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We assume a single population of {\Lya} absorbing structures $(z \sim 2)$ and simulate physical quantities measurable in the spectra of double line of sight (DLOS) quasars having various separations. We present four tests designed for diagnosing absorber mass distributions (smooth or irregular), geometries (spherical or slab--like), and kinematics (isotropic or rotational velocities).
The overall mass distribution can be inferred from the neutral {\HI} column density ($N_H$) distributions of lines coincident in both LOS. The $N_H$ distributions for lines not coincident in both LOS (anticoincidences) provide diagnostics for both the mass distribution and geometry. The distributions of line of sight velocity differences between coincident lines are strongly dependent upon the kinematics. Comparison of velocity dispersions along a single line of sight to the {\sc RMS} differences between widely separated DLOS provides supporting information for determining absorber geometries.
Comparing to existing data, we find that: (1)~The observed $N_H$ distributions of coincident lines are correlated, with an increasing scatter with DLOS separation, consistent with smooth absorber mass distributions. (2)~For smooth spherical structures (ie.~mini--halo like), the $N_H$ distributions for anticoincident lines should exhibit sharp cut--offs at small $N_H$. Thus the observed large anticoincident $N_H$ are not consistent with a single population of smooth spherical absorbers. (3)~The {\sc RMS} values of velocity differences between coincident lines increase with DLOS separation as expected for rotating disk--like absorbers. (4)~The observed velocity dispersion along a single line of sight is small compared to the {\sc RMS} difference between widely separated lines of sight. This is inconsistent with models in which absorption is produced by cloudlets moving isotropically within a spherical structure.
Overall, only a smooth, rotating slab--like model remains consistent with the inferred properties of a single population of {\Lya} absorbers.
