We investigate the dependence of the magnetopause location on the interplanetary magnetic field (IMF) cone angle (the angle between the IMF and solar wind velocity vectors) in a statistical study based on ≈6500 magnetopause crossings observed by the five THEMIS spacecraft, both at the dayside and flanks. To remove other well-known effects, we analyze the difference between observed magnetopause radial distances and those predicted by an empirical magnetopause model (scalable by the solar wind dynamic pressure and IMF BZ component). The results demonstrate a systematic increase of the magnetopause distance for radial IMF directions, from ≈0.3 RE at 90° to ≈1.7 RE at 0° or 180° cone angle. Moreover, a stronger dependence of the magnetopause location on the solar wind dynamic pressure than predicted by the current models was observed.
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 The magnetopause is a layer/region determined by the pressure balance between the total pressure on the magnetosheath side and the magnetic pressure on the magnetospheric side. A strong dependence of the magnetopause shape and location on the solar wind dynamic pressure was established and also the dependence on the strength and orientation of the interplanetary magnetic field (IMF) has been noted by Aubry et al. .
 For the shape of the near-Earth high-latitude magnetopause, Boardsen et al.  prepared an empirical model which is parameterized by the solar wind dynamic pressure, IMF BZ, and dipole tilt angle in a limited range of the XGSE coordinate and found that the dipole tilt angle and solar wind dynamic pressure are the most significant factors influencing the shape of the high-latitude magnetopause, whereas the IMF BZ dependence is separable only when the effects of the pressure and dipole tilt angle are removed. Moreover, these authors have shown that the low-latitude subsolar magnetopause is a function of the tilt angle and that this dependence becomes weaker towards the flanks. The cusp magnetopause indentation was suggested by a number of the authors [e.g., Petrinec and Russell, 1995; Sotirelis and Meng, 1999; Eastman et al., 2000] and its deepness and location were associated with the dipole tilt angle [Šafránková et al., 2002, 2005; Lin et al., 2010]. On the other hand, the presence of this indentation was questioned in several papers [e.g., Zhou and Russell, 1997; Lavraud et al., 2004].
Fairfield et al.  indicated that a radial IMF orientation may be an alternative dominant factor which can cause the magnetopause expansion in the subsolar region. They supposed that foreshock pressure fluctuations convect through the subsolar bow shock into the magnetosheath and influence the subsolar magnetopause location. The position of the foreshock behind the bow shock is controlled by the θBN angle (the angle between the IMF and local normal to the bow shock). In the subsolar region, this angle coincides with the angle between the IMF vector and the Earth-Sun line. In the case of a radial IMF, the foreshock is located upstream of the subsolar quasiparallel bow shock. Under this condition, Merka et al.  reported larger amplitude magnetopause oscillations occurring during intervals of quasi-radial IMF. Also the case studies by Suvorova et al.  and Jelínek et al.  mentioned an unusual location of the magnetopause caused by the radial IMF. Thus, our short statistical study is devoted to an average magnetopause location through intervals of the IMF aligned with solar wind velocity. To distinguish between the influence of the IMF cone angle (the angle between solar wind velocity and IMF vectors) and the θBN angle (the angle between the IMF vector and the vector of the normal to the bow shock just upstream of a particular magnetopause crossing), the analysis is carried out for the subsolar and flank magnetopauses separately. The investigation is based on the five-spacecraft THEMIS mission [Angelopoulos, 2008] that yields the opportunity to identify many magnetopause crossings being registered by the same instruments with the same solar wind monitor.
2. Data Set and Methodology
 All five THEMIS probes were launched on 17 February 2007 into very similar elliptical and near-equatorial orbits. Our analysis uses magnetopause crossings identified by a visual inspection of the plots containing plasma moments, ion, and electron spectra [McFadden et al., 2008], and magnetic field data [Auster et al., 2008] with the best available time resolution. The inspected periods were June–August and November 2007 and May–August 2008; altogether we collected 6649 magnetopause crossings for which the upstream data were available. Many of these crossings were multiple but we treated each in a series as a single crossing. The locations of all crossings are shown in Figure 1. The Petrinec and Russell  (PR96 hereafter) magnetopause surface calculated for IMF BZ = 0 and the solar wind dynamic pressure, pSW = 2 nPa is given for reference.
 To further analysis, the crossings were divided into two groups of approximately equal sizes: subsolar crossings (5 < XGSM; −5 < YGSM < +5, −5 < ZGSM < 5) and the rest of them. The latter group will be called the flank crossings hereafter.
 The WIND plasma moments [Ogilvie et al., 1995] and the ACE magnetic field [Smith et al., 1998] were used as input parameters for model predictions. These data were propagated by the two-step routine [Šafránková et al., 2002] to the location of a particular THEMIS magnetopause crossing; the deceleration in the magnetosheath was omitted. Five-minute averages of both the plasma and magnetic field centered around the time of the magnetopause crossing were then used as a proxy of the upstream conditions. The locations of observed crossings should be transformed into aberrated coordinates. The aberration is widely discussed by Šafránková et al.  with the conclusion that the best ordering of the data provides the procedure taking into account the Earth's orbital motion and omitting the transversal components of the solar wind velocity, thus we use this approach.
 Our analysis uses the differences between the radial distance of observed crossings, Robs and the distance predicted by the PR96 model, Rmod. To ensure that the results do not depend on the model used, we performed the same analysis applying the residuals of Shue et al. , Roelof and Sibeck , and Boardsen et al.  models; the results were even quantitatively very similar.
3. Data Analysis and Its Discussion
 The PR96 model includes the IMF BZ and pSW as parameters, thus we check its performance with respect to these parameters. Figure 2 shows the differences, Robs − Rmod as a function of IMF BZ. One can note that the average value of deviations is nearly constant and equal to ≈0.5 RE for −10 nT < BZ < 4 nT. It drops down to ≈−0.3 RE for larger IMF BZ but the number of crossings for such large BZ is small and they cannot spoil a further analysis.
 The differences Robs − Rmod are plotted as a function of pSW in Figure 3a. The average values shown as the yellow and blue bars reveal a systematic dependence of the difference on pSW. The crossings observed under low pSW are on ≈1 RE farther from the Earth than the predictions for both subsolar (blue points) and flank (red points) groups of crossings. From this it follows that the dependence of the magnetopause location on pSW is stronger than the sixth root that is usually expected. To show it, we plot the radial distance of subsolar crossings as a function of pSW in Figure 3b. The best fit is 12.8 × pSW1/4.8. The value of the exponent is rather high, however, Lin et al.  published a 3D magnetopause model and found this exponent ≈1/5.2 for the whole magnetopause surface. We assume that the presence of plasma in the low-latitude boundary layer can further increase the value of the exponent for the subsolar region. Consequently, the whole problem needs a deep analysis that is out of the present paper that is concentrated on the influence of the IMF direction. We think that the reason why this effect was not found in earlier studies [e.g., Šafránková et al., 2002] is an unusually low pSW in 2007–2008. The distribution of pSW in our set peaks at 1.4 nPa (not shown), whereas 2 nPa is considered as a typical pressure.
 Nevertheless, to account for the pressure and possible IMF BZ effects, we have divided both our sets (subsolar and flank) into two sub-sets according to pSW (the break point is 1.4 nPa) and then according to the IMF BZ sign. The differences, Robs − Rmod as a function of the IMF cone angle are plotted in Figure 4. As mentioned, the cone angle is defined as the angle between the IMF and solar wind velocity vectors. In Figure 4, the red points stand for low pSW and blue points for the high pSW in a) and b) panels, whereas the same colors distinguish positive (blue) and negative (red) IMF BZ in c) and d) panels, respectively. The average values are shown by the horizontal bars of corresponding colors. The top panels show the distribution of the subsolar crossings, the flank crossings are given in the bottom panels. The black parabolic curves that emphasize the trends are the fits of all data in the corresponding panel. In spite of a large spread of experimental points, one can clearly see that the crossings observed during a radial IMF (aligned with the solar wind flow) are on average about 1 RE outward from the Earth than the crossings observed during the IMF perpendicular to the solar wind velocity. This trend is clearly observed in all subsets.
 We assume that the dependence is connected with a different way of transformation of the upstream pressure to the pressure imposed onto the magnetopause behind the quasiparallel and quasiperpendicular bow shocks. There is no compression of the magnetic field at the parallel bow shock and Verigin et al.  pointed out an important role of the magnetic field tension that is vanishing behind the parallel bow shock. Moreover, Suvorova et al.  have shown that the magnetosheath plasma pressure is by a factor of ≈2 lower for such shock. For this reason, we made the plots of Robs − Rmod vs the θBN angle (not shown) but the ordering of the data was much worse, especially at the flanks. Nevertheless, the parallel subsolar bow shock is the proper cause of the magnetopause displacement. Taking into account the shape of the magnetosheath streamlines [e.g., Spreiter et al., 1966], the magnetopause is influenced by the solar wind entering close to the subsolar point and the θBN angle is equal to the cone angle at this point. The average amplitude of the cone angle effect (≈1 RE) is smaller than that following from the case studies [Suvorova et al., 2010; Jelínek et al., 2010] but as it can be seen in Figure 4, we have a large number of crossings that lie 3 or more RE from the predicted location. The large spread of the points can be partly connected with the fact that the radial IMF is difficult to propagate [e.g., Jelínek et al., 2010, and references therein] and partly with other factors. We should point out that we made the plots similar to those in Figure 4 for other quantities (e.g., in-ecliptic IMF angle, solar wind speed and density, upstream β, tilt angle, and geomagnetic indices) but without any clear effect. We believe that a possible influence of these quantities would be separable when the cone angle effect will be removed by an improved magnetopause model.
 The analysis of magnetopause locations observed by the Themis spacecraft in 2007–2008 is present. It brings a statistical evidence that the dayside magnetopause location is strongly influenced by the IMF cone angle as it was shown in the case studies [Merka et al., 2003; Suvorova et al., 2010; Jelínek et al., 2010]. The difference between the IMF aligned with and IMF perpendicular to the solar wind flow is as large as 1 RE. This effect is attributed to a less effective transformation of the solar wind dynamic pressure to the pressure imposed onto the magnetopause during intervals of a radial IMF. Another factor contributing to deviations of the observed crossings from their model predictions is a stronger dependence of the magnetopause location on the solar wind dynamic pressure than that usually suggested. However, the exact quantification of the pressure effect requires a larger number of the crossings observed under pressures exceeding 2 nPa to be complemented into the data set.
 The authors acknowledge the NASA contract NAS5-02099 and V. Angelopoulos for use of data from the THEMIS mission. Specifically, the authors thank C. W. Carlson and J. P. McFadden for use of ESA data and K. H. Glassmeier, U. Auster, and W. Baumjohann for the use of FGM data provided under the lead of the Technical University of Braunschweig and with financial support through the German Ministry for Economy and Technology and the German Center for Aviation and Space (DLR) under contract 50 OC 0302. The present work was partly supported by the Czech Grant Agency under contract 205/09/0112 and partly by the Research Plan MSM 0021620860 that is financed by the Ministry of Education of the Czech Republic. G. Granko thanks the Charles University Grant Agency (GAUK 163810) for support.