Tachyon stars

We consider a self-gravitating body composed of ideal Fermi gas of tachyons at zero temperature. The Oppenheimer-Volkoff equation is solved for various central densities and various tachyon mass parameter $m$. Although a pure tachyon star has finite mass, it cannot occur in nature because the equilibrium condition P=0 and the causality condition cannot be satisfied simultaneously. A stable configuration with tachyon content must be covered with a non-tachyon envelope. The boundary between the tachyon core and the envelope is determined by the critical pressure $P_T$, which depends on the tachyon mass $m$. The tachyon core is dominant and its mass can exceed many times the solar mass $M_{\odot}$ when $m$ is much smaller than the nucleon mass $m_p$, while at large $m$ compared with $m_p$, the main contribution to the total stellar mass is due to the envelope whose material determines the parameters of the whole star. However, the parameters of the tachyon core do not depend on the envelope material. When the tachyon core appears, its mass $M_T$ and radius $r_T$ grow up with increasing central density until maximum values are reached, after which the mass and radius slowly decrease. The redshift at the surface of the tachyon core does not depend on $m$ and never exceeds $z_{\max}\simeq 0.3$. The maximum mass of tachyon core and its maximum radius are achieved at certain central density and obey universal formulas $M_{T\max}/M_{\odot}=0.52m_p^2/m^2$ and $r_{T\max}=4.07m_p^2/m^2$ [km] that allow to estimate arbitrary supermassive tachyonic bodies at the cosmological scale.