# 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/1303.3009v1/

## Key points

- Dekel et al. present simple yet effective toy models for galaxy formation during the active phase at redshifts greater than 1
- Models tested against high-resolution hydro-cosmological simulations focusing on massive galaxies between redshifts 4 and 1
- Investigated aspects include total mass inflow rate, baryonic stream penetration, galactic disc size, gas content, star-formation rate, inflow rate towards central bulges and black holes, and equilibrium state of discs and bulges
- Findings show proportional relationship between inflow rate, galaxy mass, and redshift; significant baryonic stream penetration; galactic disc radius around 5% of virial radius; steady state with close correlation between star-formation rates and accretion rates; significant inflow through discs supporting VDI predictions; galaxies approaching equilibrium with bulge masses similar to disc masses
- Toy models offer valuable approximations for understanding average behaviors in simulated galaxies

## Summary

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In their study, Dekel et al. present simple yet effective toy models that capture essential processes involved in galaxy formation during its highly active phase at redshifts greater than 1. These models are tested against a series of high-resolution hydro-cosmological simulations focusing on massive galaxies between redshifts 4 and 1. The authors investigate the evolution of various key aspects as a function of redshift and mass, including (a) the total mass inflow rate from the cosmic web into galactic haloes utilizing the Extended Press-Schechter (EPS) approximation, (b) the penetration of baryonic streams into the inner regions of galaxies, (c) the size of galactic discs, (d) the steady-state gas content and star-formation rate within galaxies based on mass conservation and a universal star-formation law, (e) the inflow rate within discs towards central bulges and black holes derived from energy conservation and self-regulated violent disc instability (VDI), and finally, (f) the equilibrium state reached by discs and bulges. The results indicate that these toy models offer valuable approximations for understanding average behaviors observed in simulated galaxies. Noteworthy findings include: 

(a) A proportional relationship between inflow rate, galaxy mass, and redshift scaling as (1+z)^{5/2}. (b) Approximately 60% penetration of baryonic streams into inner haloes at redshifts 4 to 2. (c) Galactic disc radius being around 5% of the virial radius. (d) Galaxies achieving a steady state where star-formation rates closely follow accretion rates into galaxies. (e) Significant inflow through discs comparable to star-formation rates supporting VDI predictions. (f) Galaxies approaching equilibrium with bulge masses similar to disc masses due to replenishment of gas drained by star formation through fresh accretion. The agreement between these toy models and simulations underscores their utility in simplifying complex phenomena for insightful interpretations and quick estimations. This work not only enhances our understanding of galaxy formation processes but also provides a practical tool for making rapid predictions in related studies.