We present numerical experiments aimed to study the correlation between the magnetic field strength , B , and the density , n , in the cold atomic interstellar medium ( CNM ) .
We analyze 24 magneto-hydrodynamic models with different initial magnetic field intensities ( B _ { 0 } = 0.4 , 2.1 , 4.2 , and 8.3 \mu G ) and/or mean densities ( 2 , 3 , and 4 cm ^ { -3 } ) , in the presence of driven and decaying turbulence , with and without self-gravity , in a cubic computational domain with 100 pc by side .
Our main findings are : i ) For forced simulations , which reproduce the main observed physical conditions of the CNM in the Solar neighborhood , a positive correlation between B and n develops for all the B _ { 0 } values .
ii ) The density at which this correlation becomes significant ( \lesssim 30 cm ^ { -3 } ) depends on B _ { 0 } but is not sensitive to the presence of self-gravity .
iii ) The effect of self-gravity , when noticeable , consists of producing a shallower correlation at high densities , suggesting that , in the studied regime , self-gravity induces motions along the field lines .
iv ) Self-gravitating decaying models where the CNM is subsonic and sub-Alfvénic with \beta \lesssim 1 develop a high density positive correlation whose slopes are consistent with a constant \beta ( n ) .
v ) Decaying models where the low density CNM is subsonic and sub-Alfvénic with \beta > 1 show a negative correlation at intermediate densities , followed by a high density positive correlation .