We present a detailed analysis of the partial coverage of the Q 1232+082 ( z _ { em } = 2.57 ) broad line region by an intervening H _ { 2 } -bearing cloud at z _ { abs } = 2.3377 .
Using curve of growth analysis and line profile fitting , we demonstrate that the H _ { 2 } -bearing component of the cloud covers the QSO intrinsic continuum source completely but only part of the Broad Line Region ( BLR ) .
We find that only 48 \pm 6 % of the C iv BLR emission is covered by the C i absorbing gas .
We observe residual light ( \sim 6 % ) as well in the bottom of the O i \lambda 1302 absorption from the cloud , redshifted on top of the QSO Lyman- \alpha emission line .
Therefore the extent of the neutral phase of the absorbing cloud is not large enough to cover all of the background source .
The most likely explanation for this partial coverage is the small size of the intervening cloud , which is comparable to the BLR size .
We estimate the number densities in the cloud : n _ { H _ { 2 } } \sim 110 cm ^ { -3 } for the H _ { 2 } -bearing core and n _ { H } \sim 30 cm ^ { -3 } for the neutral envelope .
Given the column densities , N ( H _ { 2 } ) = 3.71 \pm 0.97 \times 10 ^ { 19 } cm ^ { -2 } and N ( H i ) = 7.94 \pm 1.6 \times 10 ^ { 20 } cm ^ { -2 } , we derive the linear size of the H _ { 2 } -bearing core and the neutral envelope along the line of sight to be l _ { H _ { 2 } } \sim 0.15 ^ { +0.05 } _ { -0.05 } pc and l _ { HI } \sim 8.2 ^ { +6.5 } _ { -4.1 } pc , respectively .
We estimate the size of the C iv BLR by two ways ( i ) extrapolating size - luminosity relations derived from reverberation observations and ( ii ) assuming that the H _ { 2 } -bearing core and the BLR are spherical in shape and the results are \sim 0.26 and \sim 0.18 pc , respectively .
The large size we derive for the extent of the neutral phase of the absorbing cloud together with a covering factor of \sim 0.94 of the Lyman- \alpha emission means that the Lyman- \alpha BLR is probably fully covered but that the Lyman- \alpha emission extends well beyond the limits of the BLR .