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HI column density statistics of the cold neutral medium from absorption studies

Physical properties of the tiny scale structures in the cold neutral medium (CNM) of galaxies is a long-standing puzzle. Only a few lines of sights in our Galaxy have been studies with mixed results on the scale-invariant properties of such structures. Moreover, since these studies measure the variation of neutral hydrogen optical depth, they do not directly constrain the density structures. In this letter, we investigate the possibility of measuring the properties of density and spin temperature structures of the \HI from absorption studies of \HI. Our calculations show that irrespective of the thermal properties of the clouds, the scale structure of the \HI column density can be estimated, whereas, \HI absorption studies alone cannot shed much light on either the amplitude of the density fluctuations and their temperature structures. Detailed methodology and calculations with some fiducial examples are presented.