Geosynchronous magnetopause crossings: necessary conditions

The experimental data on GOES magnetic measurements and plasma measurements on LANL geosynchronous satellites is used for selection of 169 case events containing 638 geosynchronous magnetopause crossings (GMCs) in 1995 to 2001. We study the necessary conditions for the geosynchronous magnetopause crossings using scatter plot of the GMCs in the coordinate space of Psw versus Bz. In such representation the upstream solar wind conditions demonstrate sharp envelope boundary under which no GMCs are occurred. The boundary has two strait horizontal branches where Bz does not influence on the magnetopause location. The first branch is located in the range of Psw=21 nPa for large positive Bz and is associated with an asymptotic regime of the pressure balance. The second branch asymptotically approaches to the range of Psw=4.8 nPa under very strong negative Bz and it is associated with a regime of the Bz influence saturation. We suggest that the saturation is caused by relatively high contribution of the magnetosphere thermal pressure into the pressure balance on the magnetopause. The intermediate region of the boundary for the moderate negative and small positive IMF Bz can be well approximated by a hyperbolic tangent function. We interpret the envelope boundary as a range of necessary upstream solar wind conditions required for GMC in the point on the magnetopause located mostly close to the Earth ("perigee" point). We obtain that the dipole tilt angle and dawn-dusk asymmetry influence on the "perigee" point location. We find that the aGSM latitude of this point depends linearly on the dipole tilt angle with the slope about -0.5. The aGSM longitude of the "perigee" point decreases with IMF Bz with a rate of about 2 angular minutes per 1 nT. An empirical model predicting the magnetopause crossing of the geosynchronous orbit in the "perigee" point is proposed.