We present a series of 2-dimensional ( r, \phi ) hydrodynamic simulations of marginally self gravitating ( M _ { D } / M _ { * } =0.2 , with M _ { * } = 0.5 M _ { \odot } and with disk radius R _ { D } = 50 and 100 AU ) disks around protostars using a Smoothed Particle Hydrodynamic ( SPH ) code .
We implement simple and approximate prescriptions for heating via dynamical processes in the disk .
Cooling is implemented with a simple radiative cooling prescription which does not assume that local heat dissipation exactly balances local heat generation .
Instead , we compute the local vertical ( z ) temperature and density structure of the disk and obtain ‘ photosphere temperature ’ , which is then used to cool that location as a black body .
We synthesize spectral energy distributions ( SEDs ) for our simulations and compare them to fiducial SEDs derived from observed systems , in order to understand the contribution of dynamical evolution to the observable character of a system .

We find that these simulations produce less distinct spiral structure than isothermally evolved systems , especially in approximately the inner radial third of the disk .
Pattern amplitudes are similar to isothermally evolved systems further from the star but do not collapse into condensed objects .
We attribute the differences in morphology to increased efficiency for converting kinetic energy into thermal energy in our current simulations .
Our simulations produce temperatures in the outer part of the disk which are very low ( \sim 10 K ) .
The radial temperature distribution of the disk photosphere is well fit to a power law with index q \sim 1.1 .
Far from the star , corresponding to colder parts of the disk and long wavelength radiation , known internal heating processes ( PdV work and shocks ) are not responsible for generating a large fraction of the thermal energy contained in the disk matter .
Therefore gravitational torques responsible for such shocks can not transport mass and angular momentum efficiently in the outer disk .

Within \sim 5–10 AU of the star , rapid break up and reformation of spiral structure causes shocks , which provide sufficient dissipation to power a larger fraction of the near infrared radiated energy output .
In this region , the spatial and size distribution of grains can have marked consequences on the observed near infrared SED of a given disk , and can lead to increased emission and variability on \lesssim 10 year time scales .
The inner disk heats to the destruction temperature of dust grains .
Further temperature increases are prevented by efficient cooling when the hot disk midplane is exposed .
When grains are vaporized in the midplane of a hot region of the disk , we show that they do not reform into a size distribution similar to that from which most opacity calculations are based .
With rapid grain reformation into the original size distribution , the disk does not emit near infrared photons .
With a plausible modification of the opacity , it contributes much more .