integral is over the computational volume of the model field. A second estimate of the free energy is provided by calculating \(\frac{1}{2\mu _{0}}\int {\boldsymbol {B}}^{2}\,\mathrm{d}V-\frac{1}{2\mu _{0}}\int {\boldsymbol {B}}_{0}^{2}\,\mathrm{d}V\). If \({\boldsymbol {B}}\) is divergence free, the two estimates of the free energy should be the same. A difference between the two estimates indicates a departure from \(\nabla \cdot {\boldsymbol {B}}=0\) in the volume. The test is an implementation of a procedure proposed by Moraitis et al. (Solar Phys.289, 4453, 2014) and is a simpler version of the Helmholtz decomposition procedure presented by Valori et al. (Astron. Astrophys.553, A38, 2013). We demonstrate the test in application to previously published nonlinear force-free model fields, and also investigate the influence on the results of the test of a departure from flux balance over the boundaries of the model field. Our results underline the fact that, to make meaningful statements about magnetic free energy in the corona, it is necessary to have model magnetic fields that satisfy the divergence-free condition to a good approximation.     

A Statistical Study on Photospheric Magnetic Nonpotentiality of Active Regions and Its Relationship with Flares During Solar Cycles 22?–?23

A statistical study is carried out on the photospheric magnetic nonpotentiality in solar active regions and its relationship with associated flares. We select 2173 photospheric vector magnetograms from 1106 active regions observed by the Solar Magnetic Field Telescope at Huairou Solar Observing Station, National Astronomical Observatories of China, in the period of 1988??C?2008, which covers most of the 22nd and 23rd solar cycles. We have computed the mean planar magnetic shear angle ( $\overline{\Delta\phi}$ ), mean shear angle of the vector magnetic field ( $\overline{\Delta\psi}$ ), mean absolute vertical current density ( $\overline{|J_{z}|}$ ), mean absolute current helicity density ( $\overline{|h_{\mathrm{c}}|}$ ), absolute twist parameter (|?? _av|), mean free magnetic energy density ( $\overline{\rho_{\mathrm{free}}}$ ), effective distance of the longitudinal magnetic field (d _E), and modified effective distance (d _Em) of each photospheric vector magnetogram. Parameters $\overline{|h_{\mathrm{c}}|}$ , $\overline{\rho_{\mathrm{free}}}$ , and d _Em show higher correlations with the evolution of the solar cycle. The Pearson linear correlation coefficients between these three parameters and the yearly mean sunspot number are all larger than 0.59. Parameters $\overline {\Delta\phi}$ , $\overline{\Delta\psi}$ , $\overline{|J_{z}|}$ , |?? _av|, and d _E show only weak correlations with the solar cycle, though the nonpotentiality and the complexity of active regions are greater in the activity maximum periods than in the minimum periods. All of the eight parameters show positive correlations with the flare productivity of active regions, and the combination of different nonpotentiality parameters may be effective in predicting the flaring probability of active regions.     

The seasonal variation of the newtonian constant of gravitation and its relationship with the “classical tests” of general relativity

The ratio between the Earth's perihelion advance (Δθ) _E and the solar gravitational red shift (GRS) (Δø _s e)a ₀/c ² has been rewritten using the assumption that the Newtonian constant of gravitationG varies seasonally and is given by the relationship, first found by Gasanalizade (1992b) for an aphelion-perihelion difference of (ΔG)_a?p . It is concluded that $$\begin{gathered} (\Delta \theta )_E = \frac{{3\pi }}{e}\frac{{(\Delta \phi _{sE} )_{A_0 } }}{{c^2 }}\frac{{(\Delta G)_{a - p} }}{{G_0 }} = 0.038388 \sec {\text{onds}} {\text{of}} {\text{arc}} {\text{per}} {\text{revolution,}} \hfill \\ \frac{{(\Delta G)_{a - p} }}{{G_0 }} = \frac{e}{{3\pi }}\frac{{(\Delta \theta )_E }}{{(\Delta \phi _{sE} )_{A_0 } /c^2 }} = 1.56116 \times 10^{ - 4} . \hfill \\ \end{gathered} $$ The results obtained here can be readily understood by using the Parametrized Post-Newtonian (PPN) formalism, which predicts an anisotropy in the “locally measured” value ofG, and without conflicting with the general relativity.     

Dark energy model in anisotropic Bianchi type-III space-time with variable EoS parameter

A new dark energy model in anisotropic Bianchi type-III space-time with variable equation of state (EoS) parameter has been investigated in the present paper. To get the deterministic model, we consider that the expansion θ in the model is proportional to the eigen value s² ₂\sigma^{2}_{~2} of the shear tensor s^j _i\sigma^{j}_{~i}. The EoS parameter ω is found to be time dependent and its existing range for this model is in good agreement with the recent observations of SNe Ia data (Knop et al. in Astrophys. J. 598:102, 2003) and SNe Ia data with CMBR anisotropy and galaxy clustering statistics (Tegmark et al. in Astrophys. J. 606:702, 2004). It has been suggested that the dark energy that explains the observed accelerating expansion of the universe may arise due to the contribution to the vacuum energy of the EoS in a time dependent background. Some physical aspects of dark energy model are also discussed.     

Fragmentation of the Current Sheet,Anomalous Resistivity,and Acceleration of Particles

The evolution of the current sheet in the electric current direction (in the guiding magnetic field direction) is studied numerically in the 3-D particle-in-cell model with two current sheets and periodic boundary conditions. In the regime with (where v _D and are the electric current drift and electron thermal velocities, respectively) the current sheets are unstable owing to the Buneman and kink instabilities and become strongly fragmented. During their evolution, in addition to an increase of the energy of the electric field component in the guiding magnetic field direction, the energies of the electric field components in the perpendicular direction are even more enhanced. In the current sheet the anomalous resistivity (η _anom/η _C∼7×10⁵, where η _C is the classical resistivity) is generated and thus the magnetic field dissipates. Most of the dissipated magnetic energy is transformed into the electron kinetic energy in the direction of the electric current. The associated electric field accelerates the electrons from the tail of the distribution function.     

Dissipation of modified entropic gravitational energy through gravitational waves

The phenomenological nature of a new gravitational type interaction between two different bodies derived from Verlinde’s entropic approach to gravitation in combination with Sorkin’s definition of Universe’s quantum information content, is investigated. Assuming that the energy stored in this entropic gravitational field is dissipated under the form of gravitational waves and that the Heisenberg principle holds for this system, one calculates a possible value for an absolute minimum time scale in nature t = \frac1516 \fracL^1/2(^h/_2p) Gc⁴ ~ 9.27×10^-105\tau=\frac{15}{16} \frac{\Lambda^{1/2}\hbar G}{c^{4}}\sim9.27\times10^{-105} seconds, which is much smaller than the Planck time t _P =(ħG/c ⁵)^1/2∼5.38×10⁻⁴⁴ seconds. This appears together with an absolute possible maximum value for Newtonian gravitational forces generated by matter F_g=\frac3230\fracc⁷L (^h/_2p) G² ~ 3.84×10¹⁶⁵F_{g}=\frac{32}{30}\frac{c^{7}}{\Lambda \hbar G^{2}}\sim 3.84\times 10^{165} Newtons, which is much higher than the gravitational field between two Planck masses separated by the Planck length F _gP =c ⁴/G∼1.21×10⁴⁴ Newtons.     

Iodine-Cell Spectroscopy Applied to Investigating the Solar Differential Rotation

In an attempt to examine whether the spectroscopic Doppler method with an iodine cell (which is known to be successful for precise radial-velocity determinations in stellar astronomy) could be effective for investigating the solar differential rotation, we carried out intensive observations to collect spectra at a large number of points on the solar disk by using the Domeless Solar Telescope along with the horizontal spectrograph of the Hida Observatory. Having converted the resulting line-of-sight velocity component into the angular rotational rate (ω), we derived a differential rotation law, w_sidereal  (deg day^-1) = 14.03 (±0.06)-1.84 (±0.57) sin²y-1.92 (±0.85) sin⁴y\omega_{\mathrm{sidereal}}\; (\mathrm{deg}\,\mathrm{day}^{-1}) =14.03 (\pm0.06)-1.84 (\pm0.57) \sin^{2}\psi-1.92 (\pm0.85) \sin^{4}\psi (ψ: heliographic latitude), which is reasonably consistent with other spectroscopic determinations published so far. Our analysis also revealed several practical points to note for successful application (e.g., exclusion of those data that are not well distant from the meridian; mutual data subtraction/averaging for symmetric counterparts at the eastern and western hemisphere). Considering its easiness and cheapness, this iodine-cell-featured spectroscopic method may be regarded as an effective and practical tool for studying the differential rotation of the Sun.     

Ion-acoustic double layers in magnetized positive-negative ion plasmas with nonthermal electrons

The nonlinear ion-acoustic double layers (IADLs) in a warm magnetoplasma with positive-negative ions and nonthermal electrons are investigated. For this purpose, the hydrodynamic equations for the positive-negative ions, nonthermal electron density distribution, and the Poisson equation are used to derive a modified Zakharov–Kuznetsov (MZK) equation, in the small amplitude regime. It is found that compressive and rarefactive IADLs strongly depend on the mass and density ratios of the negative-to-positive ions as well as the nonthermal electron parameter. Also, it is shown that there are one critical value for the density ratio of the negative-to-positive ions (ν), the ratio between unperturbed electron-to-positive ion density (μ), and the nonthermal electron parameter (β), which decide the existence of positive and negative IADLs. The present study is applied to examine the small amplitude nonlinear IADL excitations for the (H⁺, O₂^-)(\mathrm{H}^{+}, \mathrm{O}_{2}^{-}) and (H⁺,H⁻) plasmas, where they are found in the D- and F-regions of the Earth’s ionosphere. This investigation should be helpful in understanding the salient features of the nonlinear IADLs in either space or laboratory plasmas where two distinct groups of ions and non-Boltzmann distributed electrons are present.     

Stability of ion-acoustic waves in a pair-ion plasma with a third species of ions: application to cometary plasmas

A popular model of a cometary plasma is hydrogen (H⁺) with positively charged oxygen (O⁺) as a heavier ion component. However, the discovery of negatively charged oxygen (O^?) ions enables one to model a cometary plasma as a pair-ion plasma (of O⁺ and O^?) with hydrogen as a third ion constituent. We have, therefore, studied the stability of the ion-acoustic wave in such a pair-ion plasma with hydrogen and electrons streaming with velocities $V_{d\mathrm{H}^{+}}$ and V _de , respectively, relative to the oxygen ions. We find the calculated frequency of the ion-acoustic wave with this model to be in good agreement with the observed frequencies. The ion-acoustic wave can also be driven unstable by the streaming velocity of the hydrogen ions. The growth rate increases with increasing hydrogen density $n_{\mathrm{H}^{+}}$ , and streaming velocities $V_{d\mathrm{H}^{+}}$ and V _de . It, however, decreases with increasing oxygen ion densities $n_{\mathrm{O}^{+}}$ and $n_{\mathrm{O}^{-}}$ .     

The influence of negatively charged heavy ions on the kinetic Alfven wave in a cometary environment

Kinetic Alfven waves are important in a wide variety of areas like astrophysical, space and laboratory plasmas. In cometary environments, waves in the hydromagnetic range of frequencies are excited predominantly by heavy ions. We, therefore, study the stability of the kinetic Alfven wave in a plasma of hydrogen ions, positively and negatively charged oxygen ions and electrons. Each species was modeled by drifting ring distributions in the direction parallel to the magnetic field; in the perpendicular direction the distribution was simulated with a loss cone type distribution obtained through the subtraction of two Maxwellian distributions with different temperatures. We find that for frequencies w^* < w_{cH ⁺}\omega^{*} < \omega_{c\mathrm{H}^{ +}} (ω ^∗ and w_{cH ⁺}\omega_{c\mathrm{H}^{ +}} being respectively the Doppler shifted and hydrogen ion gyro-frequencies), the growth rate increases with increasing negatively charged oxygen ion densities while decreasing with increasing propagation angles, negative ion temperatures and negative ion mass.