DigiMat: Physical Gravitational Collapse

We continue our DigiMat study of star formation by gravitational collapse into a high density hot spot. 

 

In a fluid at rest without self gravitation a hot spot cannot develop without external forcing by transfer of energy from a cold surrounding. This is because without forcing, heat energy can only transfer from hot to cold, by the 2nd law of thermodynamics.  

We now ask if in a fluid with self gravitation a hot spot can develop by surrounding cooling. We use DigiMat to give an answer: We thus simulate the motion of a fluid with self gravitation starting with the fluid at rest with constant  density, temperature and internal energy, assuming periodic boundary conditions for fluid variables. We set the gravitational potential to zero at the boundary and thus create a gravitational force directed to the center of the domain. Here is the result at a certain time:

What do we see? We see (crosscut of) central accumulation of mass/density (blue) combined with central heating and far-away cooling given by temperature (green), with black line the initial distribution. We thus effectively see a transfer of heat energy from cold to hot. This transfer is accomplished by gravitation, which from an initial state with zero fluid velocity attracts the fluid towards the center thereby increasing kinetic energy there, which then is transfered into heat energy as pressure finally retards the flow (and reverses the flow into expansion). 

We thus find that the presence of a gravitational field can be viewed as a form of external forcing making possible transfer of heat energy from cold to warm. Gravitational collapse thus appears possible thermodynamically.   

Gravitational collapse with transfer of heat energy from a cold exterior to a hot interior fits with the observation of interstellar dust at low temperture, about 20 K. The price of shining stars is chilly space between stars, by conservation of total energy.