[Paper Review] Galactic Disk Formation and the Angular Momentum Problem

Andreas Burkert|ArXiv.org|Aug 10, 2009

Galaxies: Formation, Evolution, Phenomena2 references3 citations

TL;DR

This paper investigates the angular momentum problem in galactic disk formation, proposing that high-redshift disk galaxies with high gas velocity dispersions (40–80 km/s) and turbulent dynamics achieve stable, compact disks through gravitational instability-driven turbulence that regulates gas cooling and angular momentum loss. The key result is that viscous timescales matching star formation timescales (≈10^9 years) in z≈2 disks imply a self-regulated cycle linking turbulence, star formation, and secular evolution, resolving the discrepancy between observed compact disks and theoretical predictions based on spin parameters.

ABSTRACT

Galactic disk formation requires knowledge about the initial conditions under which disk galaxies form, the boundary conditions that affect their secular evolution and the micro-physical processes that drive the multi-phase interstellar medium and regulate their star formation history. Most of these ingredients are still poorly understood. Recent high-resolution observations of young high-redshift disk galaxies provide insight into early phases of galactic disk formation and evolution. Combined with low-redshift disk data these observations should eventually allow us to reconstruct the origin and evolution of late-type galaxies. I summarize some of the major problems that need to be addressed for a more consistent picture of galactic disk formation and evolution.

Motivation & Objective

• To resolve the cosmological angular momentum problem in disk galaxy formation, where observed disk sizes are smaller than predicted by standard spin parameters.
• To understand the origin of compact, high-redshift disk galaxies with high gas velocity dispersions (40–80 km/s) and their evolutionary link to local late-type spirals.
• To investigate how turbulence, gravitational instabilities, and viscous evolution regulate angular momentum redistribution and star formation in disks.
• To reconcile discrepancies between theoretical models (e.g., λ′ ≈ 0.035) and observations (λ′ ≈ 0.025) in low-redshift disks and high-redshift systems.
• To determine whether feedback, clumpiness, and numerical resolution in simulations can be corrected to produce realistic, large-scale disks.

Proposed method

• Uses the spin parameter λ′ = J / (√2 M_vir V_vir R_vir) to relate halo angular momentum to disk scale length R_d via R_d ≈ 8(λ′/0.035)(H₀/H)(v_max/200 km/s) kpc.
• Applies the viscous timescale model τ_visc = (1/α)(v_rot/σ)² τ_orb, with α ≈ 1, to estimate angular momentum transport in disks.
• Compares observed disk properties (R_d, v_max, σ) from low-redshift (Courteau 1997) and high-redshift (SINS) samples to theoretical predictions.
• Employs the Toomre Q parameter (Q ≈ 1) to model gravitational instability as the driver of turbulence and velocity dispersion in high-redshift disks.
• Analyzes the correlation between gas surface density and orbital timescale via Σ_g ∼ τ_orb^−2.5, linking kinematics to star formation efficiency.
• Evaluates the role of feedback, clumping, and numerical resolution in simulations to explain catastrophic angular momentum loss in disk formation.

Experimental results

Research questions

• RQ1 Why do observed disk scale lengths in low-redshift galaxies imply a lower spin parameter (λ′ ≈ 0.025) than theoretical predictions (λ′ ≈ 0.035)?
• RQ2 How can high-redshift disk galaxies with high velocity dispersions (σ ≈ 40–80 km/s) form compact, stable disks despite high turbulence?
• RQ3 What is the role of gravitational instability and turbulence in regulating angular momentum loss and star formation timescales in z≈2 disks?
• RQ4 Why do simulations often fail to produce large, late-type disks due to artificial angular momentum transfer and numerical resolution issues?
• RQ5 How do viscous evolution and star formation timescales co-evolve in high-redshift disks to maintain stability and disk structure?

Key findings

• The observed correlation between disk scale length and maximum rotational velocity in low-redshift galaxies is best fit by a spin parameter of λ′ ≈ 0.025, indicating average angular momentum loss during infall.
• High-redshift SINS galaxies show two distinct classes: dispersion-dominated (v_max/σ ≤ 3) with R_d ≈ 1–2 kpc and v_max ≈ 100 km/s, and rotation-dominated (v_max/σ > 3) with larger sizes and velocities.
• The observed scaling of high-redshift disks requires a spin parameter 3–4 times higher than in low-redshift systems due to smaller virial radii at z≈2, implying enhanced angular momentum retention or redistribution.
• Viscous timescales in high-redshift disks are ≈10^9 years, matching observed star formation timescales, indicating a self-regulated cycle of turbulence, star formation, and angular momentum transport.
• Turbulence in high-redshift disks is driven by gravitational instabilities, with gas velocity dispersions approaching the stability limit at Q ≈ 1, where gravitational instabilities saturate and regulate kinetic energy.
• The observed gas velocity dispersion in high-redshift disks correlates well with theoretical expectations based on Q = 1, supporting gravitational instability as the primary driver of turbulence and disk evolution.