Ions and electrons play an important role in various stages of the star formation process .
By following the magnetic field of their environment and interacting with neutral species , they slow down the gravitational collapse of the proto-star envelope .
This process ( known as ambipolar diffusion ) depends on the ionisation degree , which can be derived from the HCO ^ { + } abundance .
We present a study of HCO ^ { + } and its isotopologues ( H ^ { 13 } CO ^ { + } , HC ^ { 18 } O ^ { + } , DCO ^ { + } , and D ^ { 13 } CO ^ { + } ) in the low-mass proto-star IRAS16293 - 2422 .
The structure of this object is complex , and the HCO ^ { + } emission arises from the contribution of a young NW-SE outflow , the proto-stellar envelope and the foreground cloud .
We aim at constraining the physical parameters of these structures using all the observed transitions .
For the young NW-SE outflow , we derive T _ { kin } = 180 - 220 K and n ( { H _ { 2 } } ) = ( 4 - 7 ) \times 10 ^ { 6 } cm ^ { -3 } with an HCO ^ { + } abundance of ( 3 - 5 ) \times 10 ^ { -9 } .
Following previous studies , we demonstrate that the presence of a cold ( T _ { kin } \leqslant 30 K ) and low density ( n ( { H _ { 2 } } ) \leqslant 1 \times 10 ^ { 4 } cm ^ { -3 } ) foreground cloud is also necessary to reproduce the observed line profiles .
We have used the gas-grain chemical code nautilus to derive the HCO ^ { + } abundance profile across the envelope and the external regions where X ( HCO ^ { + } ) \gtrsim 1 \times 10 ^ { -9 } dominate the envelope emission .
From this , we derive an ionisation degree of 10 ^ { -8.9 } \lesssim x ( e ) \lesssim 10 ^ { -7.9 } .
The ambipolar diffusion timescale is \sim 5 times the free-fall timescale , indicating that the magnetic field starts to support the source against gravitational collapse and the magnetic field strength is estimated to be 6 - 46 \mu G .