We fit an isothermal oscillatory density model to the outer disk of TW Hya in which planets have presumably already formed and they are orbiting within four observed dark gaps .
At first sight , this 52 AU small disk does not appear to be similar to our solar nebula ; it shows several physical properties comparable to those in HL Tau ( size R _ { max } = 102 AU ) and very few similarities to AS 209 ( R _ { max } = 144 AU ) .
We find a power-law density profile with index k = -0.2 ( radial densities \rho ( R ) \propto R ^ { -1.2 } ) and centrifugal support against self-gravity so small that it virtually guarantees dynamical stability for millions of years of evolution to come .
Compared to HL Tau , the scale length R _ { 0 } and the core size R _ { 1 } of TW Hya are smaller only by factors of \sim 2 , reflecting the disk ’ s half size .
On the opposite end , the Jeans frequency \Omega _ { J } and the angular velocity \Omega _ { 0 } of the smaller core of TW Hya are larger only by factors of \sim 2 .
The only striking difference is that the central density ( \rho _ { 0 } ) of TW Hya is 5.7 times larger than that of HL Tau , which is understood because the core of TW Hya is only half the size ( R _ { 1 } ) of HL Tau and about twice as heavy ( \Omega _ { J } ) .
In the end , we compare the protostellar disks that we have modeled so far .