# Toy Models for Galaxy Formation versus Simulations

**Authors:** A. Dekel, A. Zolotov, D. Tweed, M. Cacciato, D. Ceverino, J. R. Primack  
**arXiv:** [1303.3009](https://arxiv.org/abs/1303.3009)  
**Date:** 2013-03-12  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/1303.3009v2/

## Key points

- Dekel et al. present simple toy models capturing key processes in galaxy formation at redshifts >1
- Models tested against high-resolution hydro-cosmological simulations of massive galaxies at redshifts 4 to 1
- Focus on aspects like mass inflow rate from cosmic web, baryonic streams penetration, galactic disc size, gas content, and star-formation rate
- Findings show mass inflow rate proportional to mass and scales with (1+z)^5/2; ~50% of baryonic streams penetrate inner halo at redshifts 4 to 2
- Galactic discs typically have radius ~5% of virial radius; star-formation rate correlates with accretion rate in steady state
- Investigate gas inflow through discs towards central bulges and black holes using energy conservation principles and self-regulated violent disc instability (VDI)
- Find intense gas inflow through disc comparable to star-formation rate as predicted by VDI
- Galaxies tend towards steady state where bulge mass is similar to disc mass due to balance between gas draining by star formation, outflows, and disc inflows replenished by fresh accretion
- Models offer simplified yet insightful approach aligning well with simulations for quick predictions and deeper comprehension of galaxy evolution dynamics

## Summary

In their study, Dekel et al. present simple yet effective toy models that capture key processes involved in galaxy formation during its active phase at redshifts greater than 1. These models are tested against high-resolution hydro-cosmological simulations of massive galaxies at redshifts ranging from 4 to 1. The authors focus on various aspects of galaxy evolution, including the total mass inflow rate from the cosmic web into galactic haloes, the penetration of baryonic streams into the inner galaxy, the size of galactic discs, and the steady-state gas content and star-formation rate within galaxies. Their  provide valuable approximations for understanding the behavior of simulated galaxies. Through their analysis, Dekel et al. find that the mass inflow rate is proportional to mass and scales with (1+z)^5/2, while approximately 50% of  penetrate into the inner halo at redshifts between 4 and 2. They also observe that galactic discs typically have a radius around 5% of the virial radius and that galaxies reach a steady state where the star-formation rate correlates with the accretion rate. Furthermore, they investigate the inflow rate within galactic discs towards central bulges and black holes using energy conservation principles and self-regulated violent disc instability (). Their findings suggest an intense gas inflow through the disc comparable to the star-formation rate, as predicted by VDI. Additionally, they note that galaxies tend towards a steady state where bulge mass is similar to disc mass due to a balance between gas draining by star formation, outflows, and disc inflows replenished by fresh accretion. Overall, these  offer a simplified yet insightful approach to understanding complex phenomena in galaxy formation processes. By aligning well with simulations, these models prove useful for making quick predictions and gaining a deeper comprehension of galaxy evolution dynamics.