High-latitude Bow Shock: Tilt Angle Effects

Transcription

1 WDS'7 Proceedings of Contributed Papers, Part II, 9 33, 7. ISBN MATFYZPRESS High-latitude Bow Shock: Tilt Angle Effects K. Jelínek, Z. Němeček, and J. Šafránková Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic. Abstract. This paper deals with an influence of the tilt angle on the location of the Earth s bow shock. We present statistical study of more than five thousand bow shock crossings collected by five spacecraft (INTERBALL-1, MAGION, GEOTAIL, IMP 8 and CLUSTER) for which as a monitor of the solar wind we used data from the WIND satellite. We assume that the effect of the tilt angle (which is the angle between the Earth s magnetic dipole and Z axis of GSM coordinates) on the bow shock position is significant only at high latitudes. For the study, we compare our set of crossings with an analytical bow shock model (Jeřáb et al. [5]). We found that the position of the high-latitude bow shock is also measurably governed by the Earth s tilt angle. Introduction The Earth s bow shock (BS) is very frequently seen as an example of a collisionless shock in the space plasma and it was studied by many authors (e.g., Fairfield [1971]; Formisano et al. [1973]; Tsurutani and Stone [1985]; Burgess [1995]; Russell [1995], and references therein). A great amount of BS observations has been accumulated by satellites at significantly low latitudes. An advantage of the INTERBALL project was its relative large inclination of the orbit (63 o ) and this allows us to study also high-latitude bow shocks. Also several other spacecraft (e.g., HAWKEY or CLUSTER) recorded high-latitude BS but almost in the subsolar region or near tail because of their smaller apogee. Many studies were devoted to the influence of the tilt angle on formation of the magnetosphere as a whole and a location of the magnetopause in particular. Observations as well as MHD models reveal that the magnetotail is shifted vertically for non-zero dipole tilt. As it was showed by Sotirelis and Meng [1999], the magnetopause subsolar point varies its position nearly linearly with the tilt angle ( up to 3 R E ) from the Sun-Earth line. In the paper of Boardsen et al. [], an empirical model of the near-earth high-latitude magnetopause which depended on the solar wind dynamic pressure, the interplanetary magnetic field (IMF) B Z component and the dipole tilt angle was discussed. They found that the solar wind pressure and the tilt angle are the most significant parameters which govern the shape of the high-latitude bow shock. The tilt angle influences the location of magnetospheric cusps (Zhou and Russell [1997], Zhou et al. [1999] and Němeček et al. []) and therefore, the indentation of the magnetopause in the outer cusp depends on the tilt angle (e.g., Šafránková et al. [, 5]). Fig. 1 presents an example of the MHD simulation (BATSRUS for more information about this model see web page for zero and non-zero tilt angles and shows an asymmetry of the magnetosheath plasma density for the southern and northern hemispheres in the case of non-zero tilt. Moreover, the bow shock position and shape are controlled by the upstream Mach number, the IMF orientation and the current shape of the magnetopause, therefore the findings made on the magnetopause should be also taken into account for the bow shock. Měrka and Szabo [] showed that the tilt angle effect is important for the estimation of the bow shock position, however, the corresponding changes of the bow shock shape and location with the tilt angle variations were not taken into the bow shock models. We present a short study of the bow shock locations for varying tilt angles. The study is based on a comparison of bow shock model predictions with observations of several spacecraft. 9

2 Figure 1. Ion density plots (with a linear scale) in the XZ GSM plane as an output from the MHD BATSRUS simulation. a) tilt angle = and b) tilt angle = 3 degrees. Our statistics are directed to investigation of a similar dependence of the bow shock position on the tilt angle as it was reported for the magnetopause and to correction of current analytical models on this effect. Data set For our statistical study we have used set of 571 bow shock crossings (Fig. a) from the spacecraft IMP 8, GEOTAIL, INTERBALL-1, MAGION and CLUSTER. This set covers bow shock crossings observed from 1995 till. For these, we have identified parameters of the solar wind (the plasma and the magnetic field) from the WIND satellite shifted to the position of a relevant satellite and computed a position of the bow shock using the Jeřáb et al. [5] model. 3 < X <, gray: Z GSM <, black: Z GSM > Z (GSE) [Re] MG (18) IB1 (118) GEO ( 813) CLR ( 31) IM8 (69) Y (GSE) [Re] Figure. a) Positions of observed bow shock crossings in the Y Z GSE plane, b) Dependences of difference between observed and model bow shock positions on the tilt angle for southern (gray) and northern (black) hemispheres. (Here and in the following figures the horizontal lines represent median). 3

3 BS: 5 < X < -15 dr=.*tilt-. [Re] BS: -5 < X < 5 dr=.6*tilt-.3 [Re] BS: -15 < X < -5 dr=.9*tilt-. [Re] BS: 5 < X < 15 dr=-.1*tilt+. [Re] MP: 5 < X < -15 dr=.*tilt+. [Re] MP: -5 < X < 5 dr=.36*tilt-1. [Re] MP: -15 < X < -5 dr=.8*tilt-. [Re] MP: 5 < X < 15 dr=-.*tilt-. [Re] Figure 3. a) Dependence of differences between observed and model bow shock positions on the tilt angle in the northern hemisphere for several intervals along the Sun-Earth line. b) The same figure as in the left part for the magnetopause. Tilt angle effects The study is directed to high latitudes (in our definition it means > 3 o of latitude) because the north-south shift with the dipole tilt angle is expected in this latitude range. The following figures present results as a difference between observed and predicted radial distances of a particular bow shock (or in Fig. 3b for the magnetopause) crossing from the Earth center for positive X GSM and from the Earth-Sun line for negative X GSM. Fig. b shows the dependence of this difference on the tilt angle for northern (black) and southern (gray) hemispheres. This figure shows opposite trends of the tilt angle dependence for positive and negative Z GSM coordinates. A detail investigation of these dependences is depicted in Fig. 3a where four panels present 1 R E wide layers along the X GSM axis for the northern hemisphere. In each plot, there is drawn always a linear regression and its equation. From this figure, one can see that the near and tail flank (interval of X GSM in the range of 5, 5 R E ) bow shock crossings are located closer to the Earth for negative tilt angles and further from the Earth for positive tilts. This dependence is most significant in the range of 5, -5 R E X GSM. On the other hand, the dayside bow shock location exhibits only a weak and opposite (if any) dependence on the tilt angle. We have done the same procedure for the magnetopause (Fig. 3b) and it is evident that both plots correspond each other qualitatively and almost quantitatively. The difference between observed and model bow shock positions as a function of the X GSM position for positive (black) and negative (gray) tilt angles is shown in following series of figures. Fig. a documents our assumption that the low-latitude bow shock does not response to the tilt angle changes. Fig. b shows the tilt angle dependence of high-latitude bow shock locations for a comparison. As a next step, we make correction of the bow shock model in the interval 8 < X GSM < R E. We did not include dayside crossings because there is an opposite sense of the tilt influence. From Fig. 3a it is clear that the dependence on the tilt angle decreases farther to the tail, therefore we did not involve the tilt angle as a parameter for aberration in the XZ GSM plane but we used a simple formula, R MOD = R MOD + k tilt sin latitude, with the linear dependence on the tilt angle with respect to latitude of observed crossings. To find out free parameter k, we used minimalization of standard deviations of R OBS R MOD. The best 31

4 gray: tilt >=, black: tilt < gray: tilt >=, black: tilt < 1-1 gray: tilt >=, black: tilt < 1-1 R mod =R mod +.8*tilt*sin(latitude) 1-1 (c) Figure. Dependence of difference for positive and negative tilt angle and for the northern hemisphere between observed and model bow shocks on the X GSM axis for a) low-latitude bow shock, b) high-latitude bow shock and c) high-latitude bow shock with a correction of the Jeřáb et al. [5] model in the interval of 8 < X GSM < R E. value of the k parameter is.8. Fig. c presents the result of the correction. When we compare Fig. b and c in the interval 8 < X GSM < R E, we can note a slight indentation which we consider as a result of the magnetopause deformation in the cusp vicinity, however, this is not statistically significant and it will be a subject of further study. Conclusion We have analyzed changes of the bow shock location as a function of the Earth s dipole tilt angle, and we compared the results with a similar study of the magnetopause position. Our results can be written as follows: The low-latitude bow shock does not depend on the tilt angle. The bow shock moves in the direction of the positive Z GSM axis for positive tilt angles. The displacement can reach 1R E for the maximum tilt in the range from 8 to R E along the Earth-Sun line. 3

5 The high-latitude bow shock shows a similar dependence on the tilt angle as the magnetopause. We suggested a small correction of the model (Jeřáb et al. [5]) at high latitudes and for X GSM ranges of 8, R E. We found out a signature of the bow shock indentation caused by the magnetopause deformation in a location of the magnetospheric cusp. The present results should be considered as preliminary and their confirmation requires a further investigation. Acknowledgments. The present work was supported by the Czech Grant Agency under Contracts /3/H16, and 5/5/17, by the Charles University Grant Agency under Contract 737, and partly by Research project MSM1686 financed by the Ministry of Education of Czech Republic. References Boardsen, S. A., T. E. Eastman, T. Sotirelis, and J. L. Green, An empirical model of the high-latitude magnetopause, J. Geophys. Res., 15, 3193,. Burgess, D., Collisionless Shocks, In: Introduction to Space Physics, M.G. Kivelson and C.T.Russell (eds), Cambridge: Cambridge University Press, Chapt. 5, pp , Fairfield, D.H., Average and unusual location of the Earth s magnetopause and bow shock, J. Geophys. Res., 76, 67, Formisano, V., G. Hedgecock, G. Moreno, F. Palmiotto, and J.K. Chao, Solar wind interaction with the Earth s magnetic field,, Magnetohydrodynamics bow shock, J. Geophys. Res., 87, 3731, Jeřáb, M., Z. Němeček, J. Šafránková, K. Jelínek, J. Měrka, Improved bow shock model with dependence on the IMF strength, Planet. Space Sci., 53, 85-93, 5. Měrka J. and A. Szabo, Bow shock s geometry at the magnetospheric flanks, J. Geophys. Res., 19 (1), 1, doi:1.19/ja1567,. Němeček, Z., J. Měrka and J. Šafránková, The tilt angle control of the outer cusp position, Geophys. Res. Lett., 7 (1), 77-8,. Russell, C.T. (ed.), Physics of collisionless shocks: Proceedings of the Symposium of COSRAR Scientific Commission D, Vol. D.1, Pergamon Press, Šafránková, J., Z. Němeček, Š. Dušík, L. Přech, D. G. Sibeck, and N. N. Borodkova, The magnetopause shape and location: a comparison of the Interball and Geotail observations with models Ann. Geophys., 31,. Šafránková, J., Š. Dušík, Z. Němeček, The shape and location of the high-latitude magnetopause, Adv. Space Res., 36 (1), 193, 5. Sotirelis, T. and C. T. Meng, Magnetopause from pressure balance, J. Geophys. Res. 1, 6889, Tsurutani, B.T. and R.G. Stone, Collisionless shock in the heliosphere: Reviews of current research, Washington DC, American Geophysical Union, Geophysical Monograph Series 35, AGU, Washington, D.C., Zhou, X.-W. and C. T. Russell, The location of the high-latitude polar cusp and the shape of the surrounding magnetopause, J. Geophys. Res. 1, Zhou, X.-W., C. T. Russell, G. Le, S. A. Fuselier, and J. D. Scudder, The polar cusp location and its dependence on dipole tilt, Geophys. Res. Lett. 6, 93,