The occurrence of upstream waves in relation with the solar wind parameters: a statistical approach to estimate the size of the foreshock region

We studied the occurrence of upstream waves in the foreshock region and their relationship with the solar wind and interplanetary magnetic field parameters. To this purpose, we developed a method for a careful identification of the upstream wave events. The results of the statistical analysis based on Cluster data (2003-2010 years) confirm that the angle between the bow shock normal direction and the interplanetary magnetic field is the key element for the wave generation; they also show the relationship between the wave occurrence and the solar wind speed and density. We focused our attention on the occurrence of wave events as a function of the distance from the bow shock. The results show that the foreshock region, where we can observe upstream waves, is characterized by an effective size that decreases with the increase of both the solar wind speed and the wave frequency. Due to the relationship between the solar wind speed and the wave frequency, we suggest that such distance is simply a function of the solar wind speed, becoming smaller when the solar wind speed increases, and then the occurring higher frequency upstream waves are confined in a more restricted region.