Cloud evolution for various metallicities is investigated by three-dimensional nested grid simulations , in which the initial ratio of rotational to gravitational energy of the host cloud \beta _ { 0 } ( = 10 ^ { -1 } – 10 ^ { -6 } ) and cloud metallicity Z ( = 0 – Z _ { \odot } ) are parameters .
Starting from a central number density of n _ { c } = 10 ^ { 4 } { cm } ^ { -3 } , cloud evolution for 48 models is calculated until the protostar is formed ( n _ { c } \simeq 10 ^ { 23 } { cm } ^ { -3 } ) or fragmentation occurs .
The fragmentation condition depends both on the initial rotational energy and cloud metallicity .
Cloud rotation promotes fragmentation , while fragmentation tends to be suppressed in clouds with higher metallicity .
Fragmentation occurs when \beta _ { 0 } > 10 ^ { -3 } in clouds with solar metallicity ( Z = Z _ { \odot } ) , while fragmentation occurs when \beta _ { 0 } > 10 ^ { -5 } in the primordial gas cloud ( Z = 0 ) .
Clouds with lower metallicity have larger probability of fragmentation , which indicates that the binary frequency is a decreasing function of cloud metallicity .
Thus , the binary frequency at the early universe ( or lower metallicity environment ) is higher than at present day ( or higher metallicity environment ) .
In addition , binary stars born from low-metallicity clouds have shorter orbital periods than those from high-metallicity clouds .
These trends are explained in terms of the thermal history of the collapsing cloud .