Early structure formation from primordial density fluctuations with a blue-tilted power spectrum

TL;DR

This study investigates how a blue-tilted primordial power spectrum influences early structure formation, leading to the formation of massive stars at very high redshifts, which could impact our understanding of the first stars and black holes.

Contribution

It demonstrates through simulations that a blue-tilted PPS causes early formation of massive stars and black holes at redshifts above 100, highlighting the importance of small-scale power spectrum shape.

Findings

Star-forming gas clouds form at z > 100 in models with m_s > 1.

Gas clouds remain hot and gravitationally contract without efficient cooling.

Massive stars and black holes may originate from these early hot clouds.

Abstract

While observations of large-scale structure and the cosmic microwave background (CMB) provide strong constraints on the amplitude of the primordial power spectrum (PPS) on scales larger than 10~Mpc, the amplitude of the power spectrum on sub-galactic length scales is much more poorly constrained. We study early structure formation in a cosmological model with a blue-tilted PPS. We assume that the standard scale-invariant PPS is modified at small length scales as $P(k) \sim k^{m_{\rm s}}$ with $m_{\rm s} > 1$. We run a series of cosmological hydrodynamic simulations to examine the dependence of the formation epoch and the characteristic mass of primordial stars on the tilt of the PPS. In models with $m_{\rm s} > 1$, star-forming gas clouds are formed at $z > 100$, when formation of hydrogen molecules is inefficient because the intense CMB radiation destroys chemical intermediates. Without efficient coolant, the gas clouds gravitationally contract while keeping a high temperature. The protostars formed in such "hot" clouds grow very rapidly by accretion to become extremely massive stars that may leave massive black holes with a few hundred solar-masses at $z > 100$. The shape of the PPS critically affects the properties and the formation epoch of the first generation of stars. Future experiments of the CMB polarization and the spectrum distortion may provide important information on the nature of the first stars and their formation epoch, and hence on the shape of the small-scale power spectrum.