Cold Accretion in Galaxy Formation

• Cold accretion is a process where metal-poor, ~10⁴ K gas streams along cosmic filaments directly funnel into galaxies, bypassing shock heating.
• The scenario is evidenced by uniform low metallicity and flat abundance gradients in systems like NGC 4650A via detailed spectroscopic studies.
• Quantitative methods, including the Birnboim & Dekel stability criterion and emission line diagnostics, confirm cold accretion's role in disk formation.

The cold accretion scenario describes a cosmological gas accretion process in which metal-poor, cool gas streams flow along cosmic filaments or penetrate the halos of galaxies without being shock heated to the virial temperature. This process is contrasted with hot mode accretion, where infalling gas forms a quasi-hydrostatic hot atmosphere and only becomes available for star formation after radiative cooling. Cold accretion is particularly significant in low-mass halos and at high redshift, and it can leave distinct chemical and structural signatures in galaxies. Observational evidence and chemical abundance analyses, such as those in the polar disk of NGC 4650A, reveal a low and uniform metallicity consistent with a cold accretion origin (Spavone et al., 2010).

1. Physical Principles and Characteristics of Cold Accretion

Cold accretion involves the inflow of metal-poor, cool ($T \sim 10^4$ K), and often highly filamentary gas from the intergalactic medium (IGM) directly into the halos and disks of galaxies. This process typically occurs when the cooling time of the infalling gas is less than the dynamical (free-fall) time, precluding the formation of a stable accretion shock at the virial radius. The Birnboim & Dekel stability criterion quantifies this condition with the parameter: $$\epsilon_{\rm s} = \frac{\rho_0\, r_{\rm s}\, \Lambda(T_1)}{u_0^3}$$ where $\rho_0$ is the pre-shock gas density, $r_{\rm s}$ the shock radius, $\Lambda(T_1)$ the cooling function, and $u_0$ the inflow velocity. If $\epsilon_{\rm s} > \epsilon_{\rm s,crit}$ ($\epsilon_{\rm s,crit} \approx 0.0126$ for $\gamma=5/3$ gas), the shock is unstable or fails to develop, and gas accretion proceeds in the cold mode (Benson et al., 2010).

In this regime, the gas retains much of its specific angular momentum, tends to flow along narrow streams, and can rapidly supply the star-forming regions of galaxies, sometimes leading to morphologically distinct features such as polar disks or extensive HI rings.

2. Chemical Abundance Diagnostics and Empirical Evidence

Detailed studies of galaxies provide empirical support for the cold accretion scenario by combining chemical abundance measurements with stellar population data and morphological analysis. In the case of NGC 4650A, deep long-slit spectra covering the brightest HII regions in its polar disk were used to measure oxygen abundances using both empirical and direct electron temperature ($T_e$) methods. Key calibrations include:

• $R_{23}$ parameter: $$R_{23} = ([{\rm O\,II}]\, \lambda 3727 + [{\rm O\,III}]\, \lambda\lambda 4959,5007) / {\rm H}\beta$$
• $S_{23}$ parameter: $$S_{23} = ([{\rm S\,II}]\, \lambda\lambda 6717,6731 + [{\rm S\,III}]\, \lambda\lambda 9069,9532) / {\rm H}\beta$$
• Empirical relation: $$12 + \log({\rm O/H}) = 1.53 \cdot \log(S_{23}) + 8.27$$ [Díaz et al. 2000]
• $P$-method: excitation-based refinement [Pilyugin 2001].

For NGC 4650A, the empirical and direct methods converge on $12 + \log({\rm O/H}) \approx 8.2 \pm 0.1$, corresponding to $Z \approx 0.2\, Z_\odot$, well below the typical metallicity for spirals of similar luminosity (which are near-solar). Additionally, the metallicity gradient along the polar disk is flat, indicative of little to no chemical enrichment from the more evolved central spheroid, and consistent with accretion of almost pristine gas (Spavone et al., 2010).

3. Distinction Between Cold, Hot, and Tidal Accretion Modes

In cold mode accretion, gas arrives cold and rapidly fuels star formation with little delay, while hot mode involves a hydrostatic shock-heated atmosphere and a longer cooling delay before star formation can proceed. In the presence of cold accretion, the angular momentum of infalling gas remains high, resulting in larger, lower-density disks with longer dynamical times. Contrasting formation scenarios such as tidal accretion or disruption from companions typically predict higher or more varied metallicities and possible metallicity gradients.

Key features distinguishing the cold accretion scenario in NGC 4650A:

• Low metallicity ($Z \sim 0.2\, Z_\odot$) in the polar disk.
• Flat radial metallicity gradient.
• Absence of evidence for significant gas exchange with the central spheroid.
• HI mass in the polar disk comparable to the mass of the central spheroid.

Alternative scenarios involving tidal stripping or mergers would likely produce greater metallicity diversity and possibly leave observable kinematic/structural signatures, which are not seen in NGC 4650A (Spavone et al., 2010).

4. Quantitative Methods and Observational Metrics

The chemical analysis relies on measurements of strong emission lines and faint auroral transitions, with electron temperatures derived from lines such as [O III] $\lambda4363$. The oxygen abundance can be computed using five-level atom approximations: $$12 + \log\left(\frac{\mathrm{O\,III}}{\mathrm{H}}\right) = \log\left(\frac{[\mathrm{O\,III}]\,4959+5007}{\mathrm{H}\beta}\right) + 6.2 + \frac{1.251}{t_3} - 0.55\log t_3 - 0.014 t_3$$ and similar for O II, where $t_3$ is the electron temperature (in $10^4$ K units).

The metallicity is benchmarked against a local, commonly adopted solar value: $12 + \log({\rm O/H})_\odot = 8.83$, with $Z_\odot = 0.02$.

5. Implications for Galaxy Formation and Evolution

The cold accretion scenario has significant ramifications for the large-scale baryon cycle and the evolutionary pathways of disk galaxies. The observed properties of NGC 4650A—flat metallicity gradients, low overall metallicity in the polar disk, HI-rich content, and lack of pre-enrichment—support a disk formation history dominated by accretion of intergalactic, metal-poor gas along filaments. This process may be more widespread in polar disk/ring galaxies and in systems where the central spheroid has not dominated recent chemical evolution via gas exchange or enrichment.

The model implies that:

• Disk assembly can be decoupled from the chemical history of the spheroid.
• Filamentary gas inflows are a robust mechanism for building extended, low-metallicity disks.
• Star formation in such systems can proceed in a uniform and externally regulated mode rather than through classic inside-out growth typical for spiral disks formed from already enriched, cooled gas reservoirs.
• Systems built via cold mode accretion may retain signatures of their formation over cosmological timescales, observable via chemical and kinematic surveys.

6. Broader Relevance and Future Directions

The cold accretion framework is integral to contemporary models of galaxy assembly, particularly for understanding star formation at high redshift, the metallicity evolution of galaxies, and the formation of exotic morphologies (e.g., polar disks, LSB galaxies). Cold mode accretion is predicted to be more pronounced at early times and in lower-mass halos, consistent with hydrodynamic simulations. Continued high-resolution spectroscopy, integral field observations, and comparative chemical studies across diverse morphologies are central for further constraining the prevalence and consequences of this accretion process (Spavone et al., 2010).

Further work is suggested in:

• Quantifying how feedback (stellar and AGN-driven) modulates cold versus hot mode accretion.
• Characterizing the interplay between angular momentum acquisition and disk morphology in cold accretion systems.
• Extending chemical abundance studies to larger samples of polar disk and LSB galaxies to assess universality.
• Simulating filamentary accretion flows with high spatial and temporal resolution to test detailed predictions of metallicity distributions and star formation histories in observed systems.