The ULF wave foreshock boundary: Cluster observations

The interaction of backstreaming ions with the incoming solar wind in the upstream region of the bow shock gives rise to a number of plasma instabilities from which ultra-low frequency (ULF) waves can grow. Because of their finite growth rate, the ULF waves are spatially localized in the foreshock region. Previous studies have reported observational evidences of the existence of a ULF wave foreshock boundary, which geometrical characteristics are very sensitive to the interplanetary magnetic field (IMF) cone angle. The statistical properties of the ULF wave foreshock boundary is examined in detail using Cluster data. A new identification of the ULF wave foreshock boundary is presented using specific and accurate criterion for a precises determination of boundary crossings. The criterion is based on the degree of IMF rotation as Cluster crosses the boundary. The obtained ULF wave foreshock boundary is compared with previous results reported in the literature as well as with theoretical predictions. Also, we examined the possible connexion between the foreshock boundary properties and the ion emission mechanisms at the bow shock

Relativistic electrons generated at Earth's quasi-parallel bow shock.

Plasma shocks are the primary means of accelerating electrons in planetary and astrophysical settings throughout the universe. Which category of shocks, quasi-perpendicular or quasi-parallel, accelerates electrons more efficiently is debated. Although quasi-perpendicular shocks are thought to be more efficient electron accelerators, relativistic electron energies recently observed at quasi-parallel shocks exceed theoretical expectations. Using in situ observations at Earth's bow shock, we show that such relativistic electrons are generated by the interaction between the quasi-parallel shock and a related nonlinear structure, a foreshock transient, through two betatron accelerations. Our observations show that foreshock transients, overlooked previously, can increase electron acceleration efficiency at a quasi-parallel shock by an order of magnitude. Thus, quasi-parallel shocks could be more important in generating relativistic electrons, such as cosmic ray electrons, than previously thought

Magnetic fields and cosmic rays in GRBs. A self-similar collisionless foreshock

Cosmic rays accelerated by a shock form a streaming distribution of outgoing particles in the foreshock region. If the ambient fields are negligible compared to the shock and cosmic ray energetics, a stronger magnetic field can be generated in the shock upstream via the streaming (Weibel-type) instability. Here we develop a self-similar model of the foreshock region and calculate its structure, e.g., the magnetic field strength, its coherence scale, etc., as a function of the distance from the shock. Our model indicates that the entire foreshock region of thickness $\sim R/(2\Gamma_{\rm sh}^2)$, being comparable to the shock radius in the late afterglow phase when $\Gamma_{\rm sh}\sim1$, can be populated with large-scale and rather strong magnetic fields (of sub-gauss strengths with the coherence length of order $10^{17} {\rm cm}$) compared to the typical interstellar medium magnetic fields. The presence of such fields in the foreshock region is important for high efficiency of Fermi acceleration at the shock. Radiation from accelerated electrons in the foreshock fields can constitute a separate emission region radiating in the UV/optical through radio band, depending on time and shock parameters. We also speculate that these fields being eventually transported into the shock downstream can greatly increase radiative efficiency of a gamma-ray burst afterglow shock.Comment: 10 pages, 1 figure. Submitted to Ap

Shocklets, SLAMS, and field-aligned ion beams in the terrestrial foreshock

We present Wind spacecraft observations of ion distributions showing field-aligned beams (FABs) and large-amplitude magnetic fluctuations composed of a series of shocklets and short large-amplitude magnetic structures (SLAMS). We show that the SLAMS are acting like a local quasi-perpendicular shock reflecting ions to produce the FABs. Previous FAB observations reported the source as the quasi-perpendicular bow shock. The SLAMS exhibit a foot-like magnetic enhancement with a leading magnetosonic whistler train, consistent with previous observations. The FABs are found to have T_b ~ 80-850 eV, V_b/V_sw ~ 1-2, T_{b,perp}/T{b,para} ~ 1-10, and n_b/n_i ~ 0.2-14%. Strong ion and electron heating are observed within the series of shocklets and SLAMS increasing by factors \geq 5 and \geq 3, respectively. Both the core and halo electron components show strong perpendicular heating inside the feature.Comment: 11 pages, 3 EPS figures, submitted to Geophysical Research Letter

Mainshocks are aftershocks of conditional foreshocks: How do foreshock statistical properties emerge from aftershock laws

The inverse Omori law for foreshocks discovered in the 1970s states that the rate of earthquakes prior to a mainshock increases on average as a power law ~ 1/(t_c-t)^p' of the time to the mainshock occurring at t_c. Here, we show that this law results from the direct Omori law for aftershocks describing the power law decay ~ 1/(t-t_c)^p of seismicity after an earthquake, provided that any earthquake can trigger its suit of aftershocks. In this picture, the seismic activity at any time is the sum of the spontaneous tectonic loading and of the activity triggered by all preceding events weighted by their corresponding Omori law. The inverse Omori law then emerges as the expected (in a statistical sense) trajectory of seismicity, conditioned on the fact that it leads to the burst of seismic activity accompanying the mainshock. The often documented apparent decrease of the b-value of the GR law at the approach to the main shock results straightforwardly from the conditioning of the path of seismic activity culminating at the mainshock. In the space domain, we predict that the phenomenon of aftershock diffusion must have its mirror process reflected into an inward migration of foreshocks towards the mainshock. In this model, foreshock sequences are special aftershock sequences which are modified by the condition to end up in a burst of seismicity associated with the mainshock.Comment: Latex document of 35 pages, 10 figure

A semi-analytical foreshock model for energetic storm particle events inside 1 AU

We have constructed a semi-analytical model of the energetic-ion foreshock of a CME-driven coronal/interplanetary shock wave responsible for the acceleration of large solar energetic particle (SEP) events. The model is based on the analytical model of diffusive shock acceleration of Bell (1978), appended with a temporal dependence of the cut-off momentum of the energetic particles accelerated at the shock, derived from the theory. Parameters of the model are re-calibrated using a fully time-dependent self-consistent simulation model of the coupled particle acceleration and Alfvén-wave generation upstream of the shock. Our results show that analytical estimates of the cut-off energy resulting from the simplified theory and frequently used in SEP modelling are overestimating the cut-off momentum at the shock by one order magnitude. We show also that the cut-off momentum observed remotely far upstream of the shock (e.g., at 1 AU) can be used to infer the properties of the foreshock and the resulting energetic storm particle (ESP) event, when the shock is still at small distances from the Sun, unaccessible to the in-situ observations. Our results can be used in ESP event modelling for future missions to the inner heliosphere, like the Solar Orbiter and Solar Probe Plus as well as in developing acceleration models for SEP events in the solar corona