Super Star Cluster Wind Calculator

Calculates properties of the super star cluster wind taking into account radiative cooling. The calculator solves equations given by Silich et al. (2004) Tenorio-Tagle et al. (2007) and Silich et al. (2008). The model is based on the following assumptions introduced by Chevalier & Clegg (1985) (CC85). Stars are uniformly distributed in the cluster of the radius R_SC, their winds and the mass ejected by supernova explosions collide, the mechanical energy is thermalized and the hot medium inside the cluster is formed. A difference between the high pressure inside the cluster and the zero pressure in infinity drives the SSC wind. Therefore, CC85 model the cluster as a sphere of the radius R_SC into which energy and mass are inserted uniformly at rates L_SC and dM_SC, respectively. The fundamental property of the wind solution (and necessary condition for the existence of the stationary solution) is that the wind velocity reaches the sound speed exactly at the cluster border.

The adiabatic terminal velocity of the wind v_inf = (2L_SC / dM_SC)^1/2 is used instead of dM_SC as a parameter in this model as it is more convenient. Since it is unknown how much of the mechanical energy is radiated away in the shock-shock collisions and how much is converted into the thermal energy of the ISM inside the cluster, we introduce a parameter eta which denotes the latter fraction.

Three wind regimes

The parameter space of the presented wind model is divided by the line (or hyper-surface depending on how many parameters we consider) of the critical luminosity Lcrit. According to the position of the model with respect to Lcrit, the wind evolves in one of the three qualitatively different regimes: quasi-adiabatic, radiative and bimodal. The quasi-adiabatic regime occurs if the cluster mechanical luminosity LSC is well below Lcrit. The wind density, temperature and velocity follow almost exactly the CC85 solution. If LSC approaches Lcrit, but stays below it, the wind cools down to 104 K and below at a certain distance from the cluster. This behaviour is called the radiative regime. The wind evolves in the bimodal regime if LSC > Lcrit. The cluster is divided into two regions by the stagnation radius Rst. In the outer part, the stationary wind exists starting with zero velocity at the stagnation radius and reaching the sound speed at the cluster border. In the central region, the inserted gas becomes thermally unstable and warm dense clumps are formed.

Downloads

References

Chevalier, R. A., Clegg, A. W., 1985, Nature, 317, 44

Silich, S., Tenorio-Tagle, G., Rodríguez-González, A., 2004, ApJ, 610, 226

Tenorio-Tagle, G., Wünsch, R., Silich, S., Palouš, J., 2007, ApJ, 658, 1196

Wünsch, R., Silich, S., Palouš, J., Tenorio-Tagle, G., 2007, A&A, 471, 579

Silich, S., Tenorio-Tagle, G., Hueyotl-Zahuantitla, F., 2008, ApJ, 686, 172

Wünsch, R., Tenorio-Tagle, G., Palouš, J., Silich, S., 2008, ApJ, 683, 683

Tenorio-Tagle, G., Wünsch, R., Silich, S., Muñoz-Tuñón, C., Palouš, J., 2010, ApJ, 708, 1621

Silich, S., Tenorio-Tagle, G., Muñoz-Tuñón, C., Hueyotl-Zahuantitla, F., Wünsch, R., Palouš, J., 2010, ApJ, 711, 25

Hueyotl-Zahuantitla, F., Tenorio-Tagle, G., Wünsch, R., Silich, S., Palouš, J., 2010, ApJ, 716, 324