1. About shape of the interplanetary shock front
PETUKHOV IVAN , PETUKHOV STANISLAV
Yu.G. Shafer Institute of Cosmophysical Research and Aeronomy SB RAS
The 32nd International Cosmic Ray Conference
August 11-18, 2011, Beijing

2. At present, the shape of the front of interplanetary shock is only known from model calculations (Smith and Draer, 1990; Wandas et al, 1997). To what extent do the calculations reproduce the properties of real shocks is not known, because local measurements on the spacecraft themselves do not provide information about large-scale shape of the surface.
We have determined the characteristic shape of the shock front from the analysis of the set components of the vector normal to the surface of the interplanetary shock front.

3. JGR, v. 115, A09215,2010 Eventually set consists of 257 observations
C.Wang, H.Li, J.D. Richardson, and J.R. Kan
Interplanetary shock characteristics and associated geosynchronous magnetic field variations estimated from sudden impulses observed on the ground.
Total 296 values ​​of the normals to the shock front.
10 - no data on the plasma before front
29 - structure "similar" to the shock front
Eventually set consists of 257 observations
GSE - Geocentric Solar Ecliptic -
X - the line from Earth to the Sun
Z - normal to the ecliptic plane, toward the North
GSM - Geocentric Solar Magnetospheric
Z - the projection axis magnetic dipole on the plane YZ in the GSE
Used 64-second data of ACE. Used a new method for determining the Rankine-Hugoniot relations
(Lin et. Al., 2006).

4. According to the binomial distribution with 95%
Sky plane projection
257 NE NW
For N=257; 2Sigma=0,06
Probabilities
0,52<PN<0,64; average PN=0,58
0,36<РS<0,48; average РS=0,42
0,48<РW<0,60; average РW=0,54
0,40<РE<0,52; average РE=0,46 69 80 50 58 SE SW
The reasons for the asymmetry may be:
1) different activity on the solar surface;
2) asymmetry front surface that forms during its propagation in interplanetary space;
North part nN>0
East part nT>0
If radius of curvature decreases with distance from the central region

5. Interplanetary shock fronts have a characteristic shape.
To derive the shock front shape, we need to introduce some assumptions
Interplanetary shock fronts have a characteristic shape.
The shape of the propagating front is conserved.
The radial component of the vector of the normal along the front changes monotonically.
Random distribution of measurement points on the solid angle is equally probable.

6. We introduce the heliocentric Cartesian coordinate system XOY plane which is located in the plane of the solar equator. The X axis is the axis of axial symmetry of the surface of the shock front. Let us introduce two angles: the angle measured from the X axis, the angle δ is measured in the plane YOZ from the axis Y.
Angular size of a shock front (Cane, Richardson, 2003)
The whole solid angle divided by some sectors y R
Ψmax x
Sun
Earth

7. 2) divide all values into some groups.
1) Since the curvature changes monotonically, we order the values of all radial component of the normal vector in decreasing order
2) divide all values into some groups.
The angle and number of values in each group is defined by the relation
In each group, we compute the mean and standard deviation that define the shape of the front in the XOY plane
Сама модель

8. y ni R βi Ψi x
The angle between the normal and the radius, in each interval is given by
The direction of the reference angle beta will determine which of the shock wave curvature.
Calculation of the shape of the front hold for 3 values:
1) )

9. The derived shape of the front
black lines - the circles given for estimate forms

10. the derived shape is approximated by two parabolas

11. In order to validate the method and the sufficient number of measurements to determine the shape of the surface we solve the problem using Monte Carlo simulation.
1) we set the shape of the shock;
2) we define the components of the vector normal for random points on the surface of the shock ;
3) using developed method, we obtain the surface shape.
Green line – define shape, cyan points – random points, red line – obtain shape.

12. Comparison of the calculated variant form of the front IS - Lario D
Comparison of the calculated variant form of the front IS - Lario D., Sanahuja B. and Heras A. M. / / Astrophys. J. 509, 1, 415 (1998).
with the appropriate cross section of the front.
As you can see, the form of the fronts are in good agreement.

13. Conclusion.
A new method for determining the shape of the front of interplanetary shock wave using a set of measurements of components of the shock normal. The large-scale asymmetry of the surface front is estimated. The typical front shape has been obtained. Adequacy of the method is proved by Monte–Carlo method.