The protostellar jets driven by the formation of the first stars are studied by using three-dimensional magnetohydrodynamical ( MHD ) nested grid simulations .
Starting from a slowly rotating spherical cloud of 5.1 \times 10 ^ { 4 } \thinspace M _ { \odot } permeated by a uniform magnetic field , we follow the evolution from the central number density n _ { c } = 10 ^ { 3 } { cm } ^ { -3 } ( where the radius of the object r = 6.6 pc ) to n _ { c } \simeq 10 ^ { 23 } { cm } ^ { -3 } ( r \simeq 1 \thinspace R _ { \odot } ) .
We resolve the cloud structure more than 8 orders of magnitude in spatial extent and 20 orders in density contrast .
We calculate four models that differ in initial magnetic field strengths and angular velocities .
In all models , protostars of \simeq 10 ^ { -3 } \thinspace M _ { \odot } are formed at n _ { c } \simeq 10 ^ { 22 } { cm } ^ { -3 } in accordance with one-dimensional calculations .
By this epoch , the magnetic flux density is amplified by 10 orders of magnitude from the initial value .
Consequently , the formed protostar possesses the magnetic field of \sim 10 ^ { 6 } G that is much larger than the flux density of the present counterparts , reflecting the fact that the dissipation of a magnetic field is ineffective in primordial gas clouds .
If the initial magnetic field B > 10 ^ { -9 } ( n _ { c } / 10 ^ { 3 } { cm } ^ { -3 } ) ^ { 2 / 3 } { G } , the protostellar jet is launched and its velocities reaches \sim 70 km s ^ { -1 } by the time the protostellar mass becomes ( 4 - 6 ) \times 10 ^ { -3 } \thinspace M _ { \odot } , and a fraction ( 3 - 10 \% ) of the accreting matter is blown off from the central region .
Owing to the interaction of these ejecta with surrounding matter , expanding bow shocks are created at both heads of the jet .
If this jet continues to sweep out the surrounding gas that otherwise accretes onto the central star or circumstellar disk , the final mass of the first star can be substantially reduced .
In addition , dense post-shock regions behind the bow shocks are expected to promote the chemical reactions ( formation of H _ { 2 } and HD ) , and this provides possible environments for subsequent low-mass star formation in the early universe .