An Analytical Model of the Comet's Collision with Jupiter

We employ an simplified analytical model to investigate the wave motion produced by the impact of Comt SL9 on the Jovian atmosphere and,under the assumption that all the kinetic energy of a comet fragment is completely converted in-to the energy of wave motions in the Jovian atmosphere,derive an analytical fromula describing the relation between the resulting wave motion in the atmosphere and the parameters of a comet fragment (the radius,density and speed).     

Correlation Functions of Small-Scale Fluctuations of the Interplanetary Magnetic Field

The Interplanetary Magnetic Field shows complex spatial and temporal variations. Single spacecraft measurements reveal only a one-dimensional section of this rich four-dimensional phenomenon. Multi-point measurements of the four Cluster spacecraft provide a unique tool to study the spatiotemporal structure of the field. Using Cluster data we determined three-dimensional correlation functions of the fluctuations. By means of the correlation function one can describe and measure field variations. Our results can be used to verify theoretical predictions, to understand the formation and nature of solar wind turbulence. We found that the correlation length varies over almost six orders of magnitude. The IMF turbulence shows significant anisotropy with two distinct populations. In certain time intervals the ratio of the three axes of the correlation ellipse is 1/2.2/6 while in the remaining time we found extremely high correlation along one axis. We found favored directions in the orientation of the correlation ellipsoids.     

Reconstructing the 3-D Trajectories of CMEs in the Inner Heliosphere

A method for the full three-dimensional (3-D) reconstruction of the trajectories of coronal mass ejections (CMEs) using Solar TErrestrial RElations Observatory (STEREO) data is presented. Four CMEs that were simultaneously observed by the inner and outer coronagraphs (COR1 and 2) of the Ahead and Behind STEREO satellites were analysed. These observations were used to derive CME trajectories in 3-D out to ～?15?R _⊙. The reconstructions using COR1/2 data support a radial propagation model. Assuming pseudo-radial propagation at large distances from the Sun (15?–?240?R _⊙), the CME positions were extrapolated into the Heliospheric Imager (HI) field-of-view. We estimated the CME velocities in the different fields-of-view. It was found that CMEs slower than the solar wind were accelerated, while CMEs faster than the solar wind were decelerated, with both tending to the solar wind velocity.     

Interplanetary and Geomagnetic Consequences of Interacting CMEs of 13 – 14 June 2012

We report on the kinematics of two interacting CMEs observed on 13 and 14 June 2012. The two CMEs originated from the same active region NOAA 11504. After their launches which were separated by several hours, they were observed to interact at a distance of \(100~R_{\odot}\) from the Sun. The interaction led to a moderate geomagnetic storm at the Earth with minimum \(\mathrm{D}_{\mathrm{st}}\) index of approximately ?86 nT. The kinematics of the two CMEs is estimated using data from the Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI) instrument onboard the Solar Terrestrial Relations Observatory (STEREO). Assuming a head-on collision scenario, we find that the collision is inelastic in nature. Further, the signatures of their interaction are examined using the in situ observations obtained by Wind and the Advance Composition Explorer (ACE) spacecraft. It is also found that this interaction event led to the strongest sudden storm commencement (SSC) (\({\approx\,}150\) nT) of the present Solar Cycle 24. The SSC was of long duration, approximately 20 hours. The role of interacting CMEs in enhancing the geoeffectiveness is examined.     

The “Atmosphere” Model: Analysis of the Time Series of Updates to the Deformations of the Earth Surface

RT-22 radio telescope in Katsiveli (“Simeiz” VLBI station) is used extensively in international projects aimed at supporting spacetime reference systems for monitoring global changes on the Earth and for precise navigation in space. This paper discusses the results of the analysis of the data about the variations of the updates to the deformations of the Earth surface at Katsiveli site computed in terms of the “Atmosphere” model of a DFG (Deutsche Forschungsgemeinschaft) project. Significant oscillation with a one-year period is found in the Eastern and vertical components of the update vector to the deformations of the Earth surface at Katsiveli sit and the parameters of the sine model of this oscillation are computed.     

Forecasting the Time Series of Sunspot Numbers

Forecasting the solar cycle is of great importance for weather prediction and environmental monitoring, and also constitutes a difficult scientific benchmark in nonlinear dynamical modeling. This paper describes the identification of a model and its use in the forecasting the time series comprised of Wolf’s sunspot numbers. A key feature of this procedure is that the original time series is first transformed into a symmetrical space where the dynamics of the solar dynamo are unfolded in a better way, thus improving the model. The nonlinear model obtained is parsimonious and has both deterministic and stochastic parts. Monte Carlo simulation of the whole model produces very consistent results with the deterministic part of the model but allows for the determination of confidence bands. The obtained model was used to predict cycles 24 and 25, although the forecast of the latter is seen as a crude approximation, given the long prediction horizon required. As for the 24th cycle, two estimates were obtained with peaks of 65±16 and of 87±13 units of sunspot numbers. The simulated results suggest that the 24th cycle will be shorter and less active than the preceding one.     

Oscillatory Response of the 3D Solar Atmosphere to the Leakage of Photospheric Motion

The direct propagation of acoustic waves, driven harmonically at the solar photosphere, into the three-dimensional solar atmosphere is examined numerically in the framework of ideal magnetohydrodynamics. It is of particular interest to study the leakage of 5-minute global solar acoustic oscillations into the upper, gravitationally stratified and magnetised atmosphere, where the modelled solar atmosphere possesses realistic temperature and density stratification. This work aims to complement and bring further into the 3D domain our previous efforts (by Erdélyi et al., 2007, Astron. Astrophys. 467, 1299) on the leakage of photospheric motions and running magnetic-field-aligned waves excited by these global oscillations. The constructed model atmosphere, most suitable perhaps for quiet Sun regions, is a VAL IIIC derivative in which a uniform magnetic field is embedded. The response of the atmosphere to a range of periodic velocity drivers is numerically investigated in the hydrodynamic and magnetohydrodynamic approximations. Among others the following results are discussed in detail: i) High-frequency waves are shown to propagate from the lower atmosphere across the transition region, experiencing relatively low reflection, and transmitting most of their energy into the corona; ii) the thin transition region becomes a wave guide for horizontally propagating surface waves for a wide range of driver periods, and particularly at those periods that support chromospheric standing waves; iii) the magnetic field acts as a waveguide for both high- and low-frequency waves originating from the photosphere and propagating through the transition region into the solar corona. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

An Analysis of the Sunspot Groups and Flares of Solar Cycle 23

Designing a statistical solar flare forecasting technique can benefit greatly from knowledge of the flare frequency of occurrence with respect to sunspot groups. This study analyzed sunspot groups and Hα and X-ray flares reported for the period 1997 – 2007. Annual catalogs were constructed, listing the days that numbered sunspot groups were observed (designated sunspot group-days, SSG-Ds) and for each day a record for each associated Hα flare of importance category one or greater and normal or bright brightness and for each X-ray flare of intensity C 5 or higher. The catalogs were then analyzed to produce frequency distributions of SSG-Ds by year, sunspot group class, likelihood of producing at least one flare overall and by sunspot group class, and frequency of occurrence of numbers of flares per day and flare intensity category. Only 3% of SSG-Ds produced a substantial Hα flare and 7% had a significant X-ray flare. We found that mature, complex sunspot groups were more likely than simple sunspot groups to produce a flare, but the latter were more prevalent than the former. More than half of the SSG-Ds with flares had a maximum intensity flare greater than the lowest category (C-class of intensity five and higher). The fact that certain sunspot group classes had flaring probabilities significantly higher than the combined probabilities of the intensity categories when all SSG-Ds were considered suggest that it might be best to first predict the flaring probability. For sunspot groups found likely to flare, a separate diagnosis of maximum flare intensity category appears feasible.     

Ooty Interplanetary Scintillation – Remote-Sensing Observations and Analysis of Coronal Mass Ejections in the Heliosphere

In this paper, I investigate the three-dimensional evolution of solar wind density and speed distributions associated with coronal mass ejections (CMEs). The primary solar wind data used in this study has been obtained from the interplanetary scintillation (IPS) measurements made at the Ooty Radio Telescope, which is capable of measuring scintillation of a large number of radio sources per day and solar wind estimates along different cuts of the heliosphere that allow the reconstruction of three-dimensional structures of propagating transients in the inner heliosphere. The results of this study are: i) three-dimensional IPS images possibly show evidence for the flux-rope structure associated with the CME and its radial size evolution; the overall size and features within the CME are largely determined by the magnetic energy carried by the CME. Such a magnetically energetic CME can cause an intense geomagnetic storm, even if the trailing part of the CME passes through the Earth; ii) IPS measurements along the radial direction of a CME at ～?120 R_⊙ show density turbulence enhancements linked to the shock ahead of the CME and the core of the CME. The density of the core decreases with distance, suggesting the expansion of the CME. However, the density associated with the shock increases with distance from the Sun, indicating the development of a strong compression at the leading edge of the CME. The increase of stand-off distance between ～?120 R_⊙ and 1 AU is consistent with the deceleration of the CME and the continued outward expansion of the shock. The key point in this study is that the magnetic energy possessed by the transient determines its radial evolution.     

An Impulsive Heating Model for the Evolution of Coronal Loops

It was suggested by Parker that the solar corona is heated by many small energy release events generally called microflares or nanoflares. More and more observations showed flows and intensity variations in nonflaring loops. Both theories and observations have indicated that the heating of coronal loops should actually be unsteady. Using SOLFTM (Solar Flux Tube Model), we investigate the hydrodynamics of coronal loops undergoing different manners of impulsive heating with the same total energy deposition. The half length of the loops is 110 Mm, a typical length of active region loops. We divide the loops into two categories: loops that experience catastrophic cooling and loops that do not. It is found that when the nanoflare heating sources are in the coronal part, the loops are in non-catastrophic-cooling state and their evolutions are similar. When the heating is localized below the transition region, the loops evolve in quite different ways. It is shown that with increasing number of heating pulses and inter-pulse time, the catastrophic cooling is weakened, delayed, or even disappears altogether.     

An Interpretation of the Coronal Holes’ Visibility in the Millimeter Wavelength Range

Various observations indicate that coronal holes generally appear as low brightness temperature regions (LTRs) in the centimeter and millimeter wavelength ranges. However, within their borders local enhancements of radiation, that is, high brightness temperature regions (HTRs), often occur. The theory behind the described behavior is not fully understood and therefore we analyze full-disk solar images obtained at a wavelength of 8 mm at Metsähovi Radio Observatory and compare them with data simultaneously taken in other wavelength ranges. The observational finding that the average brightness temperature of coronal holes is not much different from the quiet-Sun level (with localized deviations toward higher and lower intensities on the order of a few percent) is compared with theoretical models of the thermal bremsstrahlung radiation originating in the solar chromosphere, transition region, and corona. Special attention is devoted to the interpretation of the localized enhancements of radiation observed inside coronal holes at millimeter wavelengths. The main conclusion is that the most important contribution to the brightness temperature comes from an increased density in the transition region and low corona (i.e., at the heights where the temperature is below 10⁶ K). This can explain both the LTRs and HTRs associated with coronal holes.     

Statistical Comparison of Magnetic Clouds with Interplanetary Coronal Mass Ejections for Solar Cycle 23

We compare the number and characteristics of interplanetary coronal mass ejections (ICMEs) to those of magnetic clouds (MCs) by using in-situ solar wind plasma and magnetic field observations made at 1 AU during solar cycle 23. We found that ≈ 28% of ICMEs appear to contain MCs, since 103 magnetic clouds (MCs) occurred during 1995  – 2006, and 307 ICMEs occurred during 1996 – 2006. For the period between 1996 and 2006, 85 MCs are identified as part of ICMEs, and six MCs are not associated with ICMEs, which conflicts with the idea that MCs are usually a subset of ICMEs. It was also found that solar wind conditions inside MCs and ICMEs are usually similar, but the linear correlation between geomagnetic storm intensity (Dst _min) and relevant solar wind parameters is better for MCs than for ICMEs. The differences between average event duration (Δt) and average proton plasma β (〈β〉) are two of the major differences between MCs and ICMEs: i) the average duration of ICMEs (29.6 h) is 44% longer than for MCs (20.6 hours), and ii) the average of 〈β〉 is 0.01 for MCs and 0.24 for ICMEs. The difference between the definition of a MC and that for an ICME is one of the major reasons for these average characteristics being different (i.e., listed above as items i) and ii)), and it is the reason for the frequency of their occurrences being different.     

Expected in Situ Velocities from a Hierarchical Model for Expanding Interplanetary Coronal Mass Ejections

In situ data provide only a one-dimensional sample of the plasma velocity along the spacecraft trajectory crossing an interplanetary coronal mass ejection (ICME). Then, to understand the dynamics of ICMEs it is necessary to consider some models to describe it. We derive a series of equations in a hierarchical order, from more general to more specific cases, to provide a general theoretical basis for the interpretation of in situ observations, extending and generalizing previous studies. The main hypothesis is a self-similar expansion, but with the freedom of possible different expansion rates in three orthogonal directions. The most detailed application of the equations is though for a subset of ICMEs, magnetic clouds (MCs), where a magnetic flux rope can be identified. The main conclusions are the following ones. First, we obtain theoretical expressions showing that the observed velocity gradient within an ICME is not a direct characteristic of its expansion, but that it depends also on other physical quantities such as its global velocity and acceleration. The derived equations quantify these dependencies for the three components of the velocity. Second, using three different types of data we show that the global acceleration of ICMEs has, at most, a small contribution to the in situ measurements of the velocity. This eliminates practically one contribution to the observed velocity gradient within ICMEs. Third, we provide a method to quantify the expansion rate from velocity data. We apply it to a set of 26 MCs observed by Wind or ACE spacecrafts. They are typical MCs, and their main physical parameters cover the typical range observed in MCs in previous statistical studies. Though the velocity difference between their front and back includes a broad range of values, we find a narrow range for the determined dimensionless expansion rate. This implies that MCs are expanding at a comparable rate, independently of their size or field strength, despite very different magnitudes in their velocity profiles. Furthermore, the equations derived provide a base to further analyze the dynamics of MCs/ICMEs.     

Deflection of Coronal Rays by Remote CMEs: Shock Wave or Magnetic Pressure?

We analyze five events of the interaction of coronal mass ejections (CMEs) with the remote coronal rays located up to 90° away from the CME as observed by the SOHO/LASCO C2 coronagraph. Using sequences of SOHO/LASCO C2 images, we estimate the kink propagation in the coronal rays during their interaction with the corresponding CMEs ranging from 180 to 920 km s⁻¹ within the interval of radial distances from 3 R _⊙ to 6 R _⊙. We conclude that all studied events do not correspond to the expected pattern of shock wave propagation in the corona. Coronal ray deflection can be interpreted as the influence of the magnetic field of a moving flux rope within the CME. The motion of a large-scale flux rope away from the Sun creates changes in the structure of surrounding field lines, which are similar to the kink propagation along coronal rays. The retardation of the potential should be taken into account since the flux rope moves at a high speed, comparable with the Alfvén speed.     

On the Origin, 3D Structure and Dynamic Evolution of CMEs Near Solar Minimum

We have conducted a statistical study 27 coronal mass ejections (CMEs) from January 2007 – June 2008, using the stereoscopic views of STEREO SECCHI A and B combined with SOHO LASCO observations. A flux-rope model, in conjunction with 3D triangulations, has been used to reconstruct the 3D structures and determine the actual speeds of CMEs. The origin and the dynamic evolution of the CMEs are investigated using COR1, COR2 and EUVI images. We have identified four types of solar surface activities associated with CMEs: i) total eruptive prominence (totEP), ii) partially eruptive prominence (PEP), iii) X-ray flare, and iv) X-type magnetic structure (X-line). Among the 27 CMEs, 18.5% (5 of 27) are associated with totEPs, 29.6% (8 of 27) are associated with PEPs, 26% (7 of 27) are flare related, and 26% (7 of 27) are associated with X-line structures, and 43% (3 of 7) are associated with both X-line structures and PEPs. Three (11%) could not be associated with any detectable activity. The mean actual speeds for totEP-CMEs, PEP-CMEs, flare-CMEs, and X-line-CMEs are 404 km?s^?1,247 km?s^?1,909 km?s^?1, and 276 km?s^?1, respectively; the average mean values of edge-on and broadside widths for the 27 CMEs are 52 and 85 degrees, respectively. We found that slow CMEs (V≤400 km?s^?1) tend to deflect towards and propagate along the streamer belts due to the deflections by the strong polar magnetic fields of corona holes, while some faster CMEs show opposite deflections away from the streamer belts.     

A Detailed Study on the Equal Arrival Time Surface Effect in Gamma-Ray Burst Afterglows

Due to the relativistic motion of gamma-ray burst remnant and its deceleration in the circumburst medium, the equal arrival time surfaces at any moment are not spherical, rather, they are distorted ellipsoids. This will leave some imprints in the afterglows. We study the effect of equal arrival time surfaces numerically for various circumstances, i.e., isotropic fireballs, collimated jets, density jumps and energy injection events. For each case, a direct comparison is made between including and not including the effect. For isotropic fireballs and jets viewed on axis, the effect slightly hardens the spectra and postpones the peak time of the afterglows, but does not change the shapes of the spectra and light curves significantly. In the cases of a density jump or an energy injection, the effect smears out the variations in the afterglows markedly.     

A new law emerging from the recurrences of the ‘critical-acceleration’ of MOND, suggesting a clue to unification of fundamental forces

Keeping apart the problem, whether Modified Newtonian Dynamics [MOND] can replace ‘dark matter’, this letter considers seven different theoretical recurrences of ‘critical acceleration’ of MOND noticed by Sivaram in various physical situations; adds five more observational recurrences to the list; and arrives at a set of laws which seem to be followed by all the systems bound by different fundamental forces; suggesting a clue to unification of fundamental forces. This attempt proposes a general explanation for ‘flattening of galaxies’ rotation-curves’ as well as the ‘expansion of the universe’.     

Latitude Dependence of the Variations of Sunspot Group Numbers (SGN) and Coronal Mass Ejections (CMEs) in Cycle 23

The 12-month running means of the conventional sunspot number Rz, the sunspot group numbers (SGN) and the frequency of occurrence of Coronal Mass Ejections (CMEs) were examined for cycle 23 (1996 – 2006). For the whole disc, the SGN and Rz plots were almost identical. Hence, SGN could be used as a proxy for Rz, for which latitude data are not available. SGN values were used for 5° latitude belts 0° – 5°, 5° – 10°, 10° – 15°, 15° – 20°, 20° – 25°, 25° – 30° and > 30°, separately in each hemisphere north and south. Roughly, from latitudes 25° – 30° N to 20° – 25° N, the peaks seem to have occurred later for lower latitudes, from latitudes 20° – 25° N to 15° – 20° N, the peaks are stagnant or occur slightly earlier, and then from latitudes 15° – 20° N to 0° – 5° N, the peaks seem to have occurred again later for lower latitudes. Thus, some latitudinal migration is suggested, clearly in the northern hemisphere, not very clearly in the southern hemisphere, first to the equator in 1998, stagnant or slightly poleward in 1999, and then to the equator again from 2000 onwards, the latter reminiscent of the Maunder butterfly diagrams. Similar plots for CME occurrence frequency also showed multiple peaks (two or three) in almost all latitude belts, but the peaks were almost simultaneous at all latitudes, indicating no latitudinal migration. For similar latitude belts, SGN and CME plots were dissimilar in almost all latitude belts except 10° – 20° S. The CME plots had in general more peaks than the SGN plots, and the peaks of SGN often did not match with those of CME. In the CME data, it was noticed that whereas the values declined from 2002 to 2003, there was no further decline during 2003 – 2006 as one would have expected to occur during the declining phase of sunspots, where 2007 is almost a year of sunspot minimum. An inquiry at GSFC-NASA revealed that the person who creates the preliminary list was changed in 2004 and the new person picks out more weak CMEs. Thus a subjectivity (overestimates after 2002) seems to be involved and hence, values obtained before and during 2002 are not directly comparable to values recorded after 2002, except for CMEs with widths exceeding 60°.     

The Recovery of CME-Related Dimmings and the ICME’s Enduring Magnetic Connection to the Sun

It is generally accepted that transient coronal holes (TCHs, dimmings) correspond to the magnetic footpoints of CMEs that remain rooted in the Sun as the CME expands out into the interplanetary space. However, the observation that the average intensity of the 12 May 1997 dimmings recover to their pre-eruption intensity in SOHO/EIT data within 48 hours, whilst suprathermal unidirectional electron heat fluxes are observed at 1 AU in the related ICME more than 70 hours after the eruption, leads us to question why and how the dimmings disappear whilst the magnetic connectivity is maintained. We also examine two other CME-related dimming events: 13 May 2005 and 6 July 2006. We study the morphology of the dimmings and how they recover. We find that, far from exhibiting a uniform intensity, dimmings observed in SOHO/EIT data have a deep central core and a more shallow extended dimming area. The dimmings recover not only by shrinking of their outer boundaries but also by internal brightenings. We quantitatively demonstrate that the model developed by Fisk and Schwadron (Astrophys. J. 560, 425, 2001) of interchange reconnections between “open” magnetic field and small coronal loops is a strong candidate for the mechanism facilitating the recovery of the dimmings. This process disperses the concentration of  “open” magnetic field (forming the dimming) out into the surrounding quiet Sun, thus recovering the intensity of the dimmings whilst still maintaining the magnetic connectivity to the Sun. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.