# Virialization Heating in Galaxy Formation

## Abstract

In a hierarchical picture of galaxy formation virialization continually transforms gravitational potential energy into kinetic energies in the baryonic and dark matter. For the gaseous component the kinetic, turbulent energy is transformed eventually into internal thermal energy through shocks and viscous dissipation. Traditionally this virialization and shock heating has been assumed to occur instantaneously allowing an estimate of the gas temperature to be derived from the virial temperature defined from the embedding dark matter halo velocity dispersion. As the mass grows the virial temperature of a halo grows. Mass accretion hence can be translated into a heating term. We derive this heating rate from the extended Press Schechter formalism and demonstrate its usefulness in semi-analytical models of galaxy formation. Our method is preferable to the traditional approaches in which heating from mass accretion is only modeled implicitly through an instantaneous change in virial temperature. Our formalism can trivially be applied in all current semi-analytical models as the heating term can be computed directly from the underlying merger trees. Our analytic results for the first cooling halos and the transition from cold to hot accretion are in agreement with numerical simulations.

- Authors:

- (KIPAC, Menlo Park)
- (Santa Barbara, KITP)

- Publication Date:

- Research Org.:
- Stanford Linear Accelerator Center (SLAC)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 897734

- Report Number(s):
- SLAC-PUB-12304

arXiv:astro-ph/0701363v1; TRN: US200705%%230

- DOE Contract Number:
- AC02-76SF00515

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Astrophys.J.; Journal Volume: 672; Journal Issue: 2 (2008)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; GALACTIC EVOLUTION; KINETIC ENERGY; NONLUMINOUS MATTER; POTENTIAL ENERGY; SHOCK HEATING; MATHEMATICAL MODELS; Astrophysics,ASTRO

### Citation Formats

```
Wang, P., and Abel, T.
```*Virialization Heating in Galaxy Formation*. United States: N. p., 2007.
Web.

```
Wang, P., & Abel, T.
```*Virialization Heating in Galaxy Formation*. United States.

```
Wang, P., and Abel, T. Wed .
"Virialization Heating in Galaxy Formation". United States.
doi:. https://www.osti.gov/servlets/purl/897734.
```

```
@article{osti_897734,
```

title = {Virialization Heating in Galaxy Formation},

author = {Wang, P. and Abel, T.},

abstractNote = {In a hierarchical picture of galaxy formation virialization continually transforms gravitational potential energy into kinetic energies in the baryonic and dark matter. For the gaseous component the kinetic, turbulent energy is transformed eventually into internal thermal energy through shocks and viscous dissipation. Traditionally this virialization and shock heating has been assumed to occur instantaneously allowing an estimate of the gas temperature to be derived from the virial temperature defined from the embedding dark matter halo velocity dispersion. As the mass grows the virial temperature of a halo grows. Mass accretion hence can be translated into a heating term. We derive this heating rate from the extended Press Schechter formalism and demonstrate its usefulness in semi-analytical models of galaxy formation. Our method is preferable to the traditional approaches in which heating from mass accretion is only modeled implicitly through an instantaneous change in virial temperature. Our formalism can trivially be applied in all current semi-analytical models as the heating term can be computed directly from the underlying merger trees. Our analytic results for the first cooling halos and the transition from cold to hot accretion are in agreement with numerical simulations.},

doi = {},

journal = {Astrophys.J.},

number = 2 (2008),

volume = 672,

place = {United States},

year = {Wed Jan 17 00:00:00 EST 2007},

month = {Wed Jan 17 00:00:00 EST 2007}

}