Summary of my Ph.D. studies
My Ph.D. thesis work was all about interplanetary (IP) shocks. You may find an introduction to IP shocks in the chapter 2 of my thesis. In ordinary hydrodynamic theory, a shock occurs when a fluid tries to overcome an obstacle and the relative speed between the obstacle and the fluid is greater than the fluid sound speed. For example, in the case of a bullet traveling in the air, hydrodynamic equations give shock information for the upstream (unshocked) and downstream (shocked) regions. Such information may be used to calculate, for example, the Mach number, a quantity that gives some idea of the shock strength. In the case of solar-terrestrial interactions, things become much more complicated in relation to the previous example: now, the medium, the solar wind plasma, has a magnetic field attached to it, the interplanetary magnetic field (IMF), which is a vector. As opposed to the ordinary theory, now the hydrodynamic equations are coupled to the Maxwell equations, and, under some particular assumptions, give rise to the magnetohydrodynamic (MHD) theory. Then, for a particular region in the plasma, if one allows jumps in magnetic field, temperature, particle density, and velocity to occur, such quantities will obey the Rankine-Hugoniot conditions.
In the case of MHD shocks, an event will be a fast forward shock (FFS) if the shock travels away from the Sun and the magnetosonic speed (a combination of Alfvenic and sound speeds) is greater than the relative speed between the shock and the medium in the shock frame of reference. If the shock travels toward the Sun in the shock frame of reference and the relative speed obeys the same conditions listed above, the shock is said to be an FRS (fast reverse shock). Based on these conditions, one can obtain an SFS (slow forward shock) and a SRS (slow reverse shock).
As opposed to the gun bullet example above, shock perturbations generated at the Sun may travel away from the Sun and toward the Sun in the shock frame of reference, but in both cases the shocks travel away from the Sun in the Earth's (or a spacecraft's) frame of reference since they are dragged by the solar wind. The figure above shows, as an example, an IP shock observed by ACE on 23 June 2000. This shock is classified as FFS because all plasma and IMF quantities suffer positive jumps. In my thesis, I used only FFS because we know they are more geoeffective in comparison to the other shock categories (slow and reverse).
As opposed to the gun bullet example above, shock perturbations generated at the Sun may travel away from the Sun and toward the Sun in the shock frame of reference, but in both cases the shocks travel away from the Sun in the Earth's (or a spacecraft's) frame of reference since they are dragged by the solar wind. The figure above shows, as an example, an IP shock observed by ACE on 23 June 2000. This shock is classified as FFS because all plasma and IMF quantities suffer positive jumps. In my thesis, I used only FFS because we know they are more geoeffective in comparison to the other shock categories (slow and reverse).
IP shocks present different properties in regards their upstream region (non-shocked region) and downstream region (shocked region). Such properties determine the strength of the shock, which is usually measured by the downstream to upstream density and magnetic field ratios. At 1 AU, IP shocks are assumed to be planar structures and therefore their shock fronts have a shock normal vector. The shock normal veto gives us information about the shock propagation in the heliosphere. The angle between the shock normal and the upstream magnetic field is called obliquity. If this angle is close to 90 deg, the shock is classified as a perpendicular shock. If the obliquity angle is close to zero, the shock is said to be an almost parallel shock. If that angle is somewhere between 0 and 90 degrees, the shock is named an oblique shock. However, different authors have different criteria for this definition.
Another important aspect of IP shock geometry is the angle between the shock normal and the GSE (Geocentric Solar Ecliptic) X line. The GSE coordinate system is defined as follows: the X axis points radially from the Earth to the Sun; the Y axis points towards dusk, the direction opposite to the Earth's motion around the Sun, and Z axis perpendicular to the plane of the planetary motion, defined positive when pointing towards North. The shock impact angle is then defined as the angle between the Sun-Earth line and the shock normal. If the shock impact angle is close to 180 degrees (pointing in the anti-Sun-ward direction), the shock is an almost frontal shock. On the other hand, if there is any deviation of the shock normal in relation to the Sun-Earth line, the shock is classified as an inclined shock. During my Ph.D work, I showed that the more frontal and the more perpendicular the shock, the higher the geomagnetic activity triggered by the IP shock.
IP shocks are usually driven by transient solar disturbances when propagating in the interplanetary space. Such perturbations are CMEs (coronal mass ejections), and CIRs (correlating interaction regions). We know from an extensive literature that CMEs may drive shocks with normals all around the heliosphere, i.e., frontal and inclined shocks. In contrast, CIRs tend to drive more inclined shocks due to its geometry in the heliosphere. The animation above shows a frontal CME (most likely with a frontal shock) hitting the Earth (yellow circle). Note the peculiar radial propagation of the CME. In the case of a CIR, however, as shown by the animation below, a CIR strikes Earth with a shock normal with a large inclination in relation to the X line in the equatorial plane. This spiral CIR geometry is related to the Parker spiral generated when fast plasma streams encounter slow plasma streams in the heliosphere. These simulations were computed by the heliospheric model ENLIL and are available at the CCMC website. I thank Dr. Yihua Zheng for helping me find a nice frontal CME-driven shock and inclined CIR-driven shock.
During my Ph.D. studies, I had the opportunity to study the effects of interplanetary (IP) shock angles on the geomagnetic activity that follows the shock impacts. The title of my Ph.D. thesis is "A study of interplanetary shock geoeffectiveness controlled by impact angles using simulations and observations". The main idea of my research was that IP shocks that strike Earth frontally (shock normal vector aligned with the line that connects Earth and Sun) are followed by higher geomagnetic effects in comparison to the case in which IP shocks hit Earth with inclination angles larger than zero. The animation below shows results of my simulation paper. In this work, I used the Open Geospace Circulation Model (OpenGGCM) code to run my simulations. The simulated example at left column is a strong inclined shock, whereas the column at right shows a weak frontal shock. Even though the frontal shock was as half strong as the inclined one, the former was much more geoeffective than the latter. I attributed this effect to the geoeffective compression of the magnetosphere by the frontal IP shock in all directions at the same time. For instance, field-aligned currents (FACs) are seen to be stronger in the frontal case in comparison to the inclined case in the ionosphere nightside. This is a substorm signature. See my simulation paper and thesis for more details.
In order to support my simulation results, I looked at solar wind and IMF data and found 461 fast forward IP shocks in a time frame of almost 20 years. This list can be found in the Appendix of my thesis and can be downloaded from the link above. I used WIND and ACE data to calculate shock normals using different methods found in the literature (see my thesis). In my first observational paper, I correlated SuperMAG data (SML, SME, etc.) with the shock inclination angles and speed and found that, the faster and more frontally the shock hits the magnetosphere, the higher will the geomagnetic activity following the shock be. That paper contains statistical results of IP shocks at 1 AU as well. I found similar results in my second observational paper for auroral power intensity using SuperMAG data as well. My observational results confirmed my previous results predicted by simulations. As a result, I concluded that space weather forecasts should not only worry about the strength in which solar wind disturbances (CMEs or CIRs) hit the Earth, but also about the angle in which the magnetosphere is struck by such perturbations.