# Bulk viscosity of strongly interacting matter in the relaxation time approximation

## Abstract

Here, we show how thermal mean field effects can be incorporated consistently in the hydrodynamical modeling of heavy-ion collisions. The nonequilibrium correction to the distribution function resulting from a temperature-dependent mass is obtained in a procedure which automatically satisfies the Landau matching condition and is thermodynamically consistent. The physics of the bulk viscosity is studied here for Boltzmann and Bose-Einstein gases within the Chapman-Enskog and 14-moment approaches in the relaxation time approximation. Constant and temperature-dependent masses are considered in turn. It is shown that, in the small mass limit, both methods lead to the same value of the ratio of the bulk viscosity to its relaxation time. The inclusion of a temperature-dependent mass leads to the emergence of the β _{λ} function in that ratio, and it is of the expected parametric form for the Boltzmann gas, while for the Bose-Einstein case it is affected by the infrared cutoff. This suggests that the relaxation time approximation may be too crude to obtain a reliable form of ς/τ _{R} for gases obeying Bose-Einstein statistics.

- Authors:

- McGill Univ., Montreal, QC (Canada); Jan Kochanowski Univ., Kielce (Poland)
- McGill Univ., Montreal, QC (Canada)
- Brookhaven National Lab. (BNL), Upton, NY (United States)

- Publication Date:

- Research Org.:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

- OSTI Identifier:
- 1454832

- Alternate Identifier(s):
- OSTI ID: 1434403

- Report Number(s):
- BNL-205755-2018-JAAM

Journal ID: ISSN 2469-9985; PRVCAN

- Grant/Contract Number:
- SC0012704

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review C

- Additional Journal Information:
- Journal Volume: 97; Journal Issue: 4; Journal ID: ISSN 2469-9985

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

### Citation Formats

```
Czajka, Alina, Hauksson, Sigtryggur, Shen, Chun, Jeon, Sangyong, and Gale, Charles.
```*Bulk viscosity of strongly interacting matter in the relaxation time approximation*. United States: N. p., 2018.
Web. doi:10.1103/PhysRevC.97.044914.

```
Czajka, Alina, Hauksson, Sigtryggur, Shen, Chun, Jeon, Sangyong, & Gale, Charles.
```*Bulk viscosity of strongly interacting matter in the relaxation time approximation*. United States. doi:10.1103/PhysRevC.97.044914.

```
Czajka, Alina, Hauksson, Sigtryggur, Shen, Chun, Jeon, Sangyong, and Gale, Charles. Tue .
"Bulk viscosity of strongly interacting matter in the relaxation time approximation". United States.
doi:10.1103/PhysRevC.97.044914.
```

```
@article{osti_1454832,
```

title = {Bulk viscosity of strongly interacting matter in the relaxation time approximation},

author = {Czajka, Alina and Hauksson, Sigtryggur and Shen, Chun and Jeon, Sangyong and Gale, Charles},

abstractNote = {Here, we show how thermal mean field effects can be incorporated consistently in the hydrodynamical modeling of heavy-ion collisions. The nonequilibrium correction to the distribution function resulting from a temperature-dependent mass is obtained in a procedure which automatically satisfies the Landau matching condition and is thermodynamically consistent. The physics of the bulk viscosity is studied here for Boltzmann and Bose-Einstein gases within the Chapman-Enskog and 14-moment approaches in the relaxation time approximation. Constant and temperature-dependent masses are considered in turn. It is shown that, in the small mass limit, both methods lead to the same value of the ratio of the bulk viscosity to its relaxation time. The inclusion of a temperature-dependent mass leads to the emergence of the βλ function in that ratio, and it is of the expected parametric form for the Boltzmann gas, while for the Bose-Einstein case it is affected by the infrared cutoff. This suggests that the relaxation time approximation may be too crude to obtain a reliable form of ς/τR for gases obeying Bose-Einstein statistics.},

doi = {10.1103/PhysRevC.97.044914},

journal = {Physical Review C},

number = 4,

volume = 97,

place = {United States},

year = {Tue Apr 24 00:00:00 EDT 2018},

month = {Tue Apr 24 00:00:00 EDT 2018}

}