[Paper Review] The beginning of nonlinear stage of evolution of protostars at $ z=20

В. К. Дубрович|arXiv (Cornell University)|May 11, 2018

Astrophysics and Star Formation Studies3 citations

TL;DR

This paper proposes that the absorption signal detected by the EDGES experiment at z≈20 arises from the onset of nonlinear compression in primordial protostars, driven by self-gravity increasing photon path length and optical depth. The mechanism relies on velocity gradients in collapsing density fluctuations, with a predicted protostar mass of ~10⁴ M☉, explaining the observed 0.5 K absorption depth without requiring Lyman-α radiation or X-ray emission.

ABSTRACT

The results of the EDGES (Experiment to Detect the Global EoR Signature) experiment (Bowman et al., 2018) is interpreted as the beginning of compression stage of primary density fluctuations in a mini halo. Estimates of the mass of these objects are given.

Motivation & Objective

• To explain the EDGES experiment's unexpected 21 cm absorption signal at z≈20, which predates the formation of first stars.
• To investigate whether the observed absorption depth can be explained by nonlinear dynamics in primordial density fluctuations before star formation.
• To determine the mass and physical conditions of protostars at the onset of gravitational collapse, independent of Lyman-α or X-ray emission.
• To assess the role of velocity gradients and metric evolution in enhancing optical depth during the early nonlinear stage of protostar formation.

Proposed method

• Uses the standard 21 cm brightness temperature formula (Eq. 1) but extends it to include non-uniform velocity gradients from self-gravitating fluctuations.
• Models the effective photon path length (L_max) as a function of velocity gradient and compression dynamics, increasing optical thickness.
• Estimates the amplification factor K = L_max / L_D using observed depth (0.5 K) and theoretical baseline (0.1–0.2 K) to infer required mass enhancement.
• Applies the Dicke narrowing effect via Doppler broadening and integrates over line-of-sight fluctuations assuming a duty cycle of ~0.5.
• Considers the transition from Hubble expansion to gravitational compression, where velocity gradients shift from Hubble-like to compressive.
• Uses numerical estimates at z≈20 with ρ₀≈2×10⁻²⁵ g/cm³ and t₀≈5×10⁻¹⁵ s to derive characteristic scales and masses.

Experimental results

Research questions

• RQ1 Can the EDGES 21 cm absorption signal at z≈20 be explained by the onset of gravitational compression in protostars without invoking early stellar feedback?
• RQ2 What is the required mass scale of protostars to produce the observed 0.5 K absorption depth via enhanced optical depth?
• RQ3 How do velocity gradients and metric evolution during nonlinear collapse affect the effective path length of 21 cm photons?
• RQ4 Why is the absorption signal observed at z≈20, earlier than expected for Lyman-α or X-ray-driven mechanisms?
• RQ5 Is the observed line shape consistent with the dynamics of sound-wave-driven, self-gravitating fluctuations in the early universe?

Key findings

• The observed 0.5 K absorption depth in the EDGES signal can be explained by a 10-fold increase in effective photon path length due to velocity gradient changes during early collapse.
• The required amplification factor K ≈ 5–10 is achieved when the protostar mass reaches approximately 10⁴ M☉, based on K³ scaling from the baseline mass M_D ≈ 100 M☉.
• The redshift of z≈20 corresponds to the onset of nonlinear compression, where Hubble expansion is balanced by self-gravity, leading to reduced velocity gradients and longer photon paths.
• The blue wing of the absorption line forms due to the initiation of active compression and increasing velocity gradients, while the red wing forms during deceleration.
• The mechanism is independent of Lyman-α radiation or X-ray emission, making it applicable before the era of first stars.
• The model predicts that fluctuations with a duty cycle of ~0.5 and uniform coverage of the sky naturally lead to a coherent, deep absorption feature without requiring cold matter or exotic physics.