Bifurcation of Magnetic Field Topology Detected in Magnetospheric Multiscale (MMS) Mission in 19 September 2015 Event.

Magnetic nulls, that r eferred to a region with vanishing magnetic fields , play an important role in an energy conversion and a particle acceleration during a magnetic reconnection. Moreover, they determine magnetic field topologies, if the nulls are hyperbolic inn the system (Hartman-Grobman) Theorem. In this report, we use the linear interpolation to determine null positions of the dayside reconnection in an electron diffusion region (EDR) on September 19, 2015. The eigenvalues of these nulls determine the local magnetic field topology. In this event, we detect the local magnetic field bifurcation observing the change of eigenvalue from three real values to one complex conjugate and one real values when the null crosses one of tetrahedron boundary cells. Surprisingly, this exactly coincide with the theory to observe the null in linear approximation. This bifurcation is also evidenced by measuring the topology distances between two nulls that are just before and after the bifurcation using the earth mover's distance (EMD). We report the first in situ measurement where a magnetic null crosses the MMS tetrahedron and observed its local magnetic field bifurcation when its exits from one of four tetrahedral boundary cells.