in Fig. 1 for two fixed values of the densities: $N=10^{30} cm^{-3}$ and $N=10^{32} cm^{-3}$, respectively. These high boson densities may be assumed for compact objects. The values of the critical temperatures (the dotted lines that separate the region where the BEC appears from that where there is no BEC) are in the range of $T=10^7-10^9$ K which are also typical of compact objects. We can see from the graphics how $T_{cond}$ grows with the augment of the density and diverges when $b\rightarrow1$ ($B\rightarrow B_c$).

![\[fig5\] The phase diagram in the $T-b$ space for different values of particle density. The black dashed lines are the critical curves that separates the region of $T$ and $b$ when there is condensate (light gray region) from the region in which there is not (dark gray region). Note that the critical line also depends on the particle density.](dfases1.eps "fig:"){width="0.49\linewidth"} ![\[fig5\] The phase diagram in the $T-b$ space for different values of particle density. The black dashed lines are the critical curves that separates the region of $T$ and $b$ when there is condensate (light gray region) from the region in which there is not (dark gray region). Note that the critical line also depends 