Investigation of the Geoeffectiveness of Disk-Centre Full-Halo Coronal Mass Ejections

We studied the occurrence and characteristics of geomagnetic storms associated with disk-centre full-halo coronal mass ejections (DC-FH-CMEs). Such coronal mass ejections (CMEs) can be considered as the most plausible cause of geomagnetic storms. We selected front-side full-halo coronal mass ejections detected by the Large Angle and Spectrometric Coronagraph onboard the Solar and Heliospheric Observatory (SOHO/LASCO) from the beginning of 1996 till the end of 2015 with source locations between solar longitudes E10 and W10 and latitudes N20 and S20. The number of selected CMEs was 66 of which 33 (50%) were deduced to be the cause of 30 geomagnetic storms with \(\mathrm{Dst} \leq- 50~\mbox{nT}\). Of the 30 geomagnetic storms, 26 were associated with single disk-centre full-halo CMEs, while four storms were associated, in addition to at least one disk-centre full-halo CME, also with other halo or wide CMEs from the same active region. Thirteen of the 66 CMEs (20%) were associated with 13 storms with \(-100~\mbox{nT} < \mbox{Dst} \leq- 50~\mbox{nT}\), and 20 (30%) were associated with 17 storms with \(\mbox{Dst}\leq- 100~\mbox{nT}\). We investigated the distributions and average values of parameters describing the DC-FH-CMEs and their interplanetary counterparts encountering Earth. These parameters included the CME sky-plane speed and direction parameter, associated solar soft X-ray flux, interplanetary magnetic field strength, \(B_{t}\), southward component of the interplanetary magnetic field, \(B_{s}\), solar wind speed, \(V_{sw}\), and the \(y\)-component of the solar wind electric field, \(E_{y}\). We found only a weak correlation between the Dst of the geomagnetic storms associated with DC-FH-CMEs and the CME sky-plane speed and the CME direction parameter, while the correlation was strong between the Dst and all the solar wind parameters (\(B_{t}\), \(B_{s}\), \(V_{sw}\), \(E_{y}\)) measured at 1 AU. We investigated the dependences of the properties of DC-FH-CMEs and the associated geomagnetic storms on different phases of solar cycles and the differences between Solar Cycles 23 and 24. In the rise phase of Solar Cycle 23 (SC23), five out of eight DC-FH-CMEs were geoeffective (\(\mbox{Dst} \leq- 50~\mbox{nT}\)). In the corresponding phase of SC24, only four DC-FH-CMEs were observed, three of which were nongeoeffective (\(\mbox{Dst} > - 50~\mbox{nT}\)). The largest number of DC-FH-CMEs occurred at the maximum phases of the cycles (21 and 17, respectively). Most of the storms with \(\mbox{Dst}\leq- 100~\mbox{nT}\) occurred at or close to the maximum phases of the cycles. When comparing the storms during epochs of corresponding lengths in Solar Cycles 23 and 24, we found that during the first 85 months of Cycle 23 the geoeffectiveness rate of the disk-centre full-halo CMEs was 58% with an average minimum value of the Dst index of \(- 146~\mbox{nT}\). During the corresponding epoch of Cycle 24, only 35% of the disk-centre full-halo CMEs were geoeffective with an average value of Dst of \(- 97~\mbox{nT}\).     

The Na <Emphasis Type="SmallCaps">i</Emphasis> and Sr <Emphasis Type="SmallCaps">ii</Emphasis> Resonance Lines in Solar Prominences

We estimate the electron density, \(n_{\mathrm{e}}\), and its spatial variation in quiescent prominences from the observed emission ratio of the resonance lines Na?i?5890 Å (D₂) and Sr?ii?4078 Å. For a bright prominence (\(\tau_{\alpha}\approx25\)) we obtain a mean \(n_{\mathrm{e}}\approx2\times10^{10}~\mbox{cm}^{-3}\); for a faint one (\(\tau _{\alpha }\approx4\)) \(n_{\mathrm{e}}\approx4\times10^{10}~\mbox{cm}^{-3}\) on two consecutive days with moderate internal fluctuation and no systematic variation with height above the solar limb. The thermal and non-thermal contributions to the line broadening, \(T_{\mathrm{kin}}\) and \(V_{\mathrm{nth}}\), required to deduce \(n_{\mathrm{e}}\) from the emission ratio Na?i/Sr?ii cannot be unambiguously determined from observed widths of lines from atoms of different mass. The reduced widths, \(\Delta\lambda_{\mathrm{D}}/\lambda_{0}\), of Sr?ii?4078 Å show an excess over those from Na?D₂ and \(\mbox{H}\delta\,4101\) Å, assuming the same \(T_{\mathrm{kin}}\) and \(V_{\mathrm{nth}}\). We attribute this excess broadening to higher non-thermal broadening induced by interaction of ions with the prominence magnetic field. This is suggested by the finding of higher macro-shifts of Sr?ii?4078 Å as compared to those from Na?D₂.     

A New Solar Imaging System for Observing High-Speed Eruptions: <Emphasis Type="Italic">Solar Dynamics Doppler Imager</Emphasis> (SDDI)

A new solar imaging system was installed at Hida Observatory to observe the dynamics of flares and filament eruptions. The system (Solar Dynamics Doppler Imager; SDDI) takes full-disk solar images with a field of view of \(2520~\mbox{arcsec} \times 2520~\mbox{arcsec}\) at multiple wavelengths around the \(\mathrm{H}\alpha\) line at 6562 Å. Regular operation was started in May 2016, in which images at 73 wavelength positions spanning from \(\mathrm{H}\alpha -9~\mathring{\mathrm{A}}\) to \(\mathrm{H}\alpha +9~\mathring{\mathrm{A}}\) are obtained every 15 seconds. The large dynamic range of the line-of-sight velocity measurements (\({\pm}\,400~\mbox{km}\,\mbox{s}^{-1}\)) allows us to determine the real motions of erupting filaments in 3D space. It is expected that SDDI provides unprecedented datasets to study the relation between the kinematics of filament eruptions and coronal mass ejections (CME), and to contribute to the real-time prediction of the occurrence of CMEs that cause a significant impact on the space environment of the Earth.     

Addendum to: Strength of the Solar Coronal Magnetic Field – A Comparison of Independent Estimates Using Contemporaneous Radio and White-Light Observations

This addendum uses an alternate fit for the electron density distribution \(N(r)\) (see Figure 1) and estimates the coronal magnetic field using the new model. We find that the estimates of the magnetic field are in close agreement using both the models.

We have fit the \(N(r)\) distribution obtained from STEREO-A/COR1 and SOHO/LASCO-C2 using a fifth-order polynomial (see Figure 1). The expression can be written as

$$\begin{aligned} N_{\text{cor}}(r) &= 1.43 \times 10^{9} r^{-5} - 1.91 \times 10^{9} r^{-4} + 1.07 \times 10^{9} r^{-3} - 2.87 \times 10^{8} r^{-2} \\ &\quad {} + 3.76 \times 10^{7} r^{-1} - 1.91 \times 10^{6} , \end{aligned}$$

(1)

where \(N_{\text{cor}}(r)\) is in units of cm^?3 and \(r\) is in units of \(\mathrm{R}_{\odot}\). The background coronal electron density is enhanced by a factor of 5.5 at 2.63 \(\mathrm{R}_{\odot}\) during the coronal mass ejection (CME). The estimated coronal magnetic field strength (\(B\)) using radio data indicates that \(B(r) \approx(0.51\text{\,--\,}0.48) \pm 0.02\ \mathrm{G}\) in the range \(r \approx2.65\text{\, --\,}2.82\ \mathrm{R}_{\odot}\). The field strengths for STEREO-A/COR1 and SOHO/LASCO-C2 are ≈?0.32 G at \(r \approx 3.11\ \mathrm{R}_{\odot}\) and ≈?0.12 G at \(r \approx 4.40\ \mathrm{R}_{\odot}\), respectively.

     

The Origin of Sequential Chromospheric Brightenings

Sequential chromospheric brightenings (SCBs) are often observed in the immediate vicinity of erupting flares and are associated with coronal mass ejections. Since their initial discovery in 2005, there have been several subsequent investigations of SCBs. These studies have used differing detection and analysis techniques, making it difficult to compare results between studies. This work employs the automated detection algorithm of Kirk et al. (Solar Phys. 283, 97, 2013) to extract the physical characteristics of SCBs in 11 flares of varying size and intensity. We demonstrate that the magnetic substructure within the SCB appears to have a significantly smaller area than the corresponding \(\mbox{H}\upalpha\) emission. We conclude that SCBs originate in the lower corona around \(0.1~R_{\odot}\) above the photosphere, propagate away from the flare center at speeds of \(35\,\mbox{--}\,85~\mbox{km}\,\mbox{s}^{-1}\), and have peak photosphere magnetic intensities of \(148\pm2.9~\mbox{G}\). In light of these measurements, we infer SCBs to be distinctive chromospheric signatures of erupting coronal mass ejections.     

First integrals for the Kepler problem with linear drag

In this work we consider the Kepler problem with linear drag, and prove the existence of a continuous vector-valued first integral, obtained taking the limit as \(t\rightarrow +\infty \) of the Runge–Lenz vector. The norm of this first integral can be interpreted as an asymptotic eccentricity \(e_{\infty }\) with \(0\le e_{\infty } \le 1\). The orbits satisfying \(e_{\infty } <1\) approach the singularity by an elliptic spiral and the corresponding solutions \(x(t)=r(t)e^{i\theta (t)}\) have a norm r(t) that goes to zero like a negative exponential and an argument \(\theta (t)\) that goes to infinity like a positive exponential. In particular, the difference between consecutive times of passage through the pericenter, say \(T_{n+1} -T_n\), goes to zero as \(\frac{1}{n}\).     

The global modulation of Galactic and Jovian electrons in the heliosphere

A full three-dimensional, numerical model is used to study the modulation of Jovian and Galactic electrons from 1 MeV to 50 GeV, and from the Earth into the heliosheath. For this purpose the very local interstellar spectrum and the Jovian electron source spectrum are revisited. It is possible to compute the former with confidence at kinetic energies \(E < 50~\mbox{MeV}\) since Voyager 1 crossed the heliopause in 2012 at \(\sim 122~\mbox{AU}\), measuring Galactic electrons at these energies. Modeling results are compared with Voyager 1 observations in the outer heliosphere, including the heliosheath, as well as observations at or near the Earth from the ISSE3 mission, and in particular the solar minimum spectrum from the PAMELA space mission for 2009, also including data from Ulysses for 1991 and 1992, and observations above 1 MeV from SOHO/EPHIN. Making use of the observations at or near the Earth and the two newly derived input functions for the Jovian and Galactic electrons respectively, the energy range over which the Jovian electrons dominate the Galactic electrons is determined so that the intensity of Galactic electrons at Earth below 100 MeV is calculated. The differential intensity for the Galactic electrons at Earth for \(E = 1~\mbox{MeV}\) is \(\sim 4\) electrons \(\mbox{m}^{-2}\,\mbox{s}^{-1}\,\mbox{sr}^{-1}\,\mbox{MeV}^{-1}\), whereas for Jovian electrons it is \(\sim 350\) electrons \(\mbox{m}^{-2}\,\mbox{s}^{-1}\,\mbox{sr}^{-1}\,\mbox{MeV}^{-1}\). At \(E = 30~\mbox{MeV}\) the two intensities are the same; above this energy the Jovian electron intensity quickly subsides so that the Galactic intensity completely dominates. At 6 MeV, in the equatorial plane the Jovian electrons dominate but beyond \(\sim 15~\mbox{AU}\) the Galactic intensity begins to exceed the Jovian intensity significantly.     

Development and Parameters of a Non-Self-Similar CME Caused by the Eruption of a Quiescent Prominence

The eruption of a large quiescent prominence on 17 August 2013 and an associated coronal mass ejection (CME) were observed from different vantage points by the Solar Dynamics Observatory (SDO), the Solar-Terrestrial Relations Observatory (STEREO), and the Solar and Heliospheric Observatory (SOHO). Screening of the quiet Sun by the prominence produced an isolated negative microwave burst. We estimated the parameters of the erupting prominence from a radio absorption model and measured them from 304 Å images. The variations of the parameters as obtained by these two methods are similar and agree within a factor of two. The CME development was studied from the kinematics of the front and different components of the core and their structural changes. The results were verified using movies in which the CME expansion was compensated for according to the measured kinematics. We found that the CME mass (\(3.6 \times 10^{15}\mbox{ g}\)) was mainly supplied by the prominence (\(\approx 6 \times 10^{15}\mbox{ g}\)), while a considerable part drained back. The mass of the coronal-temperature component did not exceed \(10^{15}\mbox{ g}\). The CME was initiated by the erupting prominence, which constituted its core and remained active. The structural and kinematical changes started in the core and propagated outward. The CME structures continued to form during expansion, which did not become self-similar up to \(25~\mathrm{R}_{\odot }\). The aerodynamic drag was insignificant. The core formed during the CME rise to \(4~\mathrm{R}_{\odot }\) and possibly beyond. Some of its components were observed to straighten and stretch outward, indicating the transformation of tangled structures of the core into a simpler flux rope, which grew and filled the cavity as the CME expanded.     

GONG p-Mode Parameters Through Two Solar Cycles

We investigate the parameters of global solar p-mode oscillations, namely damping width \(\Gamma\), amplitude \(A\), mean squared velocity \(\langle v^{2}\rangle\), energy \(E\), and energy supply rate \(\mathrm{d}E/\mathrm{d}t\), derived from two solar cycles’ worth (1996?–?2018) of Global Oscillation Network Group (GONG) time series for harmonic degrees \(l=0\,\mbox{--}\,150\). We correct for the effect of fill factor, apparent solar radius, and spurious jumps in the mode amplitudes. We find that the amplitude of the activity-related changes of \(\Gamma\) and \(A\) depends on both frequency and harmonic degree of the modes, with the largest variations of \(\Gamma\) for modes with \(2400~\upmu\mbox{Hz}\le\nu\le3300~\upmu\mbox{Hz}\) and \(31\le l \le60\) with a minimum-to-maximum variation of \(26.6\pm0.3\%\) and of \(A\) for modes with \(2400~\upmu\mbox{Hz}\le\nu\le 3300~\upmu\mbox{Hz}\) and \(61\le l \le100\) with a minimum-to-maximum variation of \(27.4\pm0.4\%\). The level of correlation between the solar radio flux \(F_{10.7}\) and mode parameters also depends on mode frequency and harmonic degree. As a function of mode frequency, the mode amplitudes are found to follow an asymmetric Voigt profile with \(\nu_{\text{max}}=3073.59\pm0.18~\upmu\mbox{Hz}\). From the mode parameters, we calculate physical mode quantities and average them over specific mode frequency ranges. In this way, we find that the mean squared velocities \(\langle v^{2}\rangle\) and energies \(E\) of p modes are anticorrelated with the level of activity, varying by \(14.7\pm0.3\%\) and \(18.4\pm0.3\%\), respectively, and that the mode energy supply rates show no significant correlation with activity. With this study we expand previously published results on the temporal variation of solar p-mode parameters. Our results will be helpful to future studies of the excitation and damping of p modes, i.e., the interplay between convection, magnetic field, and resonant acoustic oscillations.     

Trigger of Successive Filament Eruptions Observed by SDO and STEREO

Using multiwavelength observations from the Solar Dynamics Observatory (SDO) and the Solar Terrestrial Relations Observatory (STEREO), we investigate the mechanism of two successive eruptions (F1 and F2) of a filament in active region NOAA 11444 on 27 March 2012. The filament was inverse J-shaped and lay along a quasi-circular polarity inversion line (PIL). The first part of the filament erupted at \(\sim2{:}30\) UT on 27 March 2012 (F1), the second part at around 4:20 UT on the same day (F2). A precursor or preflare brightening was observed below the filament main axis about 30 min before F1. The brightening was followed by a jet-like ejection below the filament, which triggered its eruption. Before the eruption of F2, the filament seemed to be trapped within the overlying arcade loops for almost 1.5 h before it successfully erupted. Interestingly, we observe simultaneously contraction (\(\sim12~\mbox{km}\,\mbox{s}^{-1}\)) and expansion (\(\sim20~\mbox{km}\,\mbox{s}^{-1}\)) of arcade loops in the active region before F2. Magnetograms obtained with the Helioseismic and Magnetic Imager (HMI) show converging motion of the opposite polarities, which result in flux cancellation near the PIL. We suggest that flux cancellation at the PIL resulted in a jet-like ejection below the filament main axis, which triggered F1, similar to the tether-cutting process. F2 was triggered by removal of the overlying arcade loops via reconnection. Both filament eruptions produced high-speed (\(\sim1000~\mbox{km}\,\mbox{s}^{-1}\)) coronal mass ejections.     

Quantum scattering of KCl with He/para-$\mbox{H}_{2}$: potential energy surface and rate coefficients at low temperature

We present new two- and four-dimensional potential energy surfaces for the KCl(\(\mbox{X}^{1} \varSigma ^{+}\))-He and KCl(\(\mbox{X}^{1} \varSigma ^{+}\))-para-H₂ systems calculated with the internuclear distances of KCl and H₂ frozen at their experimental minimum energy. The CCSD(T) level of theory with aug-cc-pVQZ/AQZP basis sets is used. The potential surfaces present well depths of about \(78~\mbox{cm}^{-1}\) and \(235~\mbox{cm}^{-1}\) below the dissociation limit of the above interacting systems respectively. With these potential surfaces, cross sections are obtained in the close coupling scheme and rate coefficients inferred by averaging the cross sections over a Maxwell-Boltzmann velocity distribution for temperature below 50 K. A propensity towards \(\Delta J = 1\) transitions is observed.     

Geomagnetic Effects of Corotating Interaction Regions

We present an analysis of the geoeffectiveness of corotating interaction regions (CIRs), employing the data recorded from 25 January to 5 May 2005 and throughout 2008. These two intervals in the declining phase of Solar Cycle 23 are characterised by a particularly low number of interplanetary coronal mass ejections (ICMEs). We study in detail how four geomagnetic-activity parameters (the Dst, Ap, and AE indices, as well as the Dst time derivative, \(\mathrm{dDst}/\mathrm{d}t\)) are related to three CIR-related solar wind parameters (flow speed, \(V\), magnetic field, \(B\), and the convective electric field based on the southward Geocentric solar magnetospheric (GSM) magnetic field component, \(\mathit{VB}_{s}\)) on a three-hour time resolution. In addition, we quantify statistical relationships between the mentioned geomagnetic indices. It is found that Dst is correlated best to \(V\), with a correlation coefficient of \(\mathrm{cc}\approx0.6\), whereas there is no correlation between \(\mathrm{dDst}/\mathrm{d}t\) and \(V\). The Ap and AE indices attain peaks about half a day before the maximum of \(V\), with correlation coefficients ranging from \(\mathrm{cc}\approx0.6\) to \(\mathrm{cc}\approx0.7\), depending on the sample used. The best correlations of Ap and AE are found with \(\mathit{VB}_{s}\) with a delay of 3 h, being characterised by \(\mathrm{cc}\gtrsim 0.6\). The Dst derivative \(\mathrm{dDst}/\mathrm{d}t\) is also correlated with \(\mathit{VB}_{s}\), but the correlation is significantly weaker \(\mathrm{cc}\approx 0.4\)?–?0.5, with a delay of 0?–?3 h, depending on the employed sample. Such low values of correlation coefficients indicate that there are other significant effects that influence the relationship between the considered parameters. The correlation of all studied geomagnetic parameters with \(B\) are characterised by considerably lower correlation coefficients, ranging from \(\mathrm{cc}=0.3\) in the case of \(\mathrm{dDst}/\mathrm{d}t\) up to \(\mathrm{cc}=0.56\) in the case of Ap. It is also shown that peak values of geomagnetic indices depend on the duration of the CIR-related structures. The Dst is closely correlated with Ap and AE (\(\mathrm{cc}=0.7\)), Dst being delayed for about 3 h. On the other hand, \(\mathrm{dDst}/\mathrm{d}t\) peaks simultaneously with Ap and AE, with correlation coefficients of 0.48 and 0.56, respectively. The highest correlation (\(\mathrm{cc}=0.81\)) is found for the relationship between Ap and AE.     

Eruptive Solar Prominence at 37 GHz

On 27 June 2012, an eruptive solar prominence was observed in the extreme ultraviolet (EUV) and radio wavebands. At the Aalto University Metsähovi Radio Observatory (MRO) it was observed at 37 GHz. It was the first time that the MRO followed a radio prominence with dense sampling in the millimetre wavelengths. This prompted us to study the connection of the 37 GHz event with other wavelength domains. At 37 GHz, the prominence was tracked to a height of around \(1.6~\mathrm{R}_{\odot}\), at which the loop structure collapsed. The average velocity of the radio prominence was \(55 \pm 6~\mbox{km}\,\mbox{s}^{-1}\). The brightness temperature of the prominence varied between \(800 \pm 100\) K and \(3200 \pm 100\) K. We compared our data with the Solar Dynamic Observatory (SDO)/Atmospheric Imaging Assembly (AIA) instrument’s 304 Å EUV data, and found that the prominence behaves very similarly in both wavelengths. The EUV data also reveal flaring activity nearby the prominence. We present a scenario in which this flare works as a trigger that causes the prominence to move from a stable stage to an acceleration stage.     

Heights of Coronal Mass Ejections and Shocks Inferred from Metric and DH Type II Radio Bursts

A set of 27 continuous events that showed extension of metric Type-II radio bursts (m-Type IIs) into the deca–hectometric (DH) domain is considered. The coronal mass ejections (CMEs) associated with this type of continuous event supply more energy to produce space-weather effects than the CMEs that produce Type-II bursts in any one region. Since the heights of shock formation at the start of m-Type IIs were not available from observations, they were estimated using kinematic modeling in previous studies. In the present study, the heights of shock formation during metric and DH Type-II bursts are determined using two methods: i) the CME leading-edge method and ii) a method employing known electron-density models and start/end frequencies. In the first method, assuming that the shocks are generated by the associated CMEs at the leading edge, the height of the CME leading edge (LE) is calculated at the onset and end of m-Type IIs using the kinematic equation with constant acceleration or constant speed. The LE heights of CMEs that are assumed to be the heights of shock formation/end of nearly 79% of m-Type IIs are found to be within the acceptable range of \(1\,\mbox{--}\,3~\mbox{R}_{\odot}\). For other events, the heights are beyond this range, for which the shocks might either have been generated at the CME flanks/flare-blast waves, or the initial CME height might have been different. The CME/shock height at the onset and end of 17 DH Type IIs are found to be in the range of \(2\,\mbox{--}\,6~\mbox{R}_{\odot}\) and within \(30~\mbox{R}_{\odot}\), respectively. In addition, the CME LE heights from observations at the onset and end of metric/DH Type IIs are compared with the heights corresponding to the observed frequency that is determined using the known electron-density models, and they are in agreement with the model results. The heights are also estimated using the space speed available for 15 halo CMEs, and it is found that the difference is smaller at the m-Type II start/end (0.02 to \(0.66~\mbox{R}_{\odot}\)) and slightly greater at the DH Type II end (0.19 to \(1.94~\mbox{R}_{\odot}\)). Finally, the possibility of CME–streamer interactions at the start of DH Type IIs is checked, and it is found that many of the events with streamers have lower start frequencies. In addition, these results are discussed in comparison with the values reported in the literature. This study will be useful to find the source region of metric and DH Type IIs and to understand the CME-shock propagation.     

Initial In-flight Results: The Total Solar Irradiance Monitor on the FY-3C Satellite,an Instrument with a Pointing System

The total solar irradiance (TSI) has been recorded daily since October 2013 by the Total Solar Irradiance Monitor (TSIM) onboard the FY-3C satellite, which is mainly designed for Earth observation. The TSIM has a pointing system to perform solar tracking using a sun sensor. The TSI is measured by two electrical substitution radiometers with traceability to the World Radiation Reference. The TSI value measured with the TSIM on 2 October 2013 is \(1364.88~\mbox{W}\,\mbox{m}^{-2}\) with an uncertainty of \(1.08~\mbox{W}\,\mbox{m}^{-2}\). Short-term TSI variations recorded with the TSIM show good agreement with SOHO/VIRGO and SORCE/TIM. The data quality and accuracy of FY-3C/TSIM are much better than its predecessors on the FY-3A and FY-3B satellites, which operated in a scanning mode.     

Discovery of GeV gamma-ray emission from the LMC B0443-6657 with the <Emphasis Type="Italic">Fermi</Emphasis> Large Area Telescope

We report the discovery of gamma-ray detection from the Large Magellanic Cloud (LMC) B0443-6657 using the Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope. LMC B0443-6657 is a flat-spectrum radio source, possibly associated with a supernova remnant in the Large Magellanic Cloud (LMC N4). Employing the LAT data of 8 years, our results show a significant excess (\(>9.4\sigma \)) of gamma rays in the range of 0.2–100 GeV above the gamma-ray background. A power-law function is found to adequately describe the 0.2–\(100\mbox{ GeV}\)\(\gamma \)-ray spectrum, which yields a photon flux of \(3.27\pm 0.53\ \text{photon}\,\mbox{cm}^{2}\,\mbox{s}^{-1}\) with a photon index of \(2.35\pm 0.11\), corresponding to an isotropic gamma-ray luminosity of \(5.3\times 10^{40}~\mbox{erg}\,\mbox{s}^{-1}\). The hadronic model predicts a low X-ray and TeV flux while the leptonic model predicts an observable flux in these two energy bands. The follow-up observations of the LMC B0443-6657 in X-ray or TeV band would distinguish the radiation models of gamma rays from this region.     

An analysis of the convergence of Newton iterations for solving elliptic Kepler’s equation

In this note a study of the convergence properties of some starters \( E_0 = E_0(e,M)\) in the eccentricity–mean anomaly variables for solving the elliptic Kepler’s equation (KE) by Newton’s method is presented. By using a Wang Xinghua’s theorem (Xinghua in Math Comput 68(225):169–186, 1999) on best possible error bounds in the solution of nonlinear equations by Newton’s method, we obtain for each starter \( E_0(e,M)\) a set of values \( (e,M) \in [0, 1) \times [0, \pi ]\) that lead to the q-convergence in the sense that Newton’s sequence \( (E_n)_{n \ge 0}\) generated from \( E_0 = E_0(e,M)\) is well defined, converges to the exact solution \(E^* = E^*(e,M)\) of KE and further \( \vert E_n - E^* \vert \le q^{2^n -1}\; \vert E_0 - E^* \vert \) holds for all \( n \ge 0\). This study completes in some sense the results derived by Avendaño et al. (Celest Mech Dyn Astron 119:27–44, 2014) by using Smale’s \(\alpha \)-test with \(q=1/2\). Also since in KE the convergence rate of Newton’s method tends to zero as \( e \rightarrow 0\), we show that the error estimates given in the Wang Xinghua’s theorem for KE can also be used to determine sets of q-convergence with \( q = e^k \; \widetilde{q} \) for all \( e \in [0,1)\) and a fixed \( \widetilde{q} \le 1\). Some remarks on the use of this theorem to derive a priori estimates of the error \( \vert E_n - E^* \vert \) after n Kepler’s iterations are given. Finally, a posteriori bounds of this error that can be used to a dynamical estimation of the error are also obtained.     

Multi-wavelength correlation studies of diffuse emission from the Aquila Rift

We present a multi-wavelength correlation study of diffuse ultraviolet radiation using GALEX observations towards the Aquila Rift. Apart from airglow and zodiacal emissions, we find a diffuse background of \(1300\mbox{--} 3700~\mbox{ph}\,\mbox{cm}^{-2}\,\mbox{s}^{-1}\,\mbox{sr}^{-1}\,\mathring{\mathrm{A}}^{-1}\) in the far-ultraviolet (FUV, 1350–1750 Å) band and \(1300\mbox{--}2800~\mbox{ph}\,\mbox{cm}^{-2}\,\mbox{s}^{-1}\,\mbox{sr}^{-1}\,\mathring{\mathrm{A}}^{-1}\) in the near-ultraviolet (NUV, 1750–2850 Å) band. The observed diffuse UV emissions are saturated with total as well as neutral hydrogen column density in the region due to high optical depth in UV (\(\tau \), 0.91–23.38). Higher values of FUV/NUV ratio in the region, greater than the threshold value of 0.6, along with the positive correlation between the ratio and FUV intensity are due to excess emission in the FUV band which is absent in the NUV band. We estimated the excess emission to be in the range \(\sim 400\mbox{--} 2700~\mbox{ph}\,\mbox{cm}^{-2}\,\mbox{s}^{-1}\,\mbox{sr}^{-1}\,\mathring{\mathrm{A}}^{-1}\), plausibly due to H₂ fluorescence, ion line emissions and two-photon continuum emissions from the region in the FUV band, which also shows saturation in optically thick regions with N(H₂) as well as \(\mbox{H}\alpha \) emissions. Since N(H₂) and \(\mbox{H}\alpha \) emissions spread all over the region, the excess emission from the field is composite in nature and a detailed spectroscopic analysis is needed to disentangle the contribution from individual components.     

An interacting new holographic dark energy in the framework of fractal cosmology

In this paper, we study an interacting holographic dark energy model in the framework of fractal cosmology. The features of fractal cosmology could pass ultraviolet divergencies and also make a better understanding of the universe in different dimensions. We discuss a fractal FRW universe filled with the dark energy and cold dark matter interacting with each other. It is observed that the Hubble parameter embraces the recent observational range while the deceleration parameter demonstrates an accelerating universe and a behavior similar to \(\Lambda \mbox{CDM}\). Plotting the equation of state shows that it lies in phantom region for interaction mode. We use \(\mathit{Om}\)-diagnostic tool and it shows a phantom behavior of dark energy which is a condition of avoiding the formation of black holes. Finally we execute the StateFinder diagnostic pair and all the trajectories for interacting and non-interacting state of the model meet the fixed point \(\Lambda \mbox{CDM}\) at the start of the evolution. A behavior similar to Chaplygin gas also can be observed in statefinder plane. We find that new holographic dark energy model (NHDE) in fractal cosmology expressed the consistent behavior with recent observational data and can be considered as a model to avoid the formation of black holes in comparison with the main model of NHDE in the simple FRW universe. It has also been observed that for the interaction term varying with matter density, the model generates asymptotic de-Sitter solution. However, if the interaction term varies with energy density, then the model shows Big-Rip singularity. Using our modified CAMB code, we observed that the interacting model suppresses the CMB spectrum at low multipoles \(l<50\) and enhances the acoustic peaks. Based on the observational data sets used in this paper and using Metropolis-Hastings method of MCMC numerical calculation, it seems that the best value with \(1\sigma \) and \(2\sigma \) confidence interval are \(\Omega _{m0}=0.278^{+0.008~+0.010} _{-0.007~-0.009}\), \(H_{0}=69.9^{+0.95~+1.57}_{-0.95~-1.57}\), \(r_{c}=0.08^{+0.02~+0.027}_{-0.002~-0.0027}\), \(\beta =0.496^{+0.005~+0.009} _{-0.005~-0.009}\), \(c= 0.691^{+0.024~+0.039}_{-0.025~-0.037}\) and \(b^{2}=0.035\) according to which we find that the proposed model in the presence of interaction is compatible with the recent observational data.     

Relative equilibria of the restricted three-body problem in curved spaces

We use a formulation of the N-body problem in spaces of constant Gaussian curvature, \({\kappa }\in \mathbb {R}\), as widely used by A. Borisov, F. Diacu and their coworkers. We consider the restricted three-body problem in \(\mathbb {S}^2\) with arbitrary \({\kappa }>0\) (resp. \(\mathbb {H}^2\) with arbitrary \({\kappa }<0\)) in a formulation also valid for the case \({\kappa }=0\). For concreteness when \({\kappa }>0\) we restrict the study to the case of the three bodies at the upper hemisphere, to be denoted as \(\mathbb {S}^2_+\). The main goal is to obtain the totality of relative equilibria as depending on the parameters \({\kappa }\) and the mass ratio \(\mu \). Several general results concerning relative equilibria and its stability properties are proved analytically. The study is completed numerically using continuation from the \({\kappa }=0\) case and from other limit cases. In particular both bifurcations and spectral stability are also studied. The \(\mathbb {H}^2\) case is similar, in some sense, to the planar one, but in the \(\mathbb {S}^2_+\) case many differences have been found. Some surprising phenomena, like the coexistence of many triangular-like solutions for some values \(({\kappa },\mu )\) and many stability changes will be discussed.