Fragmentation and binary formation processes are studied using three-dimensional resistive MHD nested grid simulations .
Starting with a Bonnor-Ebert isothermal cloud rotating in a uniform magnetic field , we calculate the cloud evolution from the molecular cloud core ( n = 10 ^ { 4 } { cm } ^ { -3 } ) to the stellar core ( n \simeq 10 ^ { 22 } { cm } ^ { -3 } ) , where n denotes the central density .
We calculated 147 models with different initial magnetic , rotational , and thermal energies , and the amplitudes of the non-axisymmetric perturbation .
In a collapsing cloud , fragmentation is mainly controlled by the initial ratio of the rotational to the magnetic energy , regardless of the initial thermal energy and amplitude of the non-axisymmetric perturbation .
When the clouds have large rotational energies in relation to magnetic energies , fragmentation occurs in the low-density evolution phase ( 10 ^ { 12 } { cm } ^ { -3 } \lesssim n \lesssim 10 ^ { 15 } { cm } ^ { -3 } ) with separations of 3–300 AU .
Fragments that appeared in this phase are expected to evolve into wide binary systems .
On the other hand , fragmentation does not occur in the low-density evolution phase , when initial clouds have large magnetic energies in relation to the rotational energies .
In these clouds , fragmentation only occurs in the high-density evolution phase ( n \gtrsim 10 ^ { 17 } { cm } ^ { -3 } ) after the clouds experience significant reduction of the magnetic field owing to Ohmic dissipation in the period of 10 ^ { 12 } { cm } ^ { -3 } \lesssim n \lesssim 10 ^ { 15 } { cm } ^ { -3 } .
Fragments appearing in this phase have separations of \lesssim 0.3 AU , and are expected to evolve into close binary systems .
As a result , we found two typical fragmentation epochs , which cause different stellar separations .
Although these typical separations are disturbed in the subsequent gas accretion phase , we might be able to observe two peaks of binary separations in extremely young stellar groups .