On the co-orbital motion in the planar restricted three-body problem: the quasi-satellite motion revisited

In the framework of the planar and circular restricted three-body problem, we consider an asteroid that orbits the Sun in quasi-satellite motion with a planet. A quasi-satellite trajectory is a heliocentric orbit in co-orbital resonance with the planet, characterized by a nonzero eccentricity and a resonant angle that librates around zero. Likewise, in the rotating frame with the planet, it describes the same trajectory as the one of a retrograde satellite even though the planet acts as a perturbator. In the last few years, the discoveries of asteroids in this type of motion made the term “quasi-satellite” more and more present in the literature. However, some authors rather use the term “retrograde satellite” when referring to this kind of motion in the studies of the restricted problem in the rotating frame. In this paper, we intend to clarify the terminology to use, in order to bridge the gap between the perturbative co-orbital point of view and the more general approach in the rotating frame. Through a numerical exploration of the co-orbital phase space, we describe the quasi-satellite domain and highlight that it is not reachable by low eccentricities by averaging process. We will show that the quasi-satellite domain is effectively included in the domain of the retrograde satellites and neatly defined in terms of frequencies. Eventually, we highlight a remarkable high eccentric quasi-satellite orbit corresponding to a frozen ellipse in the heliocentric frame. We extend this result to the eccentric case (planet on an eccentric motion) and show that two families of frozen ellipses originate from this remarkable orbit.     

On the period of the periodic orbits of the restricted three body problem

We will show that the period T of a closed orbit of the planar circular restricted three body problem (viewed on rotating coordinates) depends on the region it encloses. Roughly speaking, we show that, \(2 T=k\pi +\int _\Omega g\) where k is an integer, \(\Omega \) is the region enclosed by the periodic orbit and \(g:{\mathbb {R}}^2\rightarrow {\mathbb {R}}\) is a function that only depends on the constant C known as the Jacobian constant; it does not depend on \(\Omega \). This theorem has a Keplerian flavor in the sense that it relates the period with the space “swept” by the orbit. As an application we prove that there is a neighborhood around \(L_4\) such that every periodic solution contained in this neighborhood must move clockwise. The same result holds true for \(L_5\).     

Bandpass calibration of a wideband spectrometer using coherent pulse injection

We present a relatively simple time domain method for determining the bandpass response of a system by injecting a nanosecond pulse and capturing the system voltage output. A pulse of sub-nanosecond duration contains all frequency components with nearly constant amplitude up to 1 GHz. Hence, this method can accurately determine the system bandpass response to a broadband signal. In a novel variation on this impulse response method, a train of pulses is coherently accumulated providing precision calibration with a simple system. The basic concept is demonstrated using a pulse generator-accumulator setup realised in a Bedlam board which is a high speed digital signal processing unit. The same system was used at the Parkes radio telescope between 2–13 October 2013 and we demonstrate its powerful diagnostic capability. We also present some initial test data from this experiment.     

Preliminary assessment of the ATHENA/WFI non-X-ray background

We present a preliminary assessment of the non-X-ray background for the WFI on board ATHENA conducted at IAAT in the context of the collaborative background and radiation damage working group activities. Our main result is that in the baseline configuration originally assumed for the camera the requirement on the level of non-X-ray background could not be met. In light of the results of Geant4 simulations we propose and discuss a possible optimization of the camera design and pinpoint some open issues to be addressed in the next phase of investigation. One of these concerns the possible contribution to the non-X-ray background from soft protons and ions funneled to the focal plane through the optics. This is not quantified at this stage, here we just briefly report on our ongoing activities aimed at validating the mechanisms of proton scattering at grazing incidence.     

Spectral Trends of Solar Bursts at Sub-THz Frequencies

Previous sub-THz studies were derived from single-event observations. We here analyze for the first time spectral trends for a larger collection of sub-THz bursts. The collection consists of a set of 16 moderate to small impulsive solar radio bursts observed at 0.2 and 0.4 THz by the Solar Submillimeter-wave Telescope (SST) in 2012?–?2014 at El Leoncito, in the Argentinean Andes. The peak burst spectra included data from new solar patrol radio telescopes (45 and 90 GHz), and were completed with microwave data obtained by the Radio Solar Telescope Network, when available. We critically evaluate errors and uncertainties in sub-THz flux estimates caused by calibration techniques and the corrections for atmospheric transmission, and introduce a new method to obtain a uniform flux scale criterion for all events. The sub-THz bursts were searched during reported GOES soft X-ray events of class C or larger, for periods common to SST observations. Seven out of 16 events exhibit spectral maxima in the range 5?–?40 GHz with fluxes decaying at sub-THz frequencies (three of them associated to GOES class X, and four to class M). Nine out of 16 events exhibited the sub-THz spectral component. In five of these events, the sub-THz emission fluxes increased with a separate frequency from that of the microwave spectral component (two classified as X and three as M), and four events have only been detected at sub-THz frequencies (three classified as M and one as C). The results suggest that the THz component might be present throughout, with the minimum turnover frequency increasing as a function of the energy of the emitting electrons. The peculiar nature of many sub-THz burst events requires further investigations of bursts that are examined from SST observations alone to better understand these phenomena.     

Reconstruction of the North–South Solar Asymmetry with a Kuramoto Model

This paper applies a Kuramoto model of coupled oscillators to investigate the north–south (N–S) solar asymmetry and properties of meridional circulation. We focus our study on the asymmetry of the 11-year phase, which is slight but persistent: only two changes of sign (around 1928 and 1968) are observed in the past century. We present a model of two non-linear coupled oscillators that links the hemispheric phase asymmetry of sunspots with the asymmetry of the meridional flow. We use a Kuramoto model with evolving frequencies and constant symmetric coupling to show how asymmetry in meridional circulation could produce a persistent phase lead of one solar hemisphere over the other. We associate the natural frequencies of the two oscillators with the velocities of the meridional flow cells in the northern and southern hemispheres. We assume the respective circulations to be independent and estimate the value of the relevant cross-equatorial coupling by the coupling coefficient in the Kuramoto model. We find that a persistent N–S asymmetry of sunspots and the change of the leading hemisphere could indeed both be the result of the evolving frequencies of meridional circulation; the necessary asymmetry of the meridional flow may be small; and the cross-equatorial coupling has an intermediate range value. Possible applications of these results in solar dynamo models are discussed.     

Meridional Motion and Reynolds Stress from Debrecen Photoheliographic Data

The Debrecen Photoheliographic Data catalogue is a continuation of the Greenwich Photoheliographic Results providing daily positions of sunspots and sunspot groups. We analyse the data for sunspot groups focussing on meridional motions and transfer of angular momentum towards the solar equator. Velocities are calculated with a daily shift method including an automatic iterative process of removing the outliers. Apart from the standard differential rotation profile, we find meridional motion directed towards the zone of solar activity. The difference in measured meridional flow in comparison to Doppler measurements and some other tracer measurements is interpreted as a consequence of different flow patterns inside and outside of active regions. We also find a statistically significant dependence of meridional motion on rotation velocity residuals confirming the transfer of angular momentum towards the equator. Analysis of horizontal Reynolds stress reveals that the transfer of angular momentum is stronger with increasing latitude up to about \(40^{\circ}\), where there is a possible maximum in absolute value.     

On Flare-CME Characteristics from Sun to Earth Combining Remote-Sensing Image Data with <Emphasis Type="Italic">In Situ</Emphasis> Measurements Supported by Modeling

We analyze the well-observed flare and coronal mass ejection (CME) from 1 October 2011 (SOL2011-10-01T09:18) covering the complete chain of effects – from Sun to Earth – to better understand the dynamic evolution of the CME and its embedded magnetic field. We study in detail the solar surface and atmosphere associated with the flare and CME using the Solar Dynamics Observatory (SDO) and ground-based instruments. We also track the CME signature off-limb with combined extreme ultraviolet (EUV) and white-light data from the Solar Terrestrial Relations Observatory (STEREO). By applying the graduated cylindrical shell (GCS) reconstruction method and total mass to stereoscopic STEREO-SOHO (Solar and Heliospheric Observatory) coronagraph data, we track the temporal and spatial evolution of the CME in the interplanetary space and derive its geometry and 3D mass. We combine the GCS and Lundquist model results to derive the axial flux and helicity of the magnetic cloud (MC) from in situ measurements from Wind. This is compared to nonlinear force-free (NLFF) model results, as well as to the reconnected magnetic flux derived from the flare ribbons (flare reconnection flux) and the magnetic flux encompassed by the associated dimming (dimming flux). We find that magnetic reconnection processes were already ongoing before the start of the impulsive flare phase, adding magnetic flux to the flux rope before its final eruption. The dimming flux increases by more than 25% after the end of the flare, indicating that magnetic flux is still added to the flux rope after eruption. Hence, the derived flare reconnection flux is most probably a lower limit for estimating the magnetic flux within the flux rope. We find that the magnetic helicity and axial magnetic flux are lower in the interplanetary space by ～?50% and 75%, respectively, possibly indicating an erosion process. A CME mass increase of 10% is observed over a range of \({\sim}\,4\,\mbox{--}\,20~\mathrm{R}_{\odot }\). The temporal evolution of the CME-associated core-dimming regions supports the scenario that fast outflows might supply additional mass to the rear part of the CME.     

Forbush Decrease: A New Perspective with Classification

Sudden short-duration decreases in cosmic ray flux, known as Forbush decreases (FDs), are mainly caused by interplanetary disturbances. A generally accepted view is that the first step of an FD is caused by a shock sheath and the second step is due to the magnetic cloud (MC) of the interplanetary coronal mass ejection (ICME). This simplistic picture does not consider several physical aspects, such as whether the complete shock sheath or MC (or only part of these) contributes to the decrease or the effect of internal structure within the shock-sheath region or MC. We present an analysis of 16 large (\({\geq}\,8 \%\)) FD events and the associated ICMEs, a majority of which show multiple steps in the FD profile. We propose a reclassification of FD events according to the number of steps observed in their respective profiles and according to the physical origin of these steps. This study determines that 13 out of 16 major events (\({\sim}\,81\%\)) can be explained completely or partially on the basis of the classic FD model. However, it cannot explain all the steps observed in these events. Our analysis clearly indicates that not only broad regions (shock sheath and MC), but also localized structures within the shock sheath and MC have a significant role in influencing the FD profile. The detailed analysis in the present work is expected to contribute toward a better understanding of the relationship between FD and ICME parameters.     

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.