On the formation age of the first planetary system

Abstract

Recently, it has been observed the extreme metal-poor stars in the Galactic halo, which must be formed just after Pop III objects. On the other hand, the first gas clouds of mass ∼ 10⁶ M⊙ are supposed to be formed at z ∼ 10, 20, and 30 for the 1σ, 2σ and 3σ, where the density perturbations are assumed of the standard ΛCDM cosmology. Usually it is approximated that the distribution of the density perturbation amplitudes is gaussian where σ means the standard deviation. If we could apply this gaussian distribution to the extreme small probability, the gas clouds would be formed at z ∼40, 60, and 80 for the 4σ, 6σ, and 8σ where the probabilities are approximately 3 × 10⁻⁵, 10⁻⁹, and 10⁻¹⁵. Within our universe, there are almost ∼ 10¹⁶ (∼ 10²²M⊙/10⁶M⊙) clouds of mass 10⁶M⊙. Then the first gas clouds must be formed around z ∼ 80, where the time is ∼ 20 Myr (∼ 13.7/(1 + z)^3/2 Gyr). Even within our galaxy, there are ∼ 10⁵ (∼ 10¹¹M⊙/10⁶M⊙) clouds, then the first gas clouds within our galaxy must be formed around z ∼ 40, where the time is ∼ 54 Myr (∼ 13.7/(1+z)^3/2Gyr).

The evolution time for massive star (∼ 10²M⊙) is ∼ 3 Myr and the explosion of the massive supernova distributes the metal within a cloud. The damping time of the supernova shock wave in the adiabatic and isothermal era is several Myr and stars of the second generation (Pop II) are formed within a free fall time ∼ 20 Myr. Even if the gas cloud is metal poor, there is a lot of possibility to form the planets around such stars. The first planetary systems could be formed within ∼ 6 × 10⁷ years after the Big Bang in the universe. Even in our galaxies, the first planetary systems could be formed within ∼ 1.7 × 10⁸ years. If the abundance of heavy elements such as Fe is small compared to the elements of C, N, O, the planets must be the one where the rock fraction is small. It is interesting to wait the observations of planets around metal-poor stars. For the panspermia theory, the origin of life could be expected in such systems.