ON THE SMOOTH SURFACE OF THE NORTHERN BOW SHOCK OF MARS, BASED ON MARS GLOBAL SURVEYOR’S MEASUREMENTS N. SERGIS and X. MOUSSAS Department of Astrophysics, Astronomy and Mechanics, Faculty of Physics, National University of Athens, Panepistimiopolis GR 15783, Zografos, Athens, Greece (e-mail: nsergis@cc.uoa.gr; xmoussas@cc.uoa.gr) (Received 21 January 2001; accepted 23 April 2001) Abstract. A very smooth and time-invariable bow shock of Mars is revealed using Mars Global Surveyor’s data. The bow-shock position has been identified using magnetic and electron flux data obtained by the Magnetometer and Electron Reflectometer (MAG/ER) experiment aboard Mars Global Surveyor, in the time period between days 87 and 255 of 1998. From the magnetic field and the electron flux measurements, 148 bow-shock crossings were detected, concentrated mostly on the northern hemisphere of the planet. With these results, a 3D configuration of the bow shock is constructed and presented. The results show that part of the observed bow shock is a surprisingly smooth surface. It is possible that the bow shock is smooth only in the northern hemisphere, since the southern surface is characterized by local magnetic anomalies. Its real shape can only be revealed in a 3D representation in the planetary centered solar ecliptic coordinate system and questions the theoretically expected variation of the bow shock. 1. Introduction Mars has a very weak intrinsic magnetic field, mostly of a crustal character, believed to be the remnant of a dynamo that has now ceased, after operating for a comparatively short period of time in the early history of the planet (Acuña et al., 1998). Its main characteristic is that it consists of several highly variable magnetic dipoles or multipoles, localized in parallel stripes with alternating polarity which we call magnetic rings, in the southern hemisphere, as shown in the magnetic chart of the planet (Acuña et al., 1999). These magnetic rings produce alternating magnetic fields as strong as 500–1500 nT in the surface, therefore the planet’s interaction with the solar wind might be somehow affected by the surface magnetic anomalies, mostly in the southern hemisphere (Acuña et al., 1999). The absence of a strong, global, dipole magnetic field is supported by all relevant Mars Global Surveyor’s measurements. The MAG/ER experiment aboard Mars Global Surveyor provides fast (up to 32 samples per second) and precise (12 bit) vector measurements of the ambient field over the range of 4 to 65 536 nT per axis. The electron reflectometer measures the local electron distribution function in the range of 0.01 to 20 keV (Acuña et al., 1999). Solar Physics 202: 191–200, 2001. © 2001 Kluwer Academic Publishers. Printed in the Netherlands. 192 N. SERGIS AND X. MOUSSAS Figure 1. Example of the magnetic field behavior for a bow-shock crossing (day 104 of 1998). The exact time of the crossing is 104.1150 days. 2. The Bow-Shock Crossings From the magnetic field measurements obtained by the MAG/ER experiment of the Mars Global Surveyor, during 353 complete orbits around Mars in the time period from 28 March 1998 to 8 September 1998, we detected 148 bow-shock crossings. These crossings were characterized by a sharp and major fall of the magnetic field with increasing planetocentric distance (Figure 1). The interplanetary magnetic field outside the boundary surface was small, presenting the usual solar wind values for the distance of Mars. Inside the planet’s magnetic cavity the field was much stronger and variable, while in the post-shock area a significant compression of the magnetic field is present. The electron flux behavior also indicates simultaneously the presence of the bow shock at exactly the same position. From the electron flux measurements, an obvious and sharp increase at the bow-shock crossing was observed in all energies up to 10 keV (Figure 2). This electron intensity increase is a typical and theoretically expected feature of a bow-shock crossing, which coincides with the change of the magnetic field, indicating the plasma compression behind this boundary surface (Burges, 1995). 3. The Variability of the Solar Wind Conditions The interaction of Mars with the solar wind and the position and configuration of the bow shock strongly depend on the solar wind pressure variability with time. The solar wind total pressure in the vicinity of Mars can be calculated as Psw = κρu2 +
B2 + ni kTi ≈ κρu2 , 2µo i (1) SMOOTH SURFACE OF THE NORTHERN BOW SHOCK OF MARS 193 Figure 2. Example of the electron flux behavior for a bow-shock crossing (day 104 of 1998) and for 3 different energies (in flux descending order 314, 515, and 844 eV, respectively). The exact time of the crossing is 104.1150 days. where ρ is the mass density, u the radial velocity, and B the magnetic field of the solar wind, k is the Boltzmann constant, ni is the i-particle density, Ti is the iparticle temperature, and µo is the magnetic permeability. This assumption is safe, since the dynamic pressure is the dominant component of the total pressure. The factor κ is taken to be equal to unity for the vicinity of Mars (κ has a value close to unity for Earth and Venus). In order to study the time variation of the solar wind pressure and since we do not have direct proton velocity and density measurements near Mars, we use Ulysses’ measurements for the same time period, normalized at Mars’ distance in order to have a general idea of the solar wind pressure variability near Mars at the time period of the bow-shock crossings used. For the time period under investigation, Ulysses and Mars are both very close to the ecliptic plane, presenting very small difference in their ecliptic latitudes, while Ulysses’ heliocentric distance slightly changes from 5.4067 to 5.3416 AU. Any unusual feature of the solar wind pressure near Mars would be detected by Ulysses about 9 days later. This way we can quite accurately know the limits of the solar wind pressure variation near Mars. The equations used for the normalization of Ulysses’ measurements in Mars’ distance were (2) um ≈ uu , nm = nu  ru rm 2 , (3) 194 N. SERGIS AND X. MOUSSAS Figure 3. The variation of the solar wind dynamic pressure for the time period of the bow-shock crossings, as derived from Ulysses’ measurements normalized to the distance of Mars. Figure 4. Statistical behavior of the solar wind dynamic pressure near Mars for the time that our data covers. where um , nm , and uu , nu are the radial flow velocities and the proton densities of the solar wind near Mars and near Ulysses, respectively, while rm and ru are their heliocentric distances. The results show that the solar wind dynamic pressure varied as expected between 10−10 and 10−8 Pa (Figure 3). Furthermore, there were not any extreme solar wind conditions recorded during the same time period at 1 AU. The statistical SMOOTH SURFACE OF THE NORTHERN BOW SHOCK OF MARS 195 behavior of the solar wind dynamic pressure near Mars for the time that our data covers, is illustrated in Figure 4. At this point we should make clear that even though Ulysses’ measurements could not provide detailed knowledge of the solar wind pressure conditions in the vicinity of Mars, yet they give valuable information on its range during the period under examination. 4. Discussion During the last decade several attempts were made to predict the characteristics of the bow shock of Mars, based mostly on data fitting computer models. Slavin et al. (1991) assumed cylindrical symmetry and used conic sections to fit 94 bow shock crossings. The curve eccentricity derived from the fitting was e = 1.01 and the subsolar planetocentric distance value was rsb = 1.58 RM . Using the same assumptions but a different fitting method and 126 bow-shock positions identified by Mariner 4, Mars 2, Mars 3, Mars 5, and Phobos 2 observations, Trotignon et al. (1993) predicted a variable bow shock with slightly different parameter values (e = 1.02 and rsb = 1.57 RM ). Kallio et al. (1993) noticed that at least away from the subsolar region, a gas dynamic description may be effectively used to investigate the bow-shock characteristics, while Kallio (1996) treats the bow shock as a conic function with eccentricity e = 1.02 and rsb = 1.56 RM . In a recent work, Vignes et al. (2000), also assuming a cylindrical symmetric bow shock, used 450 MGS’s crossings to determine the conic parameters. The eccentricity presented nearly the same value as before (e = 1.02–1.03) while the subsolar planetrocentric distance appears larger (rsb = 1.64–1.67 RM ). In this work we use the sunstate, planetary centered, solar ecliptic (sse) coordinate system. This system has its x axis along the planet–Sun direction, its y axis in the ecliptic plane antiparallel to the planet’s rotation around the sun, while the z axis completes the right-hand coordinate system.  We present the bow-shock location in the usual (x, Y = x 2 + y 2 ) diagram (Figure 5), as well as in a 3D configuration. The use of the (x, Y ) diagram assumes axial symmetry of the planet’s interaction with the solar wind in the y and z directions, implying this way that the projection of the bow shock in the yz plane is a circle of radius Y (x). This often used assumption has not taken into account any deviations from the axial symmetry imposed, and was well formed in the absence of extended bow-shock evidence. Vignes et al. (2000) chose as well to present 450 MGS bow-shock crossings in an (x, Y ) diagram, where a large scattering is observed in the radial direction. Since the presentation of the bow shock in an (x, Y ) diagram cannot reveal any possible asymmetries of this surface, we concentrate in a 3D representation of the crossings. In the 3D presentation, the bow shock seems to be unexpectedly smooth and stable for the time period of six months that the measurements cover. It is surprising that there are certain view angles under which the surface appears almost 196 N. SERGIS AND X. MOUSSAS  Figure 5. 2D presentation of the bow-shock crossings in the (x, Y = x 2 + y 2 ) diagram (x towards the Sun), where cylindrical symmetry is assumed along the x axis. Notice the large scattering imposed mostly by this assumption. like an arc line, presenting much less scattering (Figures 6 and 7). This indicates that the bow shock is a relatively smooth surface and the scattering observed in the (x, Y ) diagram is mostly due to the simplified assumption of axial symmetry of the surface. From a theoretical point of view, several reasons are expected to result in at least temporal and occasionally large variability of the surface: (a) The solar wind pressure change. A bow shock caused primarily by an iono0 )) is spheric pressure exponentially decreasing with distance (P = P0 exp(− r−r H of course much less compressible than the one created by the magnetic pressure of a strong dipole (decreasing as r −6 ), but during the time period that we studied, the solar wind pressure variation with time exceeded two orders of magnitude, presenting a very large gradient too. These short time-scale variations should result in a time-dependent change in the shape and distance of the Martian bow shock, especially if we consider that the upper ionosphere is a quite disturbed plasma area, where upward ion motions are present (Lichtenegger et al., 1998). Furthermore, if a strong surface magnetic anomaly substantially affects the configuration at the bow-shock area, and a low multipole or dipole magnetic field component locally prevails, the solar wind is primarily confronted by the inside magnetic pressure, which decreases as r −6 as mentioned before. Therefore the simplified balance equation indicates that Psw r 6 = constant, where r is the planetocentric distance of the bow-shock point under consideration. In that case, the factor 20 variation SMOOTH SURFACE OF THE NORTHERN BOW SHOCK OF MARS 197 Figure 6. 3D presentation of the bow-shock crossings in the sse coordinate system. The center of the planet is located at (0, 0, 0). Notice that the scattering almost disappears when the crossings are seen under this view angle. between the median and maximum solar wind pressure (Figure 4), is consistent with a bow-shock-location change of about 1.6 and could account for the few (three) low shock positions observed (Figures 6 and 7). (b) The substantial change in the planet’s heliocentric distance during the sixmonth period. In the beginning of the time period under examination (day 87 of 1998) the heliocentric distance of Mars was 1.424 AU, while in the end (day 255 of 1998) had become 1.622 AU. Assuming that the solar radiation flux follows an r −2 decrease law, we conclude that this difference imposes a substantial 23% decrease in the solar energy flux on the planet. This radiation variation is expected to affect the planetocentric distance of the bow shock. (c) The change of martian epoch. The rotation axis of Mars has nearly the same inclination angle with respect to the ecliptic plane, as Earth. Therefore, Mars also presents epochs, characterized by changes in the atmospheric conditions and the mean surface temperature. Our data cover the spring time of the northern hemisphere. 198 N. SERGIS AND X. MOUSSAS Figure 7. The 148 points of the martian bow shock from MGS measurements (black spheres) in a 3D presentation, together with their projections (open circles) in the basic planes xy, xz, and yz. (d) The surface magnetic anomalies, combined with the rotation of the planet. The strong (up to 1500 nT) surface magnetic fields are expected to contribute to the spatial and temporal variation of the bow shock and the ionopause. These fields, being very localized, provide an additional magnetic pressure which, as the planet revolves, should result in an asymmetric configuration in the interaction of the planet with the solar wind (Acuña et al., 1999). (e) We expect a north-south asymmetry due to the existence of the southern surface magnetic anomalies (Vignes et al., 2000), or due to possible planetary ion pickup asymmetry, similar to the one detected at the magnetic barrier of Venus (Zhang, Luhmann, and Russel, 1991). The north-south asymmetry of the plasma flow and density inside the planet’s magnetic cavity, is caused mostly by the direction of the solar wind’s electric field and was succefully predicted by Luhmann et al. (1990) and Lichtenegger et al. (1998). These possible asymmetries could not easily be detected in this work because our data cover only part of the northern hemisphere. SMOOTH SURFACE OF THE NORTHERN BOW SHOCK OF MARS 199 It should also be mentioned that according to Shinagawa (2000), the upper ionosphere is characterized by very complicated dynamics, not yet fully understood, suggesting the presence of significant variability depending on the planet’s rotation and the solar wind’s conditions. Considering our results it is questionable whether the bow shock could truly present cylindric symmetry. The derived 3D shape of the bow shock implies that the fit with a conic or any other axial symmetric function might be inaccurate and even misleading. Acknowledgements We continue to be grateful to the Research Committee of the National and Kapodistrian University of Athens, for grant number 70/4/2469 for Space Physics. We continue to be grateful to Dr J. King for the excellent facilities provided by NSSDC. 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