We develop a new method to constrain the physical conditions in the cool ( \sim 10 ^ { 4 } { K } ) circumgalactic medium ( CGM ) from measurements of ionic column densities , by assuming that the cool CGM spans a large range of gas densities and that small high-density clouds are hierarchically embedded in large low-density clouds .
The new method combines the information available from different sightlines during the photoionization modeling , thus yielding tighter constraints on CGM properties compared to traditional methods which model each sightline individually .
Applying this new technique to the COS-Halos survey of low-redshift \sim L ^ { * } galaxies , we find that we can reproduce all observed ion columns in all 44 galaxies in the sample , from the low-ions to O vi , with a single universal density structure for the cool CGM .
The gas densities span the range 50 \lesssim \rho / { \bar { \rho } _ { b } } \lesssim 5 \times 10 ^ { 5 } ( { \bar { \rho } _ { b } } is the cosmic mean ) , while the physical size of individual clouds scales as \sim \rho ^ { -1 } , from \approx 35 { kpc } of the low density O vi clouds to \approx 6 { pc } of the highest density low-ion clouds .
The deduced cloud sizes are too small for this density structure to be driven by self-gravity , thus its physical origin is unclear .
The implied cool CGM mass within the virial radius is ( 1.3 \pm 0.4 ) \times 10 ^ { 10 } { M _ { \odot } } ( \sim 1 % of the halo mass ) , distributed rather uniformly over the four decades in density .
The mean cool gas density profile scales as R ^ { -1.0 \pm 0.3 } , where R is the distance from the galaxy center .
We construct a 3D model of the cool CGM based on our results , which we argue provides a benchmark for the CGM structure in hydrodynamic simulations .
Our results can be tested by measuring the coherence scales of different ions .